Sodium chloride has a Debye temperature

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

\Theta_D=321\,\mathrm{K}

. The Umklapp threshold argument gives the freeze-out factor

e^{-\Theta_D/bT}

, but the numerical prefactor

b

in the threshold energy

k_B\Theta_D/b

is only known to be of order

2

. ((a)) Estimate the factor by which the Umklapp rate falls between

300\,\mathrm{K}

and

100\,\mathrm{K}

, taking

b=2

. ((b)) Repeat, taking

b=3

. ((c)) State by what factor the two estimates in (a) and (b) differ, and comment on what this tells you about quoting an Umklapp freeze-out factor without stating

b

Browse the problem library