ORNL-2396.txt

- ORNL-2396 -
. Chemistry-General
* " TID-4500 (14th ed.)

 

GUIDE TO THE PHASE DIAGRAMS

OF THE FLUORIDE SYSTEMS.

Ty, E.Ricei | -

 

 

 

OAK RlDGE NATIONAI. I.ABQRATORY
operdted by

UNION CARBIDE CORPORATION
T for the .

U S ATOMIC ENERGY COMMISSIO“

 
ORNL-2396
Chemistry-General
TID-4500 (14th ed.)

Contract No. W=-7405-eng-26

REACTOR PROJECTS DIVISION

GUIDE TO THE PHASE DIAGRAMS OF THE FLUORIDE SYSTEMS
J. E. Ricei

Consultant to Qak Ridge National Laboratory from New York University, Department of Chemistry

DATE ISSUED

Ny

 

OAK RIDGE NATIONAL LABORATORY
Oak Ridge, Tennessee
operated by
UNION CARBIDE CORPORATION
for the
U.S. ATOMIC ENERGY COMMISSION
PREFACE

A comprehensive study of fused-salt phase equilibria has been in progress at the
Oak Ridge National Laboratory for several years in connection with reactor technology.
In the course of that study, several complex fused-salt ternary systems have become
well enough understood that nearly complete phase diagrams of the systems could be
constructed.! Detailed discussion of the phase equilibria occurring in those systems is
included herein.

Except for the LiF-BeF ,~UF, and NaF-BeF ,—UF, systems, each of the diagrams
of ternary systems included in this discussion was derived at ORNL in the Fused Salt
Chemistry Section, under the direction of W. R. Grimes.

Because it was felt that this collection of fluoride phase diagrams might prove more
valuable if accompanied with a discussion of some of the types of phase relations
illustrated in them, the following treatment was prepared. The purpose is to present
some general principles and explanations which should aid in the reading, interpretation,
and use of the actual diagrams in the collection and of other similar diagrams which
may still be determined. While the relations are usually explicitly shown, at least as
far as they are known, in the temperature-composition diagrams of the binary systems,
the corresponding relations are not always equally apparent in the usual *‘phase diagram”’
of a ternary system of any complexity. In either case, moreover, the diagram does not
show the actual data and observations upon which the diagram itself, essentially an
inference, is based, nor does it give any idea of the amount of work, in experimentation
and in thought, underlying the construction of the diagram. This aspect of the diagrams,
however, is something best presented and treated by the investigators themselves.

All the diagrams in the collection represent ‘‘condensed systems’’:

i.e., they show
the temperature-composition relations between solid and liquid phases under one atmos-
phere of open pressure. For chemical reasons the atmosphere was actually helium or
argon. No two-liquid equilibria were encountered. Limited miscibility of solids is
involved in some of the diagrams, but there are no critical solution (or consolute) points
for solid solution. The discussion will deal only with types of phase equilibria actually
represented in the systems.

We shall treat first the essentials involved in the binary diagrams of the collection,
and then, more extensively, the essential relations for the several ternary diagrams.
The last sections will consider specifically the ternary systems and their constituent

binary systems.

 

]R. E. Thoma (ed), Phase Diagrams of Nuclear Reactor Materials, ORNL-2548 (to be published).
CONTENTS

P REFACE et ettt ettt e e ea et et ettt ettt et et s eeanaee e i
LIST OF FIGURES L. ettt et et ee et e ee e e en e een e vii
PART I. GENERAL PRINCIPLES
Lo BINARY DIAGRAMS e e et ettt ettt e 3

1.1. Pure Components as Solid Phases ..........ccccoooveviiviieini, ettt 3

1.2, Pure Compounds ..ottt bt bt e, 3
Relation Between Congruence and Incongruence of Melting for a Binary Compound ................ 4

130 S0lid SOIUtION oo et et 4
Continuous Solid SolUtion ..o 4
Miscibility Gap in Solid SolUtion ... i e e, 5

Solid Solution and Polymorphism ..ottt 5

2. TERNARY EQUILIBRIUM OF LIQUID AND ONE SOLID (SURFACES) .o, 7
2.1, Fixed Solid oo e e 8
2.2, Variable Solid (Solid Solution) .o e e 8
Fractionation Path ... e bt b e oo e eseeeat e e et e et ete et e et e e e te et e eeeeae s 9
Equilibrium Path o e et st st 9

3. TERNARY EQUILIBRIUM OF LIQUID AND TWO SOLIDS (CURVES) ..o, 11
3.l REACHON T Y POS oo b ettt e, 11
3.2. Maximum and Minimum Temperature Points ..o e, 12
3.3. Equilibrium Crystallization Process for Liquid on a Two-Solid Curve ..., 12

4. TERNARY CONDENSED INVARIANT POINTS (FOUR PHASES) ..o, 14
4.1. Binary Decompositions in Presence of Ternary Liquid ... 14
PUPE T SOlidS oo ettt 14

Effect of the Third Component Entering into Solid Solution ..o, 14

4.2. Types of Ternary InVariants ... e s 15
Type A Invariant: Triangular or Terminal Type of Invariant ... 15

Type B Invariant: Quadrangular, Diagonal, or Metathetical Type of Invariant .................... 15

4.3. Relations of the Three Liquid Curves at Their Invariant Intersection...........cccevvvveivinieinicennne, 15
4.4. Congruent and Incongruent Crystallization End Points ..o 17
4.5. Melting Points of Ternary Compounds ... et st 19
4.6. Invariants Involving Solids Only . 19

5. CRYSTALLIZATION PROCESS WITH PURE SOLIDS e 20
6. CYRSTALLIZATION PROCESS WITH CONTINUOUS BINARY SOLID SOLUTION ..o, 25
6.1, Fractionation ProCess ..ottt oot e e st ean s ee st a e naeaees 26

6.2. Equilibrium Process ... e ettt e ar e 26

7. CRYSTALLIZATION PROCESS WITH SOLID SOLUTIONS AND SEVERAL INVARIANTS .............. 29
7.1, The Phase Diagram ... ettt e et e st eee st e n e enee 29

7.2. Equilibrium Crystallization Process ... 30

7.3. Process of Crystallization with Perfect Fractionation............ccoooiiiiiiiiiiiiiii e 32
7.4. Ternary Solid Selution in Compound D[ i 33
10.
1.

12.

13.

4.

15.

Vi

PART II. THE ACTUAL DIAGRAMS

SYSTEM X—U—V: LiF=UF ;=BeF , i s 37
SYSTEM Y--U~V: NaF=UF ,=BeF , . s 40
SYSTEM Y—U—R: NaF—UF j=RbF .. 44
SYSTEM Y—Z—R: NaF=ZrF [=RBF s 47
11.1. The System According to Figure 11.3 and Neglecting Solid Solution........cccccoieiiiiinicriiennnn, 47
11.2. Consideration of Solid Solution Formation .........cooieiiii e 49
11.3. The Region for Compounds G and H of System R—Z ... 49
The Region As Shown in Figures 11.6 and 11.7 e, 49
The Region As Shown in Figures 11.8 and 11.9 . 51
11.4. The Region Involving Compounds B and D of System Y—Z ..., 52
SYSTEM Y—Z—X: NaF—ZrF ;= LiF 55
12,7, Subsystem Yo AmGoX e o e e et e 56
12.2. SUBSYSEEM EmZmH oottt e et et et e e s 58
12.3. SUbsystem A—E—H—G ...ttt e s 59
12.4. Subsolidus Decompositions of Compounds G and 7 ......coooviiiiiiii i 60
Decomposition of Compound ... ..ottt ettt sa e a e 60
Decomposition of Compound G ... ettt 61
SYSTEM Y—U—X: NaF—UF [—LiF s 64
13.1. The Invariants P ,, P, P, AN P g 64
The Invariant Py oo s 64
The Invariant P o o 65
The Invariant P o s e 66
The Invariant P oo e 66
13.2. The Region DUH ..ot e e et st et e ene e aaa e, 68
13.3. The Region YD HX i ettt e s ae e 71
13.4. Fractionation Process on the Solid Solution Fields ... 73
SYSTEM Y—U=Z: NaF—UF [=ZrF | s 75
TA. 1. General CRaracteriStics .ooiiiiiiiiriiiiieeiee oottt et et e e st em e e 2eae et e eseeseen s s emteamse e aesan e e s eensees 75
14.2. Subsystem Y—A-G ....... ettt N ehteereeht s e e et et et ereehea e et et £ttt £ehe et e eh et nen e e e ene e 75
14.3. Subsystem A-—D—K—G ... s s e e 79
The Region Involving A, B, C, and D oo e e s 80
The Region Involving G, H, I, and K . ...ocoiiiiiiiii et e 87
Fractionation Processes in the Subsystem A—D—K—G .. ..o 89
Subsolidus Reactions Involving Compounds A, H, and ] ..ot e e 90
T4.4, Subsystem D—U—Z—K ...t e b e 21
Equilibrium Crystallization Along Curves ..o e 91
Fractionation Processes in the Subsystem DU—Z—K .......ccoooiiiiiriiiieiiie et 94
Equilibrium Crystallization inthe U_Field ... 95
Subsolidus Compounds F and F ...ttt et e %6
SYSTEM Y—W—Z: NaF—ThF —ZrF 97
1.1,
1.2.
1.3.
1.4.
1.5.
1.6.
1.7.
1.8.
1.9.

1.10.
1.11.
1.12.
1.13.
1.14.

2.1
2.2.
2.3.
2.4.

3.1.
3.2.
3.3.
3.4.
3.5.
3.6.

4.1.
4.2.
4.3.
4.4.
4.5.
4.6.
4.7.
4.8.
4.9.

4.10.
4.11.
4.12.
4.13.

LIST OF FIGURES

Pure components as solids.......ccccoooivioii i
Retrograde solubility curve ..oooievviiiiiiii
Binary compounds .........coocoiiiiiii e,

“Inverse’’ fusion of binary compound ...

........................................................................

Singular point between congruence and incongruence of melting ..o

Continuous solid solution without MAXimMUM OF MIMIMUT oottt reereeeree e veesereaesasnnneeeees

Continuous solid solution with minimum ....................
Discontinuous solid solution, eutectic case ..............

Discontinuous solid solution, peritectic case............

Elevation of transition temperature, involving liquid

Elevation of transition temperature, subsolidus ........

........................................................................

........................................................................

........................................................................

........................................................................

........................................................................

Depression of transition temperature, involving liquid ..o

Depression of transition temperature, subsolidus......

........................................................................

Depression of transition temperature, lower fOrm pure ..........ccovioiiiiiiiieieet e s

Liquidus surface for pure solid A ...,

........................................................................

Fractionation path on surface for liquid in equilibrium with A—B solid solution .....ccoccovvninnn

Relation between equilibrium path and fractionation

Relation between equilibrium path and fractionation

paths: for ternary solid solution..............

paths: for binary solid solution ...............

Change from even to odd reaction: two solid solutions ...

Change from odd to even reaction: two solid solutions ...

Change from odd to even reaction: two pure solids ..

Temperature maximum in reaction L — calories —> §, + S, e,

Temperature minimum in reaction L + §, ~ calories —> S, i

Three-phase triangle on curve for L. — calories —> S, + S,

Type A invariant ...
Type B invariant ...
Arrangement of curves at a eutectic ...
Arrangement of curves for case (a) and case () ........
Arrangement of curves for case (c) and case (d) ........
Impossible angles of intersection ...,

Eutectic triangle contains only the eutectic “‘point”’

........................................................................
........................................................................
........................................................................
........................................................................
........................................................................
........................................................................

E

..................................................................

Eutectic triangle also contains several peritectic “points” ...,

Invariant, €ase (@) oo
Invariant, €ase (@) ..o
Invariant, case (€) oot

Invariant, case (b)) oo e

Semicongruent melting point of ternary compound M,

........................................................................

........................................................................

........................................................................

........................................................................

........................................................................

oo o O OO OO0 LWLWW

— —
O O 0

— ot ek et od
AR MR AN ed el =

— il e ] e et el et weed med v e e
OO0 N0 N N N N O O8O OO

vii
5.1
5.2.
5.3.
5.4.
5.5.
5.6.
5.7.
5.8.
5.9.
5.10.
5.11.
5.12.

6.1.
6.2.
6.3.
6.4.
6.5.

7.1,
7.2
7.3.
7.4.
7.5.
7.6.
7.7.
7.8.
7.9.
7.10.
7.1,
7.12.
7.13.
7.14.

8.1.
8.2.
8.3.
8.4.
8.5.
8.6.
8.7.
8.8.

viii

Two three-solid arrangements for two binary compounds ... 20
Necessary arrangement of curves and invariants for the two cases in Fig. 5.1 ..o 20
Hypothetical ternary system with three binary compounds ... 21
The section A—D, of Fig. 5.3 .o 21
Isotherm between py aNd 7 ..o 2]
[sotherm between 7 QN 72 ..o e bbb bbbt e 23
Isotherm above P, and still above Eq and E, i 24
[SOEREIM Gt Py o e s s s s s s e et 24
The SeCtion D =Dy it b s s 24
The SECHon D gD 5 (oo e 24
The SeCtion C—D 5 .o e e 24
The SECHON D 1=B oot 24
Ternary system with continuous A—B solid solution and pure C ........occiviviinnniicicnce, 25
The binary system A—B of Fig. 6.1 .o e 25
Arbitrary section, from C to the AB side ... 25
Fractionation paths for the solid solution sUFFACE .. .o 26
Equilibrium paths and inflection point of fractionation path. ..., 28
Ternary system with discontinuous A—B solid solution and two binary compounds .................... 29
Binary system A—B of Fig. 7.1 .o 29
The invariant reaction planes of Fig. 7.1 e e 30
The SECHON D y=8 o 30
IS Otherm GBOVE [ . oot e e 31
[sotherm just Below P e e 31
Isotherm below m but above P and above F4 s 31
The SECHION D =D o oot 32
The SECHON D =B oot e - 32
The SEction A—D 5 .o 32
Portion of Fig. 7.3, with some ternary solid solution ot Dy ..., 33
Isotherm for Fig. 7.11, between p and P .o e 33
|sotherm [UST GDOVE P 1 oo s 33
Part of the section D =D, for Fig. 7. 1T e, 33
System X—U: LiF=UF ;o 37
System U=V UF =BeF , oo 37
System X—V: LiF=BeF , i i, 37
System X—U—=V: LiF=UF =BeF 38
Isotherm involving the fnvariant P, .. s 39
Isotherm above P, and Py o 39
The section C=V: LiF4UF ,=BeF . 39
The section B—V: 7LiF.OUF ,—BeF ., 39
8.9.
8.10.

9.1.
9.2.
9.3.
9.4.
9.5.
9.6.
9.7.
9.8.
9.9.

10.7.
10.2.
10.3.
10.4.
10.5.
10.6.
10.7.
10.8.
10.9.
10.10.

11.1.
11.2.
11.3.
11.4.
11.5.
11.6.
11.7.
11.8.
11.9.
11.10.

12.1.
12.2.
12.3.
12.4.
12.5.
12.6.
12.7.

The section B—-D: 7Li|:-6UF.4—2LiF-BeF2
The section A=D: 4LiF-UF4—2LiF-BeF2

........................................................................................

..........................................................................................

System Y—U: NaF —UF |
System Y—-V: NaF—=BeF , .. i
System Y—U—V: NaF=UF =BeF , .o,
Isotherms involving compounds E and F (NaF.2UF, and NaF-4UF )
The section F—V: NaF.4UF ,~BeF,
The section E—V: NaF.2UF ,-BeF,
The section D—=V: 7NaF.6UF ,=BeF , e,
The section B—H: 2NaF.UF =2NaF.BeF , ...,
The section D—H: 7NaF.6UF ,~2NaF.BeF,

............................................
................................................................................................

..................................................................................................

......................................................................................

System R—U: RbF-UF,
System Y—R: NaF=RbF .
System Y—U—R: NaF=UF ,=RbF .
The section D—N: 7NaF.6UF ,—RbF.6UF,
The section D—M: 7NaF.6UF (=RbF.3UF | o
The section D—K: 7NaF.6UF ,=2RbF.3UF,
The section D—I: 7NaF.6UF ,-7RbF.6UF
The section B—H: 2NaF.UF ,~2RbF.UF
The section Y—0Q: NaF—NaF-RbF-UF ;.
The section O-G: NoF-RbF-UF4—3RbF-UF4

........................................................................................................................

........................................................................................

......................................................................................
........................................................................................

..........................................................................................

....................................................................................

System Y—Z: NaF-ZrF
System R—Z: RBF=ZrF |
System Y—Z—R: NaF—ZrF ,~RbF s
The partial section M,—Z: NoF-RbF-ZrF4-ZrF4 ............................................................................
Divisions of Fig. 1.3 i et e s
Detail of binary system Z—R: ZrF ,=RbF ..o
Region involving compounds H and G: 5NaF.2ZrF, and 3NaF-ZrF ,
Detail of system Z—R, for f1 (5NaF.2ZrF ;) assumed pure ...,
Region involving H and G, for H pure: 5NaF.2ZrF , (pure} and 3NaF-ZrF .o
Region involving solid solutions in Y—7 (NaF=ZrF ;) system ...

......................................................................................................................

System X—Z: LiF-ZrF,
System Y=X: NaF =LiF e
System Y—Z—X: NaF—ZrF wLiF
Region below section A—G (3NcF-ZrF4-—3LiF-ZrF4)
The section A—G (BNGF-ZrF4—3LiF-ZrF4) ........................................................................................
Region above section E~H (7NaF-62rF4—2LiF-ZrF4)
The section F—I (3NcF-4ZrF4—3LiF-4ZrF4)

........................................................................................................................

......................................................................

....................................................................

....................................................................................

50
12.8.
12.9.
12.10.
12.11.
12.12.

13.1.
13.2.
13.3.
i3.4.
13.5.
13.6.
13.7.
13.8.
13.9.
13.10.
13.11.

14.1.
14.2.
14.3.
14.4.
14.5.
14.6.

14.7.
14.8.
14.9.

14.10.
14.11.
14.12.

14.13.

14.14.

14.15.

14.16.
14.17.

14.18.
14.19.

Middle region of system Y—Z~X: NaF=ZrF =LiF ..o, e et
Decomposition of compound 1 {SLiF4ZrF ) i,
The section F—I (3NaF-4ZrF4—-3LiF-4ZrF4) ....................................................................................
Decomposition of compound G (BLIF-ZrF,) .o
The section A-G (3NoF-ZrF4-3LiF-ZrF4) ........................................................................................

System X—Us LiF=UF ;o
System Y—U—X: NaF—UF —LiF s
The section D—H (7N0F-6UF4-7LiF-6UF4) ......................................................................................
Decomposition of compound C (SNaF-3UF ) ..
Decomposition of compound G (4LiF-UF4) ........................................................................................
Formation of compound E (NaF-2UF |} ..,
Region above section D—H (7NaF.6UF ,=7LiF.6UF ) oo,
The section E—H (NcF-ZUF4—7LiF-6UF4) ........................................................................................
Region below section D—H (7N0F-6UF4—7LiF-6UF4) ......................................................................
The section B—G (QNGF-UF4—4LiF-UF4) ..........................................................................................
Detail of Fig. 13.2, near compound C (5NaF 3UF ) ..o

System Y—7Z: NaF=ZrF ;s
System U—Z: UF [=ZrF ;o
System Y—U—Z: NaF=UF =ZrF /., et ettt e et naees
The section A—G (B_NGF-UF4—3NGF-ZI‘F4) ........................................................................................
The section D—K (7N0F-6UF4—7N0F-6ZrF4) ....................................................................................

The section between Y {(NaF) and the point on UZ that represents the
composition TUF = 1ZrF | i,

Subsystem Y~A—G: NaF=3NaF.UF ,—=3NaF.ZrF , .o
Subsystem Y—A—G (NaF-3NaF.UF ,~3NaF.Z¢F ,): fractionation paths ...,

Subsystem A—D—K—G: system NaF-UF ,~ZrF , region between 3:1 and 7:6
SOLIA SO UTIONS .o ettt et et b e e et

Scheme | for compound C (5NoF-3UF4) ..............................................................................................
Sequence of isotherms for Scheme | ...

The section between C (5N0F-3UF4) and the point on YZ that represents the
composition SNaF-3ZrF ,, in Scheme | ...

Scheme Il for compound C (5NoF-3UF4) ..............................................................................................
Sequence of isotherms for Scheme 1l ...

The section between C (SNGF-SUFA) and the point on YZ that represents the
composition SNaF=3ZrF ,, in Scheme Il ...

Lower part of subsystem A—D—K~G: the NaF-ZrF, side of Fig. 14.9 ..

Solids left after complete solidification, in region YDK

(Na F—7N0F-6UF4—7NGF-6ZrF4) ......................................................................................................
Decomposition of compound A (3NoF-UF4) ........................................................................................
Transition in compound {/ (SNQF-ZZer) ............................................................................................
14.20.
14.21.

14.22.
14.23.
14.24.

15.1.
15.2.
15.3.
15.4.
15.5.
15.6.
15.7.
15.8.

Appearance of compound ] (BNOF-QZer) .......................................................................................... 93
Subsystem D—U~Z—K: system NaF-UF ,-ZrF, between the 7:6 solid solution

and the UF ,~ZrF, solid solution...........ccccoiiiiiiiiiis e, 93
Subsystem D—U—7—K: temperature CONTOUIS .. ..ooiociiiiieiieeieieesieeieiteee oo 93
Subsystem D—U—Z—K: fractionation paths ... 94
Appearance of compounds £ and F (NaF.2UF, and NaF-4UF ) 96
System Y=W: NaF—ThF e e 97
System W2t ThF = ZrF ;oo 97
System Y—W—Z: NaF—ThF —ZrF ;.. 98
System Y—W—Z7: NcF—ThF4—ZrF4 (revised) ..o, e e e, 99
Middle region of system Y—W—7Z (NaF=ThF ,=ZrF ;) ..o, 100
Subsolidus transition in compound B (5NoF-2ZrF4) .......................................................................... 101
W—Z7 region of system Y—W--Z (ThF ,~ZrF, region of system NaF~ThF ~Z¢F,) ... .. 102
Fractionation paths for the solid solution surface of system Y—W—-Z

(NGF=ThE j=ZrF ) oo s e 103

xi
PART |
GENERAL PRINCIPLES
1. BINARY DIAGRAMS

1.1 PURE COMPONENTS AS SOLID PHASES

With the pure components as the only solid
phases in a binary system (Fig. 1.1), the melting
points (T, and T}) are lowered and the system is
always eutectic in type. In Fig. 1.1 the eutectic
e involves the high-temperature form of A (A,)
and the low-temperature form of B (Bfi); at the
temperature of e the phase reaction is:

L(e) —calories === A_+ Bg

If T:1 is the transition temperature for the forms
of A, then the two-solid mixture consists, at
equilibrium, of A  and B
Afi and B, below T7. 1f T is the transition
temperature for the polymorphic forms of B, there
will be a break in the freezing-point curve (or
solubility curve) of the B solid at the temperature
T, unaffected by the A if both forms of the B
solid are pure. Above TJ, the liquid is in
equilibrium with B , below Tj with B If the
transition B,~» B

above T{; and of

fails to occur on cooling, a
metastable eutectic e(m) is possible, for liquid in
(metastable) equilibrium with A_and B .

(It is possible for a solubility curve to show a
‘“‘:etrograde’’ temperature effect, even down to the
eutectic, in which case we would have Fig. 1.2.
Retrograde changes of solubility with temperature
were not encountered in the present systems,
whether binary or ternary, but reference will be
made to this question later.)

Liquids A and e,
such as point @ (Fig. 1.1), give A as primary
crystallization product when cooled to the curve

with composition between

T,e. At the temperature T the equilibrium
mixture consists of solid A and liquid 7 in the
ratio (by weight or by moles, depending on the
units of the diagram) x//xs. When the temperature
of e (eutectic) is reached, the remaining liquid
freezes invariantly to a secondary crystallization
product of a mixture of A_and B, crystals in the
proportion ev/eu. For liquids between b and B in
composition the primary solid will be B , changing
to By at Tp, and followed by the eutectic mixture
at e.

In a two-phase region such as T ,ue, the
coexisting equilibrium phases are joined by
horizontal tie lines (also called conjugation lines,
conodes, joins) running in this case between the
liquidus curve T,e ond the solidus curve T,u.

A
With pure solid A, the solidus is here a vertical

fine, the edge of the diagram. The horizontal line
uev is also sometimes considered part of the
solidus of the diagram.

1.2. PURE COMPOUNDS

Figure 1.3 shows three
(C; D, E) in the system A-B:
1. Compound C melts congruently at C_; it has
a congruent melting point.

binary compounds

It is stable as a solid
phase until it melts to a liquid of its own chemical
(analytical) composition. Points e, and e, are
eutectics for solids A and C_and for C_ and D,
respectively.

At TZ, the higher-temperature form
C_ undergoes transition

. to Cpe At To, Cg
decomposes on cooling into the solids A and D.

2. Compound D melts at the
temperature D.. |t decomposes as a solid phase

incongruently

UNCLASSIFIED
ORNL~LR-DWG 24748

 

 

 

 

 

 

 

 

 

 

 

T — AD+E . E+E
/H—CB C£+D
76'\ - ]
A+ D |
A C D £ B
Fig.1.3.
(into liquid p and solid B) before reaching its
own melting point [the metastable or submerged
congruent melting point D _{m)]. In contrast to a
eutectic point (e,, e,), the point p is called a
peritectic point (also meritectic, sometimes) and
the reaction:

D + calories = L(¢) + B

is a peritectic reaction.

3. Compound E decomposes as a solid phase,
into D and B, at the temperature T, before it
reaches any equilibrium with liquid. Such a solid
phase is sometimes called '*subsoclidus.”

Figure 1.3 shows a metastable eutectic, e(m),
between solids A and D, possible if compound C
fails to form on e’ (m)
metastable eutectic for solids C_and B.

It is also possible for ¢ compound to undergo

cooling; is a similar

incongruent melting on cooling (inverse peritectic,
or inverse fusion), as shown in Fig. 1.4. No
example is found in the actual binary systems
studied, but the relation will be referred to under
the ternary systems. In Fig. 1.4, T] ts the usual
incongruent melting point of C; T, is its inverse
fusion point:

C —calories=—=L({(p )+ B .

Relation Between Congruence and Incongruence of
Melting for a Binary Compound

The flatness of the freezing-point curve of a
compound at the maximum, whether exposed and
stable as at C_ in Fig. 1.3 or submerged and
metastable as at D_(m), depends on the degree of
dissociation of the compound in the liquid state.
If the compound C is not dissociated at all, the
maximum is a pointed intersection of two unrelated
curves: on one side the freezing-point curve of
the compound in the binary system A—-C, on the
other side the freezing-point curve of the compound
in the unrelated binary system C—B. OCnly when
the maximum is such a sharp intersection may the
whole diagram be said, strictly, to consist of two
adjacent binary systems. If there is any dis-
sociation of C into A and B in the liquid state,
the curve is rounded, and its maximum is lowered,
because the liquid, even at the maximum itself, is
not pure C (in the molecular sense) but C plus
A and B. The greater the degree of dissociation,
the flatter and lower is the maximum. Hence,
whether the melting point of the compound will be
exposed or submerged relative to the freezing-
point curves of adjacent solid phases depends

on the ‘‘true’’ melting point of the compound
without decomposition and on its degree of dis-
sociation in the melt.

In a comparison of corresponding compounds of
given formula, such as A.B in a series of
homologous binary systems with A fixed and B
varied, the congruence or incongruence of the
melting point of the compound will be a function
of three variables: the melting point of the second
component (B, B’ B", ...), the *‘true’’ melting
point of the compound (A:B, AB’, etc.), and the
degree of dissociation of the compound in the melt.

For a given specific binary system, moreover,
the relation may vary with the pressure, because of
several effects. Pressure causes some change in
the relative melting points of all three solids of
the system (A, C, B); it causes corresponding
changes in the compositions of the intervening
isothermally invariant liquid solutions (e, p, etc.);
and it causes changes in the dissociation of the
compound. The melting point of the compound
may therefore be exposed (congruent) at one
pressure and submerged (incongruent) at a different
pressure. At some particular or singular value of
the pressure, therefore, the diagram would pass
through the configuration in Fig. 1.5, When a
system at arbitrary pressure seems to give such
a diagram, however, it is reasonable to suppose
that the maximum is actually either just exposed

or just submerged.

1.3. SOLID SOLUTION
Continuous Solid Solution

In a binary system with continuous solid
solution, the usual relation is either an ascending
one as in Fig. 1.6, without minimum or maximum,
or, as in Fig. 1.7, one with a minimum. Continuous
solid solution with a maximum is very rare. The
space L + S between the liquidus and solidus
curves represents, at equilibrium, two-phase
mixtures, the L and § compositions being joined
by a horizontal tie line at any temperature. In
Fig. 1.6 L and S have the same composition only
In Fig. 1.7 the L and §
curves touch at the minimum; they touch tan-
gentially, however, and the two parts of the
diagram are not strictly like two binary systems
side by side.

Except for the pure components or for the
composition m, a given composition has a definite

for the pure components.

temperature range of freezing or melting, for
UNCLASSIFIED
ORNL-LR-DWG 24749

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

é
5 L
'.—
<
o
[T}
a
=
Lil
}_
4 A B
c
Fig.1.5.
L
/_+5\
s m
S
A B A B
Fig.4.6. Fig. 1.7

equilibrium conditions. Liquid x (Fig. 1.6) begins
to freeze at f,, and the solid starts with compo-
sition s,. As the temperature falls, the L and §
compositions adjust themselves, always on the
ends of a tie line, and the sclid reaches the
composition x at temperature t,, the last trace of
liquid that solidifies having the composition /,.
Such a crystallization process assumes complete
equilibrium all along, with the time for diffusion
in the solid that is formed being sufficient for the
solid to remain of uniform composition and in
equilibrium with the liquid.

As the opposite limiting extreme we may speak
of crystallization with perfect fractionation, in
which no diffusion at all is assumed to be
permitted to occur in the solid. The first trace of
solid formed is assumed to be effectively removed
from the reaction (as in removal of vapor in
distillation), and becomes merely the core of a
growing particle with a layered structure, one
with infinitesimal layers with infinitesimally
changing composition, each layer being taken out
of the equilibrium as it is deposited. In such a
process the liquid x (Fig. 1.6) begins to freeze

at t,, forming solid s, but now, with removal of
B-rich solid, the remaining liquid continues to fall
in freezing point and approaches the melting point
of A as limit. The solid formed has a core with
composition near s, and an outermost layer
approaching A in composition. As in azeotropic
distillation, such fractionation in the case of
Fig. 1.7 is limited by the minimum .

Miscibility Gap in Solid Selution

Figure 1.8 shows limited solid solubility in a
system with minimum melting point. The eutectic
of this system:

I(¢) ~calories=—a+ 6

is similar to that in Fig. 1.1 except that the solids
(a, b) are not pure. They represent the limits of
solid miscibility at the temperature e. The change
of this solid solubility with temperature is then
shown by the curves aa’ and bb’, joined by tie
lines indicating the compositions of conjugate
solid solutions. In Fig. 1.9 the miscibility gap
impinges on a system without minimum melting
point. The relation:

a + calories == L(p) + b6 ,

is called peritectic, being analogous to the
incongruent melting point of a compound (D in

Fig. 1.3).

Solid Solution and Polymorphism

We consider only a few simple relations for the
effect of B (in solid solution) on a polymorphic
transition point of A. Unlike Fig. 1.1, if B
dissolves in solid A, then the transition temper-
ature for:

Afi + calories == A

is either raised or lowered:

1. It is raised if B is more soluble in the lower
form than in the upper form of A (Figs. 1.10, 1.11).
The region «x represents equilibrium between
o phase and B phase, and with the B content in 3
greater than the B content in «, the transition
temperature is raised, from T , to T}. In Fig. 1.10
the phase reaction ot T is:

A+ calories —A_ +L{p) .

In Fig. 1.11:

M —
Afi +calories=—4A_+B_ ,

the B_ phase being o solid solution.
UNCLASSIFIED
ORNL-LR-DWG 24750

 

 

Aq + L

  

 

 

 

 

Fig. 1.10,

Fig. 4.41.

2. It is lowered if B is more soluble in the
upper form; it is, therefore, always lowered if the
lower form is pure Afl (Figs. 1.12, 1.13, and 1.14).

Polymorphic transitions of this sort apply to
solid solutions of binary compounds, as well as to
solid solutions of the components themselves.
These are only a few of the relations possible in

UNCLASSIFIED
ORNL-LR-DWG 24751

A+A

51 ey

=

 

 

  

 

 

 

 

 

 

Fig.1.42.
Ay+1—
(Aglgs |
At 4,)
A YSS| Mgt By
4 g
Fig.143. Fig.144.

transitions of solid solutions, but they suffice for
the systems under consideration. In particular,
these systems involve no case of a congruently
melting binary compound dissclving adjacent
solids on both sides; such a relation always
involves the possibility of nonstoichiometric
maxima and Berthollide compounds.
2. TERNARY EQUILIBRIUM OF LIQUID AND ONE SOLID (SURFACES)

The ternary diagrams under consideration deal
with temperature-composition (T vs c¢) relations
in additive ternary systems, each with three
fluorides as components. The special problems
of representation met with for reciprocal ternary
systems, those containing two cations and two
anions, are not involved.

The relations could presumably be completely
and explicitly shown in a transparent, ‘‘explodable®’
and sectionable three-dimensional triangular
prism model, in which the various phase spaces
and the two-, three-, and four-phase equilibria are
distinguished.  The two-phase spaces contain
(isothermal) tie lines
compositions of coexisting phases
solid, or two solids).

horizontal joining the
(liguid and
The three-phase equilibria
occupy spaces triangular in isothermal section —
spaces generated by isothermal three-phase
triangles, the corners of which move along con-
tinuous curves with changing temperature. The
four-phase  equilibria  (isobarically invariant)
constitute isothermal planes defined by the four
phases of the equilibrium.

The relations in the three-dimensional T vs ¢
prism are usvally represented and discussed by
means of plane diagrams which are either pro-
jections or sections of the prism.

The only type of projection used in the present
discussion is the polythermal projection of the
liquidus surfaces. This is a projection parallel
to the temperature axis, upon the ftriangular
composition plane, showing, therefore, the
various parts of the liquidus surface or surfaces
as viewed from the direction of high temperature.
The resulting ‘“‘phase diagram'’ thus consists of
fields (projected surfoces) for liquid saturated
with a single solid, of the boundary curves between
surfaces, for liquid saturated with two solids, and
of points for the intersection of these curves, three
at a time, for liquid in equilibrium with three
solids. The direction of temperature change can
be shown by arrows on the curves, and some
actual temperatures can be shown by means of
isothermal contours.

Such a polythermal projection shows directly
which surface will be reached by a liquid of
known composition upon cooling, and hence what
the nature, if not the composition, of the primary
crystallization product will be. The diagrams
under consideration give this information (where
it is known) unambiguously in every case because
they involve no solid phase with a retrograde

effect of temperature on its solubility (Fig. 1.2),
so that there is no overlapping, in polythermal
projection, of primary phase fields. This re-
striction is wunderstood in all the subsequent
The absence of retrograde effect
means, moreover, that the amount of liquid always
diminishes on cooling, while the total amount of
solid (or solids) always increases,

The T vs ¢ prism is further studied and
analyzed by means of plane sections, which may
be vertical T vs ¢ sections through two particular
binary compositions, or may be horizontal iso-
thermal sections which then amount to isothermal
solubility diagrams of the ternary system.

discussion.

We shall now consider the crystallization
equilibrium of liquid and one solid (the surfaces
of the liquidus); in the immediately following
sections we shall consider the equilibrium of
liquid with two solids (the boundary curves) and
the equilibrium of liquid with three solids (the
‘'condensed invariants’’ of the system).

The ‘‘surface’’ (the field, in projection) is
variously referred to as crystallization surface,
freezing-point surface, solubility surface, primary
phase region, or primary phase field.

When a liquid is cooled to one of these surfaces
it deposits one solid on cooling, as long as the
liquid is still on the surface (‘‘on the surface’’
means anywhere short of a boundary curve). Every
point on the surface represents equilibrium
between that particular liquid (point) and a
particular solid composition, and the liquid and
solid compositions or points are joined by a tie
line (isothermal). If the surface is cut in isothermal
section, the isothermal solubility curve is then
joined by a series of nonintersecting tie lines to
the composition of the saturating solid. If the
solid is one of fixed, constant composition, all
the tie lines, at any and all temperatures of the
surface, meet at the fixed composition of the solid
phase. Otherwise the tie lines, at any temperature,
simply join the liquidus and solidus curves; the
solidus ‘‘curve’ may be a straight line.

The direction of falling temperature at any
point of the surface is away from the composition
of the separating solid in equilibrium with the
liquid at that point. |f the solid is one of fixed
composition, therefore, straight lines radiating
from its composition are lines of falling temper-
ature, in every direction, and they cut contours of
lower temperature, progressively.
2.1. FIXED SOLID

In Fig. 2.1, the region Ae, Ee, is the (projected)
surface for saturation with pure solid A. The
arrows on the boundaries indicate the direction
of falling temperature, and the curves T, ..., T
are isothermal contours (T, > ... > T,). If the
liquid x, with composition falling on this surface,
is cooled, it begins to precipitate solid A ot T,
The crystallization path of the liquid, the path
followed by the liquid on the A surface while it is
being cooled and while it is precipitating 4, is
then a straight line extended from A through x.
Removal of A from the liquid makes its compo-
sition proceed in a straight line from the corner A,
The crystallization paths for a field of a solid of
fixed composition are therefore simply straight
lines radiating from the composition of the solid.
The composition of the liquid starting at x, while
precipitating A, will therefore be Ly 13 [ 4 etcy, at
the successive temperatures shown, and the ratio
of solid to liquid is given by xlz/xA, etc., at
each temperature. The quantity of liquid is always
diminishing, but the liquid is never completely
consumed while it is still on the A surface. Some
liquid must reach one of the boundary curves of the
fieid.

These relations hold, moreover, whether the
solid A is kept in contact with the liquid while it
is being cooled, or whether the solid is continually
removed as produced.

UNCLASSIFIED
ORNL -LR-DWG 24752

 

 

Fig. 21

2.2. VARIABLE SOLID (SOLID SOLUTION)

If the solid is a ternary solid solution, there is a
solidus surface, representing solid solutions
which are in equilibrium (point for point) with
liquids on the liquidus surface. The solidus
surface lies everywhere beneath the liquidus
surface in temperature, and it will not be repre-
sented at all in the usual ‘‘phase diagram.’”’ Any
point on the liquidus is connected by an iso-
thermal tie line with one individual point on the
solidus, representing the solid composition with
which it is in equilibrium.
anywhere intersect.

These tie lines never
The space between the two
surfaces is the two-phase space in which mixtures
consist, at equilibrium, of liquid and the solid
solution,

These surfaces are in contact at the composition
of a pure component (if the solid phase includes
the composition of the pure component), and
otherwise only at absolute maxima or absolute
minima of temperature, which may be at the binary
sides or in the ternary system: only at points, in
other words, and not along a whole ridge or trough
(valley). [The “‘absolute’ maximum or minimum of
““on'’ the surface —
and this means, it must be recalled, not on any

a liquidus surface is a point

one of its boundaries with another surface. The
absolute maximum or minimum may be at a unary
point (composition of a component), at a binary
point (side of the triangle), or at a ternary point,
as at the dome of a continuous ternary liquidus,
The surface, moreover, may have more than one
absolute maximum (or minimum).]

The equilibrium process of the freezing of a
liquid now involves a definite temperature range,
the vertical distance along the temperature axis,
in the T vs c prism, between the liquidus and
solidus surfaces. A liquid of composition x, let
us say, begins to freeze at T (the liquidus temper-
ature at x) and is completely solidified at T,
(the solidus temperature for the same composition
x). The composition s, of the solid, as it just
begins fo form at T,, is different from x. As the
crystallization proceeds, however, with falling
temperature, and if the liquid and solid phases
maintain complete equilibrium with each other,
both phases change in composition, so that at T
the final solid has the original composition x an
the last trace of liquid to solidify has still a
Between T, and T,
followed o separate, three-

different composition [,
each phase has
dimensional curve with respect to temperature and
composition, one along the liquidus surface and
one along the solidus surface, but such that the
two compositions joined by an
equilibrium tie line, at each temperature, passing
through the total composition x.

The path followed by the liquid, on the liquidus,
in such a process, is called its ‘‘equilibrium
path’’: the path followed by the composition of
the liquid during cooling, if the whole of the
solid phase
equilibrium with the liquid. Such a process can be
attained only as a limit, perhaps, with extremely
slow cooling, since the interior of the growing
solid can be kept uniform with the surface layer
only through diffusion in the solid.

At the opposite extreme of behavier we may
specify that no diffusion whatever takes place in
the growing solid.

were always

is at every moment in complete

The first infinitesimal amount
of solid now acts simply as an unchanging core
for a growing layered structure, each layer differing
infinitesimally in composition from the preceding
one, and each layer, because of the absence of
diffusion, being effectively
equilibrium as it is formed. In such a process
there is no longer a definite freezing range for
the liquid. As the solid produced is being ef-
fectively removed, the remaining liquid tends
toward some temperature minimum of the surface
before being consumed. The path followed by the

removed from the

liqguid in such a limiting process of perfect
fractionation we shall call a **fractionation path.”’

(When the separating solid is of fixed compo-
sition, as in Fig. 2.1, there is no distinction
between *‘‘equilibrium path'' and ‘‘fractionation

path’’; hence the one term, ‘‘crystallization path.’)

Fractionation Path

The surface may be considered to be covered
by a family of curves (fractionation paths),
following the course of falling temperature and
hence cutting contours in the order of falling
temperature, and all originating at some absolute
maximum of the surface. If there is an absolute
minimum on the surface, then these paths, after
fanning out, converge again at that minimum. All
the cases in the systems under consideration
concern solid solution surfaces having one or two
absolute maxima (in some cases the maximum is
metastable);
with an

there are no solid
absolute minimum.

submerged or
solution surfaces
Hence the fractionation paths in these systems

do not converge with falling temperature, but end,

each at a separate point, at the various boundaries
(for liquid in equilibrium with two solids) of the
surface.
there are two families of crystallization paths, one

With two absolute maxima on a surface,

originating at each maximum.

At any point on the surface, such a path starts
with a direction given by the L—S tie line at that
point of the surface, but the direction immediately
changes because, as the temperature changes, the
The direction of
motion for the liquid composition is away from the
composition of the separating solid. The fraction-
ation path is therefore such that its tangent at
any point is the L-—S5 tie line at that point
(Fig. 2.2). Here the curve Bf is a fractionation
path on a surface for precipitation of an A-B
solid solution; and the lines /, s, !

separating solid also changes.

25 v gy

are L—=S tie lines on this surface at temperatures
T >T,>T,>T,.

UNCLASSIFIED
ORNL-LR-DWG 32546

 

 

Fig 22.

Equilibrium Path

The composition x in Fig. 2.3 is liquid above
temperature ¢, and solid below tee When cooled
to t,, it just begins to produce solid of compo-
sition s.; s, is a point on the solidus surface in
equilibrium with the point [, (or x) on the liquidus
surface.  The line s,y is therefore the S—L
tie line for 7, at ¢,. With precipitation of s,, the
liquid liquidus in the
direction of this tie line (i.e., it tends, with

tends to move on the
removal of the solid phase, to follow the fraction-
ation path Pqr to which the tie line s/, is tangent
at /), but its motion is restricted by the condition
that the line joining solid and liquid compositions
must always pass through the fixed point x, at
each temperature, and that this line must always
be an equilibrium tie line. These successive
tie lines are s,1,, s,l,, etc. The solid follows
the curve s. s, ... s, (s, being the same as x),
and the liquid follows the curve (its equilibrium
path) l]l2 .o 15 (Z, being the same as x). At e
the sample is completely solidified, I, being the
composition of the last trace of liquid. Since
the lines Soly 5414, etc,, are tie lines, they are
tangent, at the liquid points, to the fractionation
paths (¢, . « . p) through these points.

[t is thus seen that the equilibrium path of the
liquid x (its path on the liquidus surface) is one
which crosses, with falling temperature, successive
fractionation paths at points where the tangent to
the path passes through the point x. The

UNCLASSIFIED
ORNL—LR-DWG 24753

 

Fig. 2.3

10

equilibrium path crosses the fractionation paths
from the convex to the concave side. |f a fraction-
ation path should be a straight line, it is not
crossed by an equilibrium path; it is itself an
equilibrium path, as in the case of precipitation of
pure solid.

In the general case of Fig. 2.3, the solid is a
ternary solid solution, and the liquid may com-
pletely solidify, as assumed in Fig. 2.3, before it
reaches a boundary curve of the surface. If, as in
Fig. 2.2, the solid solution is binary, it is
impossible for a ternary liquid precipitating the
solid solution to solidify completely before it
reaches a boundary curve of the surfoce, where a
solid involving the third component may also
But although, with binary solid
the curve s,s. ... s

precipitate.
becomes a
straight line, the relations between equilibrium
path and fractionation paths developed in Fig., 2.3
still hold (Fig. 2.4). At t, the mixture is not all
solid; it still consists of liquid and solid in the
ratio s, x/xI, .

Returning to Fig. 2.3, ony total composition,
like x itself, on the particular tie line syl will
consist, at t,, of the phases s, and /;. Hence the

3 3
equilibrium path of any total composition between

solution,

s, and [, will pass through one common point,
namely, 13. Consequently, while there is but one
fractionation path passing through any single point
of the surface, there will be an infinite number of
equilibrium paths passing through the same point.
A surface may therefore be described by the
family or families of fractionation paths on it, but
not by equilibrium paths.

UNCLASSIFIED
ORNL ~LR-DWG 24754

 

 
3. TERNARY EQUILIBRIUM OF L1QUID AND TWO SOLIDS (CURVES)

We now consider the crystallization process for
a liquid in equilibrium with two solids, §, and S,:
liquid on a curve of twofold saturation (boundary
curve, fieid boundary),

3.1. REACTION TYPES

The curve constituting the boundary between the
surface for S, and the surface for S, represents
liquid in equilibrium with both solids, but not
necessarily precipitating both solids upon cooling.
If the liquid does precipitate both solids on
cooling, and the reaction is:

[. - calories —— §

the crystallization is said to be positive for both
solids, §,(+), §,{+), and the curve is said to be
one of even reaction. [With retrograde temper-
ature effects it is possible to have both solids
dissolving on cooling, with negative crystal-
lization for both, so that the reaction may still
be even: §.(~), S,(=).] The curve is one of
odd reaction (a transition curve) if one solid (Sys
let us say) is dissolving in or reacting with the
liquid and the other, S,, is precipitating during
cooling. The crystallization is now S,(=), $,(),
and the reaction is:

L +S] -~ calories —— Sz

The sign of the reaction at a particular point
on the two-solid curve involves the direction of
the tangent to the curve at that point in relation
to the compositions of the two solid phases in
equilibrium with the liquid at that point., The
liquid is at any point simply one corner L of a
three-phase triangle. In the general case, in
which all three phases are variable in composition,
each equilibrium phase follows its own compo-
sition curve in the phase diagram, but the usual
polythermal phase diagram shows only the curve
for the liquid composition. [f the solids A and
§, are of fixed composition, then the S -5, leg
of the triangle is o fixed line and only the L-S,
and LS, legs move, with L on the liquid curve;
if one of the solids is a binary solid solution, then
the curve for that solid is a straight line; etc.
In any case the liquid curve on the ordinary phase
diagram represents simply one corner of the
three-phase triangle of the equilibrium, and the

whole triangle may in general be moving, with its
corners changing in composition, as the temper-
ature changes.

Figures 3.1, 3.2, and 3.3 show three cases:
Figs. 3.1 and 3.2, cases with curves for both A\
and 5., both of which are therefore ternary solid
solutions; Fig. 3.3, a case with fixed solids for
§, and S,. The arrows on the curves indicate the
direction of falling temperature., The surface
on the left of the L curve is that for liquid de-
positing S, on cooling; that on the right is for
liquid depositing S, on cooling.

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crystallization

Positive (precipitation) of a
solid from o liquid corresponds to a direction
vector for the motion of the liquid away from the
composition of the separating solid; for negative
solid in a
liquid, the direction vector for the motion of the
liquid is toward the solid. The resultant of the
direction vectors must make the liquid move in
the direction of falling temperature on the L curve.

crystallization or dissolving of a

Examination of the direction vectors, in Figs. 3.1,
3.2, and 3.3, required to give the indicated motion

11
on the L curve, shows that the reaction is even,
in every case, between 7 and s [S,(4), 52(+)], and
odd between s and ¢ [S,(-), S,(+)]. Equivalent to
this procedure is the test of the tangent to the
curve at any point. If the tangent extends between
the compositions of the equilibrium solids, i.e.,
if the tangent cuts the S, -5, leg of fhe three-phase
triangle, the curve is even [25 +)]; otherwise
it is odd. The sign of ‘rhe reactlon changes at
point s, where the tangent to the curve passes
through the composition of one of the solids (S,
for the cases illustrated); i.e., where one of the

-S legs of the triangle is tangent to the L curve,

A curve originating at a binary eutectic (pre-
sumably as in Fig. 3.1), whether entering the
ternary system with falling or with rising temper-
ature, always starts as an even curve, while one
originating at a binary peritectic (Figs. 3.2 and
3.3) starts as odd. But in all cases the sign may
change as the curve proceeds on its course, both
because of changing direction of the L curve and
because of variation in solid compositions. Hence
if "‘eutectic curve” or ‘‘peritectic curve'' refers
simply to the origin of the curve, the expression
does not necessarily describe the type of reaction
later on along the curve. Since the type of re-
action at any point on a curve is an important
property of the curve, it is better to speak of
““even’’ and ‘‘odd’’ curves in order to distinguish
curves for the precipitation of two solids from
transition curves,

The sign of the reaction on a liquid-solid curve
is, then, quite clear, on the ordinary phase dia-
gram, if the solids are of fixed composition; but,
when the solids are variable, the type of reaction
(precipitation of two solids or transition) is often
unknown, for it is necessary at any point to know
the compositions of the saturating solids in order
to test the tangent at that point,.

Since the direction of falling temperature on a
surface is always away from the composition of
the separating solid, it turns out that a two-solid
curve of even reaction can be reached from either
side, but if the reaction is odd [SI(-')' 52(+)] it
can be reached only from the S, side. Both the
fractionation paths and the equilibrium paths
lead to the odd curve from the S, surface, and
away from it on the S, surface. This is at once
clear in Fig. 3.3, where all the crystallization
paths on the S, surface radiate as straight lines
from the point S,, and those on the §, surface are
straight lines radiating from the point 5.

12

3.2, MAXIMUM AND MINIMUM
TEMPERATURE POINTS

A twofold saturation curve may pass through a
maximum or a minimum of temperature. This is
possible only if at least one of the solids is
variable in composition. At the maximum or
minimum the three-phase triangle becomes a line:
the three phases (L, Sy and 52) have collinear
compositions, all lying on one straight line of
the diagram. Figure 3.4 shows the case of a
maximum on a curve of even reaction, and Fig. 3.5
a minimum on a curve of odd reaction.

The leading corner of the three-phase triangle
(in the direction of falling temperature) may be
said to be the liquid. The collinearity corresponds
to the relations at a binary origin of such an
equilibrium, which is always a maximum or a
minimum for the equilibrium, and where of necessity
the three phases are on one straight line, which
then opens up into ¢ triangle on entering the
ternary diagram.

3.3. EQUILIBRIUM CRYSTALLIZATION
PROCESS FOR LIQUID ON A TWO-SOLID CURVE

When the liquid is on a two-solid curve, the
fixed total composition x of the sample being
cooled must lie inside the three-phase triangle
(Fig. 3.6). The mixture consists of three phases,

UNCLASSIFIED
ORNL- LR -DWG 24755

F Wi M
MAXIMUM

   

 

s
o
5,

2

gL 36
such that the ratio of the total solids to liquid is
xL/xy, and the ratio of S, to Sy is ySz/yS1.
As the temperature falls and L travels down the
curve, the whole three-phase triangle moves with
it, $; and §, in general following their own com-
position curves. Since the point x is fixed, it is
therefore possible (but not necessary) that one of
the three sides of the triangle may come to sweep
through x. When this happens, the mixture be-
comes a two-phase mixture, the third phase having
been consumed in the crystallization process. In
the sketch in Fig. 3.6, if the general configuration
remains the same while the triangle moves to the
right, the amount of solid increases and the liquid
diminishes (as always), and when the side .5,
sweeps through x, the liquid vanishes, leaving
§, and §,. The solidification process would then
be completed while L is still on the curve, or
before L reaches the end of the curve, J. But if
the triangle twists aond changes shape as L moves
down the curve, the point x may come to be swept
by the S.L leg (S, vanishing) or by the S,L leg
(S, vanishing). It S, vanishes and the liquid is
left saturated with only §,, the liquid leaves the
curve to travel on the §. field; if §, is consumed,
the liquid, saturated with §
curve onto the S, field.

, alone, moves off the
Some of the possible variations of behavior are

the following:

1. Curve of even reaction:

(a) |f the solids are not variable, no phase is
consumed while L is on the curve. The
liquid diminishes, but some reaches the
end of the curve; [. does not leave the
curve.

(6) If S, is variable and S, constant, either
liquid or S, may be consumed, but not §,.

Solidification may be complete on the curve,
or L may leave the curve for the §. field,
or it may reach the end of the curve,

(c) If both solids are variable, any one of the
three phases may be consumed. Solidifi-
cation may be complete on the curve, or
L. may leave the curve on either side, or
L may reach the end of the curve.

2. Curve of odd reaction [Sl(_)' 52(+)]: Now §,
may always be consumed, whatever the nature
of the solids.

(a) With fixed solids, only S, can be con-
sumed. The liquid may leave the curve for
the S, field, or it may reach the end.
Solidification cannot be completed with L
on the curve.

(6) If S, is variable (s, fixed or variable),
then any one of the three phases may be
consumed.  Solidification may be com-
pleted on the curve, L may leave the curve
for either side, or it may reach the end of
the curve,

A transition curve (odd reaction) is traveled
(L. moves along the curve} only if complete equi-
librium is maintained between the liquid and the
If this solid (S,)
is effectively cut of the equilibrium (i.e., if it is
removed as formed, if its surface is covered by

dissolving, or reacting, solid.

deposition of S,, or if the process is too rapid),
then a liquid which reaches such a curve by depo-
sition of S, merely crosses the curve. It begins
to precipitate S, without consuming any SI; it
undergoes a change in direction and enters at
surface. The new solid §, is
merely deposited upon the first (S,) in a non-
equilibrium mixture,

once upon the §

13
4, TERNARY CONDENSED INVARIANT POINTS (FOUR PHASES)

Ternary condensed invariant points are generally
the points of intersection of three curves, each
for a liquid in equilibrium with two solids, re-
sulting in the equilibrium of a liquid with three
solids. In addition we shall have to consider
reactions involving four solids, below temper.
atures of equilibrium with liquid.

The four phases of the (isobarically) invariant
equilibrium are arranged either as a triangle, with
cne phase inside (type A), or as a quadrangle
(type B). The special case which may appear
to be the limit between triangle and quadrangle,
with the fourth phase on a side of the triangle
(i.e., with three of the four phases on a straight
line), is strictly a binary three-phase invariant,
and the fourth phase, while present, is not in-
volved in the phase reaction. We shall discuss
this case before considering the true ternary in-
variant reactions.

4,1. BINARY DECOMPOSITIONS IN PRESENCE
OF TERNARY LIQUID

Given the four coexisting phases arranged as
follows:

Ph]\— Pl-|27Ph3
Ph,

with Ph,, Ph,, and Ph, collinear, then the equi-
librium:

Ph, <=2 Ph, + Ph; t calories

does not invelve Ph,. Such a situation arises for
the interaction of three solids (collinear) in the
presence of a liquid phase:

B-\— |LC7D

the liquid being saturated with all three. In the
usual examples found, the three solids are on a
binary side of the ternary diagram, but sometimes
they are on a line inside the ternary system,

14

“Pure’ Solids

If B, C, and D are three successive solids in
the binary system A~E, and if they are ‘‘pure’’ in
the sense that, although they may involve binary
solid solution among themselves, they nevertheless
do not take into (ternary) solid solution the third
component F, then the temperature (always at

constant pressure) of the equilibrium:
C == B + D + calories

is unchanged by the presence of a liquid, con-
taining F, in which these solids are dissolved
to safuration. The liquid may even contain more
than one such foreign component. Provided that
the three solids themselves remain pure in re-
spect to any of the foreign components {(F, G, . . .)
in the liquid phase, the temperature of the phase
reaction is the same as that in the binary system
A-FE itself.

Not only is the temperature independent of the
composition of the liquid phase, but, since the
liquid is not invoived in the phase reaction, the
very amount of the liquid phase is constant (com-
plete equilibrium being assumed) during the phase
reaction.

Such strictly binary invariant points will be
distinguished with a subscript identifying the
decomposing solid phase, such as P, or P, in

the above examples. A similar invariant would be
that of the transition of a binary solid solution in
presence of a ternary liquid (points T in Figs.

1.10 to 1.14}.

Effect of the Third Component Entering
into Solid Solution

|f a foreign component enters any of the three
solids, forming a solid solution, the temperature
of the phase reaction is changed, and it now varies
with the composition of the solid solution {or
solid solutions)., If C alone forms such a solid
solution with the foreign component, then the de-
composition temperature is raised if the reaction
is:

C +calories S<==B +D ,
and lowered if

C —~ calories =— B +D .
If C remains *‘pure’’ while either or both of the
other solids form a solid solution with the added
component, then the decomposition temperature is
lowered if the reaction is:

C +calories —=— B +D ,
and raised if
C - calories &=—=B +D .

If both C and one (or both) of its products form
such a solid solution, then the temperature of de-
composition may be either raised or lowered, and
it may even pass through a maximum or a minimum.

Finally, however, when such ternary solid so-
lution is involved in one or more of the three
solids, their compositions are no longer collinear,
The invariant reaction now involves all four
phases, it is no longer binary but ternary, and it
will pertain to one or other of the ternary types
now to be discussed.

4,2, TYPES OF TERNARY INVARIANTS

Type A Invariant: Triangular or Terminal
Type of Invariant

fn the case of a type A invariant (Fig. 4.1), the
phase reaction is terminal with respect to the
interior phase. The phase reaction is:

4 tcalories — 1 +2+3 .

On one side of the invariant temperature we have
the three equilibria involving 1, 2, ond 4; 29
3% and 4% and 17, 3%, and 4”; and on the other
side only the equilibrium of 17, 2"*, and 3"
The interior phase, 4, exists only on one side, and
its stable existence is terminated at the type A
invariant,

If the interior phase is a liquid and the others
are solids, the invariant is a eutectic. All four
phases may be solids, and then the invariant is the
decomposition of solid 4 into three solids. The
liquid may be an exterior phase, and then the in-
variant is an incongruent melting point of the
interior ternary solid 4; two cases arise. Case

(@):
4 + calories —1+2 + L

is a ternary analog of the incongruent melting
point of a binary solid into liquid and another

solid, Case (b):

4 — calories — 1 +2 + L

is an inverse peritectic or inverse fusion point,
like one found in rare cases in binary systems
(Fig. 1.4), and (possibly) in one case in the
present ternary systems (solid phase C in system
Y-U=Z, Fig. 14,10).

Type B Invariant: Quadrangular, Diagonal, or
Metathetical Type of Invariant

In the case of a type B invariant (Fig. 4.2},
the phase reacfion is:

1 +3 tcalories == 2 +4 ,

not terminal for any phase. On one side of the
invariant temperature we have the equilibria in-
volving 1, 2, and 3 and 1% 37, and 4’ and on the
other side the equilibria involving 17, 2%, and
4° and 277, 377, and 4°”. This invariant is re-
lated to double decomposition reactions, even
when occurring in additive ternary systems. The
combination 1 and 3 is stable only on one side
of the invariant temperature, and the combination
2 and 4 only on the other side. The stable di-
agonal of the quadrangle changes from 1-3 to 2-4;
hence the term ‘‘diagonal reaction.”

4,3, RELATIONS OF THE THREE LIQUID
CURVES AT THEIR INVARIANT INTERSECTION

On the liquidus diagram the only invariants we
see are those involving a liquid phase and three
solids, and they occur as intersections of three
curves of liquid in equilibrium with two solids.
Hence, unless the locations of the three solids
are known, relative to the position of the invariant
liquid (commonly this position is called '‘the in-
variant point,”’ but the invariant is not a point
but a plane, either triangular or quadrangular),
we cannot always know the type of invariant
involved.

If, as in Fig. 4.3, all three liquid curves fall in
temperature to their intersection, the invariant is
a eutectic (type A). The phase reaction is termi-
nal for the liquid, which is inside the three-solid
triangle:

[. - calories fis] +S2 +53 .

Conversely, if the liquid of the intersection is
known to be inside the three-solid triangle, then
the temperature must fall to the intersection on
all three curves, and the intersection is a eutectic,
the temperature minimum for the liquidus in the
area of the three-solid triangle.

15
5 2
‘.._._-- 2
——f————————
4 4/ 3.'
3!!
1
4,’1’ *
Fig. 4.1.
3
3/ 3
.
—g————
2
2
41
1 1/ 4
Fig. 4.2.

UNCLASSIFIED
ORNL-LR-DWG 24757

"t
2
—_—
_-_,___.__
i
3
I
1
T
3
4///
4 H
"
1

 

Fig. 4.3. Fig. 4.4.

16

Fig. 4.5,
But any other arrangement of temperature fall of
the three curves may mean either a type A or a
type B invariant. Thus, the arrangement in Fig.
4.4 may mean either of the following reactions:

(@) Type A: S, +calories == S, +S5, +L.

(6) Type B: S, +L +calories == §, +5,.

That in Fig. 4.5 may be either of the following:

—_—

(c) Type A: S, = calories == S, +8, +L.
(d) Type B: S, +L = calories &= 5, +S,.

These four invariants involving liquid (a, 4, ¢, d)
are usually called simply ‘‘ternary peritectics®’
as distinct from the eutectic reaction.

Moreover, the curves meeting at a eutectic are
usually all three of even reaction, but they need
not be; one may be odd in reaction. For in-
variants (a) and (b) (Fig. 4.4) one of the curves
proceeding from the invariant to lower temperature
must be odd. For invariants (¢) and (d) (Fig. 4.5)
no restrictions of reaction sign hold.

For all invariant intersections of three liquid
curves, no angle of the intersection can be greater
than 180°. This requirement holds both for the
truly ternary invariants (types A and B) and for
those explained as binary invariants with the
three soiids on one straight line. This restriction
means that the metastable extension of each
curve must extend into the field of the third
solid. The metastable extension of the curve for
liquid in equilibrium with S and S, for example,
must penetrate to temperatures below the surface
for liquid in equilibrium with S_, and this require-
ment cannot be satisfied, for all three curves
simultaneously, if any angle of the intersection is
greater than 180°. Thus, in Fig. 4.6, the extension
ia’ of the curve for liquid in equilibrium with §
and S., which is a boundary of the surface for
liquid in equilibrium with S 3+ would have to pene-
trate beneath the S, surface itself, an impossi-
bility in the absence of retrograde temperature
effects, here excluded. The same contradiction
would hold for the extension b’ of the curve for
liquid in equilibrium with §, and S,, which is
also a boundary of the § Only the
metastable extension ic” of the curve for liquid in
equilibrium with S, and S, would behave correctly.

surface.

4,4, CONGRUENT AND INCONGRUENT
CRYSTALLIZATION END POINTS

In Figs. 4.7 and 4.8, E represents a eutectic
liquid in equilibrium with the three solids Sir Sy
and ¥ (Sl)' (52), and (53) represent the fields for
liquid in equilibrium with each of the three solid
phases, With complete equilibrium always main-
tained during cooling, the point E must be reached,
along one or another of the three curves meeting
at E, by liquid from any total composition in the
triangle §,5,5,, no matter how many other in-
variant points may be traversed on the way; and,
with complete equilibrium, only liquids from
original compositions in the triangle $,5,5, will
reach E. Liquids with original composition x in
the triangle §,5,5, cannot dry up, or they cannot
be completely solidified, until some liquid finally
reaches E. Since liquid E is inside the triangle
of its three solids, so that the composition of the
liquid E is accountable in terms of its three solids,
it is said to dry up congruently; i.e., E is the
congruent crystallization end point for compositions
in the triangle §,5,5.. Also, when the liquid

UNCLASSIFIED
ORNL-LR-DWG 24758

 

 

Fig. 4.8

17
reaches FE, it is always entirely consumed; it
never leaves E. This is so whether the solids
involved in the reaction are removed as formed or
not. (Exceptions, of course, would occur if there
is supercooling with respect to some solid phase;
in such a case the liquid, approaching an in-
variant point along a two-solid curve, simply con-
tinues on the metastable extension of that curve
until the metastability is relieved.)

Invariant points other than eutectics [peritectic
points (a) and (d), Sec 4.3] may be crystallization
end points for some compositions, but they are
then, in contrast, incongruent crystallization end
points. The liquid in these cases is not inside the
triangle of its three solids, and its composition
is not accountable in terms of these solids.

The following consideration of these invariants
assumes complete equilibrium in all processes.

Case {a): Reaction of type A (Fig. 4.9):

L+5,+S, = calories — §, .
Here point P is reached by liquids traveling down
in temperature along the curve LS,S4, provided
the original total composition x is in the triangle
PS,S,. Then S, appears in the invariant reaction,
and if x is in the triangle $,5,5, the liquid is
consumed, leaving the three solids. Point P is
therefore the incongruent crystallization end point
for the composition triangle S.5.5.. As for the
rest of the quadrangle: with x in the friangle
PS.S,, the solid 5, is consumed, leaving liquid,
Sy, and S,, and the liquid enters upon the curve
LS.S,; for x in the triangle PS.S,, S, is con-
sume?), and L leaves along the curve LS.S,.

This invariant is seen to be the incongruent
melting point of the interior phase §,, which may
be either a fixed ternary compound or a ternary
solid solution. Upon heating, it decomposes or
melts incongruently, at the temperature of the
invariant, to produce liquid of composition P,
S.,, and §

2f ‘
Case (a%: Reaction of type B {Fig. 4.10):

5‘] + [ — calories — 52 +S3 .

Liquid P is reached on cooling for x in the quad-
rangle §,5,PS,, along the curve LS.S, if x is in
the triangle S.5,P and along curve LSS, for x
in the ftriangle §,5.P. If x is in the triangle
§,PSq S, is consumed and L proceeds along
curve L5, S.. But if x is in the triangle §,5,5,

18

the liquid is consumed, leaving the solids ., S,
and §S,. Point P is thus the incongruent crystal-
lization end point for the composition triangle
515253.

The invariants (b} and {c), on the other hand, are
never crystallization end points in a cooling
process.

Case (c): Reaction of type A (Fig. 4.11):

S, - calories — S,+8;+L .

This is the inverse incongruent melting point of
the solid S. (a fixed ternary compound or a ternary
solid solution), decomposing or melting incon-
gruently, on cooling, into liquid of composition
P, S,,and §,; it is somewhat like that in Fig. 1.4
for a binary system. Liquids saturated with S,
and Sa along curve LS,S,, reach P on cooling
if x is in triangle S,S.P; and liquids on curve
LS.S,, saturated with S, and §,, reach P if x is
in triangle § S, P. Then at P, solid §, decom-
poses, and when all of it is consumed, the liquid
proceeds on the curve LS, S.. This case is en-
countered later in Fig. 14,10, in system Y-U-Z,
For x in triangle §,5,5,, the system is com-
pletely solid before the temperature falls to P; but
at P the liquid phase reappears in the invariant
reaction, as a result of the decomposition of S],,
and L then proceeds along curve LSS ..

Case {(b): Reaction of type B (Fig. 4.12):
S, +8, - calories — S, +L .

At this invariant temperature the combination of
solids S, and S. reacts, on cooling, to produce
liquid of composition P and §,. Liquid saturated
with S, and §,, along curve LSS, reaches P
on cooling if x is in triangle PS_S,. Then if x is
above the diagonal PS., S, is consumed in the
invariant reaction, leaving liquid, §,, and §,, and
L then moves away on the curve LS S,; for x
below the diagenal, S, is consumed, and L leaves
upon the curve LS.S.. In this invariant, the cool-
ing of two solids, S, and S,, leads to the for-
mation of liquid and the solid S, a situation en-
countered later in Fig. 13.6, in system Y-U-X.
For «x in ftriangle § 5,5, the system is com-
pletely solid before the temperature falls to P;
but at P the liquid phase reappears in the in-

variant reaction, either S, or S, is consumed

2 3
completely, and L then proceeds along one of the

curves falling away from P.
UNCLASSIFIED
ORNL -1 R-DWG 24759

 

 

With complete equilibrium, therefore, a liquid
reaching point P may be completely solidified at
that point in case (a) or case (d), but never in
case (b) or case (c).

In the absence of complete equilibrium, however,
or if the liquid is not given time to react as re-
quired with the solid phases at the invariant
temperature, the liquid reaching P does not stop
there at all, but travels on down in temperature;
along one of the issuing two-solid curves if there
is an even curve to lower temperature, or onto a
surface, of liquid in equilibrium with one solid,
if there is noeven curve leaving P for [ower temper-
ature.  Such crystallization processes will be
completed in various ways: on a solid solution
liquidus surface (the last crystallization product
being a single solid), on a curve of even reaction
(the last product being a mixture of two solids), or
at a eutectic (the last crystallization product
being a mixture of three solids).

4,5. MELTING POINTS OF
TERNARY COMPOUNDS

There are three types of melting points of
ternary compounds,

1. Congruent melting point; The solid ternary
compound here melts to a ternary liquid of the
same composition. This will occur at an absolute
maximum of the surface for liquid in equilibrium

with the compound, not at a boundary of that
surface. The compound is here said to possess
an '‘open’’ or “‘exposed’’ maximum,

2. Semicongruent melting point: In this case
the ternary compound M, decomposes to a liquid
Ly and another solid M,, with all three compo-
sitions, M,, M,, and L, lying on a straight line
in the ternary diagram. This temperature will
be a maximum (y, in Fig. 4.13) on the boundary
curve between the surface (L + M1) and the sur-
face (L + M,), and hence on curve LM M,. The
temperature on curve LM M, falls away from y in
both directions, but, while the temperature on the
surface (L + M,) falls toward y, the temperature on
the surface (L + M,) falls away from y.

3. Incongruent melting point: In this case the
ternary compound S.r decomposes to a liquid P
and two other solids, in an invariant reaction in
which the ternary compound is the interior phase
of a triangle; case (a) above (Fig. 4.9).

4,6, INVARIANTS INVOLVING SOLIDS ONLY

Invariant reactions both of type A and of type B
may involve simply four solid phases, below
temperatures of liquid equilibrium. The usual case
would be some double decomposition of type B.
The type A reaction would apply for the decom-
position, on heating or cooling, of one solid into
three others, as already mentioned. Both types

will be encountered later.

UNCLASSIFIED
ORNL-LR—~DWG 24760

 

Fig. 4.43.

19
5. CRYSTALLIZATION PROCESS WITH PURE SOLIDS

In this and in the next two sections we shall
consider some of the relations met with in typical
ternary systems, first in systems involving only
pure solid phases and then in systems involving
solid solutions.

The ternary system of Fig. 5.1 contains two
compounds, D, and Dy, stable at the

temperature and not decomposing on

binary

liquidus
cooling. Any ternary liquid, upon complete solidi-
fication, must, if complete equilibrium is main-
tained throughout, consist finally of a mixture of
three of the five solids of the system - A, B, C,
D], and D2. But there are two arrangements of
the five solids possible: scheme (a) and scheme
(b), We know in advance that one of the three-
solid combinations will be 4, D,, and D,, but
to determine whether the coexistence of solids in
the system is {a) or (b), experiment is required,
In (@) the pair of solids D
combination, and it would react to produce D, and
C (plus excess of either D, or B), while in (&)
the pair D, and C is unstable and would react to
produce D, and B. For this reason the three-
solid coexistence triangles shown in either scheme

and B is an unstable

are sometimes called ‘‘compatibility triangles.”
Theoretically, a single experiment, upon a liquid
composition at the intersection of the lines D B
and D,C, would suffice to establish the coex-
istence relations, provided that the final solids
obtained upon complete crystallization represented
true equilibrium. In scheme (&) the experiment
would yield the pair D, and C as sole solids, and
in scheme (b) the opposite pair.
ment is an

Such an experi-
application of what is known as
Guertier's Kldrkreuzverfahren,

In either case, the phase diagram will have five
fields

equilibrium with three solids, each functioning as

and three invariant points of liquid in

a crystallization end point, congruent or incon-
gruent, for one of the three-solid triangles. The
curves of liquid in equilibrium with two solids
will be joined by three intersections, as in Figs.
5.2 (a) and (b),
Figs. 5.1 (2) and (6). The invariants are numbered
to correspond to the three-solid triangles in Fig.

5.1,

in either case, at least one of these invariants

corresponding respectively to

must be a eutectic, with the invariant liquid in-
side the three-solid triangle of corresponding
number, while the other two points may be either

20

eutectics or peritectics, together or separately.
Scheme {a) thus comes to have nine possible
arrangements of the three invariant points:

Triangle | Triangle H Triongle HI
E, E, Es
B, P, — E,
E, —_ P, E,
E, Eqye Py -=
-= 10 Eg Eq
E|s Py P, — —
10 Py 3 ~=
- Pre g Py -
- -- Pro Por By

The entry "E], P, P, —=""in line 7 means, for
example, that the first two intersections are in
triangle | and the third in triangle |, so that the
first is a eutectic and the other two are peritectics.

Although each of the curves for liquid in equi-
librium with two solids enters the ternary diagram
with falling temperature, the temperature direction
on the two interior curves depends on the nature

UNCLASSIFIED
ORNL-LR-DWG 24761

C C
{g) {5)
) 1
/1 11
e B 4 B
02 DZ
Fig. 51

  

Fig. 5.2.
of the invariant points involved, for only a eutectic
is a temperature minimum,

Moreover, each of the nine possibilities enu-
merated for scheme (a) will have several variations
depending on the congruence or incongruence of
the melting points of the binary compounds in
their binary systems, with further subvariations
(for incongruence) depending on whether the
peritectic and eutectic solutions for the incon-
gruent compound are on the side of one or of the
other component in its binary system. With a
congruent melting point, the composition of the
compound will be on the binary side of its ternary
field, at the maximum temperature of the surface,
and the crystallization paths radiate from its
composition. The compesition point of an incon-
gruently melting compound will be outside its
field, but the composition point still represents
the (metastable) maximum of its surface, and the
crystallization paths radiate, by extension, from
its composition.

in Fig. 5.3, with three binary compounds, D,

melts congruently, and e, and e, are both binary
eutectics:

L(es) - B+ D2 ’
{(Note: reactions are written for the cooling

process.) The compounds D, and D, both melt in-
congruently, and b, and p, are the peritectic
liquids of the respective binary systems:

L{p,) +C»D, ,

L(p3) +A->D, .

There are six fields, projections of surfaces for
liquid saturated with a single solid: A, D, C,
D,, B, and D, in clockwise order.

The system has four ternary invariant points,
corresponding to the four three-solid ftriangles.
Three of the invariants are eutectics (temperature
minima); however, one, P., is not, since its
liquid, saturated with the solids of triangle Ill,
falis in triangle V. The temperature along the
curve E E,, for liquid saturated with D, and D,,
has a maximum value at m, the intersection of the
boundary curve with the line joining the two solids.
This is a **collinear equilibrium,’’ and the three-
phase triangle for liquid in equilibrium with D, and
D,, starting as the straight line D,mD,, expands,
with falling temperature, to end as the triangle

D,E,D, at E, and as the triangle D, E, D, at E,.
The line D, mD,, joining the compositions of the
solids and intersecting the boundary curve between
their adjacent fields, is known as an Alkemade
line. With the temperature falling toward m on
both adjacent surfaces (for liquid in equilibrium
with D, and for liquid in equilibrium with D),
while the temperature falls away from m on the
E,E, curve, the point m is a saddle point on the
curve,

The line Am ‘D, is another Alkemade line, and
m” another saddle point, @ minimum in temper-
ature on the surfaces between A and D, but a
maximum of temperature on the curve E,P_.. The
triangle for liquid in equilibrium with A and D
expands, with falling temperature, from the line
Am’D, tothe triangle AE,D, and, also with falling
temperature, to the triangle AP D ..

The section of the diagram through the line
Am 'D2, moreover, is a quasi-binary section. The
vertical section of the T vs ¢ prism through this
line is altogether like the T vs ¢ diagram of a
simple binary system (Fig. 5.4). Such a section

UNCLASSIFIED
ORNL-LR-DWG 24762

E oy

 

Fig.5.5.

2]
divides the actual ternary system A-B-C into
two separate subsystems, A~C-D_ and A-D,-B.
The section through the line D mD,, on the other
hand, although also containing a saddle point
very similar to m’ is not quasi-binary; one of the
solid phases involved in the equilibria traversed
on this section is C (between D,
that the phase equilibria along line D mD, are

and point 7}, so

not describable on the basis of o binary system
with D, and D, as components.

From this pomf on, phase reactions involving
one or two or three solids will be written always
as occurring in the direction of falling temperature,
or in the direction of removal of heat, unless

otherwise specified. The equation:
L%, +5,,
therefore, means:
L — calories -85, 4S5, .

The reactions along the boundary curves of
Fig. 5.3 are as follows:
e F. . L - D, + A;

272

paPy L +A-D, (reaction odd);

e Byt L-D,+B;

65E4: L -8B +D2,'

eéET: L-D,+(C;

p E |+ reaction odd from p, to s: L + C - D,;re-
action even from s to E,: L - C + D, (the
line D, s is tangent to the curve);

E]mEz: LD, +D2;

E]mP 1 LA +D,;

2 .

I 3E4 L D3 +D2.

The invariant reactions are:
E]: L »D] +C +D2,'
E,: LA +D] +D,;
Pyt L+A Dy +Dy;
E4: L->Dg+ D + B.

Liquids wn'rh orlgmal composition x in triangle |
must reach E, for complete solldlhcohon, those in
triangle I mus'r reach £,; those in triangle Il
must reach P; and those in triangle |V must reach
Ed'

The peritectic P is reached by all liquids with
x in the quadrangle AD,P.D..
m D P
solld, reaches curve m P3, and then proceeds to

For x in the

For x in the region

, the liquid precipitates D, as the first

P, carrying A and D, as solids.

re3gion Am°P,, the liquid reaches curve m’P,
after precipitating A, and also reaches P carrying
AandD,. Liquids th x in the region AP D, and
hence on the A surface, precipitate A cnd reach

22

the curve P3P 5 which is then followed while some
A reacts with liquid to form D,. At P

L+A~>D3+D2

Now for x in triangle Ill, the liquid is consumed,
leaving A, D, and D, (complete solidification),

But for x in the triangle D,D,P,, A s consumed

!
and the liquid proceeds on cur\fe ?3 E,.

The eutectic F, is reached by all liquids with x
in triangle |V. Those from the triangle DD, P,
reach P Those in the
quadrangle P.D,e L, precipitate D, as the first

solid, reach one of the boundary curves, and

as already explained.

then proceed to E,, either along curve P.E,

precipitating D, and D g OF along curve e E, pre-
c:nd B. Those from the B fleld be-

have similarly, reaching E

cipitating D2
either along curve
e, E, with D and B as solids or along curve e E,
with D, and B as solids.
D, field, p3P3E4e
and reach £

Those falling upon the
" as first solid,
along either curve P,E, or curve
ek, . Original compositions in the region D P,p.,
such as point z, give A as first solid and reac

precipitate D,

the transition curve p.P. on a straight line from
33 9

A, as at point v. They then travel on the curve,
toward P, but solid A is consumed before P is
reached, os at point w, on a straight line through
D, and u. At this point the liquid is saturated
only with D,
and travels across the D
boundaries, .?3E4 or €4E4,
The transition curve p P

and it therefore leaves the curve
field to one of its
finally to reach E,.
is therefore left be-
hind, after some travel along the curve, by liquids
coming from original, total compositions x in the
region D P p,, when the tie line D,L of the three-
phase triangle for L. on curve p_P. comes to sweep
through x, for at that point the solid A will have
been consumed to leave D, as the sole solid
phase,

(We shall speak of the transition curve as thus
“‘crossed'’ by the liquid in an equilibrium
for x in a specified region. The word
““crossing’’ will be used, for brevity, to mean that

being
process,

the liquid reaches the curve from cone field, travels
along the curve for a limited range, ond then,
when the original solid is consumed, leaves it
before reaching an invariant point, to move across

the adjacent field.)

While the liquid is on any one field, precipitating
a single solid, it travels in a straight line ex-
tending from the separating solid, until it reaches

one of the boundary curves of the field.
Except for the region between point C and the
curve between p, and s, the relations in the sub-
system A~C-=D, are simple, Precipitation of a
first solid leads to a boundary curve, and along
the curve to one of the eutectics. Thus compo-
sitions in the region rsE,m give D, as first solid,
reach either curve sE, or curve mE,, and finally
point E, to end as D, C, and D,.

But p.s is a transition curve, and it is crossed,
as explained for curve p,P ., by liquids criginating
in the region p,D,s. The curve p,s is reached by
liquids precipitating C, from the region between
the curve and the corner C. Those coming from
above the tangent line D, s do not leave the curve,
but stay on the curve up to the eutectic £,. Along
the section p,s the quantity of C is decreasing
at the expense of D,, and between s and E, both
solids are being precipitated.

For solutions from the region p,D,s, solid C is
consumed when the tie line D, L of the three-phase
triangle passes through the fixed total composition,
and the liquid then leaves the curve. For x in the
region D, p. 1, the liquid then reaches either curve
e, B, or curve mE, fo end at point E,; from the
region D.ry (y being on the line D E.), the liquid
reaches curve mk and hence point E,.

For x in region D, ys, the liquid, having followed
the odd curve ys for part of its length, leaves the
curve, travels across the D, field, and then
reaches the even part of the same curve, sE..
These compositions then give the following
sequence of events. The liquid precipitates C as
the primary solid and moves on the C field on a
straight line from the corner C, to reach the curve
between p, and s. Along the curve, as L moves
toward s,

L+C—>D1 ,

and C will have been completely redissolved or
consumed when L reaches a point on the curve
between y and s, on the straight line D, x. The
liquid now traverses the D, field, precipitating Dy,
and reaches the same curve again between s and
E,, where it precipitates both D, and C. Finally,
at point E],

L—>D1 +C+D2 .

The primary solid phase C therefore disappears,
but C reappears later as a secondary crystal-
lization product together with D .

Finally, some of the relations in Fig. 5.3 will
be shown on isothermal diagrams and vertical
T vs c sections. Attending first to the isothermal
solubility curve of D., we note that between p,
and r its isothermal solubility curve (simply an
isothermal temperature contour on the D, field in
Fig. 5.3) is not cut by the line D.D,, while be-
tween 7 and m it is, The solid D, is then said to
be incongruently soluble in D, in the temperature
range between p, and r, but congruently soluble
in D, between r and m. A solubility isotherm for
this region between p, andrwould be schematically
as in Fig. 5.5. Between r and m, we have Fig.
5.6: just above m’, below e,, below e, but above
es, above p., and below the freezing point of B.
The isotherm shown in Fig. 5.7 is still above E,
and E,, below p, but still above P, and e,.
Figure 5.8 is at P ond below E,, E,, and e, but
still above e,. At the invariant P, the field of
A in equilibrium with liquid shrinks to a line
(AP3) and vanishes, in the reaction:

L(P3)+A—>D3+D2 .

The vertical T vs ¢ sections through D, D, and
D,D, are relatively simple, as shown in Figs.
5.9 and 5.10 (schematic, not in scale with Fig.
5.3). Figure 5,11 shows the vertical section
through CD,, and Fig. 5.12 the section through
DB (both schematic).

UNCLASSIFIED
ORNL-LR-DWG 24763

 

 

23
UNCLASSIFIED
ORNL~LR-DWG 32574

UNCLASSIFIED
ORNL-LR~-DWG 24765

 

 

 

 

 

 

 

 

 

 

 

Fig. 5.14.

UNCLASSIFIED
ORNL-LR-DWG 24764

 

 

 

 

 

 

 

 

 

&
j* £
| | |
L 0+, | | D3tly | B+03+0p
| |

,,f | |

e e ) 8
0, D, Dy 0,

Fig 5.9 Fig 510 Fig. 5.12

24
6. CRYSTALLIZATION PROCESS WITH CONTINUOUS
BINARY SOLID SOLUTION

The system of Fig. 6.1 involves two solid
phases, pure C and the continuous binary solid
solution A=B. The binary system has a minimum
freezing point at m, Fig. 6.2. All ternary compo-
sitions must solidify to two solids, pure C and a
binary A~B solid solution. Curve e, e, represents
liquid precipitating these two solids; M is a
temperature minimum on this curve, and it is also
the temperature minimum of the whole system.
(Curve e e, may have either a minimum or a
maximum or neither.) Liquids in the C field reach
this curve on straight lines from the corner C;
those in the solid solution field reach it along
curves on the solid solution surface. [n either
case the liquid then travels toward M, but for
complete equilibrium solidification is complete,
leaving the two solids, before L reaches M, unless
the total composition x lies on the straight line
CMs.  The three-phase ftriangles for L on the
boundary curve start as the straight lines Ce, A
and Ce,B and proceed, with falling temperature,
toward M according to the configurations shown

UNCLASSIFIED
ORNL-LR-DWG 2476€

5 F 52 54 8
372
T e e -y FoTT 5

 

 

Fig. 6.2.

in Fig. 6.1, collapsing again, from either side, to
the line CMs.

A vertical T vs ¢ section from C to the side
AB appears as in Fig. 6.3. Here the composition
of the solid solution (ss) is not on the plane of
the section. Even at point v the liquid of the
section is not in equilibrium with solid solution
of the same composition as the liquid (but point u
of course is simply the melting point of pure C).
Only for the section through Cm would v represent
liquid and solid of the same composition, but the
section through Cm would not pass through the
ternary minimum M. The region C + L + ss of
Fig. 6.3 collapses to a horizontal (isothermal) line
only for the section through M, CMs (and of course
also at the binary sides Ce, A and Ce,B).

In an equilibrium process, any liquid of original
composition x is completely solidified, while
traveling on the curve, when the C—ss leg of the
three-phase triangle passes through the point x,
to leave C and a solid solution of composition on
the extension of the line Cx. Solution y, moving
on a straight line from C, reaches the curve at /
and there begins to precipitate s,. As L travels
on the curve toward M, more C and more solid
solution will precipitate, but the solid solution
changes in composition, leaving the solids C and
s when the last trace of liquid vanishes at lqe
Liquid z, moving on a curved equilibrium path,
reaches the curve e,e, at I,, at which point the
solid solution has the composition s,. At /,, C
also begins to precipitate, and solidification is
completed with liquid at /,, leaving C and s,.

The course of the liquid on the solid solution
surface, however, is not shown by the ‘‘phase
diagram'’ of Fig. 6.1. With a minimum m in the
A=B binary equilibrium, this surface has two
families of nonintersecting fractionation paths, as
sketched in Fig. 6.4. All fractionation paths end,
without intersection, at the boundary curve €€,
The two families are separated by a limiting
fractionation path originating at m. This path
reaches the curve e,e, at a point N which may be
either on the left or on the right of M. Moreover,
the path mN may be either convex toward B,
as drawn, or convex toward A, and it may even
have a point of inflection. With the arrangement
assumed in Fig. 6.4, the fractionation paths on the
A side are always convex toward B; those on the

25

ik i e
UNCLASSIFIED
ORNL~-LR-DWG 24787

  

Fig.6.4

B side all start as convex toward A, but some of
them have an inflection point and become convex
toward B before they reach the boundary curve.
These inflection points are joined by the locus
curve mR.

6.1. FRACTIONATION PROCESS

As liquid foliows one of the fractionation paths
in a fractionation process, the composition of the
layer of solid solution being deposited at any
point is given by the tangent to the fractionation
path through that point. Then, once the liquid
reaches the curve e e,, whether from the C field
or from the solid selution field, it moves on the
curve toward M as limit.
the direction e, » M, the outermost layers of solid
solution being deposited have compositions in-
creasing in B content, approaching s as the limit,
from the A side, Those moving along the curve in
the direction e,

For liquids traveling in

-+ M deposit layers increasing in
A content, and also with s as limit.

The total process therefore varies according to
the various regions of the surface. (In this dis-
cussion it must be remembered that the fractionation
path is everywhere tangent to an equilibrium tie
fine. Hence the layer of solid being precipitated
at the point where the fractionation path reaches
the curve e e, is given by the tangent at that
point, eex're-ndeci2 to the line AB. At M itself this
tangent is the line CMs; at N the tangent goes to
z, at R to y. Also, the word *'solid’" will here

mean ‘‘the layer of solid being deposited.’’)

26

1. Region Ae,M (i.e., between e, and the
fractionation path AM): While L is still on the
surface, the ''solid’’ increases in B content, to a
limit given by the tangent to the particular frac-
tionation path involved at its intersection with the
curve e, M; and as L then travels on the curve (to
M as limit), the *‘solid’ increases still further in
B (to s as limit).

2. Region between paths AM and mN: With L
on the surface, the ‘‘solid’’ always increases in
B, with z as the possible limit for fractionation
paths reaching the boundary curve near N. The
boundary is reached in the section MN, and then,
as L moves toward M, the “*solid’’ increases in A
content, toward the limit s.

3. Region BRe,: With L on the surface, the
‘solid’’ increases in A, with y as limit for the
path BR itself; then, as L travels on the curve
(to M as limit), the **solid’’ increases still further
in A (to s as limit).

4. Region between paths BR and mN: The
‘“solid”” increases in A until the inflection point

of the fractionation path is reached (intersection
of fractionation path with curve mR), and the
composition of the '‘solid’” at that point is given
by the tangent to the fractionation path at the
inflection point. Now the ‘‘solid’’ begins to de-
crease in A content, to a limit given by the tan-
gent at the end of the fractionation path at the
boundary curve, reached in the portion NR. Then
as L moves on the curve toward M as limit, the
outermost layer of solid again moves to increasing
A content, toward s as limit,

5. Path mN: For a solution on the path mN
itself, the ‘‘solid’’ increases in B content (be-
tween limits m - z), and then moves toward s
as L, after reaching point N, moves on the curve
toward M.

6.2. EQUILIBRIUM PROCESS

process with complete
equilibrium between the total solid phase and the
liquid, the liquid, such as point @ in Fig. 6.4,
follows an equilibrium path {dotted curve a ... b)
in its course on the surface to the boundary curve
ere,. The relation of this equilibrium path to the
fractionation paths which it crosses has been ex-
plained in connection with Fig. 2.4. The point b
is fixed by a three-phase triangle with the ss—L
leg passing through point . Then as L moves on
the curve toward M, solidification is complete

In o crystailization

when the ss=C leg of such a ftriangle passes
through a.
The changes in the composition of the solid
solution as the liquid follows its equilibrium path
will depend on the region of the surface involved.
Now the word ‘‘solid’”” will mean the total solid,
assumed to be uniform in composition and in fuli
equilibrium with the liquid. We note first that all
equilibrium paths for solutions in the region AsMe,
reach the boundary curve between e, and M; those
for solutions in BsMe, reach the curve between
, and M. Point M is reached only for total com-
positions on the line CMs.

e

1. Region AMe,: The equilibrium path does not
cross the line sM on its way to the boundary
curve. The solid increases in B both before and
after L reaches the curve.

2. Region AMs: The equilibrium path crosses
the line sM on its way to e, M. The solid again in-
creases in B both before and after L reaches the
curve,

3. Region smNM: The equilibrium path does not
cross the path mN; it ends on MN. The solid in-
creases in B while L is on the surface, but the
reverse change sets in when L begins to travel on
the curve.

4. Region BRe,: The equilibrium path does not
cross the line Ry; it ends on e R; the solid in-
creases in A both before and after L reaches the
curve,

5. Region ByR: The equilibrium path crosses
Ry; it ends on e,R; the solid increases in A both
before and after L reaches the curve.

6. Region yzNR: The equilibrium path does not
cross the path mN; it ends on NR.

() Region yzdR: The solid increases in A
until the equilibrium path crosses curve mR; then
the solid increases in B until L reaches curve
NR; then the solid increases again in A while L
travels on the curve,

() Region dNR: The solid increases in B
until L reaches curve NR; then it increases in A,

7. Region mzN: The equilibrium path crosses
the path mN, to reach the boundary curve on the
left of N (between ¢ and N, curve cm being the
L-ss leg of a three-phase triangle for L at point
c). The behavior for the regions above and below
curve mR differs as described for region yzNR,

(The preceding discussion of Fig. 6.4 is based
on the analysis by Osborn and Schairer.!)

The composition of the equilibrium solid for
original liquids in the region Rmy, as just stated,
reverses its direction of change (increasing first
in A, then in B) while the liquid is still on the
surface. The equilibrium path for such a liquid
first crosses fractionation paths which are convex
with respect to A, in the order 1, 2, 3, 4, etc., and
in this region the solid is becoming richer in A.
But the rate of this composition change of the
solid decreases as the equilibrium path meets
fractionation paths of smaller and smaller con-
vexity. When the equilibrium path finally reaches
the locus curve mR, it has reached a fractionation
path exactly at its inflection point, with no con-
vexity at all at that point. This fractionation
path will not be crossed by the equilibrium path,
which here turns away and begins to recross the
fractionation paths, which are now convex with
respect to B; i.e., it now crosses the fractionation
paths in the order 1% 2% 3% ..., 7%, while the
solid increases in B content.

It has been argued by Bowen? that when the
equilibrium path just touches a fractionation path
at the point of inflection of the latter (on curve
mR), the equilibrium path undergoes an abrupt
change in direction {a ‘‘corner’’). This seems to
be incorrect. The equilibrium path crosses frac-
tionation paths only from their convex to their
concave side. The sharper the curvature of a
fractionation path, the greater is the angle of in-
tersection where the equilibrium path crosses it.
As the fractionation paths lose their curvature,
approaching their inflection points, this angle of
intersection diminishes; a zero angle of contact
is approached (no longer an intersection) when the
equilibrium path reaches a fractionation curve
exactly at the latter’s inflection point. |f an
equilibrium path has to cross the fractionation
paths 1, 2, 3 before reaching path 4 at the in-
flection point of path 4, the intersection angle de-
creases as it crosses paths nearer and nearer to
path 4, because the intersection is occurring
nearer and nearer to an inflection point of a path.

 

VE. F. Osborn and J. F. Schairer, Am. J. Sci. 239,
715 (1941).

2N, L. Bowen, Proc. Natl, Acad. Sci. U.S. 27, 301
(1941).

27
The contact at such a point must therefore be
tangential, and the equilibrium curve changes
its course smoothly, without a cusp (Fig. 6.5).
If : is the inflection point on the fractionation
path Bf, and is is the tangent at 7, then equilibrium
paths for all total compositions (@, b, c) on the
line is reach point i, changing their directions
(with respect to the family of fractionation paths)
as shown. The change in direction is more marked
the farther the total composition is from the point
i, but the equilibrium path is nevertheless tangent
to Bf at i,

28

UNCLASSIFIED
QRNL—-LR-DWG 24768

 

 

Fig. 6.5.
7. CRYSTALLIZATION PROCESS WITH SOLID SOLUTIONS
AND SEVERAL INVARIANTS

7.1. THE PHASE DIAGRAM

In Fig. 7.1 the binary system A=B forms dis-
continuous solid solution with a eutectic at o
liquid saturated with solids whose compositions
are S§_ and §7. These points are to be compared
with the binary diagram shown separateily as
Fig. 7.2.

system,C,D,, D,, are pure; D, is an incongruently

The other solid phases of the ternary

melting binary compound, D, melts congruently.
There are five fields —~ for C, Dy Dy A (the
A-rich binary solid solution of A and B), and
B (the Berich binary solid solution of A and B) -
and there are three invariant points, each per-
taining to a three-solid triangle. From the di-
rections of temperature fall, one is a peritectic,
P, and two are eutectics, £, and E .

The curve E,E. must have a saddle point m on
it, and the A_ solid solution which (together with
solid D,} saturates the liquid at point m must lie
on the extension of the straight line D m to the
side AB, at §_. The solid solutions saturating
liquid £, are somewhere close to the points §_
and Se’,
than e,, the compositions of the limiting solids of
the A-B miscibility gap at £, will depend on the
effect of temperature on the solid-solid solubility.

The three-solid triangles for any of the three in-
variant points, therefore, cannot be drawn in with-
out the experimental determination of tie lines

Since the temperature of E_ is lower

along the curves near the invariants, and ultimately
of the solid solution compositions at the in-
variants. The invariant P_, a peritectic, involves
the solids C, D, and §, (a solid solution of
composition somewhere near A) in the reaction:

L(P.!)+D] +C+S] ,

and P is outside triangle | (CD,S,). The eutectic
E, must be inside triangle |l (CDZSQ, where S, is
another unknown solid solution composition); E
must be inside triangle Il (D,S,57). In the last
case, S, and S are known points if the solid so-
lution iimits in the binary system A-=B are known
for the temperature of E, (as in Fig. 7.2).

In Fig. 7.3, we assume that these key solid so-
lution compositions have been determined and that
the three-solid triangles may therefore be drawn.
The solid miscibility gap in system A-B has been
assumed to widen with falling temperature (Fig.

7.2) so that S_ and S lie between the points
53 and S:;.

Since §,, S,, and S, are different compositions,
the three-solid 'rriangfes are not adjacent. They
do not have common sides, and they do not cover
the whole of the diagram. Only original compo-
sitions x falling inside one of these three-solid
triangles will, on cooling with complete equilibrium,

UNCLASSIFIED
ORNL-LR-DWG 24769

 

 

 

Fig. 7. 2.

29
UNCLASSIFIED
ORNL -LR-NDWG 24770

 

 

solidify to mixtures of three solids: those in
triangle | solidify incongruently at P,, those in
triangle 1l and triangle Ill solidify congruently at
E, and E,, respectively. The areas not included
in these ftriangles solidify to two-solid mixtures,
and hence these areas are shown with tie lines:
D, and a solid solution whose composition is be-
tween A and S, for the area D, AS,; C and a solid
solution between S, and § Eor the area CS,S,;
D, and a solid solution between § and S, for the
area D,S,S,; and D, and a solid solution between
§3 and B for the area D,S3B.

The three-solid triangles do not overlap unless
solid-phase interactions (here excluded) should
occur at temperatures between the invariants, But
when peritectic invariants are involved, the in-
variant planes (which include the liquid phase

30

besides the three solids) may overlap, as is the
case here for the invariant quadrangle CD,S,P,,
overlapping, on the polythermal projection, the
invariant triangle CS,D, (with E, as interior
phase). These planes are at different temper-
atures; the P, plane is above the E, plane, which
is above the E, piane.

Also, the solid solution compositions S, and
S, it must be kept in mind, are not on the solidus
curve aS_ of Fig. 7.2. They are simply compo-
sitions in the area of soiid solution below this
binary solidus curve. Liquids on the curve e,E .,
including the points e, and £, are in equilibrium
with conjugate solid solutions ~ solid solutions
defined by the miscibility gap of Fig. 7.2. But
the solid solutions involved along all other curves
(oP,,P|E,, E,E,, and e E,, with the exception of
just the point E,) are simply compositions in the
solid solution areas of Fig. 7.2.

7.2, EQUILIBRIUM CRYSTALLIZATION
PROCESS

The reactions on curves e, P, and ¢, E, of Fig.
7.3 are simple precipitations of two pure solids;
on e]P1:

L~»C+D] .

and on ezEz:

L>C+D, .

On curve e, E,, the liquid precipitates two solid
solutions, starting as §_ and S at e, and changing
in composition to §, and §7 at E,. On curve ek,
the liquid precipitates D, and a solid solution
starting as pure B at e
sition to SJ at K.
is precipitating D2

3 and changing in compo-
For curve E E,, the liquid
It s
is the composition of the solid solution for L at

and o solid solution.

m {maximum of the curve), then along curve mE,

the solid solution varies from S to § and along

’
curve mE, it varies from S to S.. %'he vertical
T vs c section on the line D mS
Fig. 7.4. It looks like a quasi-binary section but
it is not. The liquid on the curve am of Fig. 7.4
is in equilibrium, not with S, but with a solid

{not on the

is shown in

solution of changing composition
plane of the diagram) which is S only for L at
point m itself,

Along curve P.E,, the liquid precipitates C

and a solid solution changing from §, (at P,) to
S, (at E2)' Curve pP, is a transition curve, along
which the liquid reacts with solid solution and
precipitates D.. The three-phase triangle starts
as the line pD,A and ends as P,D,5,, so that
the solid solution in equilibrium with liquid on
the curve varies from A at p to §, at P,.

Since the solid solutions in the system are only
binary, solidification cannot be complete while
liquid is traveling on one of the surfaces; the
liquid must reach either a curve involving a solid
The course of
the liquid on a surface precipitating a pure solid
(C, D,, or D2) is clear: a straight line from the
composition of the separating solid (Fig. 7.1).
On the two surfaces for solid solution, the paths,
whether for fractionation or for equilibrium crystal-
are curved, Fractionation paths are

sclution or one of the invariants.

tization,
shown in Fig. 7.1; equilibrium paths cross these
curves as explained under Fig. 2.4.

In the region D,S B, only liquids from an
original composition x in triangle [l (D,5,57)
reach E,, to solidify to three solids. Those for x
in triangle E,S,S7 reach E, along curve e E,,
carrying two solid solutions, and these liquids c?o
not solidify completely until they reach E,, to
produce D, as third phase. For x in the region
D,E,SiB, the liquid reaches the curve e, E, but
if x is in triangle D, S:B, the liquid is consumed
(in complete equilibrium) before reaching the
eutectic, to leave D, and a solid solution between
B and $.. Liquids in the region D,S S.E. reach
curve mE,, and again those in triangle D, S S,
solidify completely on the curve, before reaching
E,, to leave D, and a solid solution between S
and § 5 (Similar behavior is shown in the region
D,S,S,E,.)

The curve pP, is reached by liquids originating
in the region pAS P, after first precipitating a
solid solution between A and §.. For x in triangle
D, AS,, the liquid is consumed on the curve pP’,,
leaving D, and solid solution.
pD,P, the solid solution is consumed on the
curve, leaving liquid and D ; L then leaves the
curve, crosses the D, field to curve ¢ P,, and
travels to P,. For x in triangle D,5 P., no phase
is completely consumed along curve pP,, and
the liquid reaches P.

The peritectic P,
D, field and for x in the region Ce P, - along
curve e P.; P. is thus reached only for x in
the quadrangle CD, S, P,. At P,,

For x in triangle

is also reached for x in the

L+D]~3C+S] .

Hence solidification is completed here for x in
CD,S, (triangle 1), in an incongruent crystal-
lization end point, Otherwise (for x in triangle
CSTP]) D, is consumed and L begins to move
along curve P E.. This curve is also reached
directly from the C field, for x in the region
CP|E,, and from the A_ field for x in the region
P.S,S,E,.  As L travels on this curve, pre-
cipitating C and solid solution, it completes its
solidification if the total original composition x
is in triangle CS,S,; otherwise it reaches Ey,
the crystallization end point for triangle |l.

Some isothermal relations are shown in Figs.
7.5, 7.6, and 7.7. Figure 7.5 is still above the
temperature of p, Fig. 7.6 just below p. Points
s, I, s’ and [’ in these diagrams are related to
the solidus and liquidus curves of the binary
system A-B shown in Fig. 7.2, The points s”
s*in Fig. 7.7 are between §_ and S, and between
S and 5], respectively, of Fig. 7.2, The temper-
ature of Fig. 7.7 is between m and the eutectics
E,, E,, below all the binary eutectics, but still

above P,. At P, the tie-line region for D, in

UNCLASSIFIED
ORNL~LR-DWG 24774

 

31
equilibrium with liquid shrinks to a line and
vanishes.

Some vertical sections are shown in Figs. 7.8,
7.9, 7.10. The m in Fig. 7.9 is at the temperature
of point m but does not represent its composition.

UNCLASSIFIED
ORNL-LR-DWG 24772

 

 

 

 

 

 

 

      
   
 

 

 

 

 

02
EE
01 02
Fig. 7.8.
UNCLASSIFIED
ORNL~LR-DWG 24773
L
P
(Tf &
ATEMPERATURE
A S OF m)
€3
E, =-— ,
L+ 02+A5 e
w by
oo | S
+ +
© Q
o, 5
Fig. 7.9.

32

UNCLASSIFIED
ORNL-LR-DWG 24774

 

 

 

S,+C+D,

 

 

 

 

 

 

Fig. 7.40.

7.3. PROCESS OF CRYSTALLIZATION
WITH PERFECT FRACTIONATION

The fractionation paths in the two solid so-
lution fields (Fig. 7.1) are families of curves
radiating from points A and B, respectively.
Those in the A_ field are convex with respect
to B, meaning that as L travels along such a path
on cooling, in a fractionation process, it deposits
successive solid solution layers always richer in
B content; those in the B field are convex with
respect to A, and the outermost solid solution
layer here continually increases in A content
while L is traveling on the surface.

In fractionation, a liquid in the region between
e, and the path BE, reaches the curve ¢,F ,, and
on this curve the solid solution continues to in-
crease in A content. Liquid between e, and the
path BE, reaches curve ¢ E, but now two solid
solutions precipitate, and their outermost layers
vary from S, and S’ to §, and S; in composition
(Fig. 7.3). In an equilibrium process, the curve

e B,y s reached by all liquids below the line
E,S;, which is tangent, of course, to the frac-
tionation path BE, at E,, and e,Eqis reached
only by liquids between e, and line E, S5

In a fractionation process on the A _ field, the
curve P,E, is reached by liquids between the
froctionation paths AP, and AE,, and the solid
solution continues to increase in B content along
this curve. Curve E_,m is reached by liquids
between the paths AE, and Am, but in this case
the outermost solid solution layer being deposited
begins to increase in A content as L travels on
this curve in the direction m » E,. The frac-
tionation process for the region between the paths
AP, and Am ends at E,. The curve mE 5 is reached
for liquids between paths Am and AE,, with the
solid solution increasing in B content both before
and after L reaches the curve; and curve e, L,
is reached for liquids between e, and the path
AE . In these regions the fractionation ends at
E3.

Liquid between p and the path AP, reaches the
curve pP. and immediately crosses this curve to
deposit D, on the solid solution already deposited
before the curve was reached. The liquid then
reaches curve e, P, deposits a mixture of D, and
C while traveling on this curve, reaches P, and
without stopping at P1 continues on curve P.E,,
depositing C and a solid solution. The process
ends at E,. In this process the precipitation of
the solid solution is interrupted while L is cross-
ing the D, field and then returning to P, on the
curve e, P.. There will consequently be a gap in
the composition of the solid solution finally
obtained.

In the fractionation process all liquids in the
region bounded by the lines mD,, D,B, BA, and
the fractionation path Am end at E_, to leave
three solids, A, B, and D,. Liquids in the rest
of the system end at E; of these, moreover, those
in the region bounded by lines P.C, CA, and the
path AP, end as a mixture of four solids, A,
D,, C, and D,, while the rest end as three solids,
Ay, C,and D,

7.4. TERNARY SOLID SOLUTION
IN COMPOUND D,

Finally, we shall assume that the solid D,
forms solid solution with both A and C in its
binary system and with the third component B, to
give at any temperature a small isothermal area of
solid solution of ternary composition. This will
affect all the equilibria involving solid D,. The
pertinent region of Fig. 7.3 becomes that shown
in Fig. 7.11. Figures 7.6 and 7.7 change as shown

in Figs. 7.12 and 7.13. A section like Fig. 7.8
now shows the region of homogeneous ternary
solid at the D, side, labeled D (s} in Fig. 7.14.

UNCLASSIFIED
ORNL-_R-DWG 24775

 

Fig. 7.1,

  

Fig. 7.42. Fig. 7.43.

UNCLASSIFIED
ORNL-LR-DWG 247786

 

 

01(5)~II—-

 

C+D,(5)+S5, -

 

 

 

 

 

 

 

.
PART Il
THE ACTUAL DIAGRAMS
The following sections will consider, one at a
time, the ternary diagrams which have been con-
structed. For ease of drawing and for the sake of
clarity, the diagrams used in these sections are
not according to actual scale, but schematic in
their quantitative relations. The formulas and the
actual numerical values, including the tempera-
may be obtained from the experimental
diagrams.

tures,
For brevity and simplicity, moreover,
single letters rather than chemical formulas have
been used to represent the solid phases.

The following is the key for the letters regularly
used for the components of all the systems:

Symbol Component
R RbF
U UF4

Symbol Component
Vv BeF2
W ThF,
X LiF
NaF
z Zrl:4

The letters A, B, ..., N wiil be used, as needed,
for the various binary compounds in the binary
systems. They donot represent the same compounds
from one section (ternary system) to another,
whereas the components are always referred to by
the same letters.

The letter x will be used throughout to mean
“‘the total original composition of a sample being
cooled and solidified.””

 

8. SYSTEM X~U-V: LiF-UF,-BeF,

The schematic phase diagrams for the binary
systems of the first ternary system to be dis-
cussed, system X—U-V, are shown in Figs. 8.1,
8.2, and 8.3. No solid solution is involved, either
in the binary systems or in the ternary system.
Compound A in system X—U decomposes on cooling,
at T ,, into the solids X and B; and compound E
in system X~V forms on cooling, at T, from the
solids D and V.

Every solid reaching equilibrium with liquid in
its binary system must have its own primary phase
field, bordering on the side of the triangle, in the
ternary system. The field for compound A of the
system X—U, however, will have T , (designated
P, in the ternary system) as its lower temperature
{imit of stability, inasmuch as A decomposes on
cooling to this temperature. At P, the X and B
surfaces of the ternary liquidus, separated above
that temperature by the A field, will come into
contact. The compound E of system X—V may or
may not have a field (for liquid in equilibrium with
solid E) in the ternary system. It will have a
field oniy if the ternary liquid saturated with the
two solids D and V exists down to the temperature
Ty of Fig. 8.3, the temperature for the formation
of E from D and V upon cooling.

The phase diagram of the ternary system is
given in Fig. 8.4 (schematic). There are seven
fields, identified by letters in parentheses, (U),

(C), etc. The A field vanishes with falling temper-
ature at P ,, ot the temperature of decomposition
of solid A in its binary system, T ,, but now in

presence of ternary liquid. The temperature of

UNCLASSIFIED
ORNL-LR-DWG 25579

 

 

 

 

 

 

 

 

 

Fig. 8.3.

37

 
UNCLASSIFIED
ORNL-_R-0DWG 25580

 

Fig 8.4.

decomposition is unchanged, because the com-
ponent V does not form solid solution with any of
the three solids involved in the reaction. Since
solid A decomposes before its field touches any
field involving the component V, it is not part of
one of the three-solid triangles of the system, of
which there are only four, I, I, I, 1V, with the
corresponding invariant liquids Py Py Eg Ey

The reactions on the curves are as follows (all
written as the reactions occurring upon cooling):
P Pl: L+U-C.
P, P2: L +C-B.
paP gt L+Xo A,
6‘3 PA: L A+B,

: L +X > D. But this may change to:

pgE 4
L->X+D

o it does change
if the tangent to the curve comes to fall

between X and D.

as the curve approaches F

6653: L>D+V,
€7P.|: L->U=+YV.
P]P2: L->-C+V,
P2E3: L--B+V.
EfEst L>B+D. Accordingly, m is a saddle point,

with temperature falling away both toward
E, and toward £,. But the line BD is not
a quasi-binary section, for it includes the
C field and the X field.
The invariant reactions are as follows:
Py L+ U>C+V. Point P
either of the two curves falling to it, for x in

is reached along

38

the quadrangle P, CUV. It is the incongruent
crystallization end point for triangle | (CUV).
If x is in triangle P, CV, the liquid continues,

completing its solidification at P, for x in

triangle 1lI, or continuing still further and
completing its solidification at E, for x in
triangle 1.

Py L +C> B+ V. Point P, is reached along

either of the curves p, P, or PyP,, for x in
the quadrangle P, BCV. It is the incongruent
solidification end point for x in triangle |l.

E,o L > D+ B+ V. Point Ey is the congruent
solidification end point for triangle Ifl. The
final equilibrium solids for this triangle, left
at the lowest liquid reaction (E,) of the region
(triangle Ill), are therefore B, D, and V. How-
ever, at a still lower temperature (T of
Fig. 8.3) the solids D and V react to form

Below T ., therefore, the
triangle |I| becomes two three-solid triangles,
one for B, D, and E and one for B, E, and V.

E,o L - X+ B+ D, Point E, is the congruent
solidification end point for triangle 1V.

P, A> X+ B, inthe presence of liquid P ,. The
point P, is reached by liquid for x in the
triangle XBP ,,
liquid in equilibrium with X and A) or curve
e, P 4, (as liquid in equilibrium with A and B),
At P, the solid A decomposes to produce
more X and B, and the liquid moves on along
curve P E .

Four of the boundary curves are of odd reaction

(transition curves). They are crossed by equi-

librium crystallization paths as follows. (The

the compound E.

along either curve p, P, (as

expression ‘‘crossing of ftransition curves’' is
used with the meaning explained in Sec 5 in con-
nection with curve p, P, of Fig. 5.3. For restricted
values of x, the liquid reaching a transition curve
travels along the curve only for part of its length
and then leaves it for another field.)

1. p,P,: Liquids reaching this curve for x in
p,CP, (i.e., in the region between C and the
curve p, P,) travel along the curve only until all
solid U is consumed, when the CL leg of the
three-phase triangle passes through x; L then
leaves the curve and crosses the C field.

2. p,P,: Similarly crossed by liquids reaching
it from x in the region p,BP,, L proceeding onto
the B field.

3. Py PA:
region p ,AP ,, L. proceeding to travel upon the A
field.

Similarly crossed by L for x in the
UNCLASSIFIED
ORNL-LR-DWG 25581

  

    

Fig. 8.5,

 

4. pE,: Crossed for x in the region p Ds (s is
the point of tangency of the LD leg of the three-
phase triangle with curve p E ). Then, for the re-
gion between the line Ds and the line DE ,, the
primary X solid, which has been entirely consumed
while L travels on the curve p.s, appears again
as a secondary crystallization product, mixed with
D, when L, traversing the D field, reaches the
curve sE , (cf. curve p,E, of Fig. 5.3).

The isothermal relations for the A solid are
shown in Fig. 8.5, {a) between py and ey, (b) be-
tween e, and P ,, (c) at P ,, and (d) below P ,.

Figure 8.6 is a schematic isotherm between e
and p,, above P, and F,, above p,, and below e
The L + U region will vanish as a line when the
temperature falls to P and the L + C region
vanishes similarly at P,

Some vertical T vs ¢ sections are shown in

Figs. 8.7, 8.8, 8.9, and 8.10.

UNCLASSIFIED
ORNL-LR-DWG 25582

 

Fig 8.9 Fig. 8 40

39
9. SYSTEM Y=-U-V:

For the ternary system Y—U-V, we have the
binary systems Y—U in Fig. 9.1 and Y-V in Fig.
9.2; the system U=V is as in Fig. 8.2, except that
point e, is now designated e,. The ternary diagram
is given in Fig. 9.3.

The horizontal dotted lines in Figs. 9.1 and 9.2
represent polymorphic changes in pure phases:
one in solid A, two in H, and one in G. Even
when these transitions occur at liquidus tempera-
tures, as in the transition T~ for compound G,
there is hardly any effect in the ternary diagram.
Strictly, the freezing-point curve of G in the binary
system Y—V has a slight break at ¢ This break
becomes an isothermal crease on the G surface
in the ternary system. The crease starts at ¢t and
enters the ternary diagram to look simply like an
isothermal contour on the surface. |t represents
liquid in equilibrium with both forms of G. Above
this temperature the surface is for liquid in equi-
librium with G, and below this temperature it is
the surface for liquid in equilibrium with G ..
This crease has been sketched in Fig. 9.3 as ’rfie
curve t 't ”” across the G field.

UNCLASSIFIED
ORNL-LR-DWG 25583

 

~
)
hq
o
~

 

NoF-UF ~BeF,

In the system Y—U, Fig. 9.1, we note two binary
compounds, A and C, decompesing upon cooling
and two, E and F, forming from other solids upon
cooling. The first two decompose before reaching
an invariant involving a solid containing component
V,; hence, as in the case of compound A in system
X—U=V, these solids have primary phase fields
but do not take part in the three-solid triangles of
the ternary system. The compounds E and F of
the present system, unlike the similar compound E
of system X-U-V (Fig. 8.4), do have ternary
fields in the system, because the curve for liquid
in equilibrium with D and U extends down to the
temperature T . for the formation of E from D and
U, and the resulting curve for liquid in equilibrium
with £ and U further extends down to the tempera-
ture T . for the formation of I from E and U.

The ternary diagram thus has eleven fields and
seven three-solid triangles (with corresponding in-
variant liquids). It also has four invariant points
for liquids accompanying binary solid-phase re-
actions: P, and P for the decompositions of
sclids A and C on cooling, and Pp and P for
the formation of solids E and F on cooling.

The limited A field is divided into two regions
by an isothermal crease, wv on Fig. 9.3. This
crease is at the temperature T’ of Fig. 9.1, the
transition temperature for:

A_ - calories = Ag .

The higher-temperature region of the field repre-
sents liquid in equilibrium with A _, the lower
region liquid in equilibrium with Afi; the form
decomposing at P , is A 5.

The similar transitions in the solid H are assumed
to occur below the temperature of equilibrium with
any ternary liquid, and hence are assumed to have
no effect on the phase diagram.

Five curves are of odd reaction. (The even
curves simply precipitate the solids of both ad-
jacent fields.) The transition curves are as
follows:
pgPci L+Do C; crossed by L for x in region

CpyP
pyPct L +CoB; crossed by L for x in region
Bp3 PC.
P P L+U>E; crossed forx!n EP P
PPyt L+U>F,; crossed for x in FP o P,.
PpoPy L+F-E,; crossed for x in EP P .
UNCLASSIFIED
ORNL-LR-DWG 25584

\
\
\\
'\
F \
AN \
\
N\ I
" \\ \\
£ AN \
N N \
\\\ \\

. n \

: Ay

€5 \\ \\ \
S () N N\
N,
. \
S \\ \\
. ~,
. N\ \
. \
\\\\ N :
\\\
N
. SN\
®c - N
- o \\
. L
Fr N .

 

 

 

(F) S
. f” \\\. \\\
{£) p b T \
Es i‘m(G)\ EaNG \2 - - — *‘3 9
Lo e (V) N V
eTf’ G €q
Fig. 9.3.

Invariant reactions are:

P,: L +U->F +V;incongruent crystallization end
point for triangle .

L +F s E +V; same, for triangle Il

L +E D +V; same, for triangle Il

L +B »D 4+ H; same, for triangle VI.

E, Eg, E,i eutectics for triangles IV, V, VII.
There are two saddle points: m on curve E E
and m” on curve P E. But only the line DG isa
quasi-binary section, dividing the whole diagram

(Note:

P,:
P
P,

into essentially independent subsystems.

The composition diagram of a ternary system does
not have to be a triangle. As long as it is a plane,
with only two independent composition variables,
it may have any shape.)

Some relations in the subsystem D—U—~V—G may
be illustrated by consideration of the equilibrium
crystallization process for solution a4, Fig. 9.3.
This point is located on the left of line UP o, in
the region FP P, in the region EP P, in the
quadrangle P, DEV, and in triangle IV. The first
solid on cooling is U, and the liquid travels on the

41
straight line Ua to the curve P P . With L on
the curve,

L+U-E ,

but not all the U solid is consumed, and L reaches
P . At this point all the E solid so fa. produced
is consumed in reaction with U, to form F, and
then the liquid, saturated with U and F, begins to
travel on the curve P _P .. On this curve, the rest
of the U solid is consumed, and L leaves the
curve to traverse the F field on the straight line
Fa. When L reaches the curve P P,

L+F->FL ,

and now when all the F is consumed the liquid
leaves this curve to traverse the E field, on the
straight line Ea, until it reaches the curve P, P,.
Now precipitating E and V, the liquid reaches P,,
where

L +E->D4+V

Here F is consumed, and L. moves on down the
curve P, E,, precipitating D and V. |t reaches
E, and there solidifies completely to G, D, and V.
The original sclution a thus gives only three
solids upon solidification with complete equi-
If the phases are not given sufficient
time for reaction during the cooling process, the
licuid from the composition @ would still reach
E, before complete solidification, but the final
mixture would contain all the csolids of the sub-
system: U, E, F, V, D, and G.

The point P is reached, in equilibrium crystal-
lization, for x in the region DP _ U, by L on curve
e P . carrying solids D and U; at P these solids

librium,

react to form E, leaving one of them in excess.
Hence, if x is in the region DEP , U is consumed
and L takes the curve P P,; for x in the region
EUP., D is consumed and L travels on curve
PP The point P is similarly reached, for x
in the region EP U, by L on curve P P carrying
solids E and U. Then for x in the region EFP .,

42

U is consumed and L leaves on curve PP,
while for x in FUP, E is consumed and L takes
the curve P P,.
Isotherms near P
above P

are shown in Fig. 9.4 (a) just
£ and (b) just below Pp. At P the equi-
librium area for liquid in equilibrium with F
appeats as the line FP .

Vertical T vs ¢ diagrams for three sections of
this subsystem are shown in Figs. 9.5, 9.6, and
9.7, and two T vs c sections for the subsystem
Y—D—G are shown in Figs. 9.8 and 9.9.

UNCLASSIFIED
ORNL-LR-DWG 25585

 

() ‘<

A\

£ \ .

0 .\ ;

L ‘ L
ey . /
G G
Fig. 9.4.

UNCLASSIFIED
ORNL-LR-DWG 25586

 

Fig. .5,
UNCLASSIFIED
ORNL-LR-DWG 25587

 

 

 

 

 

 

ol
o
L+ E+V
Fs
D+v
D Vv
Fig. 9.7.

UNCLASSIFIED
ORNL-LR-DWG 25588

 

Fig. 9.8. Fig. 9.9.

43
10. SYSTEM Y-U-R: NaF-UF ~RbF

For the ternary system Y—U—R, Fig. 10.1 shows
the binary system R—U, and Fig. 10.2 the system
Y—R. The binary system Y—U is that of Fig. 9.1,
with the same lettering.

Figure 10.3 is the ternary diagram.

We note first the restricted fieids for the binary
compounds A and C of the system Y-U, ending at
points P, and P, respectively, at the tempera-
tures of decomposition of these solids on cooling
(Fig. 9.1). The isothermal curve uv on the A field
has been explained in connection with Fig. 9.3.
The low-temperature compounds E and F of Fig.
9.1 do not appear at liquidus temperatures in Fig.
10.3, since the curve of liquid in equilibrium with
D and U (esE] ) ends at a temperature higher
than T . of Fig. 9.1.

The new item in the present ternary system is
the ternary compound (, with P,P3E,P, as its
primary phase field. This compound is stable
When heated
it decomposes in a
into the
If the ternary compound Q is not

only below the temperature of P ..
to the temperature of P
strictly binary
solids B and H.
pure, but is mixed either with a little Y or with a
little R, it still decomposes as a solid phase into

solid-phase reaction,

UNCLASSIFIED
ORNL-LR~DWG 25589

 

 

Fig. 10.2

the same solids, B and H, at the same tempera-
ture, namely that of point P, but now in the
presence of the liquid Py The invariant point
P is therefore entirely analogous to P in Fig.
9.3, where solid E decomposes, when heated, into
D and U in the presence of the liquid P .

Figure 10.3 shows fifteen primary phase fields
and eleven three-solid triangles with corresponding
invariant liquids. There are five saddle points:
m, on curve E]Ez, m, On curve ESPQ' M, On
curve P E, m, on curve E,Eg, and m, on curve
PloEqr Two of these saddle points, m, and m,,
are on quasi-binary sections,Ym, G and Dm, J; Fig.
10.3 therefore consists of three subsystems.

The subsystem D—U~] is relatively simple, with
two eutectics, Fy and F,,, and two peritectics,

Py and Plo Three of the curves are transition
curves:
py3E 1 L + U~ N;crossed by liquids originating

in region Np,,E,,. This curve may
become even in reaction close to point

Eyy

P1oP 0t L + N~ M;crossed by liquids originating
in region Mp,, P ..
p11Pet L+ M- K;crossed by liquids originating

in region Kp,,P,.

Compositions in triangle X| solidity to D, U, and
N, but at T of Fig. 9.1, D and U react to form £,
and the triangle DUN is divided into two triangles
of three coexisting solids, DEN and EUN. At a
still lower temperature (T of Fig. 9.1), the
triangle EUN divides into EFN and FUN.

In the middle subsystem, Y—D—]J—G, there are
the following transition curves:

pyP ot L+C o B crossed for x in Bp, P .
Py P L +D - C; crossed for x in Cp, P .
py P, L+ G- Hjcrossed forx in Hp, P ,.
pgEqsr L +] > 1 crossed for x in Ipg E .

PoPy L+ H -0 crossed for x in OP P,

PP L+D B, upto point s {line Bs tangent
to the curve). The relations along this
curve are like those explained for curve
p‘sE,l in Fig. 5.3.

Point P, is reached by liquid from original

compositions x in the triangle BP _H. The liquid
reaches the curve m, P either from the left side,
carrying solid B, or from the right side carrying
solid H. It then travels on the curve, precipitating
both B and H, and reaches P .. At this point, B
and H react to form solid O, ang one of the original
UNCLASSIFIED
ORNL-LR-DWG 25590

 

 

 

Fig. 10.3.

solids will be completely consumed. For x in the
triangle P,BQ, H is consumed and the liquid
travels down the curve PQP3,‘ for x in the triangle
PQQH, B is consumed and . moves onto curve
PP 4

Consider a total composition x in the region
QP ,P,. On cooling, the first solid is H, and L
moves on a straight line from H to reach either
curve P P, directly, or first curve m,P ,, then

2 !
point P, and then the curve PoP,. Vfi-nile L

travels along this curve, H reacts with liquid to
form O, and eventually L leaves the curve, when
all H is consumed, to enter the Q field. Traversing
this field on a straight line from O, it can reach
any one of the three other boundaries of the @
field. These are all even curves, and liquid cannot
leave them. If x is in triangle Hl, L will reach P
along curve P P, and complete its crystallization
at P, to leave solids Y, B, and Q; for x in triangle
I, L ends at E,, leaving Y, O, and G.

45
For a liquid with composition O itself, the first
solid is H, and L travels to the saddle point m,,
where the liquid solidifies completely into B and
H, which solids will be present at the end in the
exact proportions corresponding to Q. Then at
the temperature of Po these solids combine to
produce Q.

Compositions in triangle V complete their crystal-
lization at Eg, into a mixture of B, H, and I. But

UNCLASSIFIED
ORNL-LR-DWG 255914

L+ U
LN+~

46

on cooling further, B and H combine to produce Q,
leaving, below the temperature of P o either B,
O, and I or Q, H, and 1.

Some T vs c vertical sections are shown in

Figs. 10.4-10.10.

UNCLASSIFIED
ORNL-LR-DWG 25592

L+G~ ‘
(+G+H -

   
 
 
 
   
   

P
1. SYSTEM Y-Z-R: NaF-ZrF ,~RbF

For the ternary system Y-Z-~R, the binary
system Y~Z is shown (schematically) in Fig. 11.1
and R-Z in Fig. 11.2. The system Y-R is as in
Fig. 10.2, but now with e 3

In each of the first two compounds, A and B, of

in place of e, ,.

the system Y~Z, there is some solid solution on
the Z side of the stoichiometric composition. In
the case of B, solid solution is limited to the
upper form, B,
The transition temperature is accordingly lowered,
from T’ to T”.
solid solution extending in the direction of the
Y side. The subsolidus compound D, which forms
from the solids € and E (a solid solution) at T',
forms solid solution on the Z side. The compounds
D and E, in other words, may be said te form a
[imited series of solid solutions with each other.

The compound E forms similar

The 1:1 compound will not be considered in con-
nection with the ternary system. It is observed
to be formed at relatively low temperature, but
its relation to the established phase equilibria
of the binary system has not been even tentatively
clarified.

The phase diagram for the system R-Z shows
some solid solution, on the Z side, for the two
At T’ the compound H is
polymorphic transition:

compounds G and H.
shown as undergoing a
H, ~ calories ——= H[3 ,

and the transition temperature is shown as being
lowered to T " as the result of the solid solution
formation. The relations for compound H, however,
It seems possible
that it may in fact be a pure solid phase, without
any solid solution, and moreover, without any

are experimentally not clear.

polymorphic transition,

The ternary diagram for the system is given in
Fig. 11.3.

With regard to this diagram, which is shown as
it has so far been worked out, we note the absence
of any primary phase field for the incongruently
melting compound B of the system Y=Z and for
the subsolidus compound D of the same system.
Both of these solids should have primary phase
fields in the ternary system. The regions involved
were investigated before the relations for these
compounds were definitely established in the
binary system, and they have not yet been rein-
vestigated.

while the lower form, B g, is pure.

We shall first discuss briefly the relations for
the ternary system as reported in the diagram of
Fig. 11.3, assuming, moreover, that the solids
form no solid solution. This will serve as a basis,
then, for a more detailed discussion of special
regions of the system involving the missing solids,
together with the solid solutions formed.

11,1. THE SYSTEM ACCORDING TO FIGURE
11.3 AND NEGLECTING SOLID SOLUTION

There are primary phase fields for three ternary
compounds, My, M, and M,, all with the same
(1:1) ratio of the components Y and R, and varying
only in Z content. They lie on a line with the
corner Z, Both M, and M, have congruent melting
points, with a temperature maximum in each field
at the composition of the compound itself, Crystal-
lization paths in each of these two fields radiate
in all directions as straight lines from the maxi-
Liquid can be in equilibrium with solid
M, and any of seven other solids (the M, field has
seven boundaries). The M, field has five bound-
aries (but the field for the here missing compound
B will probably add a sixth boundary).

The ternary compound M, has a semicongruent
melting point, at the temperature of point y on the
boundary curve between the M, and M, fields
(cf. Fig. 4.13). Instead of reaching a congruent
melting point, the compound M,, when heated to
the temperature of y, decomposes, or melts incon-

mum.

gruently, into compound M, and liquid y, collinear
with M.
toward y, the M, surface falls away from y, and
the temperature on the boundary curve PP,
falls away from y in both directions.

With saddle points (m’ and m "} on each of the
other two boundary curves crossed by the line
M M,M,Z, this line is a quasi-binary section
(from M, to Z) of the ternary system (Fig. 11.4);
y is seen to be simply the incongruent melting

The M, surface falls in temperature

point for the compound M. in this binary system.

Figure 11.3 shows fifteen primary phase fields
and sixteen three-solid triangles with corresponding
invariant liquids, There are ten saddle points
(m-points), only one of which, with all solids
assumed pure, is not on a quasi-binary section;
this is on the curve E, E, .. The nine quasi-
divide the diagram into eight
quite simple ternary subsystems, shown as the

eight areas of Fig. 11,5,

binary sections

47
UNCLASSIFIED
ORNL-LR-DWG 25643

 

Pg

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F

(1:1)

£

Fig 111,

 

 

 

 

 

 

 

11.2.

Fig.

48
“NCLASSIFIED
CRNL-.®-DW5 25

502

 

 

Only five of the boundary curves in Fig. 11.3
seem to be of odd reaction (pPB, PP ror P19F 110
PgP gt and P5P16); all the others seem to be

even. The curve P P, ., for

L+M »M,,

is crossed by L for x between the curve and the
lines P .M, and P My

The binary peritectic peint p has been left un-
numbered in Fig. 11.3, because it may represent
either p, or p, of Fig. 11.1; and the invariant
PS’ has been primed, because there must be two
invariants here (P, and P,) in place of just the
one., Also, a primary field for compound D of
Fig. 11.1 should make its appearance somewhere
along the curve e P/, the prime on P. being used
because there should be two invariants here also,
P, and P..

11,2, CONSIDERATION OF SOLID
SOLUTION FORMATION

If the actual solid solutions in this system are
considered, the phase diagram is no longer divided
into as many independent subsystems as assumed
in Fig. 11.5. Five of the areas of Fig, 11.5 re-
main simple, involving only pure solids: EZM,
with just P, and Eg as invariants; M Z] with
Py, and E,,; M ]I with E YGR with E
YAG with El'

However, although the solids A and G are present
as pure solids in their equilibria below the line

and

137 187

AG, they both form solid solutions, containing
excess Z, in their binary systems. |n cther words,
the liquid on curve m, - E, precipitates pure
A and pure G, but the liquid on the part my > E,
(of the same curve) precipitates two solid so-
lutions, starting as pure A and pure G at m, and
ending as A, (on the side YZ} and G, (on the side
RZ), for E,. The A solid solution extends be-
yond A,, toward Z, for the equilibrium with liquid
on curve P.E,, and the saddle point m, is no
longer on a quasi-binary section. At My, the
liguid is in equilibrium with M, and a solid so-
lution of composition Ama, between A, and Ags
the composition corresponding to L at P,. Simi-
larly, the saddle point mg is no longer on a quasi-
binary section, since here the liquid is in equi-
librium with M. and a solid solution of composition

G, , between G, and G the composition for L

17¢
at Ig”. On the other hand, Moy ON the curve E,E,,
is exactly on the line AG, o quasi-binary section.

The fractionation paths in the A field, then,
originating from point A, are straight lines for the
line Am, and below, but they are curves convex
with respect to the Z corner above the line Am,,
with the limiting paths Ap and Am, both straight
(sketched on Fig. 11.3). The paths for the G
field are similar: straight lines from G below the
line Gm,, and curves, convex with respect to Z,
above this line.

The region AEM,IG, then, although it contains
the quasi-binary line M,M,, is not subdivided
into separate subsystems; the line MM, does
not cut the region into two parts, For convenience,
however, the right and left portions will be dis-
cussed separately,

1.3, THE REGION FOR COMPOUNDS
G AND H OF SYSTEM R-Z

The Region As Shown in Figures 11.6 and 11.7

The relations for compounds G and H, as assumed
in Fig. 11,2, are shown in schematic detail in
Fig. 11.6. On the basis of these relations the
region M M,IG of the ternary system would be
schematically as sketched in Fig. 11.7. For the
H solid solution field the fractionation paths are
curves, convex with respect to Z, originating by
extension from the point .

On the curve my » P, the liquid precipitates
M, and solid solution on the binary side starting

1

at Gm8 for L. at mg and ending ot G, for P,

49

e
<
@
L
o0
W
w
==
w0
@
o
=1
29
.ML
=z
@
o

 

G 7
-
~ \\\jgw/
> 7 S
7 foi
\ 7 H\,\ \.\ _,,
\ 7_ ,.\ .;.\_ ,,,_,
N Lh\ \_\ \
; - _,_,
Z ///./“‘\‘\\‘ = - A.,,,M .,,.,,
e = ,,, \ , \
: \ N
) Y §
s I Y
=l S
"~ } / |
Wt \
. |
b
~

 

 

Fig. 11.5.

4.

11

Fig.

T

 

—

SN Q\qu

 

mi:4|1x

L\J.v.l\.fi\

F+L—

TH

 

6.

14

Fig.
UNCLASSIFIED
ORNL-LR-0OWG 25595

 

These solid solutions are not on the ‘‘solidus’’
curve of Fig. 11.6, but G, itself is. On the curve

bg > Pz

L + G (solid solution) » H, (pure) .

The three-phase triangle starts as the line pBHaGp

(see Fig. 11.6), and ends as the triangle P HG, S
This curve is crossed for x in the region Hpgt |4

The invariant reaction at P17 is
L+G M +H, .

This is an incongruent crystallization end point
for x in triangle XVII (MlHG”); for x in M, P, .H,
the liquid moves onto curve P, P
M, and an H,
and ending as H, .

14¢ Precipitating
solid solution starting as pure H
(As shown on Fig. 11.6, H,

is not on a solidus curve of the binary system.

Cn curve y » P,
L +M1 -—>M2 ;

this curve is crossed for x in the region M,yP, ..
The point P, is reached for x in the quadrangle
M1M2P]6H]6; its reaction is

L+M] ~>M2+H‘6 .

and it is the incongruent crystallization end point
for triangle XVIi (M]MzH]é).

"\'12P16H1Qa L. then travels on curve 1_316 - E_15'
precipitating M, and an H solid solution starting

For x in the region

at H, . and ending at H, .. Along curve e, > E, ,
the liquid precipitates I and an H, sclid solution

starting at H_ and ending at H, . (see Fig. 11.6).

9
Along curve E,,»E

L - M2 +1 .
The point E, . is reached for x in triangle XV
(M IH, ).

For x in the regions M, G,.G, MH, H, and
MoH, (Hy liquid is consumed, to leave two solids,
while traveling on curves E,P.., P P, ., and
P ¢E s respectively,  The H solid solution

produced in these processes, with compositions
ranging from H to H, ., is the a form of H. As the
temperature is lowered, however, the solid so-
lution undergoes transition to the 3 form, starting
at T’ for pure H and ending at 7", as shown in
Fig. 11.6; and these temperatures are unaffected
by the coexistence with solid M
since the H, and Hyg solid solutions are purely
binary.

We have here assumed the order of decreasing
temperature to be: T’ = Pig >eg > E s >T7%
But if T > E,, then there is an isothermal
crease, at temperature T, running across the H
surface between curves e £, and P, E .. The
surface between this crease and E, . represents
solid solution; the
rest of the H field represents liquid in equilibrium

or solid M,

liquid in equilibrium with H

with H, solid solution.

For the relations assumed in Fig. 11.7, liquid
of composition @ gives M, as first solid, and L
moves on a straight line from M, (i.e., on the
extension of the straight line M,a) to the curve

yP Here

16°

L+M »M,

M, is consumed; . leaves the curve, traverses the
M, field on a straight line from M, and reaches
curve m,E, .. Here

L—»M2+I .

and at E, ., H

The Region As Shown in Figures 11.8 and 11.9

The other possibility for the region M, M,IG
seems to be, as already stated, that H forms no
solid solution, and has but one form. Then Fig.
11.6 becomes Fig. 11.8, and Fig. 11.7 becomes
Fig. 11.9. In Fig. 11.9, the first solid for liquid

also precipitates.

51
UNCLASSIFIED
ORNL-LR-DWG 2559¢

 

 

Fig. 1.9

a is the G solid solution, between G and G,,.

The liquid reaches the curve m P,., traveling on
a curved equilibrium path over the G surface. On
the curve, the liquid precipitates M, and more
solid solution, ending at G, AtP,_,

L+G”»M] +H ;

G is consumed; the liquid travels on curve

17

P17P16' precipitating M] and H, and reaches Plé'

where the liquid is consumed in the reaction

L+M] ->M2+H .

1.4, THE REGION INVOLVING COMPOUNDS
B AND D OF SYSTEM Y -Z

Figure 11,10 shows a probable arrangement for
the missing primary phase fields for compounds
B and D of system Y~Z, Also, since four of the
solids of system Y-Z form binary solid solutions,
there must be various two-solid areas reached upon
complete solidification in this region, whenever
one of these solids crystallizes together with a
solid involving the third component R; i.e., for
every case of a boundary curve invelving one of

52

these solids and a solid containing component K.
These areas are shown with tie lines, the relations
being essentially as already explained schemati-
cally for Fig. 7.3.

The field for compound B is introduced as
p,p 5P P4, and that for compound D as PP P..
There are now two more three-solid triangles, for
The compo-
is simply the ternary

the two added ternary invariants.
sition represented by P,
solution present when the compound D forms on
cooling from solids C and E (a solid sclution); it
is similar to P and P, in Fig. 9.3, where, how-
ever, only pure solids are involved.

As explained for the solid phase H under Fig.
11.7, the solid form of B involved on the B field
and along its boundaries is the solid solution in
the upper polymorphic form B, ranging in compo-
sition from pure B to the solid solution limit indi-
cated in Fig. 11.10. As the temperature is lowered,
however, the B, phase undergoes transition to the
pure 3 form, starting at T’ for pure B, and ending
at T” for the solid solution (Fig. 11.2). As in
the case of compound H these temperatures are un-
affected by the coexistence with solid M.

Wherever the compound C is invelved as a solid
phase, its form is €, above the temperature of
(Fig. 11.1), C, between 3 and t,, C.,, between
t, and tas and Cj5 below t,. The C surface, (C),
is, strictly, divided into four parts, by the special
isothermal contours at ¢,, t,, and t;. These con-
tours constitute slight creases in the surface,
defining the regions for liquid in equilibrium with
Co Ca Cy,cnd Cs, respectively.

Since A, B, D, and E are binary solid solutions,
the fractionation paths on the fields for these
solids are curved. Those for the E field are
are similar to those on the A field: above the
they are straight lines from F, and below
this line they are curves convex with respect to
For the B and D fields the paths
originate by extension from the points B and D

line Em4
the corner Y,

respectively, and they are convex toward Z in
both cases,

Along the binary curve Ee, (from the congruent
melting point of E to e,), the liquid precipitates a
solid solution starting as pure E at the melting
point of E and ending at E_ for L at ¢,. Along
the ternary curve e, P, the liquid precipitates
C and a solid solution of E, strictly varying in
composition between the temperatures of e, and
P, but practically constant because the solidus
UNCLASSIFIED
ORNL-LR-DWG 25597

 

 

 

 

 

 

 

 

 

Fig. 11.10.

(Fig. 11.1) is practically vertical, At P, there-
fore,

C+E_ - calories » D ,

For x in the region CDP ,, E_

L. travels on curve P P,

is consumed, and
precipitating D in the
reaction

L+C->D .

For x in the region DE P, Cis consumed, and

L. travels on curve N

DI
precipitating two solid

solutions, conjugate solid solutions of the com-
pounds D and E. The D solid starts as pure D at
P and ranges to D_ when P is reached, and the
E solid, already at E_, changes slightly but is
still practically constant at E_, The point P is
then the invariant liquid for the solids D, E
and M,, in the reaction

st

L+DS—>ES+M2 .

For x in the region £ _P_M,,

L. moves along curve P7E8, precipitating M, and

D_ is consumed, and

53
E_ (still practically constant, we are assuming).

The saddle points m,, m,, m,, and m” involve
liquid saturated with two pure solids, as does
also the special point y; m, and mgy, as already

discussed, involve M, and a solid solution (A

and G, reSpecfiveiy]).

For liquid of composition @ ir Fig. 11.10 the
first solid on cooling is a solid solution of A,
and A,.

between A The liquid reaches curve

p,P 4 where 3

L +A(ss)->B .

The A solid solution is consumed; L {eaves the
curve, traverses the B field precipitating solid
solution B, and reaches the curve p.P,. Here

L ""IB(SS)—)C‘~ .

The B solid solution is consumed; [ leaves the
curve, traverses the C field on a straight line from
C, and reaches curve P P.. Here

L—yC+M] .

L +MT - +M2 ;

M, is consumed, and L moves to P, where D also
precipitates to leave C, D, and M,., The path of
the liquid on the solid solution fields (A and B)
is curved, convex with respect to the corner Z.

Liquid & gives M, as first solid, reaches curve
PP, precipitates C and M, and reaches P,

where M] is consumed in the reaction
L +M] > C +z\"12 .

Now [. moves on P5P6

sumed in the reaction

to P, where C is con-

L+C—~>D+M2 .

The liquid now starts out on curve P P, pre-

‘ 7
cipitating M, and solid solution, but the liquid
vanishes on the curve to leave a two-solid mixture
of M, and a solid solution between D and D, on a

straight line through # and M,
12, SYSTEM Y=Z~X: NaF-ZrF -LiF

For the ternary system Y=Z-X, the diagram of
the binary system Y=Z, already considered under
Fig. 11,1, is used here with the same lettering.
The binary systems X-Z and Y=X are shown,
schematically, in Figs. 12.1 and 12,2. Two of the
compounds
cooling, one of them, G, also showing a polymorphic
transition, at T°,

The ternary diagram, as far as it has been worked
out, is shown in Fig. 12,3. Like Fig. 11,3, the
diagram does not show the primary phase fields
for compounds B and D of the Y=Z system, which
should appear.

of the system X-Z decompose on

This system involves several series of solid
solutions. It has not only the binary solid so-
lutions of the system Y~Z (Fig. 11.1), but also

solid solutions, with compositions on straight
lines (crosshatched on Fig. 12.3) across the
diagram, formed between corresponding binary

compounds of the systems Y-Z and X-Z. The
compound A of system Y-Z (3Y.1Z) forms solid
solution with G (also 3:1 in composition) of
system X—=Z. The solid solution is not continuous,
Since both compounds
melting points and since the

but has a miscibility gap.

have congruent

UNCLASSIFIED
ORNL-LR-DWG 25598

 

 

 

 

section Am,G of Fig. 12,3 is quasi-binary, it is
clear that the ternary system may immediately be
divided at this point into separate subsystems,
With m, a femperature minimum between A and G,
the binary system A=G is eutectic in nature,

Solid A, however, also forms solid solution
(with excess Z in its composition) in the binary
Y-Z system. The solid solution originating at
point A of Fig, 12,3 is therefore actually ternary
in composition, occupying an area of the diagram,
and one edge of this area is the straight line from
point A to point G.

The corresponding compounds F and I, both 3:4
in composition, also form solid solution with a
miscibility gap. Both have incongruent melting
points, however, and the section FI of Fig. 12.3
is of course not quasi-binary, even though the
solutions formed are strictly on the, line FI. The
section EH, however, through the
on the curve E E, divides the
upper part of Fig. 12.3 into two independent sub-
systems. This is so since E forms solid solution
with D (Fig. 11.1) but not with F, and H is pure.

We shall therefore discuss this system part by
part, for it consists of three practically inde-
pendent subsystems: Y=A=G=X, A=E=H=G,
and E~Z~H. (Note: This independence holds at
least to just below liquidus temperatures, but not
all the way, since compounds G and | of system
X—7 decompose at low temperature.)

We shall first describe the fractionation paths
for the solid solution surfaces, The field for the
A-rich solid solution of A and G, i.e., the surface
for liquid in equilibrium with A _, is e, ApP [P E E,.
The maximum of this surface is point A itself,
since this

quasi-binary
saddle point m

compound melts congruently.  The
fractionation paths therefore radiate as curves
from point A, and they may be said to consist of
two families of paths, divided by the straight-line
fractionation path running from A to m,. All the
paths, diverging from this line, are convex with
respect to point G, A similar arrangement holds
for the G_ field (field for liquid in equilibrium
with Gerich solid solution), e,Ge P E,, with a
and all
other paths diverging from this line and convex
with respect to the point A, For the surface
estyP1oPors for liquid in equilibrium with F_
(F-rich solid solution of F and I}, the temperature
maximum for the origin of the fractionation paths

straight-line path running from G to m,

is the metastable congruent melting point of F.

55
 

 

Hence the fractionation paths do not show & common
origin on the field itself, but radiate, as curves
convex toward I, from point F. The fractionation
paths for the I_ surface, ep, (P, PoEg, similarly
radiate, as curves convex toward F, from the sub-
merged maximum at point I,

The fractionation paths for the fields for solid
solutions of the compounds B, D, and E of system
Y—-Z, to be considered later, will be as described
for the same fields in the preceding system (Sec

11.4).

UNCLASSIFIED
ORNL-LR-DWG 25599

(Z) A

 

 

 

 

12,1, SUBSYSTEM Y-A-G-X

The region YAGX is shown in Fig. 12.4, ond
the vertical T vs ¢ section AG is given, sche-
matically, in Fig. 12.5,

Liquid on the curve
solid

starting as s

moE, precipitates two

mutually saturating solutions, with con-

jugate compositions and s’

»
and S5

These limiting solid so-
lutions may be identified on the miscibility gap in

at the temperature of m, and ending as s,

at the temperature of F .
UNCLASSIFIED
ORNL-LR-DWG 25600

 

 

 

 

 

Fig.

Fig. 12.5, which shows the solid-solid solubility
as diminishing with decreasing temperature. On
curve e £, liquid precipitates Y and solid so-
; ot E};
similarly, liquid on curve e,E, precipitates X
and solid solution G _ ranging from G to 55. Liquid

lution A_ ranging from pure A at e, to s

on curve E.E, precipitates X and A_ solid so-

lution starting at s for sclution m, and ranging

]
to s, for liquid following curve m E, and ranging
to s, for liquid following curve m,E,. The solid

are not related

solution compositions s, and s _

1
1
to the miscibility gap of Fig. 12.5; they are merely

 

12.0.

points inthe A _ solid solution area of that diagram,
Also, as explained under Fig. 7.3, the line s_ m, X
is not a quasi-binary section. 1

Liquids with original composition x in the region
s,GX reach the curve e, L, and solidify com-
pletely before reaching E,, to leave X and G_.
Similarly, liquids from x in the s s, X solidify

on the curve m E, to leave A_ c1nd X. Only
liquids for x in the triangle s,s7X reach E, to
give the three solids s,, sJ, and X. Similarly,
only liquids for x in the triangle Ys, X reach E,
to form the three solids of triangle I.

57
Summarizing the equilibrium crystallization

process for the curves: curve e E, is reached for
x in region YAs I, but the liquid vanishes on
the curve for x in Yas,; curve e E_ is reached
for x in XGsJE,, but the liquid is consumed for x
in XGsz',' curve E.E, s reached for x in
s 5,E XE, but the liquid is consumed for x in

s,X; curve e, E, is reached for x in YE X,

for x in 5252'52, but on these
curves the liquid does not vanish,

Sy

and curve m_E

12.2. SUBSYSTEM E~Z~H

The region EZH is shown in Fig. 12.6, and the
vertical T vs ¢ section FI is shown in Fig. 12.7.
The miscibility gap in the F=I solid solution is
shown as
The three invariant planes in Fig. 12.6 are seen
The quadrangle P, s, Zs{, is the

widening with falling temperature.

to overlap.

UNCLASSIFIED
ORNL-LR-DWG 258601

 

 

 

Fig. 12 7.

58

highest in temperature. Below it is the quadrangie
g° is the
triangle for Eg, Es H. (This diagram has certain
similarities to the hypothetical case of Fig. 7.3.)

Polsys The lowest in temperature

In the relations as assumed in these figures,
liquids in the field DgZp 4Py, give pure Z as
primary solid, and travel on a straight line from Z
to one of the transition curves p P, and p, P, ..
On the curve p P, ,

L+Z~»F_,

the F-rich solid solution. The three-phase triangle
for this equilibrium starts as the line p,FZ and
ends as the triangle P $y0Z. For xin the region
FZsyq the liquid vanishes on the curve, leaving
Z and F_ (between [ and Sm).

region Petsy 0P

For x in the
, Z is consumed while L is on
the curve, and the liquid then leaves the curve to
travel, on o curved path, across the F_ field.
Similar relations hold on the | side, with respect
to curve p, P, ., with the reaction

L+Z—>IS

For x in the region IZS]’O, the liquid vanishes on

the curve, leaving Z and [_ (between | and SI’O)'

and for x in pwls' P L. leaves the curve when

107 10
all Z is consumed, to travel, on a curved path,
across the I_ field. Only liquids for x in the

quadrangle s, Zs/ P reach P,., where the

) ) 10
reaction 1s

L +Z~»s]0 +S1g -
For x in s, Zs]’ , therefore, the liquid is consumed
at P, to leave the three solids of triangle X,
Sy o 51’0, and Z; and otherwise, with Z consumed,
L moves down along curve P. P

107 9/
two conjugate solid solutions with compositions

precipitating

changing from s, ¢ and 59', according
to the miscibility gap in Fig. 12.7.

The curve P, P may also be reached directly
from either the F_ field or the I_ field, for x in

and 5'0 to s

the regions 89.510P]OP9 and 51059_P9%)10’ re-
spectively. Foint P is reached by liquids for x

in the quadrangle Es_ s/P., and with the reaction

979" 9!

L + Sg > E +59' ,
this is the incongruent crystallization end point for
triangle 1X, Esgsg. If sg
reaction, the liquid moves down on curve Polg,

is consumed in the P9
precipitating E and I_ solid solution ranging from
59' to sg. (With reference to Fig. 12.7, s_ is in the
I_ area but not on the solidus edge of the misci-
bility gap.) Also, liquids reaching curve egE
travel on it precipitating H and I_ (between I ang
sy)»  For x in Hsgl, the liquid vanishes on the
curve to leave f/ and 1. The point E_, then, is
reached for x in triangle VIl EsgH, for which it
is the eutectic.

Finally, liquid traveling on curve e Py, but with
x in the region EFs,, vanishes on the curve to
leave E and F_; liquid traveling on the curve
PyEg and with x in ES;SB vanishes to leave E
and I _ between s and s,.

As an example of some of the relations we con-
sider point @ in Fig. 12.6. For liquid of this
composition, the first solid on cooling is Z, and
L. reaches curve p P, on a straight line from Z,

On the curve,

0

L+Z-F_,

starting between F and s, and moving toward
But before the composition of the solid

S .
of
solution reaches s Z is consumed; L leaves

10/
the curve and travels on a curved path, convex

with respect to I, across the F_ field. While L

 

 

is on the F_ surface, the solid solution continues
to become richer in I. When [ reaches curve
PP, the I-rich solid solution begins to pre-
cipitate together with F_, the compositions of the
solid solutions being given at each temperature by
the miscibility gap of Fig. 12.7. When L reaches
P,

L+sg>F+sg,
and sg vanishes. The liquid then travels on the
curve PoE ., while s changes toward Sge Crystal-
lization is completed at Eg to leave the solids

E, Sgs and H,

12,3. SUBSYSTEM A-E~-H-G

The phase diagram as constructed in Fig. 12.3
omits fields for the binary compounds B and D of
the system Y=Z (Fig. 11.1). We shall, however,
discuss the region AEHG, not as shown in Fig.
12.3, but as it might probably appear with the
necessary fields for B and D (Fig. 12,8), as was
done for the system Y=Z~R in Fig. 11,10.

o and s” of Fig. 12.8 are

The points s, m
2
the same as those so labelled in Fig. 12.4. The

UNCLASSIFIED
ORNL-LR—-DWG 25602

 

 

 

 

 

59
and s, (like s

12.4) are also conjugate solid solutions of the

solid solutions s and s, in Fig.
A~G solid solution miscibility gap, identifiable in
Fig. 12.5,
As liquid travels on the curve m, » P,
cipitates solid solutions beginning as s and
2
s, and ending as s, and sJ. The solids of

triangle |11, S 31 53’, and /{, are in equilibrium with

it pre-

,

the invariant liquid P,, where the reaction is

»
L+53~953+H

If 53: is consumed in this reaction, the liquid moves
down the curve P.P,, precipitating A_ solid so-
lution and H., The A_ solid solution, however,
is here shown as ternary in composition, and
it has the composition s, when L reaches Py
Point a is the limiting composition in the binary
system Y=Z at the temperature of .
Compositions x in the area Aas s, would
solidify (in full equilibrium} to a single ternary
solid solution phase while the liquid is traveling
on the A_ field, before the liquid reaches any
boundary curve (cf, Fig. 2.3). For x in the region
aBs,, L reaches the transition curve o 4 aleng

which
L +AS~+B ’

and the liquid vanishes while on that curve, to
leave A_(on the curve as,) and B.

The rest of the relations in this diagram are
altogether similar to those in Fig. 11.10, with H,
so to speak, in place of the various ternary com-
pounds of that diagram,

12,4, SUBSOLIDUS DECOMPOSITIONS OF
COMPOUNDS G AND |

As shown in Fig. 12,1, for the binary system
X-Z, the compounds G and I undergo solid-phase
and T,
respectively. In the ternary system Y-Z-X, both
of these compounds form solid solution with the
third component, Y, while their products of de-
composition do not. The decomposition temper-
ature is therefore lowered, in both cases, and we

decompositions at the temperatures TG

shall say to T/ and T/, respectively. The com-
pound [ is considered first,

Decomposition of Compound [

The changes in the two- and three-solid equilibria
accompanying the low-temperature decomposition
of compound I are shown in the successive iso-
therms of Fig. 12.9. Isotherm (a) is just below
[, of Fig. 12.6, and it represents the various two-
and three-solid mixtures which will be obtained

UNCLASSIFIED
ORNL-LR-DWG 25603

 

Fig. 12.9.

60
upon complete solidification of any composition
in this subsystem. Only the number of phases
is shown inthe figure; the phases may be identified,
if necessary, from Fig. 12,6. Figure 12,9 () is
just below T, of Fig. 12,1, where the three-solid
area for Z, H, and I_ appeared on cooling. Figure
12.9 (c) is at the temperature of a four-solid in-
variant, for the reaction

F+l - F +H
S 5

on cooling, and Fig. 12.9 (d) is just below this
invariant, Figure 12.9 (e) is at the temperature
T,, the lowest temperature for the existence of
the I_ solid phase (point s). Figure 12.9 (/) is
below this temperature. The T vs ¢ section FI
(Fig. 12.10) shows little of all these changes.

Decomposition of Compound G

According to Fig. 12.1, the compound G under-
goes a fransition on cooling, at 77, from G, to
Gy before the 3 form decomposes at 7 .. In the
successive solid-phase isotherms of Fig. 12.11

it is assumed that, as in the case of the aecompeo-
sition temperature itself, the transition temper-
ature is also lowered, from T to T, as the result
of the presence of the third component in solid
solution. The temperature-composition relations
assumed, then, for the section AG are shown in
Fig. 12.12.

The first isotherm, (a), of Fig. 12.11 represents
the two- and three-solid combinations for equi-
librium just below the temperature of point P, of
Fig. 12.8, for the region YBHX (the ternary solid
solution area for A_ is omitted). At T’ there
appears a length of G, solid solution, with four
new equilibria for H and (G ) ; X and (G ) ; H,

(G.), and (G ) ; and X, (G ), and (GS)B. Figure
a

12.]?(b)showslfhese new combinations, at a temper-
ature between 7 7and I'”, Figure 12.11(c) isat T”,
the lowest temperature for existence of the ternary
G, solid solution, Figure 12.11(d) is between
77 and T, where the 3 form begins to decompose
(into H and X) in the binary system. Figure
12.11(e) is between T . and T(';. Figure 12.11(/)
is at 7., the lowest temperature of existence of
the G, solid solution in the ternary system.
Figure 12.11(g) is below 7.

UNCLASSIFIED
ORNL-LR-DWG 25604

 

 

 

 

 

61
UNCLASSIFIED
ORNL-LR-DWG 25605

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 12 1.

62
 

L+ A

 

Ac+(6)q

 

 

 

 

=
b 7

UNCLASSIFIED

ORNL-LR-DWG 32522

7!
///’(63)3

1

/“‘\*

s B+ X+H

 

D

 

Fig. 12 12.

63

 
13. SYSTEM Y-U-X: NaF-UF,-LiF

For the ternary system Y—U—X, the binary system
Y—U is used with the lettering shown on Fig. 9.1.
The binary system Y—X is that of Fig. 12.2, with
e, Mow in place of e,,. The binary system X-U,
already given in Fig. 8.1, is repeated here in Fig.
13.1 to show the new lettering tequired in the
present section. We note the binary compounds A
and C of system Y—U and G of system X-U, de-
composing on cooling. The system Y-U also has
two compounds, E and F, which form below the
liquidus temperature.

UNCLASSIFIED
ORNL-LR-DWG 25606

 

 

 

 

Fig. 13 1.

The ternary diagram is given in Fig. 13.2. There
are no binary solid solutions involved in this
system, but there are two large primary phase
fields for solid solutions formed across the diagram
by corresponding 7:6 compounds D and H. These
compounds form discontinuous solid solution with
a considerable miscibility gap. The primary phase
fields for D (the D-rich solid solution) and for
H, {the H-rich solid solution) are in contact along
the boundary curve £, E,, and the point m,; on this
curve is a saddle point, being on the line DH.
However, compound D has a congruent melting
point, while compound H melts incongruently, so
that the line Dmy H is not a quasi-binary section.
The system has three saddle points but no quasi-
binary section at all. The fine Dm, X looks like
one but is not, because of the solid solution in
the D solid phase. The extent of solid-solid
solubility at the liquidus temperatures, across the
section DH, is suggested by the crosshatching on

this line in Fig. 13.2.

64

The fractionation paths on the D _ surface origi-
nate at point D and radiate, on either side of the
straight-line path Dm,, as curves convex with
respect to point H. The paths on the H field must
be imagined as radiating by extension from point H
(the submerged, metastable maximum of the field);
they curve similarly on either side of the straight-
line path Hm, (of which only the portion r » m, is
on the stable surface for liquid in equilibrium with
H_) and are convex with respect to point D.

The vertical T vs c relations for the section DH
of the ternary system are shown in Fig. 13.3. The
point 7 is on curve pg P, of Fig. 13.2, and s s
the composition of the solid solution in equilibrium
with liquid 7. The solids s and s/ are the

conjugate solid solutions in equilibrium w3i’rh liquid
m., the minimum of the section. The compositions
below this temperature on Fig. 13.3 correspond to
liquids at the ternary eutectics £, and E,, and
will be referred to later.

The system (Fig. 13.2) has ten primary phase
fields and ten invariant points. Four of these
invariants, however, involve simply the decompo-

There

are consequently only six three-solid triangles for

sition or formation of binary compounds.

ultimate combinations of solids on complete solidi-
fication, related to two ternary peritectics and four
ternary eutectics. We shall consider first the four
invariant points for appearance or dis-
appearance of binary compounds and then the
trelations involved in the principal invariants.

special

13.1. THE INVARIANTS P, P Pe. AND P_

Cl
The Invariant PA

The decomposition of compound A involves pure
solids:

A—bY+B

r

and the temperature of the invariant P, is there-
fore the same as T , in Fig. 9.1. (The changes in
isothermal relations near P
to those shown in Fig. 8.5.) The curves ¢, P, and

esz are both curves of even reaction,

L—)A+Y

are entirely similar

and
[.A+B

I

respectively; the first is reached by liquid for total
composition x in the region YAP ,, the second for

x in ABP ,. At P ,, solid A decomposes, and the
 

UNCLASSIFIED
CRNL-LR-DWG 25607

 

 

Fig 13.2.

liquid travels on curve P ,E, precipitating B and
Y. The isothermal curve wv represents liquid in
equilibrium with A_and A ; and divides the A field
into regions for liquid in equilibrium with A_ and
for liquid in equilibrium with AB' lts temperature
is T’ in Fig. 9.1.

The Invariant P _

The temperature of the invariant P~ for the
decomposition of compound C in the presence of
ternary liquid, is higher than T . of Fig. 9.1, be-
cause C is here decomposing not into pure solids

but into B and a solid solution of D and H. The
isothermal relations involving P . are shown in
Fig. 13.4: {(a) between Py and P () at P
(c) between P and T ., and {d) below T The

Cl
reaction on curve p, P i

cis
L+D »C ,
s
the three-phase triangle starting as line p,CD and
ending as P-Cy (isotherm &). This curve is

reached for x in the region p,DyP . For x in
CDy, the liquid is consumed on the curve to leave

65
UNCLASSIFIED
ORNL-LR-DWG 25608

 

Fig. 13 3.

C and D _ (between D and y). For x inp,CP ., D_
is consumed on the curve, and L then traverses
the C field on a straight line from C, to reach
curve p, P . Forcurve p, P,

L+C->»B

The curve is reached for x in p, CP ; then for x in
p4BP -, C vanishes on the curve and L leaves the
curve to travel on the B field. The point P, with
the invariant reaction

L+C-sB+y ,

is reached only for x in the quadrangle BCyP . For
x in the triangle BCy, the liquid is consumed to
leave the three solids, while for x in ByP ., C is
consumed and the liquid moves away on curve
P-E,, precipitating B and D _, the solid solution
ranging from point y at P to s, {Fig. 13.9) at E,.

At P _ the equilibrium between C and liquid,
shown in isotherm (a), is replaced by the equi-
librium between B and D _, shown in isotherm (c),
with the D_ composition ranging between limits
y’ and y”. The limit y” reaches pure D aof T .
and the limit y " reaches s, ot E,.

As the temperature begins to fall below P,
compositions in the region BDy have already been
completely solidified, either as C and D _ (from D
to y) or as B, C, and y.
of Fig. 13.4 (c) moves to the left, the C vanishes
from the three-solid mixtures to leave B and D,
and the two-solid (C and D) mixtures first change

A

66

Now as the tie line By~

to B, C, and y“ and then lose the C phase to leave
B and D_. The lowest temperature for coexistence
of C with liquid is P, but C finally vanishes from
coexistence with solids B and D_at T, to leave

Fig. 13.4 (d).

The Invariant PG

The relations at P . are similar, except that one
of the boundaries of the G field is a curve of even
reaction. At P, the decomposition of G involves
pure X and H_ solid solution, and the temperature
is higher than T _ of Fig. 13.1. The isothermal
relations are shown in Fig. 13.5: (4) between e,
and P, (b) at P, {c) between P and T, and
(d) below T . The reaction on curve p, P is

L+X-G ;

the curve is reached for x in Xp, P, and crossed
for x in Gp, P.. Oncurvee, P,

L—>G+H
S

’

the solid solution starting as pure H and ending at
z [Fig. 13.5 (b)]. The curve is reached for x in
P zHG. For x in zHG, the liquid vanishes on the
curve to leave G and H_. The point P, for the
reaction

L+Gasz+X

I

is reached for x in the quadrangle P . zGX. For x
in the triangle zGX, the liquid vanishes to leave
the three solids; for x in P =zX, G is consumed,
and the liquid travels on curve P _F, precipitating
X and H_ solid solution ranging from z to s
(Fig. 13.9) ot E;.

In the two- and three-solid mixtures containing
G, left in region zHX as the temperature falls
below P, solid G vanishes to leave simply X and
H_, as the tie line z”X of Fig. 13.5 (¢} moves to
the side of the diagram, which it reaches at T .,
to leave the isotherm of Fig. 13.5 (d).

The Invariant PE

The invariant P . represents the formation of the
binary compound E in the presence of ternary
liquid, not from pure solids but from U and D _
solid solution; the temperature of P is therefore
g in Fig. 9.1. The pertinent isothermal
relations are shown in Fig. 13.6: {(a) between e
and T, (b) between T and P, (c) at P, and
{d) below P Curve es P with the reaction

lower than T

1

L->U+D
s

is reached for x in the region e, UP . by liquid
UNCLASSIFIED
ORNL-LR-DWG 25609

 

Fig. 13.4.

precipitating U or for x in De P _d by liquid
precipitating D _ solid solution which starts as
pure D at e, and ends as 4 at P [Fig. 13.6 (c)].

For x in the region DUd, the liquid vanishes
while on the curve between e and P, when the
tie line 4’U, moving from DU at e. to dU at P,
comes to pass through x, to leave D_and U. At
T, however (between es and P in temperature),
the tie lines d”'E and d U also begin to enter the
diagram [Fig. 13.6 (b)]. When x comes to be swept
by the line d”'U, solid E appears in the mixture,
and the two-solid mixture of D and U becomes a
mixture of D _, E, and U. Moreover, if x is in the
region DEd [Fig. 13.6 (c)}, it comes next to be
swept by the line d”’E, when solid U vanishes
from the mixture, to leave D_and E.

Mixtures in the region DUd are therefore com-
pletely solidified before L reaches P, and at
that temperature, when d°" and 4’ meet to give
point d of the invariant quadrangle in Fig. 13.6 (c),
and when the region for D_ and U has shrunk to
the line dU, the solids present are either D_and E
in DEd, or D_ (of composition 4), F, and U in
dEU.

Liquids traveling on the curve e, P reach P
only if x is in the triangle JUP .

The reaction at the temperature of P ., however,
is

D (d)+U-E+L(P,) ;

it requires simply the solids d and U, and proceeds
whether or not the liquid phase is present. Hence

67
 

UNCLASSIFIED
ORNL~-LR-DWG 25610

 

Fig. 13 5.

those mixtures which had already solidified to E,
d, and U now produce liquid of the compesition
P . again, in the invariant reaction. The invariant
P, is an example of the type of invariant dis-
cussed as case (b) under Fig. 4.12.

Now for x in the region EUP ., the solid solution

d is consumed and L travels away on curve P _ P

E 6

along which
L+U-»E ;

and for x in JEP _, U is consumed and L moves

onto curve P o E , for

r

L-E+D
s

the solid solution starting at 4 and ending at s

4
(Fig. 13.7).

68

13.2. THE REGION DUH

Figure 13.7 gives the schematic arrangement for
the reactions involving the invariant points in the
upper half of the ternary system, the region DUH.
The invariant quadrangle pertaining to P is
shown by dashed lines.
seen to overlap in various ways.
temperature is PE > P6 > P5 > E4.

are dEUP , EUIP ,, Elsg P,

The invariant planes are
The order of

The planes
and 54554 {for E4).

The transition curve P _P for the reaction

E" &
L+U—>E '

is reached, directly or indirectly, by liquids for x
in the region P EUP; but for x in PpEP,, L
then leaves the curve when U is consumed, to
UNCLASSIFIED
ORNL—-LR—-DWG 2561414

 

”/

/

/ ///
/)

7
y Z

 

 

 

 

 

69
UNCLASSIFIED
ORNL-LR-DWG 25642

~

VI

 

Fig 13 7.

travel across the E field.
pg P4 for the reaction

L +U->1

The transition curve

r

is reached from the region pgo UP , ond it is left
by liquid for x in poIP,. The point P, is reached
only for x in P EUI its reaction is

L+U-E+1

i

and it is the incongruent solidification end point
for triangle VI (EUI). At a still lower temperature,
solid F of system Y-U forms from the solids F
and U, and then we have either E, F, and [ or F,
U, and [,

The reaction on curve P Pg is odd,

L+E-T,

if, as assumed in Fig. 13.7,
to the right of 1. In this case the curve is reached
either from P, (for x in the region PéEI) or directly
from the E field for x in P.EP,. But for x in
P 1P, the curve is left by the liquid when E is
consumed, when the liquid, saturated only with I,
moves onto the [ field.

Next, the transition curve pgP, is reached,
directly or indirectly, for x in the region /P p..
The reaction on this curve is

L+I"HS

its tangent extends

The three-phase triangle for liquid in equilibrium
with H_and [ starts as the straight line p4 HI and

70

extends into the diagram to end as P s I. Conse-
quently either the liquid or the solid I may be
completely consumed while L is on the curve.
For x in s.IH, the liquid is consumed when the
H _~I leg of the three-phase triangle sweeps through
the point x, to leave [ and H_ (between H and ss).
For x in the region p, P s, H, solid I is consumed
when the L—H_ leg passes through x; this leg starts
as the line p °H and sweeps around to become rs,
for L at 7, and finally Pgs.. When I has vanlshed
L leaves the curve to travel upon the H < field,
on a curved path (a straight path only between 7
and m,, but otherwise curving always away from
this line). The invariant P_ is reached only for x
in the quadrangle P, Els,. Its reaction is

I

L+I»E+55

and it is the incongruent crystallization end point
for triangle V (Els).

For x in the region P, Es,
down the curve P E precipifo'ring E and solid
solution H_, beginning at s. and ending at s
The curve P E, is also reached directly, from the
E field for x in £, EP, and from the H _ field for x
ins.PgE s, Forx m Es’s., the liquid vanishes
on f?'ue curve to leave F and a solid solution {be-
tween s/ and s_.). The curve P.E, is reached
from the E field for x in PLEE,, from P itself
for x in dEP (d shown in Fig. 13.6); and from the
D_ field for x in dP L E s . Liquid on the curve
P o E, precipitates F and D, starting at 4 and
ending at s,. Compositions in dEs, solidify com-
pletely on the curve to leave E and D _. (It will
be recalled that compositions in DEd solidify
completely on the curve e  P..) The invariant E
is also reached along curve m, E,, with the liquid
precipitating two mutually saturated solid soiufions
ranging from s and sm at m, to s, and s, (cf.

"3
Fig. 13.3). From the D side, m  E
for x in saEgmyi from fhe H_

the liquid moves on

is reqched
side, directly or
The invariant EA' a
is therefore reached for x in triangle IV

indirectly, for x in my E s,.
eutectic,
(54 Es‘;).

The vertical T vs c section through EH is shown
schematically in Fig. 13.8.

Solution of composition a, in Fig. 13.7, gives U
as first solid, and L reaches curve P,P, ona
straight line from U. On the curve,

L +U>E

The solid U is consumed; L leaves the curve,
UNCLASSIFIED
ORNL-LR-DWG 25613

 

 

Fig. 13.8.

travels on a straight line from E, and reaches
curve P, P,. On this curve

L +E->I

The liquid reaches P, where

L+I¢E+s5

The compound I is consumed, and the liquid follows
curve P » E , precipitating E and a solid solution
ranging from s to s ;. At E sy also precipitates,
and the liquid vanishes to leave sg E and s /.

Liquid b gives U as first solid and reaches curve
pg P4 On the curve,

L +U->1

The solid U is consumed; L leaves the curve,
crosses the I field, and reaches curve pgP.. On
this curve

L+I—»H$ ,

the solid solution starting with composition just
to the right of s and reaching s; when L is at Pq.
Now

L+1~>E+55

The compound [ is consumed, and L starts out on
curve P, E,, but the liquid is consumed before
reaching E,, to leave E and a solid solution be-

tween s and sy

Liquid c gives U as first solid and reaches curve
On the curve

L-U+D_,
s

eSPE'

and the liquid vanishes, on the curve, to leave U
and a solid solution between D and d, fixed by the
straight line Uc. As the temperature continues to
fall, solid E forms to give E, U, and D _, the compo-
sition of the solid solution moving toward point 4.
The D_ solid reaches point d at the temperature
of P . Here

U+d»E+L(PE)

The solid U is consumed, and liquid reappears,
therefore, with composition P .. Now the liquid
travels along curve P E,, precipitating E and
D, with D _ starting at d; but the liquid vanishes
while on this curve to leave E and a solid solution
between d and s, fixed by the line Ec.

Finally, consider a liquid of composition x on
the line DH. The first solid is I, and liquid
reaches curve pg P, for the reaction

L +I1I-H
s

If x is between r and s, then when L reaches
point r, I will just have been consumed, and the
solid solution has the composition s_. Now the
liquid leaves the curve and travels to m,, where
it vanishes to leave the conjugate solid solutions
s_ and s But for x between s_ and H, the
liquid and I vanish simultaneously, leaving H_ as
sole solid phase, before L reaches point r on the
curve, when the H _ corner of the L—H —I three-
phase triangle passes through point x.

13.3. THE REGION YDHX

The lower part of the ternary system is repre-
sented in Fig. 13.9. The relations involving the
fields of the decomposing solids A, C, and G have
already been discussed. The Y, B, and X fields
involve pure solids, with straight-line crystal-
lization paths radiating from the points Y, B, and
X, respectively. The transition curve pg P, was
discussed under Fig. 13.7. Liquids reach this
curve on straight-line paths from the point I (Fig.
13.7), but for x in the portion of the I field in-
cluded in Fig. 13.9, I is completely consumed
while L is still on the curve. On leaving the
curve, L then travels across the H_ field, on a
curved path, to reach one of its boundaries m  F,
PGE

31 OF e7PG.

71
 

UNCLASSIFIED
ORNL-LR-DWG 256414

Fig. 13.9)

The eutectic E, is reached for x in triangle
(YBX). The reaction on the curve E\m E, is

L—»B-}-X

r

in both directions. The reaction for curve E,m, E,
is

L-X+D_,
the solid solution ranging from s for L at m,,

to s, at E, and to s, at E,. For x in the region
5,54 X, the liquid is consumed on the curve,
before reaching a eutectic, to leave X and D
{between s, and s3). The point m, is a saddle
point, but the section s, m, X is not quasi-binary;
the liquid with composition s_ is in equilibrium
2
with a solid solution not of composition s but
between D and s . 2
The reaction on curve P _E, is probably of even
sign,

L-B+D_ ,
£

along its whole length. The solid D _ for this curve

72

starts as point y (see Fig. 13.4) for L at P _ and
ranges to s, for L at E£,. For x in the region CDy,
solidification is complete on curve p, P . to leave
C and D_; compositions in BCy solidify at P . to
leave B, C, and y. As the temperature falls further,
C then begins to vanish from these solid mixtures,
disappearing completely on the binary side of the
system at T .. For x in Bys,, solidification is
complete on the curve P.E, to leave B and D .
The point E, is reached onfy for x in triangle Il
(BS2X).

Similarly, compositions in the region zHG solidify
completely on curve e, P to leave G and H_, and
those in zGX solidify at P .
Then as the temperature falls further, G begins to
decompose in these solid mixtures, vanishing last
on the binary side ai T .
liquid vanishes on the curve P E, to leave X and
H_. On curve my E,, the liquid precipitates conju-
gate solid solutions ending at s, and s;. The
point E; is reached for x in triangle Ill (535?: X).

The vertical T vs ¢ section BG is shown in

Fig. 13.10.

to leave G, X, and =z.

For x in s/ zX, the
 

j L+B+ X

 

 

X+0, —¥

 

UNCLASSIFIED

ORNL—LR-DWG 25615

1
:

o

—-—— TEMPERATURE OF m,
e £y

)

 

 

 

Fig. 43 .10.

Liquid a in Fig. 13.9 gives X as first solid,
reaches curve p, P, reaches P . carrying G and
X, and there solidifies to G, X, and z. With falling
temperature, the composition of the solid solution
moves to the right from z, and G vanishes to leave
X and a solid solution fixed by the line Xa.

Liquid & gives G as first solid, reaches curve
e P and solidifies on this curve to leave G and
a solid solution z” [Fig. 13.5 (c)] between z and

H. Then as the temperature falls further and z~

moves to the right, X appears as third solid when
the line Gz’ passes through &, and finally G
vanishes when the line Xz’ passes through &.
Liquid ¢ gives C as first solid, reaches curve
py P, leaves this curve when C is consumed,
reaches curve e, P, on the left of v, and begins
to precipitate A _together with B. At v, A changes

to A, At P, Afi decomposes, and the liquid
travefia on curve P, » E, to solidify at E, to Y,
B, and X.

13.4. FRACTIONATION PROCESS ON THE
SOLID SOLUTION FIELDS

In a fractionation process, L follows one of the
fractionation paths to a boundary of the field; the
solid increases in H on the D _ field and increases
in D on the H_ field. The fractionation end point
is E, above the line DH. Liquids starting in the
region between e, and the path DP . end as four
solids, D, U, E, and H_, but all others starting
in the solid solution fields above line DH end as
DS, E, and H _.

Below the line DH the fractionation process for
the H_ field ends at E, leaving H_, X, and D

73
the same holds for the D _ field above the path
Dm,. The rest of the D_ field is divided by the
fractionation path Dg of Fig. 13.11; ¢ is the
intersection of p, P with line Ct, and ¢ is the
intersection of curve p, P . with line Bm,. Liquid
in the region between p, and the path Dg reaches
curve p, 4. Without stopping on the curve, L
crosses it and traverses the C field in a straight
line from C to reach curve p,i. Without stopping
on this curve, L crosses it and traverses the B
field to one of its boundaries, e, P ,, P, E,, and
m,E,. The process ends at E, to leave D, B,

Y, and X, since solids C and A will have de-
composed. The fractionation end point for the D _
field between the paths Dg and Dm, is E,, the
final solids being D_, B, and X. For the region
between the paths Dg and DP ., the precipitation
of the solid solution is interrupted while I. crosses
the C field and then the B field between curve
tP . and curve m E,, finally reaching E,, where
D_ begins to precipitate again with the composition
s,. Consequently, there is then a gap in the
composition of the D_ solid solution finally ob-
tained.

UNCLASSIFIED
ORNL-LR-DWG 25616

 

 

Fig. 13 .11,

74
14. SYSTEM Y-U-Z: NoF_-UF,_Z(F,

For the ternary system Y-U-Z, the binary
system Y-—U appears in Fig. 9.1, and it is here
used with the same lettering. The Y—Z binary
diagram was given in Fig. 11.1, but it is redrawn
here (Fig. 14.1) to show the different lettering
necessary in the preseni section. The system U-—Z
is given in Fig. 14.2.

14.1. GENERAL CHARACTERISTICS

The phase diagram of the ternary system is
given schematically in Fig. 14.3.

The principal feature in this system is the
existence of three continuous series of solid
solutions: that between the components U and Z,
with @ minimum at m’, that between the congruently
melting corresponding 7:6 compounds D and K,
aond that between the congruently melting corre-
sponding 3:] compounds A and G. For brevity
these solid solutions will be called U_, D_, and
A, respectively. The primary phase fields for
these solid solutions are the three largest fields
of the diagram.

Moreover, each of the sections AG and DK
constitutes a quasi-binary section of the system
(Figs. 14.4 and 14.5). At least as far as the
equilibria involving the liquidus are concerned,
therefore, the system as a whole may be divided
into three independent subsystems, Y-A-G,
A=-De-K-G, and D-lU..Z-.K, whick will thus be
considered separately.

In the subsystem Y—~A—G, with only two fields
(pure Y and A ), there is only one boundary curve
(66 » e,), and the temperature on this curve falls
in the same direction as for the quasi-binary
section G » A itself, In the subsystem D-U~-Z-K
the liquidus pertains almost entirely to the primary
fields for two continuous (effectively binary) solid
solutions. The boundary curve is slightly compli-
cated by the field for compound M, but it has no
minimum of temperature. The temperature of the
boundary curve falls continvously from the YU
to the YZ side, as in the section DK itself, despite
the minimum m” in the U~Z system. The middle
subsystem, however, is unusual in having opposite
directions of falling temperature in its bounding
quasi-binary solid solution systems, D » K and
A « G. No ““normal’’ behavior can be predicted for
the boundary curve between the solid solution
fields. This boundary curve is complicated by the
minor fields of the four other solids of this sub-
system, but essentially it falls in temperature

from the AD to the GK side, with a slight maximum
m near point e..

The A—G and DK solid solutions, moreover
(as shown in exaggerated form in Fig. 14.6), are
actually ternary in composition on the YZ side.
They occupy small areas of ternary composition
near points G and K, respectively, not lying
simply on the straight lines AG and DK. This is
so because the compounds G and K form solid
solutions in the Y—Z system itself, besides
forming the continuous solid solutions with the
analogous compounds of the Y—U system,

The only invariant points (for liquid in equilibrium
with three solids) in the entire system are five
peritectic points. There is no eutectic, nor is
there a minimum on any curve of liquid in equi-
librium with two solids.

The vertical T vs ¢ section of the system from
the corner Y to a point midway between U and 7 is
merely a section passing successively through the
three  adjacent but independent subsystems
(Fig. 14.6). Details of this diagram will be

mentioned later.
14.2. SUBSYSTEM Y_A_G

The relations in the subsystem Y-~A—G (Figs.
14.7 and 14.8) are similar to those discussed
under Figs. 6.1 to 6.4, but simpler, since there is
here no minimum either in the binary edge AG or in
the boundary curve e, ey

All  mixtures in the system solidify to two
solids, Y oend A_. The reaction on the curve

(2]66 IS

LY+ A
s

t

and the three-phase triangle, starting as the line
Ye G, moves, with the configuration shown in
Fig. 14.7, across the diagram to end as the line
Ye A. All liquids reach the boundary curve, and
they are completely solidified on that curve when
the total composition x is swept by the leg YA of
the three-phase triangle. Liquid « (Fig. 14.7)
gives Y as first solid and reaches the curve on a
straight line from Y. On the curve, the liquid
precipitates Y and a solid solution starting with
composition s;. The liquid vanishes on the curve,
while moving toward e, when the solid solution
reaches a composition on the extension of the
straight line Ya. Liquid & precipitates a solid
solution beginning between G and s,. The liquid
reaches the curve on a curved equilibrium path

75
UNCLASSIFIED
ORNL-LR-DWG 25617

 

214

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(1.4} M

K

14 1.

Fig.

 

 

 

14.2.

Fig.

76
 

UNCLASSIFIED
ORNL-LR-DWG 25618

 

™N

77
 

UNCLASSIFIED
ORNL-LR-DWG 25619

 

 

 

 

 

 

 

 

 

, G
A.S‘
G
Fig. 14 .4. Fig.14.5.
L
,’ L+ U,
v/ | Os+L

| ' |

L+ A J \ \ :

Y+ L+A, \ll ' L+ D : De+ L+ Ug
| |
;|A5+L |
) |
PN A
| N
¥+ A | |

N
| A5+ D f
|
I ,;

 

Fig. 14 .6.

 
 

Fig.14.7.

(as discussed in Sec 6) convex with respect to
point A, When it reaches the curve, the liquid is
at I, and the solid at s;. Now Y begins to pre-
cipitate with the solid solution; the liquid moves
toward e, and vanishes when the solid solution
reaches a composifion on the extension of line Y&,
The vertical T vs ¢ section (first third of
Fig. 14.6) is similar to Fig. 6.3; but in the present
case the area for liquid in equilibrium with Y and
A_ collapses to a line only at e, and at ¢,, since
there is no minimum in the boundary curve.
Crystallization paths in the Y field are straight
lines from Y. Fractionation paths in the A_ field
are a family of curves originating at G, diverging
from the line G » A, convex with respect to A, and
each ending at the boundary curve (Fig. 14.8).

4.3, SUBSYSTEM A_D_K-G

The two large fields in the subsystem A-D—K—-G
(Fig. 14.9) pertain to solid solutions A_and D_.
Part of the A_ field is in the subsystem Y-A-G
already discussed, and part of the D_ tield is in
the subsystem D—-U—-Z—K, The line G » A is
simply the line of maximum temperature running
from G to A, and it is the limiting fractionation
path of the field dividing the curved paths of the
two subsystems. The line D » K is a similar

 

UNCLASSIFIED
ORNL-LR-DWG 25620

 

Fig.14.8.

UNCLASSIFIED
ORNL-LR-DWG 25621

 

79
limiting straight-line fractionation path running
from the melting point of D to the melting point of
K, and dividing the curved families of fractionation
paths of the two
fractionation paths in the A_ field (on either side
of the line AG - i.e., both in Fig. 14.8 and in
Fig. 14.9) are convex with respect to point A, and
those in the D_ field are convex with respect to
point K. The tangents for the two fractionation
curves meeting from two sides at the curve PP,
must be such that the three-phase triangle for this
curve points toward P, (direction of falling
temperature), as shown for point 2 in Fig. 14.9.
The vertical T vs ¢ section across the curve
P,P, is shown as the middle part of Fig. 14.6.
There is theoretically a single-phase ternary solid
solution band reaching very slightly into the
section both from the AG line and from the DK
line; the dimensions are exaggerated in order to
show the schematic relations. The region “A_ +

adjacent subsystems. The

L + D" is a cut through the space generated by
the moving three-phase triangles of curve PP ..
The coexisting phases are not on the plane of the
diagram. The order of temperature for the three
corners of this cut (L. > A_ > D) results from the
fact that the section involved, from Y to the 1:1
ratio on the UZ side, is reached, with falling
temperature, first by’the L corner of the three-phase
triangle, next by the A_ corner, and last by the
D_ corner, according to the configuration of the
triangle drawn on Fig. 14.9.

The solid H_ of system Y~Z forms some binary
solid solution on the side of compound /, and hence
the fractionation paths in the H_field are curved
and are convex with respect to K. The common
origin of these paths, extended back, is the
metastable congruent melting point of H_ in the
Y—Z binary system. The fransition from H_solid
solution to pure H,, all occurring below liquidus
temperature, will be discussed later. The compound
¢, as will be explained shortly, also forms solid
solution with composition extending into the
diagram toward the GK side; hence the paths on the
C field are also curved, are convex with respect
to K, and originate by extension from the point C.
Only the solids B and ! are pure, in Fig. 14.9.
The 1 field is divided into three portions, by
isothermal creases at the temperatures f, and ¢
of Fig. 14.1; the portions represent, with falling
temperature, liquid in equilibrium with [, liquid
in equilibrium with 1., and liquid in equilibrium
with I_ . The t, transition, to I, occurs at a [ow
temperature and does not affect the liquidus
surfaces.

80

The crosshatched lines in Fig. 14.9 indicate
where the solid solution compositions are found.

The Region Involving A, B, C, and D

With regard to the evidence for solid solution
formation by compound C, we note that this
incongruently melting 5:3 compound decomposes
on cooling, at T -(630°), into the pure solids B
and D in the binary system Y—-U, But its primary
phase field in the ternary system Y-U~—Z extends
down to the temperature of P_ (610°). Since D is
known to form solid solution with K in the ternary
system, the decomposition temperature of C is
expected to be raised in the ternary system unless
the solid phase C itself forms a solid solution
third This solid
solution, which the compound C must therefore
form, may be imagined as involving the hypothetical
corresponding 5:3 compound in the Y—Z system, so
that the composition of the solid phase to be
called C_ (solid solution of 5:3 compounds
originating at point C) probably extends on a line
into the diagram paralle! to the edges AG and DK,

Morecever, the point P, may either represent the
lowest temperature of existence of this solid phase

containing the component,

in the ternary system; or it may represent simply
the lowest temperature for its equilibrium with
ternary liquid, while the lowest temperature for its
may be still (in subsolidus
In absence of the information required

existence lower
relations).
for deciding between these alternatives, we shall
consider both relations for this region of the
system, referring to the first as Scheme | and to
the second as Scheme |l.

Scheme |. ~ The point P, is here assumed to be
the lowest temperature of existence of the C_
solid solution, with the third compenent, in other
lowering the decomposition
temperature of C. The schematic relations for
the invariant four-phase planes would be as shown
in Fig. 14.10. There are three such planes. The
highest-temperature plane is the quadrangle for
P], involving B, C,, Ay, and L(P,); the next, in
dashed lines, which will be referred to as the
invariant Q_, is a quadrangle involving B, A,, D,
and C,; the lowest is the triangle for P,, for the

phases A,, D,, L(P,), and C, as the interior

words, continually

phase.
The order of decreasing temperature for the
fixed points involved is assumed to be:

py>bg>m>e, > P >T>0,>P, .

A series of isotherms relating these points is

in Fig. 14.11: (a) between P4 and pg;

given
UNCLASSIFIED
ORNL-LR-DWG 25622

 

Fig. 14 .10,

(b) between P, and m; (c) between m and e,; (d) at
P.i (e) between P, and T; (f) between T - and
O, (g) at Q. () between Q_ and P,; (i) at P,;
(j) below P,.

The reactions on the curves (of liquid in equi-
librium with two solids) and at the invariants are
as follows:

1. Dy L +D_» C_. The three-phase
triangle, triangle 1 in Fig. 14.11(a), starts as the
line ?,CD and ends as P,C,D,. This curve is
reached by liquids from the region p,DD,P,,
precipitating D_. But for original, total compo-
sition x in the region CDD,C,, the liquid vanishes
while traveling on the curve, before reaching P,
to leave C_ and D_ when the C _—D_ leg of the
three-phase triangle comes to pass through =x.
(The appearance and disappearance of phases to
be considered in this section will most easily be
visualized through the sequence of isotherms in
Fig. 14.11. The disappearance of the liquid
phase is not necessarily the end of the phase
changes.) For x in the region p,CC,P,, the D

- P2:

phase vanishes while L is still on the curve,
when the L—C_ leg of the triangle passes through
x. Then the liquid, saturated only with C_,
traverses the C_ field to reach one of its other
boundaries, p,P, or P,P,.

2 py » Pyt L+ Cg » B. The three-phase
triangle, [triangle 2 in Fig. 14.11(b}], starts as
line p,BC and ends as P BC,. The curve is
reached for x in p,CC,P,, by liquid precipitating
C,e For x in BCC,, the liquid vanishes on the
curve to leave B and C_ when the leg B—C|
passes through x; for x in p,BP,, C_ vanishes on
the curve when the L—B leg passes through x, and
then L traverses the B field.

3. m>e,: LB+ A,. Point mis the temper-
ature maximum on the curve e,P,. For this
o the three-phase triangle starts
as the line A _mB and ends as Ae,B [triangle 3°
in Fig. 14.11(c)]. The curve is reached from the
B field for x in me,B or from the A_ field for x in
AezmAm.
reaching e,, to leave B and A, (between A and A )
on a line passing through x.

4. m>F.: L+ B+ A, The three-phase triangle
[triangle 3 in Fig. 14.11(c) ] starts again as the
line A_mB ond ends as A BP,. The curve is
reached from the B field, by liquid precipitating B,
for x in mBP ; and it is reached from the Ag field
by liquid precipitating A_, for x in A mP,A,.
Now if x is in AjA B, the liquid vanishes on the
curve to leave B and A_ (between A, and A,)
on a line passing through x,

Invariant P : The triangles 2 and 3 are seen, in
Fig. 14.11{c), to be separated by a region in which
B is in equilibrium with liquid. This equilibrium
shrinks to a line at P], in the invariant reaction

section, m -» ¢

The liquid always vanishes before

LPY+B=»A, +C, ,

and it is replaced by the equilibrium between
A and C, which now separates two new three-
phase triangles [4 and 5 in Fig. 14.11(e)] for B,
C., and A_ and for liquid, A, and C_. Point P,
represents a type B diagonal invariant reaction,
the triangles 2 and 3 being replaced by 4 and 5.
The point P, is reached for x in the quadrangle
AyBC,P,. For x in A{BCy, the liquid is consumed
in the reaction to leave A,, B, and C, (triangle 4);
for x in A,C,P,, the solid B is consumed, and L
travels on the curve P, » P, representing the
traveling of triangle 5 (L--A_~C ).

5, P, » Pyr L » A, + C,o The three-phase
triangle (friangle 5) starts, as just explained, as

81
 

 

UNCLASSIFIED
ORNL-LR-OWG 25623

 

  

5.:\_\4 5 ’ °
2 W }
Fig 1414 (part 1)
A C P, and ends as A,C,P,. This curve is Fig. 14.11(f), to separate triangles 4 and 6]

reached from the C_ field for x in P,C,C,P,, and
from the A_ field for x in AP\ P,A,. For xin
A[C,C,4A,, the liquid vanishes on the curve to
leave A_ ond C_ when the A —C_ leg of the
triangle passes through x.

Between the temperatures of P, and P,, however,
at T (the decomposition temperature of C in the
binary system) the equilibrium between B, C_, and
D_ appears as a three-phase triangle [triangle 6
in Fig. 14.11(f)]1. It starts as the line BCD at
T and ends as the triangle BC,D, at the invariant
temperature O .

The invariant O involves four solid phases
(three of them variable) in another quadrangular or
diagonal invariant reaction of type B. As the Q
temperature is approached,
equilibrium between B and C_ [which is seen, in

z
the region for the

82

shrinks to a line, the two triangles come into
contact, and we have the reaction

B+Cz"Az+Dz .

The equilibrium between B and C_ is replaced by
one between A_ and D_, now separating the two
new triangles originating at Q_ : triangles 7 and 8
of Fig. 14.11(), for B, A,, and D, and for A_, D,
and C_.

In all the three-phase triangles of Fig. 14.11,
the corners representing variable phases (C_, A,
D_, L) move continually to the right with falling
temperature. Triangle 7, however, will be assumed
to remain constant with further decrease of temper-
ature; at any rate it will not be involved in any
more of the phase changes now under discussion.
 

 

 

 

UNCLASSIFIED
ORNL-LR-DWG 25624

 

 

Fig. 14 11 (part 2)

The invariant reaction Q_ will occur for x in
the quadrangle BD,C,A,, leaving B, D,, and A,
for x in triangle BD_A_, and otherwise A_, D,
and C_, as triangle 8, which continues to move to
the right.

Finally, the three remaining moving triangles,
1, 5, and 8, come together at P,. The range of
existence of the C_ solid phase, in other words,
here shrinks to a point, C,e The invariant P,,
then, is of type A, triangular, with C, as interior
phase; it is terminal for the phase C_. It is an
example of the case c¢ invariant discussed under
Fig. 4.11. It may be said to be the decomposition
point, on cooling, for the C_ solid solution in the

ternary system. The reaction is
Cy,» D,y + Ay + L(P,)

whereupon the liquid then travels down the curve
P, » P, with its three-phase triangle 9 [Fig.
14.11(j)f.

Some of the relations may be shown, in different
fashion, in the T vs c vertical section of Fig. 14.12,
between C in system Y-U and the 5:3 ratio in
system Y—Z. This section cuts triangles 1, 6,
7, 8, and 9 of the foregoing discussion.

The sequence of phase changes upon cooling,
for complete equilibrium, starting with a liquid of
specified composition in Fig. 14.10 may be followed

83
UNCLASSIFIED
ORNL-LR-DWG 25625

 

 

 

 

 

 

with the aid of Fig. 14.11. The fixed composition
point x will fall successively in the various two-
phase regions (tie line areas) and three-phase
triangles (numbered and explained above) as these
move through the point with falling temperature.
A few particular compositions will be considered,
for illustration.

Point a (Fig. 14.10): The first solid on cooling
is A_, starting between A, and A,. The liquid
reaches curve P]P2 and precipitates A and C_
(C, starting between C, and C,). The liquid
vanishes before reaching P,, leaving A  and C_
on a line through point @. Point 4, in other words,
finds itself in the two-solid region between

triangles 8 and 5 of Fig. 14.11(h). With further

84

=53 IN Y/

Fig. 14 12

cooling, this region moves to the right, and point
a enters triangle 8, with three solids, A, C_, and
D_. The solid C_ thus decomposes into 4  and
D_ on cooling, and the residual C approaches
C, in composition. When the temperature reaches
le liquid reappears, in the invariant reaction:

C, ~calories » L(P,) + 4, + D,

[ This reaction is case (c) of Sec 4, Fig. 4.11, but
now with solids of variable composition.] When
all C, is consumed, the liquid starts out on curve
P,P,, vanishing to leave A  and D on a line
through point a.
Point 6: The first solid is D_, between D and
D,. The liquid reaches curve p,P,. Here

’

L+DS—>CS

Cs starting between C and C,. The liquid is
consumed on the curve, leaving C_ and D, on a
line through 5. Point b now comes to be in the
region for C_ and D_, between triangles 6 and 1.
When triangle 6 reaches b, B appears as a solid

phase. Thenat O,
B+C,»A_+D, ,

B is consumed, and b ends as A_ and D, in the
region between triangles 7 and 8 [Fig. 14.11(%)1.

Point ¢c: As in the case of point b, the liquid
reaches curve p,FP, and vanishes to leave C_
and D_. But below T, C begins to decompose;
point ¢ comes to be in triangle 6, and finally into
the area for B in equilibrium with D_ as triangle 6
moves on.

Point d: The first solid is C_, between C and

C,. The liquid reaches curve p3P], where

L+CS—;B .
At P,, A, appears, and
L+B->A, +C, .

The liquid is consumed, and point 4 finds itself in
triangle 4. Next, A_ vanishes, leaving B and C.
Then D_ appears, and point d enters triangle 6. At
o

=~ o

B+C_ A _+D, ,

leaving B, A_, and D, d being in triangle 7.
Point e: The first solid is B, and L reaches
curve mP,, where

L—>B+AS

!

the solid solution being between A~ and A,.
At P,

L+B-A,+Cy,

the liquid is consumed, and point e is now in
triangle 4. As this triangle moves on, however,
the C_ phase vanishes, to leave B and A, on a
line through point e.

Point f: The first solid is C_, L reaches curve
p4P 1, Cs is consumed on the curve, and L traverses
the B field to reach curve mP,. At P,

L+B~ A, +C, ,

B is consumed, and the liquid travels on curve

PP, precipitating A_ and C_ (triangle 5). The
liquid vanishes, however, to leave A_ and C,
between triangles 4 and 5, and point f next comes
to be in triangle 4, as B, A_, and C_.. Then at Q_,

st

B+Cz—>Az+Dz

/

leaving the solids of triangle 7.

Scheme ll. — The point P, is here assumed not
to be the lowest temperature of existence of the
Cs solid solution (with composition C,). The C,
phase is assumed to vanish, on cooling, at some
intermediate composition (C_, between C and Co)
at a still lower temperature, that of a four-solid
invariant to be called O_, The relations would be
those shown schematically in Fig. 14.13. The
highest-temperature invariant plane is again the
P, quadrangle, assumed to be identical with that
in Scheme | (Fig. 14.10). Next is the P, plane,
now a quadrangle, an example of the case (d)
invariant discussed under Fig. 4.10. Below these
is the triangular plane of the O invariant
reaction, terminal for Cy, the interior phase. We
now have the temperature order:

Py>Te>Py>0,

The first six isotherms of Fig. 14.11 apply to
Scheme It as they are. The subsequent isotherms
are given in Fig. 14.14, and to preserve continuity
these will be lettered as follows: (g) at P,, (h) be-
tween P, and Q , (i) at Q,, (7) below Oy

Excepf for ’rge pOSIfIOjl:IS of the composmons
Ay, C, and Dy, involved at P, the crystallization
processes on the liquidus surfaces and on the
curves of twofold saturation are the same in both
schemes. The schemes differ only in the reactions
of the solid phases left after complete solidi-
fication.

Triangles 1-6 originate as in Scheme |, and they
again move to the right with falling temperature.
The relations in the isotherm (f) (which is between

and P, in Scheme Il and between T . and O,

in Scheme 1) are topologically the same for both
schemes. This is now followed by isotherm (g),
at P,. The triangles 1 and 5, separated in (f) by
the equilibrium between C_ and liquid, here come
into contact, in the reaction

L(1‘)2)4-C2~>142+D2 ,

giving rise to the equilibrium between A_and D,
separating the two new triangles 8" and 9% These
involve the same phases as the triangles of the
same number in Scheme |, but the compositions
are different. Also, while triangle 97, like triangle 9

85
UNCLASSIFIED
ORNL-LR-DWG 25626

D

 

Fig. 14 .13.

in Scheme |, now continues to move to the right as
the liquid travels on the curve P,P, precipitating
Ao and D, the triangle 8 begins to move to the
feft with falling temperature. Eventually it makes
contact with triangles 6 and 4, in the O
reaction, in the arrangement shown in Fig. 14.14(:).
The ternary C solid solution, the interior phase of
the triangular, type A invariant reaction, simply
decomposes into the solids B, A and D, leaving
triangle 77 which corresponds to ftriangle 7 of
Scheme .

invariant

The vertical T vs ¢ section through C and the
5:3 ratio inthe system Y—Z is shown in Fig. 14.15,
which is to be compared with Fig. 14.13. In both
cases there are two solid-state decomposition

reactions for C.:

CS_’B+DS

86

and
CS-+A5+DS .

In Scheme |, the decomposition into B and D_
extends from the binary temperature T . to the
invariant Q_, and the decomposition into A_ and
D, falls in temperature from Q, to the invariant
P,. In Scheme li, the decomposition into B and
D falls in temperature from T to Qe and the
decomposition into A and D, rises in temperature
from Qy to P,.

Point a (Fig. 14.13): The first solid is D_. The

liquid reaches curve p 4P, where

L+DS—>C5

(triangle 1), and the liquid vanishes on the curve
to leave C_ and D_. Below T, the point a is
reached by triangle 6 (for B, C_, and D), and
finally remains as B and D_ when it is left behind
by triangle 6.

Point b:  The first solid is C_.
reaches curve p4P,, where

The liquid

L +C$ > B
(triangle 2). At P,
L +B-> A] + Cy

The compound B is consumed, and the liquid
moves on curve P P, precipitating A, and C_
(triangle 5). The liquid vanishes on the curve to
leave A_ and C_, and point & is next reached by
triangle 4 (for B, C_, and D). At Qy, the C.
phase decomposes to leave B, Ay, and D,
(triangle 7).

The liguid

Point ¢: The first solid is D_.

reaches curve D 4F o, where
[+ DS > CS
(friangle 1). At P,

The liquid is consumed, and point ¢ is left in
triangle 8" (for A_, C_, and D ). But this triangle
moves to the left with falling temperature, and
before the temperature of O is reached, C_ will
have vanished to leave A and D_.

Point d: The first solid is C,+ The liquid
reaches curve P, P, where L » A_ + C_ (triangle 5).
The liquid vanishes on the curve to leave A_ and
(g) (A}

 

    

‘ frbyra—~—L+¢+ N \‘

‘ \6,2: T

LN

 

C.. But point d is next reached by triangle 87
from the right, to give A, C_, and D_. At Q,
the C_ phase decomposes to leave the three solids
of triangle 77 (B, Ay, and Dy).

The Region Involving G, H, I, and K

The lower part of the subsystem A-D-K-G
is shown in Fig. 14,16, Liquids on curve P, P,
precipitate the solid solutions A_ and D, solidi-
fying completely, while on the curve, for x above
the line A;D, (joining the solid solution compo-
sitions for liquid at P;). (We continue here to
call the A~G solid solution A_ and the D—K solid
solution D_, even down to the limits G and K.)
As the composition of G is approached, the A_
solid solution is shown as occupying an area in
composition, since G also forms solid solution in
the binary system Y—Z, varying from G to the
composition G, at the temperature of p,. The

same situation holds at K, which forms solid

UNCLASSIFIED
ORNL-LR-DWG 25627

 

  
 
   

 

Fig. 44 44,

solution in the binary system Y—Z, extending from
K to the limit Ko at the temperature of €ge
For the curve p 3+ Which is reached for x in

the region p.G the reaction is

733’
L+ASH’HG.

The solid solution starts at G, for L at p, and
ends at A, for L at P;. The three-phase triangle
starts as The line G Hp7 and ends as A HP,.
Hence liquid on the curve is completely solidified,
leaving H, and A, (between G, and A,), for x in

HG,A;. For x in the area of the ternary solid
solution, ss, solidification is complete with L
still on the A_ surface, before any curve is
reached. The curve p,P 4, moreover, is crossed

for x in HP3p7, when, after the A_ phase has been
consumed, the liquid leaves ’rhe curve to travel
across the H field, but now precipitating not pure

H, but the H_solid solution ranging from H to H,.

<0
~
 

 

UNCLASSIFIED
ORNL-LR-DWG 25628

As+Cot D¢

L+A+D,

 

 

The point P, is reached for x in the region
HA,D,P,, by way of either curve P,P, or curve
p4P,. Liquids with x in the triangle A;D,H then
solidify completely in the reaction

L(P3)+A3~»HG+D3 ,

while the others travel down the curve P, » P,
precipitating two solid solutions, one of H
(H to H,) and one of D, (D to D,). Complete
solidification is therefore effected on this curve
for x in HD,D ,H,. The curve is reached from the
H, field for x in HP,P ,H, and from the D_ field for

- 3474
xin 3D3D41'34.

On the transition curve p P,

L+HCI_-’IG .

88

—w53INYZ

Fig. 14.15.

The H, solid solution in equilibrium along this
curve is, strictly, variable in composition, starting
just to the right of H, at p. and ending at H,.
(Since P, is below pg in temperature, the compo-
sition of H, must be just to the left of that for
the binary peritectic po of Fig. 14.1.) Since the
variation is probably very slight, we have here
assumed this solid to be constant at H, for the
whole curve. This curve is reached for x in
HyP,pg and it is crossed for x in IPpg.  The
point P, is thus reached, either from curve PP,
or from curve p P, for x in the quadrangle H,D P I.
The reaction is

L(P)+H,»1,+D, ,

so that liquidus for x in the triangle H,D,I here
UNCLASSIFIED
ORNL-LR-DWG 25629

 

Fig. 14.16.

solidify completely. The rest move on down the
curve P e,, precipitating [ and D_ (between D,
and Kg); the form of the compound I deposited will
be I down to temperature t,, then I 5 to temperature
ty and I, to the temperature e,. All liquids
reaching curve F e  solidify completely betfore
reaching €,. The curve is reached from the I
field for x in IP ey and from the D_ field for x in
P,D4Kgege Liguids with x in the ss area near K
solidify completely while L is still on the D_
surface.

For composition a in Fig. 14.16 the first solid
to form on cooling is D_. The liquid reaches

curve P, where

L+AS+DS .

L+A3->H+D3

I

A3 is consumed, and L starts out on curve PP,

on this curve the liquid vanishes, to leave H

and D solid solutions on a line through point a.

Point &:  The first solid is D_. The liquid
reaches curve P.P , where it precipitates a solid
solution between H and H, and a solid solution
between Dy and D,. At Py

L+H, 14D, ,

leaving the three solids H,, 1, and D,.
The first solid is H,
to the left of H ). The liquid reaches curve p P,

Point c: (strictly slightly

where

L+H4~>]a.

The solid H, is consumed, and L crosses the [

field to curve P Here

469.
L41+DS

!

and the liquid vanishes to leave Iand D_on a line
through point c; the polymorphic form of I depends
simply on the temperature.

Point d: The first solid is A, between G, and
A, . The liquid reaches curve p,P,, where

L+AS—»Ha .

The solid A_ is consumed; L leaves the curve,
crosses the H field, and reaches curve PP,
Here

L->H +D_ .

At P,,

L+H4H;.'Q+D4 ;

H, is consumed; the liquid starts out on curve
P eq, and vanishes to leave I and D_ on a line
through point 4.

Fractionation Processes in the Subsystem

A-D-K_G

The phase changes so far discussed have been
those for crystallization with complete equilibrium.
We shall now consider crystallization with perfect
fractionation, as explained in Sec 6, simply for
the two principal solid solution fields of Fig. 14.9.

In a fractionation process, the liquid on a surface
follows a single fractionation path (as sketched
in Fig. 14.9). These paths are here curves in
every case except for the B and I fields, where
they are straight lines radiating, by extension,
from points B and I, respectively. When the liquid,
following such a fractionation path, whether curved
or straight, reaches a boundary curve of even
reaction (one on which the liquid precipitates
two solids on cooling), the liquid travels along
this curve. But if it reaches a curve of odd
reaction (transition curve), it immediately crosses
the curve and begins to travel along a fractionation
path — curved or straight — on the next fieid.
(See Sec 4-D for the behavior at invariant points.)

In the fractionation process, the outermost layer

of solid solution being deposited by liquid on the

89
D_ field continually increases in K content. It
continues to change in the same direction,
moreover, whichever of the four boundary curves
is reached, while L travels on the boundary curve.
But the boundary curve p,F, is a transition curve;
L does not travel on it but immediately crosses it,

Hence the ultimate mixture of solids (non-
equilibrium mixture) produced by liquid in a
fractionation process varies according to the

various regions into which the D_ surface may be

divided.

There is first a very narrow region, close to the
p 4D side, from which L will cross the curve p,P,,
traverse the C_ field, cross the curve P3P
traverse the B field, and reach curve m -» e..
The final mixture of solids obtained therefore
contains D, C_, B, and A (although C_ may have

decomposed on cooling).

Next to this region there is one from which L
will traverse the same curves and fields but end
on the boundary m » P of the B field. The liquid
then follows boundary curves all the way to e, to
leave a mixture of all six solids of the subsystem:
D,, C,, B, A;, H_ solid solution, and 1. The
next region will send L to curve P P,, missing the
B field, and now solid B will be missing in the
final five-solid mixture, except as formed by
decomposition of C_  For these two regions the
composition of the D_ solid solution finally
obtained will have a discontinuity (a gap), since
precipitation of D_ is interrupted between the
point when L reaches and crosses the curve p P,
and the point when it reaches P, along curve
PP, (as explained also in Sec 7.3).

The next region, between the fractionation paths
DP, and DP,, will miss the C_ field entirely and
end as four solids: D_, A_, H, and I. The region
between paths DP3 and DP, will give only D, H,
and I, and that between the path DP, and the
corner K only D_ and I.

On the A_ field the outermost layer of solid
solution continually increases in A content while
L is still on the surface. For the region between
A and the fractionation path Gm, the solid
deposited continues to in A content
while L moves on the curve m > e,, ending as a
mixture of B and A_. For the region between the
paths Gm and GP, the depositing solid reverses
its direction (of composition change) and moves
toward G as L travels on the boundary curves
m > P, » P, > P, The liquid then follows the

increase

90

curves Py » P, 5 ey, and finally leaves a mixture
of all six solids of the subsystem (counting C_,
which, however, may have decomposed). For the
region between Py and the path GP,, L crosses
the curve p P, but ultimately reaches either P,P,
or P,eq, to approach, in either case, eg as the
fimit of the process; the final mixture consists of

A, H_ solid solution, I, and D_.

Subsolidus Reactions Involving Compounds
A, H, and J

The two- and three-solid regions left on complete
solidification in the two subsystems so far con-
sidered, below the temperatures of all the phase
reactions discussed, are shown in Fig. 14.17.
There are also two single-phase regions ss near
points G and K.

At T, (Fig. 9.1), the compound A of the system
Y—U (atter changing from A_to A, at T”) decom-
poses on cooling into Y and B. £cau5e A forms
ternary solid solution (A_, with G), the decompo-
sition temperature is lowered in the ternary
system. This decompesition involves changes in
the upper part of Fig. 14.17, and the pertinent
isotherms are shown in Fig. 14.18: (&) just below
T ,; (b) at a four-solid invariant of type B, where

B+S]4Y+52_

on cooling; and (c) below this invariant.

UNCLASSIFIED
ORNt - LR-DWG 25630

o
*
E'TDS
fecva.+
B4 A Ly
~
4 e )
/45 +D§
Hylssi+ D,
/
Y+ A
Ach Dot Hy = o
(55)\ i - ),-;ss\:
Ye oM . . . i
G #H /
Holss)+ 0.+ /
At Hy O 5
Fig. 1417
UNCLASSIFIED
ORNL- LR-DWG 25634

0 D

45

Fig 4418

At T’ (Fig. 14.1), H_ undergoes transition to
H 5, which is a pure solid instead of a binary solid
solution, and the binary transition temperature is
lowered to T". Since the solid solution is not
ternary, these temperatures are not changed in the
ternary system. Figure 14.19 shows the ac-
companying changes in the solid phase combi-
nations: (a) above T’ (b) between T’ and T”,
(c) below T".

At T, (Fig. 14.1), the compound ] of system
Y—Z appears on cooling, forming from I and K,
(the binary solid solution composition for K at the
temperature of T.,). Because K forms ternary
solid solution (D, with D), the formation temper-
ature is lowered in the ternary system. The
changes affecting Fig. 14.17 are shown in the
isotherms of Fig. 14.20: (a) just at T,, where the
point | appears as pure | in equilibrium with I and
K].; and (b) below Ty With decreasing temperature
the three-phase equilibrium of I + | + D_ moves
into the diagram as the triangle IJK". The two-
phase equilibrium between ] and K, (Fig. 14.1)
becomes the two-phase tie-line bancf Jo + D_ of
Fig. 14.20(6), with tie lines running from the
binary solid J—]” to the ternary solid K" —K"

The solids | and K’ vary with temperature ac-
cording to the miscibility gap in the J—K solid
solutions shown in Fig. 14.1.

14.4. SUBSYSTEM D..U-.Z_.K
Equilibrium Crystallization Along Curves

The relations for complete equilibrium solidi-
fication in the subsystem D—-U—Z—~K are shown,
schematically, in Fig. 14.21, and Fig. 14.22 shows
approximate temperature contours for this region.

There are three primary phase fields: one for
the D~K solid solution D_, one for the U-Z solid
solution U_, and one for the incongruently melting,
pure compound M. The reaction on the curve
eP. is L » D, + Ug, the three-phase triangle
starting as the line De U and ending as the
triangle DgP Uc. This curve is reached from the
D_ field for total composition x in the region
De P D, and from the U field for x in e UU,P..
Solidification is complete on the curve for x in
DUUSDS'

The third part of Fig. 14.6 shows the vertical
T vs c¢ section through this part of the system.
It is similar to the middle part of Fig. 14.6 except
that the solid solutions are strictly on vertical
lines, D_ being on a vertical line through DK and
U_ on a vertical line through UZ,

On the curve p1Ps from py, to t, the reaction
is one of transition,

L+US—’M

I

with U_ ranging from pure Z at p,, to U, at t. For
the section of the curve from ! to P, the reaction
is even:

L—>M+US

(ranging from U, to Ug). The three-phase triangle
L-M-U_ starts as the line p, MZ ond ends as
P .MU,  The sign of the reaction changes at
point t, where the L—M leg of the triangle is
tangent to the curve.

The odd-reaction section of the curve, p,.¢, is
reached only from the U_ field, for x in the region
?11tU,Z, by liquids precipitating U  as primary
crystallization product. Then if x is in the region
p11tM, U, is consumed while L is traveling on the
curve, between p,, and #, and the liquid leaves
the curve to traverse the M field, on a straight line
from M. Compositions for x in p, ,yM (y being on
the line P_M) then reach the curve P.e , while
those for x in ytM reach the curve (P, where U,

91
UNCLASSIFIED
ORNL—-LR—-DWG 25632

 

Fig. 14 .49.

now richer in U, appears again as a secondary
crystallization product mixed with M.

The even portion of the curve, tPS, is reached
from either side: from the U_ field directly for x
in the region 1P U.U, and from the M field for x
in MP ¢z, either directly or after the crossing of
the yt curve.

Liquids for x in the region MU.Z solidify
completely while traveling on this curve, somewhere
between p., and P, when x comes to be swept
by the M—U_ leg of the three-phase triangle.

The point P is therefore reached only for x
in the quadrangle D U MP, and, with the reaction

L+U5->D5+M ,

92

it is the incongruent crystallization end point for
x in the triangle DgUgM, to leave the three solids
D¢, Ug, and M. For xin P.D M, Ug is consumed,
and L travels down the curve P e, to solidify
completely, before reaching e, into M and D_
solid solution between D, and K. The curve

Pe, o along which

IL-M+D
5

I

is reached from the D_ field directly for x in
KD Pge,, and from the M field for x in e P M,
either directly or after the crossing of the p |y
curve.

The compositions of points D, U, and U, are

5'
hypothetical.
 

UNCLASSIFIED
ORNL-LR-DWG 25634

UNCLASSIFIED
ORNL-LR-DWG 25633

 

Fig. 14.20.

154

 

 

UNCLASSIFIED
ORNL-LR-DWG 25635

Fig. 14.22.

93
The minimum m” of the U—Z binary system is
not involved in any of these considerations, for
the points U, and U, involve temperatures and
compositions not on the solidus curve of Fig. 14.2.

Point a: For liquid with original composition
at point a in Fig. 14.21, the first solid on cooling
is D_, with composition between D and D.. The
liquid reaches curve e P, where

L+D_+U,
(between Uand U,). At P,
L +U5~>D5+M .

The solid Ug is consumed; the liquid moves onto
curve Pe, o and vanishes to leave M and D_on a
line through a.

Point b: The first solid is U_ (below U.). The
liquid reaches curve 0115 where

L-»M+US .

The solid U, now moves up to reach U, when L
reaches P, Thereafter, the solidification occurs
as for point a.

Point c: The first solid is U_ (below U). The
liquid reaches curve p,,P.. As L follows this
curve, the quantity of U_ first diminishes — until
L. reaches ¢t — and then increases as L moves
from ¢ to P.. But all the while the composition
of U_ is moving toward U.. At P, the liquid is
consumed to leave D, U, and M.

Point d: (This point is not shown on the diagram;
it is in the area between M and curve p, P,
between the lines MP_ and MD..) The first solid
is U_, near Z. The liquid reaches curve p, Py,
and U_ is now entirely consumed in the reaction

L+U oM
5

I

while L is moving on the curve, before it reaches
point t. The liquid then leaves the curve, travels
across the M field precipitating more M, and
reaches the same curve again near P, Here

LM+ U

s
(now near U; in composition). At P, U, is
consumed; the liquid moves onto curve P_e.  and

5710
vanishes to leave M and D_ on a line through

point d.

Fractionation Processes in the Subsystem

D-U-Z-K

Figure 14.23 shows schematic fractionation
paths in the subsystem D—U—-Z-K. These are
hypothetical, for we have no information on the

94

UNCLASSIFIED
ORNL-LR-DWG 25636

 

Fig. 14.23.

liquid-solid tie-line directions for points on the
surfaces (and we can make only uncertain infer-
ences for the directions of tie lines at the boundary
curves). However, we shall assume the relations
shown schematically in Fig. 14.23 and discuss
them along the lines followed under Figs. 6.1

fo 6.4.

The paths on the M field are simply straight
lines originating by extension from point M. Those
on the D_ surface originate from the maximum D
and diverge from the straight line DK, always
convex with respect to K. This means that when
a liquid is traveling over this surface, whether in
complete equilibrium with the whole solid phase
or in a fractionation process, the solid solution is
always changing in composition toward K. More-
over, the same direction of change in the solid
continues here when either of the boundary curves
is reached: e P or Peey.

The U_ surface, with two maxima (U and Z), has
two families of fractionation paths, separated by a
limiting fractionation path originating at the binary
minimum m*% This path, m'N, must reach one of
the two boundary curves, e P, or p P We
assume that it reaches the curve p, P. at the
point N between P, and ¢, and that it is convex
with respect to the corner Z. Accordingly, the
paths on the U side of m "N are convex with respect
to Z through their entire length, but some of those
on the Z side, while starting out as convex with
respect to U, pass through a point of inflection
and become convex with respect to Z before
reaching the boundary curve. The dashed curve
m’R is the locus of these inflection points, and
R is assumed to be between N and ¢. The paths
between ZR and Zp,, have no inflection point
and are simply convex with respect to U,

For further orientation we note that the line
PgUg of Fig.14.21 is tangent at P to the fraction-
ation path UP,, Nr is tangent at N to the path
m ‘N, and Rv is tangent at R to the path ZR, Point
y is on the line P M,

The sequence of changes in the fractionation
process varies according to the regions into which
the U, surface is divided by the lines and curves
just defined. The outermost layer of U_ solid
solution being deposited will be referred to as
“*solid."”’

1. Region e UP . (meaning between e, and the
fractionation path UP.): While L is still on the
U_ surface, the ‘*solid’’ increases in Z content to
a limit given by the tangent to the particular
fractionation path involved at the curve ecPe. At
the same point of the curve, the tangent to the D_
fractionation path gives the initial composition of
the D_ **solid’” precipitated, together with U,
while L follows the curve e, + P.. Then, as L
travels on the curve, the ‘‘solids’’ reach Dg and
Ug when L reaches P.. Then L follows curve
Pgey, towards e, as limit, depositing M and D
ranging from D to an outermost layer approaching
pure K.

2. Region between paths UP. and m'N: The
““solid’ increases in Z while L is on the surface,
reaching a point between U and r when L reaches
the curve between P_ and N. Then, as the liquid
moves toward P, precipitating M and U, the
outermost ‘‘solid'’ reverses its direction, reaching
Ug when L reaches P Thereafter the solidi-
fication occurs as for region 1. (Note: Once L
reaches PS in fractionation, it continues onfo
curve Pe, .)

3. Region p,,Zy: The ‘'solid"’ increases in U
content while L is on the surface, to a limit, fixed
by the tangent to the fractionation path, when L
reaches the curve between p,, and y. The liquid
crosses the curve at once in a straight line from
5€1g+ Ihere-
after the solidification occurs as for region 1.

M, precipitating M, to reach curve P e

4. Region between paths Zy and Z:: The
“*solid'’ increases in U for L on the surface, to
a limit, fixed by the fractionation path, when L
reaches the curve between y and ¢, The liquid
crosses the curve at once on a straight line from
M, precipitating M, to reach the curve again along
tP . This curve is followed to P, with the liquid
precipitating M and U again, the *‘solid’’ starting
at a higher U content than when its precipitation
ceased on the curve yt, lts composition reaches
U5 when L reaches P ¢; thereafter the solidification
occurs as for region 1.

5. Region between paths Zt and ZR: The
“‘solid"’ increases in U both before and after L
reaches the curve. The limit is U, at P There-
after the solidification occurs as for region 1.

6. Region between paths ZR and m’N: The
““solid’’ increases in U until the inflection point
of the fractionation path is reached (intersection of
path with curve m”R), and the ‘‘solid’’ at that
point is given by the tangent to the path at its
inflection point.  Now the ‘‘solid’’ begins to
decrease in U content, to a limit, given by the
tangent to the end of the fractionation path at the
boundary curve, reached between N and R. Then,
as L follows the curve to P, the ‘‘solid” again
moves to higher U content, reaching U, for L at
P..  Thereafter the solidification occurs as for
region 1.

7. Path m’N: For a liquid on the path m’N
itself, the ‘‘solid’’ increases in Z (between the
limits m” > ), and then moves, in reverse, to U,
as L moves on the curve from N to P.. Thereafter
the solidification occurs as for region 1.

Equilibrium Crystallization in the U_ Field

We finally consider the behavior of liquid on
the U_ surface under conditions of complete
equilibrium with the whole of the solid phase.
For such crystallization with complete equilibrium,
involving equilibrium paths crossing the fraction-
ation paths, the behavior for the various regions
would be as follows (all entirely analogous to the
discussion of the regions in Fig. 6.4). When the
liquid reaches a boundary curve, of liquid in
equilibrium with two solids, it proceeds according
to the equilibrium relations already considered
above for Fig. 14.21. We are here dealing only
with L on the surface itself.

1. Region between e_. and the fractionation
path UP.: The equilibrium solid always increases
in Z content. The equilibrium path does not

95
cross the line Pl
boundary curve el .

The liquid reaches the
(It reaches it at a point
where the L—U_ leg of the three-phase triangle
for L on the curve passes through the total original
composition x.)

2. Region between path UP, and line UgPg: The
solid always increases in Z. The equilibrium path
crosses the line U P on its way to the boundary
curve, which is reached between ¢_ and P
and path m’N:
The solid always increases in Z. The equilibrium
path does not cross the fractionation path m’N,
and it reaches the boundary curve between P,
and N.

4. Region between p,, and the path ZR: The
solid always increases in U content. The equi-
librium path does not cross the line Rv, and it
reaches the boundary curve between Rand p, .

5. Region between the path ZR and the line Ru:
The solid always increases in U. The equilibrium
path crosses the line Rv, and it reaches the
boundary curve between R and p,,.

6. Region between line Rv and line Nr: The
equilibrium path does not cross the path m’N, and
it ends on the curve between N and R.

(¢) Region rvRd: The solid increases in U
until the equilibrium path crosses the curve m'R;
then the solid increases in Z content until L
reaches the boundary curve.

(b)) Region dNR: The solid always increases in
U content for L on the surface.

7. Region between path m’N and
The equilibrium path crosses the fractionation
path m“N, to reach the boundary curve on the left
of N, between N and a point ¢, where cm” is the
L-U_ leg of the three-phase triangle for the curve
with U_ at composition m" The behavior above
and below the curve m’R differs as under region 6.

3. Region between line UgP,

line Nr:

Subsolidus Compounds E and F

The solid equilibria after complete solidification
of liquid will be affected, with further fall of

96

temperature, by the appearance of the subsolidus
compounds E and F of the system Y-U (Fig. 9.1).
The pertinent isothermal relations are shown
schematically in Fig. 14.24: (a) above T (temper-
ature of formation of E from D and U in the binary
system); (b) between TE and T g (c) below T
(temperature of formation of F from E and U in the
binary system)., Only the upper part of Fig. 14.21
is involved.

UNCLASSIFIED
ORNL-LR-CWG 25637

(a) U (&) u -

F+lg
) EX&

Os + g Dot £+
d &
/ Do+l

£+ 0,
{c) u

far
ErFtl, ’
£ L
£ N
Dot &+l
I
< Do+
£+ 0O TS
Fig 14 24,
15. SYSTEM Y=WaZ:

The binary system Y~W is shown schematically
in Fig. 15.1, and W=Z in Fig. 15.2. We note com-
pound G in Fig. 15.1, decomposing on cooling at
T.. System W~Z forms continuous solid solution
with a minimum at m, The diagram for the system
Y-Z is used with the same lettering as shown in
Fig. 11.1. It has the subsolidus compound D,
solid solution in four compounds (A, B, D, and
F), and transitions in two compounds (B and C).

The ternary diagram, as at present reported, is
that of Fig. 15.3.

Despite the continuous solid solution in the
W~2Z system there seems to be no solid solution
formed across the diagram between the corre-
sponding 2:1 compounds H and C.

The phase diagram as represented in Fig. 15.3
has two principal items of uncertainty. The first
is the absence of a field for compound B of system
Y-Z. The field now attributed to compound C

UNCLASSIFIED
ORNL-LR-DWG 25638

 

&
1
|
1
|
|

Fig. 451
V
=
(WS)
W WZ
Fig. 15.2.

NaF=ThF ~ZrF

pertains, actually, practically entirely to the 5:2
compound B, and only a small region of the ‘*C
field’’ of Fig. 15.3, near the boundary curve ¢ ,E ,
pertains to the 2:1 compound C. There must be
another three~solid triangle in the diagram, and
another invariant point between m, and E,. The
second uncertainty concerns the invariant point
E,, reported as eutectic, |f a temperature maxi-
mum definitely exists on the curve P_Eg, then
E_ must be a eutectic. This temperature maximum,
however, if it does exist (and its existence seems
to be experimentally uncertain, actually), will not
be, as now drawn, on the line WE, for the solid
phase in the large field is not pure W but a con-
tinuous solid solution of W and Z. The curve
P_Eg, then, may or may not have a maximum on it,
and if it does, the maximum must be on the right
of the line WE. The mere position of E; in the
triangle EWZ does not tell us whether it is a
peritectic or a eutectic, for it is necessary to
know its position in relation to the particular
solid solution composition saturating the liquid
at EB'

In Fig. 15.4 we assume, principally for the sake
of clarity of discussion, that this invariont, now
called F_, is a eutectic; and an additional field
is introduced between those for A and E, so that
both B and C are now represented with primary
fields.

In this schematic diagram, then, there are eleven
fields and nine three-solid triangles (not all
shown in Fig. 15.3) with corresponding invariant
liquids. There are only two saddle points, m,
between the A and the H fields, and m, between
the fields for E and W_ (solid solution of W and Z)°.

Because of the binary solid solutions formed
by the solid phases A, B, and F, the triangles in
Fig. 15.4 are not drawn for the actual compositions
of the solid phases involved at the invariant so-
lutions, The probable relations will be discussed
separately for the two principal regions of the
system, shown in Figs. 15.5 and 15.7.

We shall assume that the saddle point my s
exactly on the line HA, although compound A
forms solid solution in the direction of B. With
this assumption, the line Hm. A becomes a quasi-
binary section (the only one in the system), and
the region YHA an independent, simple subsystem,
with two invariants, P, and E,, involving pure
solid phases. The final solids are either Y, G,

97
 

and A or G, i, and A; but below 7' of Fig. 13.1,
G decomposes into Y and H, leaving Y, H, and A
for the whole corner.

Some solid solution is involved at each of the
other invariants of the system.

The region between the section HA and roughly
JE is shown in detail, in Fig. 15.5, schematically,
and distorted for clarity, The reactions along the
curves are as follows:

1. mPyr L > H + A, the A solid starting as
pure A and ranging to A, at P .

98

 

UNCLASSIFIED
ORNL-LR-DWG 25639

 

2. €9P3: L >H+I1,

3. pyoPs: L+ -1

4. p,P,i L +A > B, the A solid starting with
the composition given by Fig. 11.1 at temperature
p, and ranging to A, at P .

5. P,P,: L -1+ A, the A solid ranging from
AB to A,.

6. P,P.: L>1+B8, the B solid starting as pure
B and ranging to B..

7. P.P,: L ] +B, the B solid ranging from
Bs to B,.
Fig.

8. p,P,: L + B C, the B solid starting with
the composition given by Fig. 11.1 at temperature
Py and ranging to B, at P,.

9. e,E,r L 5 C +E, the E solid starting with
the composition given by Fig. 11.1 at temperature
e, and ending at E 7) (not to be confused with
the eutectic point £, }.

10. P.E,: L »] +C. (Note: the solid for the
C field is C, above the isothermal curve at ¢
CB below it.)

1 ond

 

UNCLASSIFIED
ORNL-LR~-DWG 25640

15.4.

1. p Pg: L +W_ > ], the W_solid starting as
pure W and ranging to Wy (of Fig. 15.7).

12, PgE,: L » ] + E, the E solid starting as
pure E and ending at F,,. (But the compositions
of the solids at P_ will be discussed further under

Fig. 15.7.)

The invariant reactions are as follows:

Pyt L +H - A, + 1 incongruent crystallization
end point for triangle [l (HA ;1).

99
UNCLASSIFIED
ORNL-LR-DWG 25644

 

 

Fig. 15.5.

P L + A‘1 R B; incongruent crystallization
end point for triangle 1V (4,IB).

P, L + 1 > By + ]; incongruent crystaliization
end point for triangle V (BI]).

P L +B, > C, +]; incongruent crystallization
end point for triangle VI (B, CJ).

Eyi L > Cg+ ] + E i congruent crystallization

end point for triangle VI [CEJEU)]'

Liquids with original compositions in the tie-
line areas of Fig. 15.5 complete their crystal-
lization on the various curves, leaving two-solid
mixtures of one pure compound and one solid

solution.

The B solid involved in the liquid equilibria of
Fig. 15,5 is the B form. Figure 11,1 shows this
form undergoing transition to the pure Bfi between
the temperatures T’ and T’ in the binary system
Y-7, These temperatures are unaffected by the
third component W. The changes in the solid-phase

100

combinations brought about by this transition are
shown in the series of schematic isotherms of
Fig. 15.6: (a) between P, and T ; (b) between T’
and O; {c) at Q; (d) between O and T""; (e) below
T”. The point Q is a four-solid invariant of type
B, the reaction being:

I +B,(ss) - calories == ] +Bg .

The two-solid equilibrium between I and B (ss)
here shrinks to a line on cooling, to be replaced
by the two-solid equilibrium between | and B
(@ line). At T, between isotherms (d) and (ei
the equilibrium between | and B (ss) shrinks to
a line and vanishes.

Also, at temperature T, of Fig. 11.1, below E,
of Fig. 15.5, the compound D of system Y-Z7
appears, forming from C and E ,, (more exactly it
forms from compound E of the composition given
by Fig. 11.1 at the temperature 7). This simply
divides the triangle V|| [which involves, at this
temperature, C., ], and E,.] into two triangles:
one for i I and D {pure D), and one for | and
conjugate solid solutions of D and E, with compo-

sitions given in Fig. 11.1. At ¢, of Fig. 11.1,

o further changes to Cj. ’

The remaining region of the system is shown
schematically in Fig. 15.7, with a temperature
maximum m, assumed to occur in the curve Pato,
and E_ therefore a eutectic. The point E, there-
fore lies in a three-solid triangle (IX) involving
the solids E, F, and a W—Z solid solution assumed

The W

composition in equilibrium with liquid at mar W,

and E. Although
m4, then, is a saddle point, the section Em, W

to have the composition shown as W_.

is, of course, on a line with m

is not quasi-binary, since the point W does noBT
represent liquid and solid of the same composition
in equilibrium. The point Wg represents the W_
composition for triangle VI, for the peritectic
point P, together with the two solids | and E.
It is assumed that the solid phase E is pure for
liquids along the whole length of the curve PoE,,
and that the binary scolid solution of E (in the
direction of C) enters only beyond P, on curve
P8E7'
solid phase may begin to vary in composition even
before P tn this case the line W_E
would end slightly to the left of E, as would also
the line W myE. We assume, therefore, that the

[t seems possible, however, that the FE

is reached.

spread inthe composition of solid F is insignificant
along the curve Palig.
UNCLASSIFIED
ORNL-LR—-DWG 25642

   

.“ffi"yf‘/f"(,‘ N
i
I+ J+ BQ(SSF)/;’#,/‘H \

  

(v il .
///f/ /.‘ \ /+BB+BQ(5$)

! :" "f‘l‘w' Ilr‘I\ N
'i"w\\‘\\.\ /f"/-"'/\“ N\

[ \

H\\\'\\ i HJ+C+ B i
}‘!w\‘!\\‘\\\f“f ///I + + Q(SS)
TT\\TrTF |

—

 

  
 

J+BB+ Bqelss)

P J+C+Ba(55)

 

B — ¢

 

o / \
/ // \\

7 'y
IS+ By, \
| /

\ /
L/
|

BB c

Fig.15.6.

101
UNCLASSIFIED
ORNL-LR~-DWG 25644

Py

      

)
o
o
o

}:

P2 Pses L7l
£ F

Fig. 45.7

We consider this region, then, on the basis of
the relations as drawn in Fig. 15.7.
The reaction on curve p, P is

L+WS—>] '

and the three-phase triangle starts as the line
p11JW and ends as p JW,. The curve is reached
by liquids for original composition x in the region
P WWPg. For x in JWWg, the liquid vanishes
on the curve to leave J and W_. For x in p,,]P,
W vanishes on the curve, and L leaves the curve
to traverse the | field on a straight line from J.
On the curve m P,

L->-E+W_,
5

the three-phase triangle starting as Em W _  and

ending as EP W, For x in the region EW W

m I
the liquid vanishes on the curve to leave E and
w.. The curve is reached from the W field for x
in P8W8Wm msy and from the E field for x in EP8m3.

The point P, is reached for x in the quadrangle
P JWgE; the invariant reaction is

L+Wgo]+E .

102

This is the incongruent crystallization end point,
then, for triangle Vil (]WBE),' but for x in EP.],
L moves onto curve PBE7' Along this curve,

L-]+E ,

with the three-phase triangle starting as JPGE
and ending as ]PBE(7)’ so that for x in E(7)]E
the liquid vanishes on the curve to leave | and a
solid solution between E and E7ye

Along curve m E,

LsE+W_,

the W_ solid ranging between W and W,. For
x in the triangle EW _W_, the liquid vanishes on
ma 9

the curve to leave P2 and W_. Along curve e E,

L>sE+F .

Curve p E, starts as
L+W_»F,

from p, to point s, where the line Fs is tangent to
the curve; between s and £,

L>F+W_ .
S

The three-phase triangle starts as the line p, FZ
and ends as the triangle FE Wy, For x in FW,Z,
the liquid vanishes on the curve to leave FF and W _
between Z and W,. For x in the region Fp s, W,
vanishes on the curve, and L traverses the F field

to reach either curve eSE or the even section of

9

the original curve, sE,, when W_ appears again,
bu* as a secondary crystallization product mixed
with F. The point Eg is reached only for x in

triangle 1X, with the reaction

L—)E+W9+F .

Compositions in the region covered in Fig. 15.7,
then, upon cooling in complete equilibrium, solidify
either to a mixture of three solids (the corners of
one of the triangles VIl, Vill, and IX) or to mix-
tures of two solids, in the tie-line areas for | and
W, for | and E, for E and W_, and for I7 and W_.

The fractionation paths on the surface for liquid
in equilibrium with W _ are sketched in Fig. 15.8,
on the basis of the assumptions made in Fig. 15.7.
Line WgPg is tangent to the fractionation path
Wm m

3

ending at P, , is tangent to the path Wm,
 

UNCLASSIFIED
ORNL-LR-DWG 25645

 

Fig. 15.8.

and WoE, is tangent to the path Wi . Curve mN
is the ?imiting fractionation path dividing the
separate families of paths originating at W and at
Z. The path mN is assumed to be convex with
respect to Z and to end (at N) on the curve poEge
The paths onthe W side of mN are convex, through-
out, toward Z; the solid solution being precipitated
on this surface continually increases in Z con-
tent. Those on the Z side start as convex with
respect to W, but some of them (nearing mN)
pass through an inflection point before reaching
the boundary curve between p, and N. For these
paths the sclid solution precipitated by liquid
traveling on the surface first increases and then
decreases in W content before reaching the curve.

The complete fractionation process tends toward
one of the eutectics E, and E, as limit. |t must
be remembered that on reaching a transition curve
in such a process L. does not travel on the curve
but immediately crosses it. This occurs, there-
fore, in a narrow region between Z and the curve

where the odd section of the curve (pbs)
be crossed. Liquids reaching the boundary

PyLg
wou?d
curves between m, and Pg all end at Eg, however,
whether or not they cross the transition curve, and
the final solids consist of E, F, and W_.

The curves p, P, and p, P are also crossed in
the fractionation process.  Consequently in a
narrow region between W and the beginning of the
curve p P, liquids will end on the curve e P,
then proceeding to E, as limit, leaving W, J, I,
H, A, B, C, and E in the final nonequilibrium
mixture, For liquids a little farther out from the
YW side, the curve e P, will just be missed, and
the solid H will not be present at the end. |if the
curve p, P is just missed, then both A and I
will also be absent, |f the liquid misses the curve
P.P,, and ends to the right of P, then the final
solids will be W_, J, C, and E; this will be the
mixture obtained for liquids up to the fractionation
path W .

103
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WTODYONZIEONOEETCTOTOINOPOXREIFPP>PTNINCONITOmMME - >
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TEOFAUEP-AEAAMANC>EQAICPIOPIALIOEIAIPAZA-~~FPAO0000 ML

ORNL-2396
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TID-4500 (14th ed.)

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MMOMUODARP>TCLOAMUIOEDOSATMIPTAmMmE-><-IVom=—m

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