docs/2_debye_model_solutions.md

+---
+search:
+  exclude: true
+jupyter:
+  jupytext:
+    text_representation:
+      extension: .md
+      format_name: markdown
+      format_version: '1.0'
+      jupytext_version: 0.8.6
+  kernelspec:
+    display_name: Python 3
+    language: python
+    name: python3
+---
+
+```python tags=["initialize"]
+from matplotlib import pyplot as plt
+from mpl_toolkits.axes_grid1 import make_axes_locatable
+
+import numpy as np
+from scipy.optimize import curve_fit
+from scipy.integrate import quad
+
+from common import draw_classic_axes, configure_plotting
+
+configure_plotting()
+```
+
+# Solutions for lecture 2 exercises
+
+### Warm-up exercises
+
+1. For low T, $1/T \rightarrow \infty$. The heat capacity is then given as:
+
+    $$
+    C \overset{\mathrm{low \: T}}{\approx} 9Nk_{\mathrm{B}}\left(\frac{T}{T_{D}}\right)^3\int_0^{\infty}\frac{x^4{\mathrm{e}}^x}{({\mathrm{e}}^x-1)^2}{\mathrm{d}}x.
+    $$
+
+2. See plot below (shown for $T_{D,1} < T_{D,2}$)
+3. The polarization describes the direction of the motion of the atoms in the wave with respect to the direction in which the wave travels. In 3D, there are only 3 different polarizations possible.
+4. The integral can be expressed as
+    $$
+    \int dk_x dk_y = \int k dk d\phi
+    $$
+
+5. The Debye frequency $\omega_D$ is the frequency of the vibrational mode with the highest eigenfrequency. It has corresponding Debye temperature $T_D = \hbar\omega_D/k_B$, which is the temperature above which all the vibrational modes in the system become excited
+6. The wavelength is of the order of the interatomic spacing:
+
+    $$
+    \lambda = (\frac{4}{3}\pi)^{1/3} a.
+    $$
+
+```python
+fig, ax = plt.subplots()
+T = np.linspace(0.1, 3)
+T_D = [1,2]
+ax.plot(T, (T/T_D[0])**3, 'b-', label = r'$T_{D,1}$')
+ax.plot(T, (T/T_D[1])**3, 'r-', label = r'$T_{D,2}$')
+ax.set_ylim([0,3])
+ax.set_xlim([0,3])
+ax.set_xlabel('$T$')
+ax.set_xticks([0])
+ax.set_xticklabels(['$0$'])
+ax.set_ylabel('$C$')
+ax.set_yticks([0])
+ax.set_yticklabels(['$0$'])
+ax.legend();
+```
+
+### Exercise 1: Deriving the density of states for the linear dispersion relation of the Debye model
+
+1. $\omega = v_s|\mathbf{k}|$
+2. The distance between nearest-neighbour points in $\mathbf{k}$-space is $2\pi/L$. The density of $\mathbf{k}$-points in 1, 2, and 3 dimensions is $L/(2\pi)$, $L^2/(2\pi)^2$, and $L^3/(2\pi)^3$ respectively.
+3. Express the number of states between frequencies $0<\omega<\omega_0$ as an integral over k-space. Do so for 1D, 2D and 3D. Do not forget the possible polarizations. We assume that in $d$ dimensions there are $d_p$ polarizations.
+
+    \begin{align*}
+    N_\text{states, 1D} & = 1_p \frac{L}{2\pi} \int_0^{k_0} 2 dk \\
+    N_\text{states, 2D} & = 2_p \left(\frac{L}{2\pi}\right)^2 \int_0^{k_0} 2\pi k dk \\
+    N_\text{states, 3D} & = 3_p  \left(\frac{L}{2\pi}\right)^3 \int_0^{k_0} 4\pi k^2 dk
+    \end{align*}
+
+4. We use $k=\mathbf{k}| = \omega/v_s$ and $dk = d\omega/v_s$ to get
+
+    \begin{align*}
+    N_\text{states, 1D} & = 1_p \frac{L}{2\pi} \int_0^{\omega_0} 2 \frac{1}{v_s} d\omega  := \int_0^{\omega_0} g_{1D}(\omega) d\omega \\
+    N_\text{states, 2D} & = 2_p \left(\frac{L}{2\pi}\right)^2 \int_0^{\omega_0} 2\pi \frac{\omega}{v_s^2} d\omega := \int_0^{\omega_0} g_{2D}(\omega) d\omega \\
+    N_\text{states, 3D} & = 3_p  \left(\frac{L}{2\pi}\right)^3 \int_0^{\omega_0} 4\pi \frac{\omega^2}{v_s^3} d\omega := \int_0^{\omega_0} g_{3D}(\omega) d\omega
+    \end{align*}
+
+    The integral boundaries set the frequency region in which you calculate the density of states.
+
+5. The density of states is the number of states per unit frequency. It has units of 1 over frequency
+
+### Exercise 2: Debye model in 2D
+
+1. The energy stored in the vibrational modes of a two-dimensional Debye solid is:
+
+    \begin{align*}
+    E & = 2_p \frac{L^2}{4\pi^2}\int_0^{\infty}(n_B(\omega(\mathbf{k}))+\frac{1}{2})\hbar\omega(\mathbf{k}) d\mathbf{k} \\
+    & = \frac{L^2}{\pi v^2\hbar^2\beta^3}\int_{0}^{\beta\hbar\omega_D}\frac{x^2}{e^{x} - 1}dx + E_0
+    \end{align*}
+
+2. The high-$T$ limit implies $\beta \rightarrow 0$. Therefore, $n_B \approx k_B T/\hbar\omega$, and the integral becomes particularly illuminating:
+
+    $$
+    E = \int_{0}^{\omega_D} \hbar\omega  n_B(\omega) g(\omega) d\omega \approx \int_{0}^{\omega_D} k_B T g(\omega) d\omega = N_\text{modes} k_B T
+    $$
+
+    where we neglected the zero-point energy. In 2D, we have $N_\text{modes} = 2_p N_\text{atoms}$, so that we recover the 2D law of Dulong–Petit $C_v = dE/dT = 2 k_B$ per atom.
+
+3. In the low temperature limit, the high-energy modes are not excited so we can safely let the upper boundary of the integral go to infinity. For convenience, we write $g(\omega) = \alpha \omega$, with $\alpha = \frac{L^2}{\pi v_s^2}$. We get
+
+    $$
+    E = \int_0^{\omega_D}\frac{\hbar\omega g(\omega)}{e^{\hbar\omega/k_B T}- 1}d\omega \approx \alpha\frac{k^3 T^3}{\hbar^2}\int_0^\infty\frac{x^2}{e^x-1}dx
+    $$
+
+    From which we find  $C_v = dE/dT = K T^2$, with
+
+    $$
+    K = 3\alpha\frac{k^3}{\hbar^2}\int_0^\infty\frac{x^2}{e^x-1}dx
+    $$
+
+### Exercise 3: Longitudinal and transverse vibrations with different sound velocities
+
+1. The key idea is that the total energy in the individual harmonic oscillators (the vibrational modes) is the sum of the energies in the individual oscillators: $E = \int_0^{\omega_D}\frac{\hbar \omega g(\omega)}{e^{\beta\hbar\omega} - 1}d\omega + E_Z$, where $g(\omega) = g_\parallel(\omega) + g_\perp(\omega)$. Using
+
+    \begin{align*}
+    g_\parallel & = 1_p  \frac{L^3}{2\pi^2} \frac{\omega^2}{v_\parallel^3}, \\
+    g_\perp     & = 2_p  \frac{L^3}{2\pi^2} \frac{\omega^2}{v_\perp^3},
+    \end{align*}
+
+    we get
+
+    $$
+    E = \frac{L^3 k_B^4 T^4}{2\pi^2\hbar^3}\left(\frac{2}{v_\perp^3} + \frac{1}   {v_\parallel^3}\right)\int_{0}^{\beta\hbar\omega_D}\frac{x^3}{e^{x} - 1}dx.
+    $$
+
+2. As in exercise 1, in the high-T limit, we have $\beta \rightarrow 0. Therefore, $n_B \approx k_B T/\hbar\omega$ and the integral for $E$ becomes:
+
+    $$
+    E = \int_{0}^{\omega_D} \hbar\omega  n_B(\omega) g(\omega) d\omega \approx \int_{0}^{\omega_D} k_B T g(\omega) d\omega +E_Z = N_\text{modes} k_B T + E_Z
+    $$
+
+    and we are left with the Dulong-Petit law $C = 3N_\text{atoms} k_B$.
+
+3. In the low temperature limit, we can let the upper integral boundary go to infinity as in exercise 1. This yields
+
+    $$
+    C \approx \frac{2\pi^2 k_B^4 L^3}{15\hbar^3}\left(\frac{2}{v_\perp^3} + \frac{1}{v_\parallel^3}\right)T^3
+    $$
+
+    where we used $\int_{0}^{\infty}\frac{x^3}{e^{x} - 1}dx = \frac{\pi^4}{15}$.
+
+### Exercise 4: Anisotropic sound velocities
+
+In this case, the velocity depends on the direction. Note however that, in contrast with the previous exercise, the polarization does not affect the dispersion of the waves. We get
+
+\begin{align*}
+E =& 3_p\left(\frac{L}{2\pi}\right)^3 \int \frac{\hbar\omega(\mathbf{k})}{e^{\beta\hbar\omega(\mathbf{k})}-1} dk_x dk_y dk_z + E_Z \\
+=&   3_p\left(\frac{L}{2\pi}\right)^3\frac{1}{v_x v_y v_z} \int \frac{\hbar\kappa}{e^{\beta\hbar\kappa} - 1}d\kappa_x d\kappa_y d\kappa_z + E_Z,
+\end{align*}
+
+where we made the substitutions $\kappa_x = k_x v_x,\kappa_y = k_y v_y, \kappa_z = k_z v_z$ so that $\omega = \kappa$. Going to spherical coordinates:
+
+\begin{align*}
+E &=  \frac{3_p L^3}{2\pi^2}\frac{1}{v_x v_y v_z}\int_{0}^{\kappa_D} \frac{\hbar\kappa^3}{e^{\beta\hbar\kappa} - 1} d\kappa + E_Z
+\end{align*}
+
+To calculate the specific heat $C = \frac{dE}{dT}$, let's differentiate this expression directly:
+
+\begin{align*}
+C &= \frac{dE}{dT} = \frac{3_p L^3}{2\pi^2}\frac{1}{v_x v_y v_z}\int_{0}^{\kappa_D} \frac{d}{dT}\left(\frac{\hbar\kappa^3}{e^{\beta\hbar\kappa} - 1}\right) d\kappa \\
+&=  \frac{3_p L^3}{2\pi^2}\frac{1}{v_x v_y v_z}\int_{0}^{\kappa_D} \frac{\hbar\kappa^3 \cdot \hbar\kappa \cdot e^{\beta\hbar\kappa}}{(e^{\beta\hbar\kappa} - 1)^2} \cdot \frac{d\beta}{dT} d\kappa
+\end{align*}
+
+Since $\beta = \frac{1}{k_B T}$, we have $\frac{d\beta}{dT} = -\frac{1}{k_B T^2} = -\frac{\beta}{T}$. Substituting this:
+
+\begin{align*}
+C &= - \frac{3_p L^3}{2\pi^2}\frac{1}{v_x v_y v_z}\int_{0}^{\kappa_D} \frac{\hbar^2\kappa^4 e^{\beta\hbar\kappa}}{(e^{\beta\hbar\kappa} - 1)^2} \cdot \frac{\beta}{T} d\kappa \\
+&= - \frac{3_p L^3}{2\pi^2}\frac{1}{v_x v_y v_z} \cdot \frac{\hbar^2\beta}{T}\int_{0}^{\kappa_D} \frac{\kappa^4 e^{\beta\hbar\kappa}}{(e^{\beta\hbar\kappa} - 1)^2} d\kappa
+\end{align*}
+
+Now, we can make the substitution $x = \beta\hbar\kappa$, which gives $d\kappa = \frac{dx}{\beta\hbar}$ and changes our limits to $\int_{0}^{\beta\hbar\kappa_D}$:
+
+\begin{align*}
+C &= - \frac{3_p L^3}{2\pi^2}\frac{1}{v_x v_y v_z} \cdot \frac{\hbar^2\beta}{T} \cdot \int_{0}^{\beta\hbar\kappa_D} \left(\frac{x}{\beta\hbar}\right)^4 \frac{e^x}{(e^x - 1)^2} \cdot \frac{dx}{\beta\hbar} \\
+&= - \frac{3_p L^3}{2\pi^2}\frac{1}{v_x v_y v_z} \cdot \frac{\hbar^2\beta}{T} \cdot \frac{1}{(\beta\hbar)^5} \int_{0}^{\beta\hbar\kappa_D} \frac{x^4 e^x}{(e^x - 1)^2} dx \\
+&= - \frac{3_p L^3}{2\pi^2}\frac{1}{v_x v_y v_z} \cdot \frac{1}{T\beta^4\hbar^3} \int_{0}^{\beta\hbar\kappa_D} \frac{x^4 e^x}{(e^x - 1)^2} dx
+\end{align*}
+
+Since $\frac{1}{T\beta^4} = \frac{k_B^4 T^3}{1} = k_B^4 T^3$, we get:
+
+\begin{align*}
+C &= -3_p \frac{3_p L^3}{2\pi^2}\frac{1}{v_x v_y v_z} \cdot \frac{k_B^4 T^3}{\hbar^3} \int_{0}^{\beta\hbar\kappa_D} \frac{x^4 e^x}{(e^x - 1)^2} dx \\
+&= 3_p \frac{3_p L^3 k_B^4 T^3}{2\pi^2\hbar^3}\frac{1}{v_x v_y v_z} \int_{0}^{\beta\hbar\kappa_D} \frac{x^4 e^x}{(e^x - 1)^2} dx
+\end{align*}
+
+This is similar to the result with isotropic linear dispersion, with the difference being the factor $1/(v_x v_y v_z)$ instead of $1/v^3$.

docs/code/elements.json

+[{"number": 1, "abbr": "H", "full_name": "hydrogen", "remark": "(H 2 , gas)", "c": 28.836}, {"number": 2, "abbr": "He", "full_name": "helium", "remark": "(gas)", "c": 20.786}, {"number": 3, "abbr": "Li", "full_name": "lithium", "remark": "", "c": 24.86}, {"number": 4, "abbr": "Be", "full_name": "beryllium", "remark": "", "c": 16.443}, {"number": 5, "abbr": "B", "full_name": "boron", "remark": "(rhombic)", "c": 11.087}, {"number": 6, "abbr": "C", "full_name": "carbon", "remark": "(graphite)", "c": 8.517}, {"number": 6, "abbr": "C", "full_name": "carbon", "remark": "(diamond, nonstd state)", "c": 6.115}, {"number": 7, "abbr": "N", "full_name": "nitrogen", "remark": "(N 2 , gas)", "c": 29.124}, {"number": 8, "abbr": "O", "full_name": "oxygen", "remark": "(O 2 , gas)", "c": 29.378}, {"number": 9, "abbr": "F", "full_name": "fluorine", "remark": "(F 2 , gas)", "c": 31.304}, {"number": 10, "abbr": "Ne", "full_name": "neon", "remark": "(gas)", "c": 20.786}, {"number": 11, "abbr": "Na", "full_name": "sodium", "remark": "", "c": 28.23}, {"number": 12, "abbr": "Mg", "full_name": "magnesium", "remark": "", "c": 24.869}, {"number": 13, "abbr": "Al", "full_name": "aluminium", "remark": "", "c": 24.2}, {"number": 14, "abbr": "Si", "full_name": "silicon", "remark": "", "c": 19.789}, {"number": 15, "abbr": "P", "full_name": "phosphorus", "remark": "(white)", "c": 23.824}, {"number": 15, "abbr": "P", "full_name": "phosphorus", "remark": "(red, nonstd state)", "c": 21.19}, {"number": 16, "abbr": "S", "full_name": "sulfur", "remark": "(rhombic)", "c": 22.75}, {"number": 16, "abbr": "S", "full_name": "sulfur", "remark": "(monoclinic, nonstd state)", "c": 23.23}, {"number": 17, "abbr": "Cl", "full_name": "chlorine", "remark": "(Cl 2 gas)", "c": 33.949}, {"number": 18, "abbr": "Ar", "full_name": "argon", "remark": "(gas)", "c": 20.786}, {"number": 19, "abbr": "K", "full_name": "potassium", "remark": "", "c": 29.6}, {"number": 20, "abbr": "Ca", "full_name": "calcium", "remark": "", "c": 25.929}, {"number": 21, "abbr": "Sc", "full_name": "scandium", "remark": "", "c": 25.52}, {"number": 22, "abbr": "Ti", "full_name": "titanium", "remark": "", "c": 25.06}, {"number": 23, "abbr": "V", "full_name": "vanadium", "remark": "", "c": 24.89}, {"number": 24, "abbr": "Cr", "full_name": "chromium", "remark": "", "c": 23.35}, {"number": 25, "abbr": "Mn", "full_name": "manganese", "remark": "", "c": 26.32}, {"number": 26, "abbr": "Fe", "full_name": "iron", "remark": "(alpha)", "c": 25.1}, {"number": 27, "abbr": "Co", "full_name": "cobalt", "remark": "", "c": 24.81}, {"number": 28, "abbr": "Ni", "full_name": "nickel", "remark": "", "c": 26.07}, {"number": 29, "abbr": "Cu", "full_name": "copper", "remark": "", "c": 24.44}, {"number": 30, "abbr": "Zn", "full_name": "zinc", "remark": "", "c": 25.39}, {"number": 31, "abbr": "Ga", "full_name": "gallium", "remark": "", "c": 25.86}, {"number": 32, "abbr": "Ge", "full_name": "germanium", "remark": "", "c": 23.222}, {"number": 33, "abbr": "As", "full_name": "arsenic", "remark": "(alpha, gray)", "c": 24.64}, {"number": 34, "abbr": "Se", "full_name": "selenium", "remark": "(hexagonal)", "c": 25.363}, {"number": 35, "abbr": "Br", "full_name": "bromine", "remark": "", "c": 75.69}, {"number": 36, "abbr": "Kr", "full_name": "krypton", "remark": "(gas)", "c": 20.786}, {"number": 37, "abbr": "Rb", "full_name": "rubidium", "remark": "", "c": 31.06}, {"number": 38, "abbr": "Sr", "full_name": "strontium", "remark": "", "c": 26.4}, {"number": 39, "abbr": "Y", "full_name": "yttrium", "remark": "", "c": 26.53}, {"number": 40, "abbr": "Zr", "full_name": "zirconium", "remark": "", "c": 25.36}, {"number": 41, "abbr": "Nb", "full_name": "niobium", "remark": "", "c": 24.6}, {"number": 42, "abbr": "Mo", "full_name": "molybdenum", "remark": "", "c": 24.06}, {"number": 43, "abbr": "Tc", "full_name": "technetium", "remark": "", "c": 24.27}, {"number": 44, "abbr": "Ru", "full_name": "ruthenium", "remark": "", "c": 24.06}, {"number": 45, "abbr": "Rh", "full_name": "rhodium", "remark": "", "c": 24.98}, {"number": 46, "abbr": "Pd", "full_name": "palladium", "remark": "", "c": 25.98}, {"number": 47, "abbr": "Ag", "full_name": "silver", "remark": "", "c": 25.35}, {"number": 48, "abbr": "Cd", "full_name": "cadmium", "remark": "", "c": 26.02}, {"number": 49, "abbr": "In", "full_name": "indium", "remark": "", "c": 26.74}, {"number": 50, "abbr": "Sn", "full_name": "tin", "remark": "(white)", "c": 27.112}, {"number": 50, "abbr": "Sn", "full_name": "tin", "remark": "(gray, nonstd state)", "c": 25.77}, {"number": 51, "abbr": "Sb", "full_name": "antimony", "remark": "", "c": 25.23}, {"number": 52, "abbr": "Te", "full_name": "tellurium", "remark": "", "c": 25.73}, {"number": 53, "abbr": "I", "full_name": "iodine", "remark": "", "c": 54.44}, {"number": 54, "abbr": "Xe", "full_name": "xenon", "remark": "(gas)", "c": 20.786}, {"number": 55, "abbr": "Cs", "full_name": "caesium", "remark": "", "c": 32.21}, {"number": 56, "abbr": "Ba", "full_name": "barium", "remark": "", "c": 28.07}, {"number": 57, "abbr": "La", "full_name": "lanthanum", "remark": "", "c": 27.11}, {"number": 58, "abbr": "Ce", "full_name": "cerium", "remark": "(gamma, fcc)", "c": 26.94}, {"number": 59, "abbr": "Pr", "full_name": "praseodymium", "remark": "", "c": 27.2}, {"number": 60, "abbr": "Nd", "full_name": "neodymium", "remark": "", "c": 27.45}, {"number": 62, "abbr": "Sm", "full_name": "samarium", "remark": "", "c": 29.54}, {"number": 63, "abbr": "Eu", "full_name": "europium", "remark": "", "c": 27.66}, {"number": 64, "abbr": "Gd", "full_name": "gadolinium", "remark": "", "c": 37.03}, {"number": 65, "abbr": "Tb", "full_name": "terbium", "remark": "", "c": 28.91}, {"number": 66, "abbr": "Dy", "full_name": "dysprosium", "remark": "", "c": 27.7}, {"number": 67, "abbr": "Ho", "full_name": "holmium", "remark": "", "c": 27.15}, {"number": 68, "abbr": "Er", "full_name": "erbium", "remark": "", "c": 28.12}, {"number": 69, "abbr": "Tm", "full_name": "thulium", "remark": "", "c": 27.03}, {"number": 70, "abbr": "Yb", "full_name": "ytterbium", "remark": "", "c": 26.74}, {"number": 71, "abbr": "Lu", "full_name": "lutetium", "remark": "", "c": 26.86}, {"number": 72, "abbr": "Hf", "full_name": "hafnium", "remark": "(hexagonal)", "c": 25.73}, {"number": 73, "abbr": "Ta", "full_name": "tantalum", "remark": "", "c": 25.36}, {"number": 74, "abbr": "W", "full_name": "tungsten", "remark": "", "c": 24.27}, {"number": 75, "abbr": "Re", "full_name": "rhenium", "remark": "", "c": 25.48}, {"number": 76, "abbr": "Os", "full_name": "osmium", "remark": "", "c": 24.7}, {"number": 77, "abbr": "Ir", "full_name": "iridium", "remark": "", "c": 25.1}, {"number": 78, "abbr": "Pt", "full_name": "platinum", "remark": "", "c": 25.86}, {"number": 79, "abbr": "Au", "full_name": "gold", "remark": "", "c": 25.418}, {"number": 80, "abbr": "Hg", "full_name": "mercury", "remark": "(liquid)", "c": 27.983}, {"number": 81, "abbr": "Tl", "full_name": "thallium", "remark": "", "c": 26.32}, {"number": 82, "abbr": "Pb", "full_name": "lead", "remark": "", "c": 26.65}, {"number": 83, "abbr": "Bi", "full_name": "bismuth", "remark": "", "c": 25.52}, {"number": 84, "abbr": "Po", "full_name": "polonium", "remark": "", "c": 26.4}, {"number": 86, "abbr": "Rn", "full_name": "radon", "remark": "(gas)", "c": 20.786}, {"number": 87, "abbr": "Fr", "full_name": "francium", "remark": "", "c": 31.8}, {"number": 89, "abbr": "Ac", "full_name": "actinium", "remark": "", "c": 27.2}, {"number": 90, "abbr": "Th", "full_name": "thorium", "remark": "", "c": 26.23}, {"number": 92, "abbr": "U", "full_name": "uranium", "remark": "", "c": 27.665}, {"number": 93, "abbr": "Np", "full_name": "neptunium", "remark": "", "c": 29.46}, {"number": 94, "abbr": "Pu", "full_name": "plutonium", "remark": "", "c": 35.5}, {"number": 95, "abbr": "Am", "full_name": "americium", "remark": "", "c": 62.7}]
\ No newline at end of file

docs/code/scrape_wiki.py

+# -*- coding: utf-8 -*-
+# ---
+# jupyter:
+#   jupytext:
+#     text_representation:
+#       extension: .py
+#       format_name: light
+#       format_version: '1.3'
+#       jupytext_version: 0.8.6
+#   kernelspec:
+#     display_name: Python 3
+#     language: python
+#     name: python3
+# ---
+
+# +
+from pathlib import Path
+import json
+
+import wikitables
+
+raw, = wikitables.import_tables('Heat capacities of the elements (data page)')
+
+# +
+elements = []
+for index, row in enumerate(raw.rows):
+    if not row[''].value.startswith('<'):
+        continue
+    description = row[''].value
+    description = description[description.index('>') + 2:]
+    c = raw.rows[index+1]['J/(mol·K)'].value
+    if not isinstance(c, float):
+        c = float(c.split()[-1])
+    number, abbr, full_name, *remark = description.split()
+    element = {
+        'number': int(number),
+        'abbr': abbr,
+        'full_name': full_name,
+        'remark': ' '.join(remark),
+        'c': c,
+    }
+    elements.append(element)
+    
+Path('elements.json').write_text(json.dumps(elements))

docs/common.py

+./code/common.py
\ No newline at end of file