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Solid state physics
lectures
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a571e85c
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a571e85c
authored
5 years ago
by
T. van der Sar
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Update 1_einstein_model.md typo
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@@ -332,10 +332,10 @@ ax.set_ylim((0, 3));
## Conclusions
1.
The law of Dulong–Petit is an observation that all materials have $C≈3k_B$ per atom.
2.
Oscillations of atoms are
*quantum*
, and they
*freeze out*
when $k_BT
\l
l
\h
bar
\o
mega_0$, leaving only zero-point motion
.
3.
The
Einstein model describes each atom in a solid as a quantum harmonic oscillator
.
2.
The Einstein model describes each atom in a solid as a quantum harmonic oscillator
.
3.
The
refore, oscillations of atoms are
*quantum*
, and they
*freeze out*
when $k_BT
\l
l
\h
bar
\o
mega_0$, leaving only zero-point motion
.
4.
Using the Bose–Einstein distribution, we derived the thermal energy and heat capacity per atom in the Einstein model.
5.
The Ei
s
ntein model correctly predicts that the heat capacity drops to 0 as $T
\r
ightarrow 0$.
5.
The Ein
s
tein model correctly predicts that the heat capacity drops to 0 as $T
\r
ightarrow 0$.
## Exercises
...
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