Phonons in solids

1
Phonons in solids
First Brillouin zone
2
Heat capacity
3NkB
T/Q
T3
3
Thermal conductivity
L
S
T1
T2

• Heat transfer is performed by the gas of
  phonons
• Umclapp process creates resistance to heat
  transfer
• ( gradient of temperature inside solid is due to
  
• this resistance)

x
L
V
S1
E
E-
T(x)
x
4
Thermal conductivity
Crystal T, K K,Wcm-1 deg-1 C,Jcm-3 deg-1 L, A Q, K
Quartz 273 0.13 2.00 40
83 0.5 0.55 540
NaCl 273 0.07 1.88 23
83 0.27 1.0 100

• Thermal conductivity of NaF crystal
• at TgtQ thermal conductivity KLT-1
• at TltQ thermal conductivity KCT3

NaF
5
Thermal expansion
Solids increase in volume as their temperature is
raised uniform displacement of all atoms
R0
6
Thermal expansion
Crystal K, 10-6K-1
Cs 97
K 83
Li 45
Ag 20
Ni 13
W 4.5
C(diamond) 1.2