Aluminium has a single mode Gruneisen parameter (its three acoustic branches

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

Solid State Physics, Ch Anharmonicity: expansion, phonon lifetimes and thermal conductivity

Problem

Aluminium has a single mode Gruneisen parameter γG=2.17\gamma_G=2.17 (its three acoustic branches, the only ones a monatomic fcc crystal has, have similar γi\gamma_i, so the single-parameter relation applies). At 300 K300\,\mathrm{K} its measured molar heat capacity is CV=23.1 J mol−1K−1C_V=23.1\,\mathrm{J\,mol^{-1}K^{-1}}, its isothermal bulk modulus is BT=76 GPaB_T=76\,\mathrm{GPa} and its molar volume is Vm=9.99 cm3 mol−1V_m=9.99\,\mathrm{cm^3\,mol^{-1}}. ((a)) Use α=γGCV/(3BTVm)\alpha=\gamma_G C_V/(3B_TV_m) to predict aluminium's linear thermal expansion coefficient at 300 K300\,\mathrm{K}. ((b)) The measured value at 300 K300\,\mathrm{K} is 23.4×10−6 K−123.4\times10^{-6}\,\mathrm{K^{-1}}. State the percentage difference between the prediction and the measured value.

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