Mean-square atomic displacements in f.c.c. crystals

The mean-square displacements of volume atoms, surface atoms and atoms near a vacancy are calculated for f.c.c. metals and rare gas solids, using a simple series expansion of the Wallis formula. We employ a model with rotationally invariant bond bending forces, unlike the de Launay model used by Masri and Dobrzynski. For atoms near a vacancy and for rare gas solids this method has been applied for the first time. The calculations are done to the R⁴ term in the expansion. The inclusion of the R⁴ term together with temperature-dependent elastic constants give results which are in better agreement with experiment. For rare gas solids Lindemann ratios calculated by this method agree closely with the values obtained from elaborate computations as well as those deduced from entropy data. The present calculation also supports the view that the melting of solids is initiated at the crystal surfaces and in the neighbourhood of vacancies.