A crystal contains point defects

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Lattice dynamics and thermal properties of solids

Thermal Physics, Ch Two-level systems, paramagnets and the Einstein solid

Problem

A crystal contains point defects. Each defect can sit in only two states: a ground state, taken as zero energy, and one excited state of energy

\varepsilon

with

\varepsilon/k_B = 600\,\mathrm{K}

. The defects are weakly coupled to the lattice, which acts as a reservoir at temperature

T

. ((a)) For

T = 300\,\mathrm{K}

, find the heat capacity of one defect, as a multiple of

k_B

and in

\mathrm{J\,K^{-1}}

. ((b)) A sample of silver is described by the Einstein model with

\theta_E = 215\,\mathrm{K}

. Find

C_V/3Nk_B

300\,\mathrm{K}

and say whether silver sits on the Dulong-Petit plateau to within

5

per cent. Count only the lattice vibrations.

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