9780030839931, Chapter 30, Problem 1P

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Chapter 30, Problem 1P Problem Phonon Correction to the Density of Vacancies A more accurate treatment of the equilibrium number of vacancies in a monatomic Bravais lattice would multiply (30.11) by a phonon correctsion (see (30.9)): n = (30.29) Make a simple Einstein theory of the normal modes of the crystal with vacancies, i.e., treat each ion as an independent oscillator, but let the oscillator frequency be either or according to whether the ion has or does not have one of its (z) nearest neighboring sites vacant. Show that in this model (30.29) becomes: n = (30.30) Since