Notes

Slide Show

Outline

1	QuantumTheoryPhonons The quantum mechanics of harmonic crystals, Including thermal properties
2	Planck distribution for phonons
3	Typical dispersion curves along general direction in k-space: 2 ion
4	Debye Approximations
5	Comparison of Debye and Einstein Specific Heats
6	Low Temperature Specific Heat of Solid Argon: Debye Theory
7	Low Temp. Specific Heat For Solid Potassium: Electrons+Phonons
8	Wavevector selection rules `Elastic scattering of x-ray photon
9	Inelastic scattering: creation of phonon of wavevector K
10	Absorption of phonon
11	Phonon “Momentum” For most practical purposes phonon acts as if it had momentum hK
12	Thermal Expansion of Crystals There is no thermal expansion if one considers only the harmonic crystal. It is possible to understand thermal expansion, however, by taking into account the effect of anharmonic terms in the potential energy on the mean separation of a pair of atoms at a temperature T
13	Anharmonic potential energy Consider as the potential energy of the atoms at a displacement x from their equilibrium separation
14	Average displacement We use statistical physics to calculate the average displacement (thermal expansion). The probability of finding a given energy U(x) is just the Boltzmann distribution function, so
15	Evaluation of numerator and denominator With this approximation we can evaluate both the numerator and denominator:
16	Thermal Expansion in Classical Region
17	Lattice constant of solid argon as function of temperature