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correction in the typos #71

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48 changes: 24 additions & 24 deletions getting-started/unit-converter.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -21,7 +21,7 @@
"metadata": {},
"source": [
"## CGS to SI\n",
"`Ubermag` uses SI units for all of the system parameters. Experimentally, material parameters are can often be measured in CGS units SI units, or a mixture of the two. Firstly, we show a convinent way of converting from CGS to SI units and other useful quantities.\n",
"`Ubermag` uses SI units for all of the system parameters. Experimentally, material parameters can often be measured in CGS units, SI units, or a mixture of the two. Firstly, we show a convenient way of converting from CGS to SI units and other useful quantities.\n",
"\n",
"To do this, we make use of `astropy.units`, a package aimed at the astrophysics community for its unit converting functionality. `astropy` is not installed by default. We can install it (e.g. with `pip`) directly from the notebook. Generally, you will not install `astropy` from inside the notebook (using either `pip` or `conda`) but for the sake of demonstration we run the command in here."
]
Expand All @@ -44,11 +44,11 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Requirement already satisfied: astropy in /home/mlang/miniconda3/envs/ubermagdev310/lib/python3.10/site-packages (5.3.4)\n",
"Requirement already satisfied: numpy<2,>=1.21 in /home/mlang/miniconda3/envs/ubermagdev310/lib/python3.10/site-packages (from astropy) (1.26.0)\n",
"Requirement already satisfied: pyerfa>=2.0 in /home/mlang/miniconda3/envs/ubermagdev310/lib/python3.10/site-packages (from astropy) (2.0.1)\n",
"Requirement already satisfied: PyYAML>=3.13 in /home/mlang/miniconda3/envs/ubermagdev310/lib/python3.10/site-packages (from astropy) (6.0.1)\n",
"Requirement already satisfied: packaging>=19.0 in /home/mlang/miniconda3/envs/ubermagdev310/lib/python3.10/site-packages (from astropy) (23.1)\n"
"Requirement already satisfied: astropy in /home/zulfigak/anaconda3/envs/ubermagdev3/lib/python3.8/site-packages (5.2.2)\n",
"Requirement already satisfied: numpy>=1.20 in /home/zulfigak/anaconda3/envs/ubermagdev3/lib/python3.8/site-packages (from astropy) (1.24.3)\n",
"Requirement already satisfied: pyerfa>=2.0 in /home/zulfigak/anaconda3/envs/ubermagdev3/lib/python3.8/site-packages (from astropy) (2.0.0.3)\n",
"Requirement already satisfied: PyYAML>=3.13 in /home/zulfigak/anaconda3/envs/ubermagdev3/lib/python3.8/site-packages (from astropy) (6.0.1)\n",
"Requirement already satisfied: packaging>=19.0 in /home/zulfigak/anaconda3/envs/ubermagdev3/lib/python3.8/site-packages (from astropy) (23.2)\n"
]
}
],
Expand Down Expand Up @@ -230,7 +230,7 @@
"$0.001 \\; \\mathrm{m^{2}\\,A}$"
],
"text/plain": [
"<Quantity 0.001 m2 A>"
"<Quantity 0.001 A m2>"
]
},
"execution_count": 7,
Expand All @@ -247,7 +247,7 @@
"id": "e6ac0a10",
"metadata": {},
"source": [
"If we wish to detach the numervical value for its units, we can do this using `.value`"
"If we wish to detach the numerical value for its units, we can do this using `.value`"
]
},
{
Expand Down Expand Up @@ -278,7 +278,7 @@
"source": [
"### Equivalencies\n",
"\n",
"The `astropy.units` also enables conversions of units with different equivalencies i.e. temperature and energy. To use this we can create a variable with the relevant units of temperature and use the `to` function to convert to the relevant units with the relevant equivalency.\n",
"`astropy.units` also enables conversions of units with different equivalencies such as temperature and energy. To use this we can create a variable with the relevant units of temperature and use the `to` function to convert to the relevant units with the relevant equivalency.\n",
"\n",
"For example, if an exchange interaction has a temperature of 4.15 K we can calculate the equivalent energy in J."
]
Expand Down Expand Up @@ -313,7 +313,7 @@
"id": "3b9b4a7a",
"metadata": {},
"source": [
"While `astropy` handles a variety of units and conversions, it does not currently have an equivalency for magnetic induction and magnetic field strength i.e. B to H . As this is a very useful for the magnetism community, we have provided the conversion here."
"While `astropy` handles a variety of units and conversions, it does not currently have an equivalency for magnetic induction and magnetic field strength i.e. B to H . As this is very useful for the magnetism community, we have provided the conversion here."
]
},
{
Expand Down Expand Up @@ -380,7 +380,7 @@
"J = \\frac{3k_\\text{B}T_\\text{C}}{\\epsilon z},\n",
"\\end{equation}\n",
"where $k_\\text{B}$ is the Boltzmann constant, $z$ is the number of nearest neighbours, and $\\epsilon$ is\n",
"a structural depended correction factor. The values of this correction factor has been calculated in Table I of [Garanin 1996](https://doi.org/10.1103/PhysRevB.53.11593)."
"a structurally dependent correction factor. The values of this correction factor have been calculated in Table I of [Garanin 1996](https://doi.org/10.1103/PhysRevB.53.11593)."
]
},
{
Expand Down Expand Up @@ -440,7 +440,7 @@
"\\begin{equation}\n",
"A = \\frac{zJl^2}{12V},\n",
"\\end{equation}\n",
"where $J$ is the Heisenberg exchange, $z$ is the number of nearest neighbour atoms, and $l$ is the distance between neighbor atoms and $V$ is the crystal volume per magnetic atom."
"where $J$ is the Heisenberg exchange, $z$ is the number of nearest neighbour atoms, and $l$ is the distance between neighbouring atoms, and $V$ is the crystal volume per magnetic atom."
]
},
{
Expand Down Expand Up @@ -547,7 +547,7 @@
"\\begin{equation}\n",
"D = \\frac{zdl}{12V},\n",
"\\end{equation}\n",
"where $d$ is the atomistic DMI, $z$ is the number of nearest neighbour atoms, and $l$ is the distance between neighbor atoms and $V$ is the crystal volume per magnetic atom."
"where $d$ is the atomistic DMI, $z$ is the number of nearest neighbour atoms, and $l$ is the distance between neighbouring atoms, and $V$ is the crystal volume per magnetic atom."
]
},
{
Expand Down Expand Up @@ -616,7 +616,7 @@
"id": "5709f726",
"metadata": {},
"source": [
"For a system with a micromagentic exchange of $6\\times 10^{-14}$ Jm$^{-1}$ and a helical period of 20 nm"
"For a system with a micromagentic exchange of $6\\times 10^{-14}$ Jm$^{-1}$ and a helical period of 20 nm."
]
},
{
Expand Down Expand Up @@ -651,7 +651,7 @@
"\\begin{equation}\n",
"P = \\frac{4\\pi J l}{|d|},\n",
"\\end{equation}\n",
"where $J$ is the Heisenberg exchange, $d$ is the atomistic DMI, and $l$ is the distance between neighbor atoms."
"where $J$ is the Heisenberg exchange, $d$ is the atomistic DMI, and $l$ is the distance between neighbouring atoms."
]
},
{
Expand All @@ -661,11 +661,11 @@
"source": [
"### Saturation Magnetisation\n",
"#### Micromagnetics\n",
"The saturation magnetisation is often measured in $\\mu_\\text{B}/f.u.$ but is needed in A/m in micromagnetics. A simple converstion can be used\n",
"The saturation magnetisation is often measured in $\\mu_\\text{B}/f.u.$ but is needed in A/m in micromagnetics. A simple conversion can be used\n",
"\\begin{equation}\n",
"M_s [ \\text{A}/ \\text{m}]= \\frac{\\mu_\\text{B} M_s[\\mu_\\text{B}/f.u.]}{V},\n",
"\\end{equation}\n",
"where $M_s[\\mu_\\text{B}/f.u.]$ is the saturation magnetisation in $\\mu_B$ per formula unit, $\\mu_B$ is the Bohr magneton in J/m, and $V$ is the volume of the formula unit in m$^3$."
"where $M_s[\\mu_\\text{B}/f.u.]$ is the saturation magnetisation in $\\mu_B$ per formula unit, $\\mu_B$ is the Bohr magneton in J/T, and $V$ is the volume of the formula unit in m$^3$."
]
},
{
Expand Down Expand Up @@ -704,7 +704,7 @@
"metadata": {},
"source": [
"#### Atomistic\n",
"In atomistic simulations the saturation magnetisation $M_s$ in micromagnetic simulations can be related to the magnetic moment $\\mu$ simply by\n",
"In atomistic simulations, the saturation magnetisation $M_s$ in micromagnetic simulations can be related to the magnetic moment $\\mu$ simply by\n",
"\\begin{equation}\n",
"\\mu = M_s V,\n",
"\\end{equation}\n",
Expand Down Expand Up @@ -752,7 +752,7 @@
"source": [
"### Anisotropy\n",
"#### Micromagnetic\n",
"Anisotropy can can be measured experimentally in a variety of different ways. The results torque magnetometry, for example, can give correct value for the anisotropy in units of Jm$^{-3}$."
"Anisotropy can be measured experimentally in a variety of different ways. The results torque magnetometry, for example, can give correct value for the anisotropy in units of Jm$^{-3}$."
]
},
{
Expand All @@ -761,12 +761,12 @@
"metadata": {},
"source": [
"#### Atomistic\n",
"Similarly to the saturation magnetisation the conversion between micromagnetic $K$ and atomistic anisotropy $k$ is simply volume weighted\n",
"Similarly to the saturation magnetisation, the conversion between micromagnetic $K$ and atomistic anisotropy $k$ is simply volume weighted\n",
"\\begin{equation}\n",
"k = K V,\n",
"\\end{equation}\n",
"where $V$ is the crystal volume per magnetic atom.\n",
"This atomistic anisotropy $k$ can also be calculated from the difference in energy of $J$ in different directions. i.e. $J_{\\perp} = 6\\times 10^{-23}$ J and $J_{\\parallel} = 5 \\times 10^{-23}$ J gives an atomistic anisotropy $k=1\\times 10^{-23}$ J."
"This atomistic anisotropy $k$ can also be calculated from the difference in energy between $J$ in different directions, i.e. $J_{\\perp} = 6\\times 10^{-23}$ J and $J_{\\parallel} = 5 \\times 10^{-23}$ J, gives an atomistic anisotropy $k=1\\times 10^{-23}$ J."
]
},
{
Expand Down Expand Up @@ -816,8 +816,8 @@
"id": "2da69916",
"metadata": {},
"source": [
"Here FeGe will be used as example for how to obtain micromagnetic parameters. FeGe has a cubic crystal structure with four Ge and four Fe atoms per unit cell with a lattice constant of $a=\t\n",
"4.6995$ Å and the distance between Fe atoms is 2.881 Å \\[[Wilhelm 2007](http://doi.org/10.1016/j.stam.2007.04.004)\\]. The saturation magnetisation is $1.07 \\mu_\\text{B}/f.u.$ \\[[Yamada 2003](https://doi.org/10.1016%2FS0921-4526%2802%2902471-7)\\] and magnetic ordering temperature is 278 K \\[[Lebech 1989](https://iopscience.iop.org/article/10.1088/0953-8984/1/35/010/meta)\\]. The helical period of FeGe is $\\sim 70$ nm \\[[Yu 2011](https://doi.org/10.1038/nmat2916)\\]."
"Here, FeGe will be used as example for how to obtain micromagnetic parameters. FeGe has a cubic crystal structure with four Ge and four Fe atoms per unit cell with a lattice constant of $a=\t\n",
"4.6995$ Å, and the distance between Fe atoms is 2.881 Å \\[[Wilhelm 2007](http://doi.org/10.1016/j.stam.2007.04.004)\\]. The saturation magnetisation is $1.07 \\mu_\\text{B}/f.u.$ \\[[Yamada 2003](https://doi.org/10.1016%2FS0921-4526%2802%2902471-7)\\], and magnetic ordering temperature is 278 K \\[[Lebech 1989](https://iopscience.iop.org/article/10.1088/0953-8984/1/35/010/meta)\\]. The helical period of FeGe is $\\sim 70$ nm \\[[Yu 2011](https://doi.org/10.1038/nmat2916)\\]."
]
},
{
Expand Down Expand Up @@ -978,7 +978,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.12"
"version": "3.8.19"
},
"widgets": {
"application/vnd.jupyter.widget-state+json": {
Expand Down