Thermodynamics, Statistical Physics, and Quantum Mechanics

226 SOLUTIONS

4.98 Schottky Defects (Michigan State, MIT)

WhenNatoms are displaced to thesurface, they leave thesamenumber

of vacancies. Nowthere areNvacancies and atoms in lattice

points. Theentropy asa function ofNis

where we have used Stirling’s formula

The freeenergy may bewritten

The minimum of thefreeenergy can befound to be

or

general, but since and thenumber ofdefects it can

Since we have

which iswhat onewould expect.

4.99 Frenkel Defects (Colorado, MIT)

We assumethat the number ofdefectscreatedaround one latticesite does
not affect theprocess ofcreating new defects. In otherwords, all configu-
rations of thesystem areindependent(not a very realisticassumption in