Aluminium's Debye temperature

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Lattice dynamics and thermal properties of solids · Lattice dynamics and thermal properties of solids

Condensed Matter Physics, Ch Thermal expansion and lattice thermal conductivity

Problem

Aluminium's Debye temperature, found by the method of Chapter 6, is ΘD=428 K\Theta_D = 428\,\mathrm{K}. Using the T3T^3 law CV=1944(T/ΘD)3 J mol−1K−1C_V = 1944(T/\Theta_D)^3\,\mathrm{J\,mol^{-1}K^{-1}} and aluminium's own γG=2.17\gamma_G = 2.17, Bmod=76 GPaB_{\rm mod} = 76\,\mathrm{GPa} and Vm=9.99×10−6 m3 mol−1V_m = 9.99\times10^{-6}\,\mathrm{m^3\,mol^{-1}} (Section 7.3), predict aluminium's linear expansion coefficient at 20 K20\,\mathrm{K}, and say by roughly what factor it is smaller than the room-temperature value of 2.31×10−5 K−12.31\times10^{-5}\,\mathrm{K^{-1}}.

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