Displacement ratios, lattice vibrations

Vibrations in the surface plane, however, will be rather similar to those in the bulk because the coordination in this plane is complete, at least for fee (111) and (100), hep (001) and bcc (110) surfaces. Thus the Debye temperature of a surface is lower than that of the bulk, because the perpendicular lattice vibrations are softer at the surface. A rule of thumb is that the surface Debye temperature varies between about 1/3 and 2/3 of the bulk value (see Table A.2). Also included in this table is the displacement ratio, the ratio of the mean squared displacements of surface and bulk atoms due to the lattice vibrations [1]. 

The lattice-vibration instability model [40, 55-59] extends Lindemann s vibrational-lattice instability criterion [60]. The melting behavior of a nanosolid is related to the ratio (/ ) of the root-mean-square displacement (RMSD, of an atom at the surface to the RMSD of an atom inside a spherical dot. p is a size-independent parameter ... 

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