ME 381R Lecture 6: Lattice Specific Heat

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ME 381R Lecture 6 Lattice Specific Heat
Dr. Li Shi Department of Mechanical Engineering
The University of Texas at Austin Austin, TX
78712 www.me.utexas.edu/lishi lishi_at_mail.utexas.
edu

• Reading 1-3-2 in Tien et al
• Reference Ch5 in Kittel

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Density of Phonon States in 1D
A linear chain of N10 atoms with two ends
jointed
a
Only N wavevectors (K) are allowed (one per
mobile atom)
K -8p/L -6p/L -4p/L -2p/L 0
2p/L 4p/L 6p/L 8p/L p/aNp/L
Only 1 K state lies within a DK interval of
2p/L of states between K and K dK is
(L/2p)dK of K-vibrational modes between w and
wdw
D(w) density of states
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Density of States in 3D
N3 of atoms
Kz
Ky
Kx
2p/L
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Lattice Specific Heat
p polarization(LA,TA, LO, TO) K wave vector
Dispersion Relation
Energy Density
Lattice Specific Heat
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Debye Model
Debye Approximation
Debye Density of States
Number of Atoms
Debye cut-off Wave Vector
Debye Temperature K
Debye Cut-off Freq.
Debye Temperature
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Lattice Specific Heat
Energy Density
Specific Heat
When T ltlt qD,
Classical Regime
Quantum Regime