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Commit 7a9aa772 authored by T. van der Sar's avatar T. van der Sar
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Update 1_einstein_model.md

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......@@ -305,13 +305,13 @@ ax.set_yticks([1])
ax.set_yticklabels(['$k_B$'])
pyplot.hlines([1], 0, 1.5, linestyles='dashed')
draw_classic_axes(ax)
ax.text(1.01, 0.5, r'$k_{\rm B}T = \hbar \omega$', ha='left', color='r');
ax.text(1.01, 0.5, r'$T= T_E= \hbar \omega_0/k_{\rm B}$', ha='left', color='r');
```
The dashed line is the classical value, $k_{\rm B}$.
Shaded area $=\frac{1}{2}\hbar\omega_0$, the zero point energy that cannot be removed through cooling.
This is for just one atom. In order to obtain the heat capacity of a full material, we would have to multiply $C$ (or $\langle E \rangle$) by $3N$, _i.e._ the number of harmonic oscillators according to Einstein model.
This is for just one atom. In order to obtain the heat capacity of a full material, we would have to multiply $C$ (or $\langle E \rangle$) by $3N$, _i.e._ the number of harmonic oscillators according to Einstein model. The plot below shows a fit of the Einstein model to the experimental data for the heat capacity of diamond.
```python
fit = curve_fit(c_einstein, T, c, 1000)
......
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