Figure by MIT OCW.
Figure by MIT OCW.
Figure by MIT OCW.
Density of states g(w)
ωD
0
g
g
t
v
vml
v
(a)
(b)
Frequency distribution g(v) for crystal. (a) Einstein approximation. (b) Debye approximation.
Figure by MIT OCW.
1
2
3
4
ω/1013 radians s-1
5
The Debye distribution of frequencies, with
the experimental distribution of frequencies
for copper. The distribution is shown as a
function of ω = 2πv. The experimental distribution
is obviously complicated enough that a theory
to reproduce such a distribution would likely
be difficult to produce.
Figure by MIT OCW.
25
Cv, joules/degree.mole
20
15
10
Debye
Einstein
Al θD = 385 K
5
0
0
.4
.8
1.2
1.6
2.0
T/θ
Comparison among the Debye heat capacity, the Einstein heat
capacity, and the actual heat capacity of aluminum.
Figure by MIT OCW.
Cp, J/ mol.K
90
80
NiSe2
9R-
70
60
50
6R-
NaCl
40
30
3R-
Ge
20
10
0
0
50
100
150
200
Temperature, K
250
300
350
Molar heat capacity at constant pressure of
three crystalline nonmetals.
Figure by MIT OCW.
cv /3R
NaCl FeS
2
Rbl
1.0
MgO
0.8
Diamond
0.6
0.4
0.2
0
0
100
200
300
400 500 600
Temperature, K
700
800
900
1000
Temperature variation of cv /3R of nonmetals. (1 mol of diamond, 12mol of Rbl, NaCl,
and MgO; and 1 mol of FeS2.)
3
Figure by MIT OCW.