Update 2_debye_model.md - polish

src/2_debye_model.md

@@ -41,8 +41,9 @@ _(based on chapter 2.2 of the book)_
     After this lecture you will be able to:
 
     - Describe the concept of reciprocal space and allowed momenta
-    - Write down the total energy of phonons given the temperature and the dispersion relation
-    - Estimate heat capacity due to phonons in high temperature and low temperature regimes of the Debye model
+    - Describe the concept of a dispersion relation
+    - Derive the total number and energy of phonons in an object given the temperature and dispersion relation
+    - Estimate the heat capacity due to phonons in the high- and low-temperature regimes of the Debye model
 
 
 ## Deficiency of the Einstein model
@@ -70,6 +71,8 @@ T_E = fit[0][0]
 fig, ax = pyplot.subplots()
 ax.scatter(T, c)
 ax.plot(temp, c_einstein(temp, T_E), label=f'Einstein model, $T_E={T_E:.5}K$')
+ax.text(T_E, 2, r'$T=T_E$', ha='left', color='r');
+ax.plot([T_E, T_E], [0, 3], 'r--')
 ax.set_ylim(bottom=0, top=3)
 ax.set_xlim(0, 215)
 ax.set_xlabel('$T(K)$')
@@ -95,7 +98,7 @@ Peter Debye (1884 – 1966) suggested to instead consider _normal modes_: sound
 Each normal mode has a _wave vector_ $\mathbf{k}$.
 All wave vectors are points in _reciprocal space_ or _k-space_.
 
-These waves don't have a fixed frequency $\omega_E$, but rather a _dispersion relation_
+These waves don't all have the same frequency $\omega_0$ as the atoms did have in the Einstein model, but rather a _dispersion relation_
 $$
 \omega = v|\mathbf{k}|.
 $$