ORNL-2982.txt

 

 

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ORNL=-2982
UC-4 - Chemistry=General

 

SELF-DIFFUSION OF CHROMIUM

IN NICKEL-BASE ALLOYS

R. B. Evans Il
J. H. DeVan
Go Mp Wafson

 

 

 

OAK RIDGE NATIONAL LABORATORY
o operated by

UNION CARBIDE CORPORATION
for the

U.S5. ATOMIC ENERGY COMMISSION

   
. ORNL-2982
UC-4—Chemistry-General
TID-4500 (15th ed.)

Contract No. W-7405-eng-26

REACTOR CHEMISTRY DIVISION

SELF-DIFFUSION OF CHROMIUM IN NICKEL-BASE ALLOYS

R. B. Evans I11
J. H. DeVan
G. M. Watson

DATE ISSUED

JAN 20 1961

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

GY SYSTEMS LIBRARIES

, U

] 3 4456 031525 &
CONTENTS

Abstract...........O...O...l..........l.....Ol..l.................. l

Introduction.....Q.O........................I............‘.....O... 2

EXperimental ApproaCh..O.l..................0......................
Diffusion Coefficien-tso..OQO.......0.0........................

Tracer Techniques Applied to Diffusion MeasurementSeececesseces

<N P W W

Present Experimental MethOdSeeeceeeescoeeccsceccescsscosssoscses

Measurement of Over-All Diffusion CoefficientS.cececcccceccccocecses

Depletion Method..............O...........O..........C.....l‘.

O N

Constant-Potential Me-thod.....................................
Results.......................................!............... lO

DiSCU.SSion a‘nd ConclusionSO....l.O....QOOOOQO................. 13

Chromium-51 Diffusion Coefficients from Electropolishing
Experiments...............O..000....O.....C......O....Q......0... 16

IntrOduC tion. ® 0 0 0 00 00 00 00 OGSO S DO OO OO OO OO B SO OO OO OCE SO S OO OOSOPOSCPOEODS 1-6
De Sc ription Of Method- 6 8 6 00 0 0 00 88 088 OO OO LSOO 00O 0N E BSOS SO R 0o 16
Re S‘ll]—ts ® 6 0 6 00000 0 0 05 00 &8 0 00 0P PO OSSO0 OO0 OO O S OO SO SO O OO O ON PO POS DSOS OPOODS 17

DiSCUSSI1ONeesesescevssosssssossscssscsosscsssssasacsssssosscscssss 19
Analysis Of Diffusion Dal8eeececosccsccccsscescscssscccccossscsscsssssns 20
CONClUSLONSeeeassasasscssssssssscssscsasosssscssssssssssscssscssossssosnss 24
NOMENC la Ul e esseesescsscscscsscsscscssossscsosssssossscssocsscssosssssses 26

AppendiX.O....l..Q.......0.......0........l...l............‘....... 27

iii
SELF-DIFFUSION OF CHROMIUM IN NICKEL-BASE ALIOYS

 

R. B. Evans III J. H. DeVan G. M. Watson
ABSTRACT

The self-diffusion coefficients of Cr°! in Inconel and INOR-8, which
are alloys suitable for use at high temperatures, were measured by con-
tacting the alloys with fused salt mixtures containing radioactive chro-
mous fluoride. These data are pertinent to the interpretation of cor-
rosion behavior occurring in polythermal systems consisting of molten
fluorides contained in nickel-base alloys. The diffusion coefficients
were determined both by direct monitoring of the Cr’l intake by the al-
loys and in some cases by an analysis of the Cr®! concentration profile
below the exposed surfaces of the metals. The experiments were designed
to provide data over the temperature range 600 to 900°C, where relatively
low diffusion coefficients (10716 to 10712 cm?/sec) were obtained. At
temperatures above 800°C the magnitudes of the diffusion coefficients ob-
tained by both techniques were the same. At temperatures below 800°C the
diffusion coefficients obtained from the concentration profiles were
higher and had a lower temperature dependence than those obtained by di-
rect monitoring of the intake of Cr®l. This was interpreted as implying
that at the lower temperatures, diffusion occurs largely through selective
paths, while at the high temperatures, homogeneous diffusion occurs. The

observed diffusion coefficients can be expressed by the equation

D - Doe—E/RT

The values of Dg and E were found to vary, depending on the history of
the specimen. For Inconel specimens annealed at 1150°C for periods of
2 hr or longer, the values of E ranged from 62 to 66 kcal/mole, and Dy
from 1.0 to 2.8 cm?®/sec. For the two alloys studied the observed dif-

fusion coefficients were the same.
INTRODUCTION

Two primary requilsites to be considered when selecting a suitable
container material for molten fluoride mixtures are availability and com-
patibility with the salt. Based on these requisites alone, pure nickel
is an obvious choice for many container applications. Additional require-
ments, such as air oxidation resistance and strength, are imposed when
the applications involve polythermal reactor systems. Development work
has clearly indicated that nickel-base alloys are suitable materials for
reactor applications and constitute a workable compromise for the diverse
requirements mentioned.t

Inconel and INOR-8 are two nickel-base alloys which have received a
considerable degree of research attention during the last few years —
particularly regarding fluoride corrosion resistance. It has been found
that the corrosive attack incurred is selective toward chromium® and is
initiated through chromium oxidation at the surface by traces of HF, NiF,,
FeF,, and UF,. The attack is relatively mild when the salt is properly
purified. The residual attack may be due to UF, alone, the effects of
which cannot be completely eliminated.

Past work also suggests that the over-all rate of the selective at-
tack is primarily governed by the diffusion rates of chromium within the
alloys.

The work covered in the present report deals with a series of experi-
ments which should be directly related to the corrosion problem under dis-
cussion. The experiments had as their objectives the measurements of
various "self-diffusion" coefficients of Cr®! in Inconel and INOR-8 at
temperatures ranging from 600 to 900°C. It should be pointed out that
the first experiments were performed elsewhere> through a subcontract
arrangement.* These data have been utilized and considerably extended

by the present investigators.

 

'W. D. Manly et al., "Construction Materials for Molten Salt Re-
actors,” p 595 in Fluid Fuel Reactors (ed. by Lane, MacPherson, and
Maslan), Addison-Wesley, Reading, Mass., 1958,

°Ibid., p 599.

’R. B. Price et al., A Tracer Study of the Transport of Chromium
in Fluoride Fuel Systems, BMI-1194 (June 18, 1957).

“W. R. Grimes, ORNL, private communication, 1956.

 
This report is divided into three major sections: a presentation
of experimental results involving over-all cr’l diffusion rates, a pres-
entation of the corresponding cr’l concentration profiles, and an inter-

pretation of the data in terms of a simple diffusion model.

EXPERIMENTAT, APPROACH
Diffusion Coefficients

The diffusion coefficient is a flow-resistance parameter used in
diffusion rate—time relationships. It is defined by the linear flow

equation (Fick's first law)

1AM ¢
5t D (1)

which, if steady-state conditions are established and D is assumed to

be independent of concentration, may be written as

LA A
it~ PT (2)
where
MM/At = constant rate of diffusion, g/sec,

A = area through which diffusion takes place, cm?,

L = length, cm, of system in x direction (L is zero at the sur-
face and increases with penetration of the metal wall),

&

concentration change of diffusing material across L,

_ 3
Crm0 7 Cxa1 g/en?,

D = diffusion coefficient, cm?®/sec.

The diffusion coefficient is a function of temperature, the diffusing
material, and the material through which diffusion takes place. It does
not depend on the macroscopic geometry of the flow system.

The steady-state equation (2) is useful for discussion and forms the
basis for the determination of flow constants in analogous systems (flow
of heat, flow of electricity, and fluid flow in porous media); however,
its use in solid-state diffusion studies has been discouraged because of
the extremely low values of AM/At and D involved. The only alternative

is utilization of experiments and equations based on unsteady-state flow.
The basic linear flow equation for this case is

If self-diffusion measurements are to be made, for example, diffusion
of radioactive silver into pure silver, and/or if the values of OC/dx
involved are not high, the diffusion coefficient can be treated as a
constant. Under such conditions and at fixed temperature and pressure,

Eq. (3) woy be written as’

¢ 9°C
gg:D—B_XZ . (4)
Equation (4) is known as Fick's second diffusion law.

In the case of one-dimensional diffusion, applicable integrated forms
of the above differential equations contain two independent variables, the
time t and the coordinate x along which diffusion takes place. Conse-
quently, development of equations relating the diffusion coefficient to
measured variables requires knowledge of either the concentration profile
along the path of diffusion at a given time or the variation of concentra-
tion with respect to time at a given coordinate. Both methods have been

successfully employed for diffusion studies.

Tracer Techniques Applied to Diffusion Measurements

Several established techniques based on the use of radioactive iso-
topes as tracers are available for measuring diffusion coefficients in
metals. All the methods strive to establish experimental conditions such
that the diffusion behavior can be conveniently described by using the
fundamental diffusion equations discussed in the preceding section. The
techniques differ widely, however, in the method of tracer placement and
in the method of data analysis.

In the case of self-diffusion measurements, the method of tracer
placement has generally involved the use of a diffusion couple, that is,

a material containing a high percentage of radioactive atoms physically

 

°J. H. Wang, "Radioactivity Applied to Self-Diffusion Studies," in
Radioactivity Applied to Chemistry (ed. by Wahl and Bonner), Wiley, New
York, 1951,
joined to a material of similar chemical composition but of lesser radio-
activity. The simplest mathematical solution describing the movement of
diffusing atoms in such a couple results if the material of higher radio-
activity is in the form of an infinitely thin layer (or plane source) and
if the diffusing medium may be considered infinitely thick. The solution

of Eq. (4) for this condition (assuming one-dimensional diffusion) is
Qo
C_.

_ e—X2/4Dt
(nDt)1/2

, (5)
where C refers to tracer concentrations at depth x after time t, and the
quantity Qo refers to an impulse (g/CmZ) of tracer supplied to the metal
from the thin layer source. These boundary conditions are met experi-
mentally only if the penetration distance is large compared with the orig-
inal thickness of the tracer layer.

A convenient set of boundary conditions results from an experimental
standpoint when both the tracer layer and the diffusing medium approach
a thickness which can be regarded as infinite. The solution in this case

becomes

T = % 1 + erf ’—X——- . (6)
0 2(D.t)l/2
In certain experiments placement of tracer atoms is effected through
surface reactions. If by such a method the surface concentration of tracer
atoms is brought instantaneously to and maintained at a constant level, a

convenient solution of Eq. (4) results; namely,

C = Cq erfc —= . (7)
2(Dt)1/?
Carburizing experiments in which labeled carbon activities are established
at surfaces of metal specimens by exposing them to CO,-CO or CH,-H, gas
mixtures are well-known example56 of this technique.
Three basically different apprvaches have been utilized to analyze

the experimental results once the diffusion of tracer has been effected.

 

61,. S. Darken and R. W. Gurry, Physical Chemistry of Metals, p 450~
51, McGraw-Hill, New York, 1953.
Most commonly the diffusion medium has been sectioned and the sections
analyzed to obtain a concentration profile as a function of distance be-
low the diffusion interface. In certain cases a surface counting tech-
nique has been employed;7 in this technique the diffusion coefficient is
calculated from the decrease in activity of the face of the specimen on
which a thin layer of the radiocactive isotope was originally deposited.

A more recently advanced method for determining the extent of tracer
penetration is based on the use of autoradiography.8 The experimental
procedure is similar to that used in the sectioning technique except that
a single section is cut on a plane which is slightly less than normal to
the direction of diffusion. A film which is sensitive to the type of ra-
diation emitted by the tracer is placed over this section. The exposed
film results in a photograph of the distribution of the tracer. The photo-
graphic density can be correlated with tracer concentration to give a com-

plete penetration curve.

Many of the previous experimental methods were developed to obtain
magnitudes of the diffusion coefficientsand, more basically, to gain an
understanding of the mechanism of tracer invasion. In the present studies,
however, it was desired foremost to determine the amount of chromium which
would enter or leave the alloy as a function of surface concentration,
time, and temperature, and the method selected was aimed at determining
the rate at which the tracer entered the diffusion medium as well as the
distribution of tracer within the medium. Accordingly, the experimental
information determined includes all the processes which occur as the dif-
fusion medium adjusts to the concentration driving force, not just the
unit atomic process by which an atom moves to a neighboring lattice site.?
The importance of this distinction becomes evident when it is realized
that at least two distinct processes contribute to the diffusion of atoms

in polycrystalline metals — diffusion occurring along grain boundaries

 

7G. Hevesy and W. Seith, Z. Physik 57, 869 (1929).

83. T. Kishkin and S. Z. Bokstein, "Distribution and Diffusion of
Components in Metal Alloys Studied by the Autoradiographic Method,"
Peaceful Uses of Atomic Energy, p 87, A/Conf 8/15, United Nations, 1955.

°C. Zener, "Theory of Diffusion," p 289 in Imperfections in Nearly
Perfect Crystals (ed. by W. Shockley), Wiley, New York, 1952.

 
and diffusion through the grain matrix. In these studies no efforts were
made to separate directly the effects of these two processes, although

certain indirect observations of their relative magnitudes were permitted.

Present Experimental Methods

In the experimental methods employed for the present studies, the
placement of radiotracer (Cr°l) was accomplished by means of the exchange

reaction
cr® + Cr*F, = CrF, + Crox (8)

for which AF® = O, K, =1, and K _=1. The Cr*F, was dissolved in a car-
rier salt composed of NaF-ZrF, (53-47 mole %). This approach was sug-
gested by the relative inertness of CrF,, NaF, and ZrF, with respect to

the primary constituents of Inconel (Ni, Cr, and Fe) and INOR-& (Ni, Cr,
Fe, and Mo). The chemical reaction between the salts and the metals under
investigation was inconsequential;lo hence the only reaction resulting at
the surface was the exchange reaction (8) noted above, which created ratios
of activated to nonactivated chromium atoms at the surface of the material
identical with the ratios of activated to nonactivated chromium ions in

the salt.

MEASUREMENT OF OVER-ALL DIFFUSION COEFFICIENTS
Depletion Method

If consideration is given to an alloy—molten salt system in which
the molten salt initially contains dissolved CrFp; and Cr*F, and the alloy
contains Cr® and no Cro*, a random exchange will take place as shown by
Eq. (8), although the net change of total chromium is zero. The combined
action of the exchange reaction and the diffusional forces within the

alloy will result in a gain of crO% in the alloy and a loss of Cr*F, from

 

107, Glassner, The Thermochemical Properties of the Oxides, Fluo-
rides, and Chlorides to 2500°K, ANL-5750.

 

 
the salt. If the fractional depletion of Cr*F, activity in the salt (cor-
rected for time decay) is measured as a function of time, a diffusion co-
efficient for chromium in the metal may be calculated by means of the fol-

lowing relationship:

b, . —D 2 2
—E:%——-—E =1 -t erfc atl/? = 1 — &% erfe u , (9)
t=0
where
t = time, sec,
b, = counts/g-min (at time count is made) of a filtered
=0 salt sample taken at t = O,
bt = counts/g-min (at time count is made) of a filtered
salt sample taken at t,
a = depletion parameter, sec"1/2,
_Afer®] Pmoag
) |CI‘F2] ps ?
A/V = ratio of the salt-exposed area of alloy to the salt
Wflwm,cmd,
[Cro]/[Cng] = weight fraction+£atio of chromium in alloy to chromous
fluoride (as Cr ') in the salt,
pm/ps = density ratio of metal to salt,
D = diffusion coefficient, cmz/sec,
u = atllz.

Equation (9) is based on a simultaneous solution of Eq. (4) and the
equation resulting from a balance of the instantaneous transfer rates of

labeled chromium from the salt to the metal, or

0 o
St (MCr*F2) = {-DA % [Cop0x (0,£)1} . (10)
The variable x is distance within the alloy measured in the direction of

diffusion, in cm; C is concentration of Cr®*, in g/em3; and M is

crOx Cr*F,

the amount of Cr’! as Cr*F, in the melt.

The boundary conditions applied to obtain this solution are: (1) the
alloy is infinitely thick in the x direction, (2) the initial concentra-
tion of Cr%* in the alloy is zero, and (3) the concentration of Cr®* at

the alloy surface at any t > 0 is governed by Eq. (10) and varies with
time according to the relationship

_ [Cr*F, ]
[CCrO*]x=o - Qm[cro] TE?F;%‘ ’ (11)

which stems directly from Eq. (8). Large-scale plots of u vs fractional
depletion were used to convert the experimental data to the corresponding
diffusion coefficients.

Experimental data have been obtained for two series of experiments,
designated isothermal and polythermal, which satisfy the boundary condi-
tions for Eq. (9). In the isothermal experiments, u was varied by varying
t; all other parameters were held constant by charging an identical amount
of salt to capsules of identical geometry and imposing isothermal condi-
tions during the exposure period. These experiments afforded a direct
verification of the time-dependence relationship for the depletion-type

experiments.ll

Constant-Potential Method

Initial experimentation indicated that the Cr*F,; content of the molten
salts in alloy containers will remain constant if, prior to the experiment,
the temperature of the system is raised to 900°C for a few hours and then
lowered. Depletion of Cr¥*F, is essentially stopped at the lower tempera-
ture by this procedure. Specimens in the form of 1/4-in.-OD Inconel ther-
mocouple wells subsequently immersed in the salts absorb labeled chromium
under conditions of a constant surface potential; that is, the cr®* con-
centration at the specimen surface remains constant with time. The cor-

responding Cr9* transfer equationl? is

Dt 1/2
AMCI'O* = ZACCI‘O* <;—T—> . (12)

 

11p description of the experimental details and the time-dependence
curves may be found in the Appendix.

127. H. Wang, "Radioactivity Applied to Self-Diffusion Studies,"
in Radioactivity Applied to Chemistry (ed. by Wahl and Bonner), Wiley,
New York, 1951.
The variable C denotes concentration as g/cm”®. Rearranging Eq. (12),

/1 [y [crFa] 1V
D = <_l6fl‘t> <Z [Cro] rhpm> s (13)

where

h = height of the immersed specimen,
r = radius of the immersed specimen,

vy = total counts of the entire specimen (without alteration) per
minute at t, '

z = counts of the salt per gram-minute at t.

The variable y is a measure of the total amount of tracer gained by the
specimen; z is an indirect measure of the tracer concentration which is
maintained on the specimen surface during immersion.

Four series of experiments were performed by means of the constant-
potential method. Three series involved Inconel specimens which had been
subjected to three types of pretreatment conditions; the fourth series
involved INOR-8 specimens. The development and utilization of this method
was partially stimulated by the need for tracer-containing alloy specimens
for subsequent electropolishing experiments. Specimens from a constant-
potential experiment were desirable in this respect as they were related
to a convenient set of solutions of the diffusion equations. PFurther in-

formation regarding experimental details is presented in the Appendix.

Results

Over-all coefficients, as a function of temperature and grain size,
were obtained from six series of experiments. The experiments could be
conveniently grouped according to experimental method, alloy pretreatment,
and type of alloy. For brevity of presentation, an outline of the experi-
ments is shown in Table 1.

Experimental points for groups I-IV and reportedl3 high-temperature
values for a similar alloy are plotted in Fig. 1. The experimental points
for groups V and VI are not shown, since the general appearance, scatter,

and slope of a plot of these points are very similar to those of Fig. 1.

 

13p, Gruzin and G. Federov, Doklady Akad. Nauk S.S.S.R. 105, 264
(1955). '

10
[l

 

 

Table 1. Summary of Experiments to Determine Over-All Diffusion Coefficients
. Chromium
Experiment Type of Content Solvgn? Alloy Material Alloy Pretreatment or
Group ) Composition . . . ., . Remarks
Experiment of Alloy and Dimensions Annealing Conditions
Number (mole %)
(vt %)
I Isothermal 16.0 NaF-Zr¥, Inconel: sides, Welding temperature, then  Previously uncorrelated data
capsule (50-50) 3/8—in. tubing; normalized under H, for obtained from ref 3 at 3
(depletion) bottom, plate 4 hr at 900°C temperatures
1T Polythermal 14,4 NaF-ZrF, Inconel: capsules Annealed under H, for 8 Experiment performed to
capsule (53-47) machined from bar hr at 1150°C verify and augment
(depletion) stock 3/8-in. OD, group I results
5/16-in. 1ID,
25/64-in. inside
length
TiT Constant 15.2 NaF-ZrF, Inconel: l/4-in. Annealed under H, for 2 Several groups of isothermal
potential (53-47) tubing, 0.035-in. to 4 hr at 1150°C experiments performed to
wall verify Eq. (12) and to
evaluate the experimental
method
Iv Constant 15.1 NaF-ZrF, Inconel: 1/4-in. Annealed under He for 2 Single l-day exposure timej;
potential (53-47) tubing, 0.035-in. to 4 hr at 1150°C experiments performed to
wall show effects of H, vs He
annealing
M Constant 14.8 NakF-Zrl, Inconel: l/4—in. Annealed under H, for 8 Single 2-week exposure-time
potential (53-47) tubing, 0.035-in. to 12 hr at 800°C experiments performed to
wall show effects of lower an-
nealing temperatures and
to provide specimens for
electropolishing experi-
ments
VI Constant 7.03 NeF-ZrF, INOR-8: l/4-in. Annealed under H, for &8 Single 2-week exposure-time
potential (53-47) tubing, 0.028-in. to 12 hr at 800°C experiments performed to

wall

obtain preliminary INOR-8
over-all coefficients
comparable to Inconel co-
efficients

 
TEMPERATURE (°C)

UNCLASSIFIED

ORNL—LR—~DWG 47491 R

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1200 1100 1000 900 800 700 600
v | [ I [ [ l l
\\\\\V
—10 \
\
\\>\\\
A8
A
—1{2 B\\A
S ‘\\\Q\ GROUPS III, IV
N{ -
o —13 ™,
o oNe \0
- O GROUP I (REF 3) 8
3 ® GROUP II 0
—44 A
O GROUP II =0
A GROUP IV ®
v 19.8% Cr IN Ni ( REF {3)
—15 | ‘;
\\
GROUPS I, 11 j:\\\\\\
—16 \
@
o)
—17
6.5 70 7.5 8.0 8.5 9.0 9.5 TeXe 10.5 11.0 1.5
10,000 /7 (°K)
Fig. l. Experimental Results for 1150°C Annealed Inconel. Over-

all coefficients.

It should be mentioned that an isothermally determined over-all co-

efficient depends on the measurement, control, or knowledge of ten vari-

ables.

Seven of these variables are squared in the final equation; also,

the coefficient changes approximately 4% per degree centigrade at 700°.

The maximum error in any single coefficient could be #0.4 of a cycle on

Figs. 1 and 2.

tions.

The effect of temperature on the observed diffusion coefficients can

This estimate excludes the effects of grain size varia-

be expressed by the equation

12

D =

Do F /RT
For the two solid lines labeled "groups I, II" and "groups III, IV," the
values of E are 66 and 62 kcal/mole, and the values of Dg are 2.8 and 1.0
cmz/sec respectively.

In view of the over-all precision involved, the most realistic sum-
mary of the results might consist of a comparison of the average curves

for all available data. Such a comparison is presented in Fig. 2.

Discussion and Conclusions

A comparison of results obtained with an unannealed Inconel specimen
(point A, Fig. 2) and those obtained with three annealed specimens (point
B, Fig. 2) presents a pointed illustration of effects associated with grain

UNCLASSIFIED
ORNL—LR—DWG 47492R2

TEMPERATURE (°C)
1200 1100 1000 900 800 700 600
I l | [ I | l

o \\
N

 

 

 

N A
N

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- \
QO
(2]
€
O —13 ™ A
S N N °
5 CURVE
= {  GROUPS I(REF 3),1I \
= N
—14 2 GROUPS III, IV ‘\\\
3 GROUPS V, VI 3
4  Ni WITH 20.4% Cr, 2.6 % Ti (REF 13) .f 5
15 —— 5  Ni WITH 19.8% Cr ( REF 13) N ~
6 Ni PURE (REF13) ‘ \1\
—16 \\
—17
6.5 7.0 75 8.0 8.5 9.0 9.5 10.0 10.5 1.0 11.5

10,000/ T (°K)

Fig. 2. Chromium-51 Diffusion Coefficients in Nickel-Base Alloys.

Over-all values.,

13
size. DPhotomicrographs showing the grain size of these specimens may be
found in Fig. 3 (ref 14). Both the unannealed and the annealed specimens
were exposed to the same pot-salt system at the same temperature. The
same trend was shown by all the experimental results, in that increases
in the time and temperature of pretreatment increased the grain size,
which, in turn, led to a decrease in the over-all coefficient. It was
concluded that grain size effects had a marked influence on the over-all
diffusion coefficient.

The above conclusion formed the basis for another interpretation;
that is, specimens with the highest number of grains also contained the
highest number of "grain boundaries"”; accordingly, one might suspect that
a certain fraction of the diffusion took place along grain boundaries at
temperatures around 700°C.

Thus there would be reason to think in terms of two coefficients,
for example, volume and grain boundary. A treatment of a similar case
by Fisher!® and by Whipple16 revealed that the time dependence of the
penetration relationships would be altered when both mechanisms are com-
bined. Such was not the case in this investigation. The data appeared
to follow the equations presented. These equations were based on a single
phenomenological coefficient which could be used to represent a homogeneous
diffusion process taking place in an isotropic medium.

An encouraging feature of the results shown in Fig. 2 is the rela-
tively good agreement between the high- and low-temperature data. A
"preak" in the over-all coefficient curves indicating a change in mechanism
was not found for the Inconel specimens. The breaks noted in previous in-
vestigations (generally obtained from concentration profiles) result in
relatively flat curves at low temperature regions.

Coefficients presented in Fig. 2 represent alloys with chromium con-
tents ranging from O to 20.4 wt %. In view of the precision of the meas-
urements and grain size effects, it was concluded that the over-all co-
efficients above 700°C did not depend on the chromium concentration in
the INOR-8 and the Inconel. The amount of diffusion did depend on the

concentration in a manner predicted by Egs. (9) and (12).

 

14pdditional photomicrographs are included in the Appendix.
153. S. Fisher, J. Appl. Phys. 22, 74 (1951).

16R, T. P. Whipple, Phil. Mag. 45, 1225 (1954).

14
 

UNCLASSIFIED
T 159714

 

 

 

 

 

 

 

 

 

 

 

 

 

UNCLASSIFIED
T 16051

 

 

 

 

 

 

D10

 

 

 

 

 

 

 

» o P
y ~ - ’ c L/ Lo
" ./ 5
. , » e j 014
. / \‘ o o8
. B ‘

. % # *
R | | o]
(b) 1! . ; “ B - (t\ . o

- Ll T

 

 

 

Fig. 3. Photomicrographs of Annealed and Unannealed Inconel Speci-
mens. (a) Specimen unannealed (point A, Fig. 2); D = 78 X 10727 cm?/sec.
(b) Specimen annealed at 1150°C for 4 hr; D = 1.7 X 10715 cm?/sec, T =

salt
675°C for both experiments.

15
CHROMIUM-51 DIFFUSION COEFFICIENTS FROM
ELECTROPOLISHING EXPERIMENTS

Introduction

Practically all the solid-state diffusion data reported in the 1lit-
erature are based on the experimental determination of tracer concentration
profiles as a function of penetration distance. The experiments differ
as to the boundary conditions, tracer placement techniques, and sectioning
procedures employed. However, determination of the tracer profile is the
basic objective common to all experiments of this type. The profile data
are then converted to diffusion coefficients through a knowledge of the
proper concentration equations.

It was felt that a series of experiments of this type would consti-
tute an interesting complement to the Inconel experiments discussed in
the preceding section of this report. Two types of coefficients for a
given specimen would be available. One would be based on the measurement
of the over-all amount of tracer which diffused into the specimen under
a known surface potential; the second would be based on the tracer con-

centration profile within the specimen.

Description of Method

Three major considerations governed the choice of a method for sec-
tioning the tracer-containing specimens. First, very shallow tracer pene-
trations (very steep tracer concentration vs distance curves) would be in-
volved; second, the operation should be fast and should not require parti-
cular skills; third, the specimens would be cylindrical in shape since they
would originate from capsules, pots, or loops. It appeared that an elec-
tropolishing technique would satisfy all these requirements.

Based on the first two requirements mentioned, an integral method*”
was employed to correlate the data. This avoided the necessity of taking
a large number of minute "cuts" and then having to calculate a large num-

ber of "average" concentrations. The experiments were conducted in the

 

173, D. Gertsricken and I. Y. Dekhtyar, Proc. Intern. Conf. Peaceful
Uses Atomic Energy, Geneva, 1955 15, 99 (1955).

16
following manner. After salt exposure, the specimens were counted, pol-
ished, re-counted, polished again, etc., until less than 10% of the orig-
inal count was present. The percentages of total counts remaining after
each polishing were plotted as a function of the cumulative penetration
distances. The experimental plot was compared with a generalized plot

of an equation applicable to the experimental procedure (constant poten-
tial, semi-infinite system, initial tracer concentration zero, etc.), The
equation is

y(x) = 100(x)1/? fx‘” erfc w dw (14)

where y(x) is percentage of original activity remaining, and w = x/2(Dt)1/2.
Values of Eq. (14) are available in the linterature.® A detailed
description of the apparatus and procedures used to perform the electro-

polishing operation may be found elsewhere.1?

Results

Present Investigation

 

Electropolishing experiments were performed on duplicate specimens
obtained from 13 separate experiments mentioned in the preceding section
(see group V). Of all the constant-potential specimens processed, this
series contained the largest amount of tracer at the deepest penetrations.
The final results are presented in Fig. 4 (open circles) immediately above
the average curve, which represents the over-all coefficient obtained with
the same specimens. It was interesting to note that the deviations ex-
hibited by these data were faithfully reproduced by the over-all values

on the lower curve.

Battelle Data

0

Electropolishing data submitted by Price?? are shown on Fig. 5. 1In

addition to the 800°C data shown, a meager amount of data was obtained

 

18, . Carslaw and J. C. Jaeger, Conduction of Heat in Solids, p
373, University Press, Oxford, 1950.
' 197, H. DeVan, An Evaluation of Electro-Machining for the Analysis
of Metal Surfaces, ORNL CF-59-6-109 (June 25, 1959).
20R. B. Price et al., A Tracer Study of the Transport of Chromium
in Fluoride Fuel Systems, BMI-1194 (June 18, 1957).

 

 

 

17
V2o

TEMPERATURE (°C)

UNCLASSIFIED
ORNL-LR-DWG 47494 R

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

866~ #00 1000 900 850 800 750 700 650 600
-9 I 1 I I
A
-40 \\
A\\\
A
-44 \\
\A d
\ \~
-42 \\
\\‘
i - 1
~
€ O GROUP ¥V ELECTROPOLISHING RESULTS
. —.— GROUP ¥ OVER-ALL COEFFICIENTS
S vl ® GROUP I ELECTROPOLISHING RESULTS (REF 3)
2 —— GROUP I OVER-ALL COEFFICIENTS (REF 3) (
L A 198 % Cr IN Ni (REF13) 4\
-5 —— | | } ; ! \\ L
| N
-16 | r ‘ ~
’ 1
! 1 \ |
\ l . \
_47 i
6 7 8 9 10 "

10,000/, (o)

Fige. 4. Chromium Diffusion Coefficients for Inconel Based on Elec-

tropolishing Data.

for 700 and 600°C., The capsules used in the over-all depletion experi-
ments served as the electropolishing specimens which led to these results.
The rigorous profile equation for a depletion experiment is
/2 X

+ — exp
2(Dt)1/2 <Dl/2

Since the required relationship would involve integration of Egq. (15)

1
c(x,t) = Cg erfc |at

 

; a2t> . (15)

with respect to x, a decision was made to approximate the rigorous solu-
tion by means of Eq. (14). Past work had shown that analogous approxima-
tions with respect to the over-all transfer equations were acceptable.

As it turned out, the approximate equation accurately described a major
portion of the experimental profiles (see Fig. 5). Coefficients based

18
UNCLASSIFIED
ORNL — LR— DWG 47495R
100

 

 

 

 

 

 

90

EXPERIMENT [cro] [cr*t]
50 NUMBER (wt%) (ppm)
0 5q 16.0 700
\ ® 55 160 1080

A 5S¢ 16.0 1380

CURVE 4 197 hr
CURVE B T768hr
EQUATION (14)
T ——— EXPERIMENTAL

 

70

 

60 \‘
RN

2 O \ \\

 

 

 

\ DATA OBTAINED BY _
\ PRICE. efa/ (REF 20)
o
A
°

 

 

TRACER (Cr®¥*) REMAINING IN WALL (%)

 

 

 

 

 

 

 

 

 

 

 

Ng
\ 0\\
2NN\ NA
10
\\~\O \\\::\
* \‘4‘~ Q ‘ii'-—
0 [
0 2 4 6 8 10 12 14

THICKNESS REMOVED BY ELECTROPOLISHING ()
Fig. 5. Concentration Profiles in 800°C Depletion Capsules.

on the 800°C data®® are shown in Table 2. All the available Battelle

data are presented in Fig. 5.

Discussion

The 800°C data of Table 2 are of considerable importance, since the
results of two independent series of experiments at this temperature
established the equality of coefficients obtained from electropolishing
experiments and over-all measurements. It is presently thought that
equality of coefficients is a necessary condition for a homogeneous dif-

fusion process.

The values given in Table 2 represent the results of three depletion
experiments and six electropolishing experiments. The two profile coef-
ficients shown were obtained from the average of three similar experiments.
The number of over-all coefficients available corresponded to the number

of capsule experiments (involving several capsules exposed for various

19
Table 2. Comparison of Diffusion Coefficients for cr9¥®
in Inconel at 800°C

 

 

 

 

O% . . a
By CfseeC;?;enZ§atlon Profiles By [Crt+*] Depletiofib
) [Crtt] D
D

Salt Ex?fii?re Time (cmz/sec) (ppm) (cm?/sec)
x 10~14 % 10~14

197 3.47 700 4.25

768 4,75 1080 6.22

1380 4.21

 

 

 

%pverages of curves for 700, 1080, and 1380 ppm Crt+ (see Fig. 5).

bAverages of several determinations with different exposure times
at specific [Crtt] (see Fig. A.3).

times) that were performed, that is, three. It is important to note that
the initial [Cr*F,]/[CrF,] ratio and the A/V ratio were identical for all
experiments in the 800°C series. Thus, profiles for capsules with ident-
ical salt exposure times should be the same i1f the over-all diffusion equa-
tions previously presented and the assumed constant-potential boundary
conditions were correct. It appears that these propositions are verified
by the proximity of experimental points to the curves on Fig. 5.

As indicated by the curves of Fig. 4, the long anticipated "breaks"
in the log D vs l/T plots were finally acquired through the profile ex-
periments. A discussion of the difference between these profile curves
and curves for the companion over-all experiments will be given separately

in the next section of this report.

ANATYSTS OF DIFFUSION DATA

It is observed from Fig. 4 of the preceding section that, at tem-
peratures less than 800°C, the "diffusion coefficients" obtained from
tracer concentration profiles are higher than those which were based on
the total amount of tracer transferred. In order to correlate both kinds

of coefficients, it is useful to visualize a diffusion specimen, wherein

20
the entire diffusion process occurs in intergranular chammels. If it is
assumed that all the chamnels can be grouped together to give a certain

fraction, £, of the bulk volume, Vb’
and (1 — f)Vb will be the "inactive'" or dead volume. The next step con-

cerns the selection of a reference coefficient for the active volume.

then be will be the "active" volume

One of two sultable reference coefficients might be chosen; they

are: a bulk coefficient, D., resulting from steady-state diffusion ex-

periments, and a grain boufigary (or channel) coefficient, Dg, which is
based on studies of single grain boundaries. To precisely illustrate

the meaning of the two hypothetical coefficients, a numerical example
incorporating both coefficients was prepared. The example involved
steady-state diffusion of tracer M through a metallic membrane 1.5
thick, 1.025 cm? in cross-sectional area, 10 wt % M, and 0.1 volume
fraction, f. The membrane contained four active channels with dimensions

given in Table 3. Both coefficients are based on the same driving force,

NC, as indicated by

 

 

AL _ A
At Dg<z L >ACM ? (16)
g
since
Cy = C atx=0and L ,
and
Cb = ng, 0<x<L .
Table 3. Channel Parameters for Hypothetical Membrane
Channel Length Area Volume A/L,
Number (n) (cm?) (cm?) (cm)
x 10™2 x 10~6
1 3.0 2.50 7.500 83.3
2 1.5 1.25 1.875 83.3
3 2.0 1.75 3.500 87.5
4 5.0 0.50 2.500 10.0

A, = 6.00 W, = 15.375 S(A/L) = 264.1

 

21
Subscript b refers to bulk values; subscript g refers to channel or grain
boundary values. For the example, D and ACM'were assumed to be 2 x 10710
cm?/sec and (10 g/em?) (0.1) (1.0 — 0.2) (1078) respectively. The weight
fractions were 1.0 X 1078 and 2.0 x 1072 at the surfaces. The correspond-

ing rate was 4.23 X 1071® g/sec. The bulk coefficient was obtained through

SCHER

with the assumed D and membrane dimensions given in Table 3; the Db

value was 7.73 x 10712 cm?/sec, which is considerably lower than the

the relationship

Dg value.
In many instances it will be very difficult to obtain individual
A/L values, which are necessary for the utilization of a true Dg. How-

ever, a model Dg or (D) may be estimated by visualizing a parallel

g model
series of chamnnels with equal lengths and areas. By using the example

values for NAg, Ab’ f, and D. and the equations

b

NAng =fAL (18a)
A, DA

ND £ = b_‘ 2 (le)
g Lg Ly

which describe the model, a (Dg)model value of 2.255 X 10710 cm?/sec was
obtained. This value is in very good agreement with the original value
of 2.0 x 10719 cm?/sec.

The foregoing example demonstrates that utilization of the model
Dg would require information as to the average internal geometry of the
diffusion media. This is not required for Db' Nevertheless, reasonable
estimates of channel behavior (Dg) can be made through D, , since large
errors are not introduced by the model when reasonable channel-size dis-
tributions are involved. Accordingly, Db was selected as the reference
coefficient for present interpretations.

The active-volume concept implies that tracer does not accumulate

in the dead volume. Thus, Fick's law, from which equations describing

22
the experiments are developed, must be modified such that

2
dx 2
Applicable boundary conditions are
lim ¢(x,t) =0 , (20a)
X0
c(x,0) =0 |, (20Db)
c(0,t) =Cq , (20c)
which lead to a solution
¢(x,t) = fCq erfc —— = (21)
2(Dbt/f)l/2

The corresponding equations for over-all tracer transfer, AM, and fraction

of tracer remaining after electropolishing, y, are

 

1/2
Dbft
AM = 2AC, < ~ > , (22)
y(x) = 100(x)1/? j;w erfc w dw (23)
W —— (24)
2(Dbt/f)l/2

These equations are compatible with the data in that the basic form of
the time-dependence curves corresponding to Eq. (22) and the shape of the
polishing profiles of Eq. (23) are not altered by the introduction of f.
Furthermore, "low" over-all coefficilents are predicted by Dbf and "high"
polishing coefficients by Db/f' From the data and the present interpre-

tation, values of D f and Db/f were measured during the experiments. Thus,

b
= . 1/2
Db (Dover-all Dpolish) ? (25)
5 1/2
f = < 5929£:§££ > . (26)
polish

23
The term "grain boundary diffusion,”" as it is generally used, refers
to the portion of the electropolishing curves which have been ignored in
this investigation, that is, the residual 5 to 15% of the total tracer
transferred which undergoes comparatively deep penetration.

This interpretation applies to 85 to 95% of the material normally
classified as "volume" diffusion. We submit that this fraction of the
transferred tracer follows selective diffusion paths given by be. Further,
the value of f is unity at approximately 800°C for chromium in Inconel and

decreases markedly with temperature reductions below 800°C.

CONCLUSIONS

As a result of the present investigation the following conclusions
are apparent:

1., Self-diffusion coefficients of chromium in Inconel in the temper-
ature range 600 to 900°C were conveniently determined (a) by monitoring
the total intake of Cr2l by the alloys exposed to salt solutions containing
Cr¥F, and (b) by measuring the tracer concentration profiles through
successive electropolishing of the specimens.

2. The experimental precision of the measurements was +0.4 cycle,
exclusive of effects related to the history of the specimen.

3. The self-diffusion coefficients of chromium in Inconel were found
to be strongly dependent on annealing conditions at low temperatures. Con-
ditions leading to large grains led to low diffusion coefficients and vice

versa within this temperature range.

4, At temperatures above 800°C the magnitudes of the self-diffusion
coefficients of chromium obtained by the different techniques were the
same. At lower temperatures the diffusion coefficients calculated from
the concentration profiles were higher and had a lower temperature depend-
ence than those obtained by direct monitoring of the intake of Crol.

5. Deviations exhibited by the diffusion coefficients obtained by
direct monitoring of the intake of Cr’l were faithfully reproduced by the
corresponding values obtained from the concentration profiles, showing
that specimen variations were not completely overcome by annealing pre-

treatment.

24
6. From the determination of the Cr’! concentration profiles, it
was apparent that about 15% of the tracer penetrated deeper than calcu-
lated, using a single diffusion coefficient. This effect is believed to
be due to "grain boundary diffusion.” The bulk of the tracer penetration
(85%) could be calculated in terms of a single coefficient.

7. No change in the time dependence of the penetration relationships
was found at any temperature investigated.

8. The change in the temperature dependence noted for the coeffi-
cients obtained from concentration profiles indicates a change in the dif-
fusion mechanism at about 800°C from homogeneous volume diffusion at high

temperatures to diffusion along selective paths at low temperatures.

25
Q o = o

Q

0
[CrF,]
[crP]

N RN o H O U
5 0 o |\

=2 =2 ¢

S’O‘:U*"Sé@

n

N ¢ X o5 < © KH1 ¢ D

26

NOMENCLATURE

depletion parameter, sec™1/?
cross-sectional area normal to diffusion, cm?

count rate of depletion salt sample, counts/g-min

cr®* (tracer) concentration, g/cm3

cr®* (tracer) concentration initially at alloy surface, g/cm?
chromous fluoride concentration in salt, ppm or weight fraction
chromium concentration in alloy, wt % or weight fraction
self-diffusion coefficient for chromium in alloy, cm?/sec
bulk self-diffusion coefficient, cm?/sec

channel self-diffusion coefficient, cm?/sec

frequency factor, cm?/sec

activation energy, cal/mole

fraction of bulk volume engaged in diffusion process

height or length of alloy specimen, cm

thermodynamic equilibrium constant, dimensionless

equilibrium quotient in terms of weight fractions of the compo-
nents, dimensionless

length along path of flow, cm

total amount of Cro* present in alloy, g
number of channels involved in diffusion
amount of Cr®* per unit area of surface, g/cm?
radius of cylindrical alloy specimen, cm
gas constant, cal mole™* (°K)™%

alloy density, g/cm?

salt density, g/cm?

diffusion time, sec

temperature, °K

dimensioniess diffusion time, atl/?

salt volume, cm’

dimensionless diffusion variable, x/2(Dt):/?
diffusion coordinate along L, cm

count rate of alloy specimen, counts/min

count rate of constant-potential salt sample, counts/g-min
APPENDIX

Materials

Chromium Tracer

 

Chromium tracer was introduced to the alloy-salt systems as Crol-
labeled chromous fluoride for all the experiments mentioned in this re-
port. This material was prepared initially in small amounts by a method
described in detail by Sturm.t:?

1 to 2 cm? of dissolved Cr°*Cl; (as received from the ORNL isotope facil-

Briefly, the procedure involved adding

ities) to a suitable amount of CrCl,; (approx 10 to 20 g), fusing with
NH,HF,, decomposing in a hydrogen atmosphere, and then reducing with hydro-
gen; the resulting CrF, was found to contain metallic chromium in variable
amounts with additional materials whose 1dentities were not established.
To obtain a pure material, crystals from large batch preparations were
carefully selected and analyzed by Sturm;l:? these crystals were ground

to pass 100-mesh screens and then subjected to neutron irradiation for

one to two weeks. The Cr*F,-CrF, mixtures thus obtained were used without
further dilution (with unlabeled chromous fluoride) for the experiments.
At concentrations of 1500 to 3000 ppm in the base salt, the dissolved
labeled material resulted in initial base salt count rates of 5 X 10° to

1 x 10° counts/g-min.

Molten Fluoride Solvent

 

Continued use of NaF-ZrF, mixtures as the molten salt solvent or
base salt for all experiments was dictated by several considerations.
Of primary importance were the noncorrosive and relatively nonhygroscopic
properties of the solidified salt, since it was necessary to manipulate
and store the alloy specimens after salt exposure. Further, the zirconium-
base salts scavenge oxygen which might be inadvertently introduced to the
system via moisture or structural metal oxides; the resulting HF can be
rapidly removed through stripping with hydrogen, which also represses the

buildup of NiF, and FeF,. Alloy surfaces exposed to these solvents were

 

1B. J. Sturm, MSR Quar. Prog. Rep. Oct. 31, 1958, ORNL-2626, p 107.
°B. J. Sturm, ORNL, private communication.

 

27
in excellent condition even after two-week exposure periods. The solvent

densities as functions of temperature are given by the equations?

o (g/cm?) = 3.79 — 0.00093t (°C)
for NaF-ZrF, (50-50 mole %) and
o (g/em®) = 3.71 — 0.0008% (°C)

for NaF-ZrF, (53-47 mole %).

Alloys

Information regarding the chromium content, type of alloy, and pre-
test treatments of the alloy specimens studied may be found in the main
body of this report (see Table 1 and Fig. 3). In addition, averages of
several analyses of the alloys are presented as nominal values in Table
A.l. Photomicrographs of typical specimens of experimental groups IIT,
IV, V, and VI are shown in Figs.A.l and A.2; corresponding annealing
conditions are repeated in the titles for the reader's convenience. In

the calculation of the results, the numerical values used for the alloy

 

3s. I. Cohen, W. D. Powers, and N. D. Greene, A Physical Property
Summary for ANP Fluoride Mixtures, ORNL-2150 (Aug. 23, 1956).

 

 

Table A.1l. Nominal Composition of Alloys Used for Experiments

 

 

Inconel INOR-8

Cr 15.1% 7.0%

Fe 8.4% 5.1%

Ni 75.6% 71.0%

Mo 700 ppm 16.0%

Mn 3200 ppm 3700 ppm

Si 1800 ppm 3900 ppm

Ti 2800 ppm Trace

Al 1500 ppm 200 ppm
Trace

C 800 ppm 700 ppm

 

28
UNCLASSIFIED

 

INCHES

0.02

 

0.03

 

 

 

UNCLASSIFIED
T18751

 

 

 

 

 

Fig. A.1. Photomicrographs of Typical Group III and Group IV Speci-
mens. (a) Group III specimen Hy: Inconel ammealed under hydrogen for 2
to 4 hr at 1150°C; (b) group IV specimen I-2: Inconel annealed under
helium for 8 to 12 hr at 1150°C.

29
 

 

 

010

 

JOll

 

Oi2

 

013

 

0l4 7

 

018

 

016

 

017

 

.08

 

 

 

 

- UNCLASSIFIED|
T18761 W

. O

z

 

 

.009

 

.010

 

0t

 

0l2

 

013

 

0l4

 

0I5

 

018

 

 

 

 

 

 

 

Fig. A.2. Photomicrographs of Typical Group V and Group VI Speci-
mens. (a) Group V specimen J-13: Inconel annealed under hydrogen for
8 to 12 hr at 800°C; (b) group VI specimen K-5: INOR-& annealed under
hydrogen for 8 to 12 hr at 800°C.

30
densities*:? at 20°C were 8.43 and 8.79 g/cm® for Inconel and INOR-8 re-
spectively. Correspondingly, the coefficients for thermal expansion em-
ployed were 16.1 X 107° and 13.7 x 107 (°c)™t,

Counting Techniques

A well-type scintillation counter was employed for all count-rate
determinations which involved the gamma-emitting, 27.5-day-half-life Crol,
Undesirable geometry and shielding effects which might introduce counting
errors were minimized in the capsule (depletion) experiments, since the
ratio of the count rates of equal amounts of salt in identical containers
was employed.

Error considerations were somewhat more complex for the case of the
constant-potential experiments; here, the measured coefficient depended
on the count rate ratio of the Cr®* embedded in a metal to the Cr*F,
present in 1 g of salt. Although the same type of glass tubes was used
to contain the metals and salts during counting, this was not sufficient
to cancel all the shielding and geometry effects present. A series of
metal specimens (1-in., lengths of l/4-in. tubing) was counted with and
without close-fitting nickel and Inconel slugs in the inside opening.

No appreciable change in counts was obtained. It was concluded that little
could be done to improve the accuracy of the measurement, such as increas-
ing the inner diameter or dissolving the Cr9* prior to counting.

An experiment was then performed to determine the effect of specimen
height, since the relative positions and heights of the salt samples and
alloy specimens were not the same while undergoing count-rate determina-
tions. Successive counts of an alloy specimen of uniform activity were
obtained as the length was decreased. The same approach was applied with
respect to the salt by addition of salt. Based on these data an appropri-
ate correction was determined and applied to all constant-potential data.
Additional doubts as to the effectiveness of this correction were dispelled
through comparisons of the experimental coefficients for similarly annealed

constant-potential data and those for the capsule data.

 

“Pechnical Bulletin T-7: Engineering Properties of Inconel and In-
conel-X, International Nickel Co., Inc. (June 1953).

JA. Taboada, ORNL, private communication.

31
Wall Exchange Reaction
Use of the wall exchange reaction
Cr® + Cr¥F, =CrF, + Cro*
implies that no dilisproportionation such as
3(CrF, + Cr*F,) =2(CrF; + Cr¥F;3) + (Cr® + crf%)

exists. The latter possibility caused concern during the early stages

of this work and thus merits some discussion. Prior to the reported poly-
thermal capsule experiment, a dummy run using tracer and welded nickel
capsules was performed ostensibly to check manual procedures and the tem-
perature profile in the polythermal block, with loaded capsules to obtain
proper heat capacity, conductivity, etc. At the conclusion of the run

it was found that the tracer initlially present in the salt had undergone
slight depletion in capsules which had been at 700°C or higher. The pos-
sibility of the formation of insoluble chromium oxides was rejected, since
ZrF, was present in large amounts. Thus the observed depletion could have
been due to the disproportionation reaction; even though the calculated
standard free energy change for this reaction does not give evidence of
disproportionation, the fact remains that the initial cr9 content of the
metal was zero. In any event, other observations during experiments with
alloys present lead to the conclusion that disproportionation is completely
repressed when chromium is initially present in the walls and ZrF, is pre-
sent in the solvent. For example, good agreement was obtained between
high-temperature over-all and polishing coefficients. Also, the chromium
concentration in salts continually exposed to fresh alloy specimens and
variable temperatures remained constant with time. This might not be

true if solvents other than those utilized were employed.
Procedures for Capsule Experiments

Isothermal Experiments

 

A detailed description of the procedures utilized to perform the
isothermal capsule (depletion) experiments is given by Price.® The sa-

lient points are presented here for the reader's convenience.

 

6R. B. Price et al., A Tracer Study of the Transport of Chromium
in Fluoride Fuel Systems, BMI-1194 (June 18, 1957).

 

 

32
Equal amounts of a prepurified solvent containing ildentical concen-
trations of Cr¥F, and CrF, were charged to several Inconel capsules of
the same dimensions. A portion of the solvent was retained for the "time-
zero" standard. The charged capsules were then sealed by welding and
placed in an isothermal furnace. At various time intervals a single cap-
sule was removed until the entire series had been transferred. The cap-
sules were opened, the salt was removed, and the percentage or fraction
of the original counts which had been lost was determined. These data
were presented in graphical form as percentage loss vs time at tempera-
ture. The present investigators carefully transposed these data to plots
aé shown in Fig. A.3; the curves represent Eq. (9) evaluated with the

average coefficient for a given experiment.

It should be noted that the points follow the curves reasonably well.
Thus Fig. A.3 demonstrates that the time-dependence characteristics pre-
dicted by Eq. (9) are followed. Also, the data of Fig. A.3 show that in-
creases in the amount of unlabeled material present result in decreased
rates of depletion as predicted by the definition of a a.nd/or u [see Eq.

UNCLASSIFIED
ORNL-LR—-DWG 53655

 

70 | | |

TEMPERATURE (°C)  [Cr* "] (ppm) _—

60 800, a 700 ° _~T o

o2
800, b 1080 oC.
' o) @
800, ¢ 1380 /A{//
G
o 700 1340 p 0% o
600 1280 7 ~
. e |
”
40 s

7’ /O

- _

20 S o, & et

V4 =

10
L~
0/
~ 600°C ©
0 O

0 5 10 5 , 20 25 30
EXPOSURE TIME (hr) /2

 

 

 

 

 

 

 

 

 

Cr*F, DEPLETION (%)
(CORRECTED FOR TIME DECAY)
\\\;

 

 

O

 

 

 

 

 

 

 

 

 

Fig. A.3. Depletion of Cr¥F, from NeF-ZrF, (50-50 Mole %) Con-

tained in Inconel.

33
(9)]. The average diffusion coefficients were obtained by comparing the
experimental curves with a generalized plot of fractional depletion vs
u (see curve A, Fig. A.4). This procedure was repeated until a satis-
factory fit was obtained. The average values of the coefficients are

presented in Fig. 1.

UNCLASSIFIED
ORNL—-LR~-DWG 53656

| corvea |
] CURVE A

PER CENT Cr* F DEPLETED VS v
80

o\ M!

4 1) (Pyerar! o7
_V_ er

] (PSALT)

100

 

 

 

 

-~

40 ——— —

— CURVE B \
PER CENT Cr° REMAINING VS w
o L |

0 04 0.8 1.2 1.6 2.0 24 2.8 3.2
v OR w {orbitrary units)

 

 

 

 

1

PER CENT DEPLETED OR REMAINING

 

 

 

 

Fig. A.4. Theoretical Curves for Depletion and Electropolishing

Experiments.

Polythermal Experiments

 

The polythermal depletion experiments were based on the use of a
thermal gradient block similar to those described by Barton” for use in
molten salt phase studies. With this device, over-all diffusion coeffi-
cients at several temperatures could be obtained from a single series of
capsules.

Approximately 250 g of prepurified solvent was melted in an Inconel
container, the labeled chromous fluoride was added (approximately 1 g),
and the melt was then subjected to a stream of hydrogen at 700°C for 30
min., Portions of this mixture were then withdrawn by means of hydrogen-
fired copper filter sticks. The filtered material was removed, ground
to pass a 100-mesh screen, and transferred to pretared glass containers;
these operations were carried out in an air-filled dry box., After initial
counting and weighing, the salts and capsules were placed in a helium-

filled dry box, wherein all caps were removed. The box was evacuated

 

c. J. Barton et al., J. Am. Ceram. Soc. 41, 63 (1958).

34
overnight, refilled with helium, and the salt transferred to the capsules,
which were then sealed by means of 3/8—in. Swagelok fittings. A hydrogen-
fired nickel disk was placed on top of the capsules (prior to closure) to
avoid contamination of the salt by removal of the oxidized fittings at
the end of the experiment. All capsules were placed in the preheated
furnace simultaneously by means of an Inconel tray. The temperature gra-
dient was re-established within 30 min without overheating any of the
capsules. At the end of several weeks, the tray was removed and all cap-
sules were immediately quenched. The capsules were opened and the final
counts and weighing were performed in the glass tubes used at the start
of the experiment. Depletions were based on a portion of the starting
material. The salts and alloys were then analyzed for total chromium
content.®

Before the actual determination, a calibration run was made for de-
termining the temperature gradient within the block as a function of cap-
sule position for a given set of furnace conditions. Fach capsule was
charged with a different amount of salt containing the same labeled and
unlabeled chromium fluoride concentration. All capsules were exposed to
molten~salt temperatures over the same time interval. The amount charged
was varied such that the factor Ampm/MSpS would be constant, even though
the temperatures of each capsule would be different. Thus the depletion
equation could be used, with temperature acting as the independent var-
iable.

The experimental points are plotted in Fig. A.5. The curve is based
on a plot established on semilog paper. It can be shown that a semilog
plot of depletion (as per cent) vs 1/T [(°K)™}] will approximate a straight
line at low values of depletion (low temperatures), deviating slightly at
higher depletion values. This results from the exponential variation of
D with respect to 1/T and affords a convenient method for correlating the
experimental data.

Depletion values at the experimental temperatures were taken from
the curve of Fig. A.5 and compared with the generalized plot of Fig. A.4.
The data, thus smoothed, formed the basis for the group II coefficients

presented in the main body of this report.

 

8This work was performed by W. F.Vaughan of the Analytical Chemistry
Division.

35
UNCLASSIFIED
ORNL—LR-DWG 53657

 

 

A~ [cr°]1=14.4 wt %
[Cr++] =1820 ppm o
P -
4, TMETAL _ 45,97 (cm)
30 | PsaLt

 

U,
t=596.4 hr /

20 o/

o /
/O

0

600 650 700 750 800

TEMPERATURE (°C)

 

PER CENT CrF2 DEPLETION

 

 

 

 

 

 

 

Fig. A.5. Results of Polythermal Experiments with Inconel Cap-
sules.,

Procedures for Constant-Potentlal Experiments

As mentioned previously, the results of experiments based on deple-
tion methods revealed that the CrF, content of the salt will remain essen-
tially constant if the alloy container is first equilibrated with respect
to Eq. (1) for several hours at 900°C, then subjected to lower temperatures.
A small specimen of the identical alloy subsequently immersed in the salt
will pick up labeled chromium under conditions of a constant surface po-
tential; that is, the Cr® concentration at the specimen surface, Cy, is
constant with time.

A diagram of the constant-potential apparatus is shown in Fig. A.6.
The alloy specimens were isothermally exposed to the salts in the form
of a closed, 1/4-in.-0D thermocouple well. The container or "pot" resided
in a standard l-in. tube furnace which was controlled to within *3°C of
the desired temperature. Temperatures within the well were periodically'
measured with a standard Pt vs 90% Pt—10% Rh thermocouple and a K-2 poten-
tiometer. Filtered salt samples for counting and CrF, analyses were oOb-
tained when the wells were changed. An argon sweep created a "blanket"
for these manipulations and also created agitation during short-term
experiments. The argon sweep was discontinued during long-term tests

to minimize plugging by the slightly volatile ZrF,. Temperature gradients

36
thus introduced were negligible. Periodic hydrogen reduction of the system
between runs kept the concentrations of corrosive NiF, and FeF, near theilr

lower limit of detection.

The results of typical experiments conducted under comparable condi-

tions are shown graphically in Fig. A.7. The curves indicate that Eq. (12)

UNCLASSIFIED
ORNL-LR-DWG 31809

He 7/
INLET
‘ | . Y4-in. INCONEL TUBING

[5 AQ\THERMOCOUPLE WELL
4 B

E TEFLON PACKING GLAND

— He OUTLET

 

 

 

 

 

 

ot
I 4 AMCr"* =24 cCr°* -
DIP LEG —{f= —5 [credler***] Dt
il AMe ox = 2AppyETAL [cr*t] s
L~ Z jfi 1 AMeoex fcre] 2
=4 2 Ter v (2 PMETAL [cr++] . '\/_,_
o AMG, 0%
; T“METAL SPECIMEN FOR Q2

 

 

 

 

 

 

Fig. A.6. Apparatus and Equations for a Constant-Potential Diffusion
Experiment.

UNCLASSIFIED
2 ORNL-LR-DWG 53658
(x140™ =)

10

POINT 4, Fig. 2

X e TEMPERATURE (°C)
3% 0 700
'l‘ O 750

® 675

A 640

 

0 2 4 6 8 10 12 14 16
EXPOSURE TIME (hr) /2

Fig. A.7. Time Dependence Curves for Constant-Potential Experi-

ments.,

37
is followed, although the intercept of many of the curves did not occur
precisely at the origin. In these cases the slopes of the lines as shown
were utilized to obtaln the corresponding coefficlents.

Pretreated wells were stored in evacuated tubes before and after salt
exposure; caution was exercised during removal of the well from the salt
to avoid surface oxidation. At a convenient time the exposed wells were
cut up to furnish specimens for counting, electropolishing, and Ccr® anal-
yses. The generalized curve used to correlate the electropolishing data

is shown as curve B in Fig. A.4.

38
V-0t W

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