Two independent quantities for copper at its melting point,

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction

Condensed Matter Physics, Ch Real crystals: vacancies, dislocations and the strength of metals

Problem

1358\ \mathrm{K}

, are both set by a Boltzmann factor

e^{-E/k_BT}

: the equilibrium vacancy fraction (Section 13.2,

\varepsilon_v = 1.28\ \mathrm{eV}

), and, for a vibrational mode of energy quantum

\hbar\omega = 25\ \mathrm{meV}

, the ratio of the population of its first excited level to its ground level,

e^{-\hbar\omega/k_BT}

(Chapter 6). ((a)) Compute the vacancy fraction

n_v

1358\ \mathrm{K}

. ((b)) Compute the oscillator's population ratio at the same temperature. ((c)) Which is larger, and by roughly what factor? Explain in one sentence, in terms of the two energies compared with

k_BT

, why the same mathematical form gives such different-sized answers.

Browse the problem library