Irrelevance of atomic masses for Debye-Waller B values in the limit of high temperatures

An expression that approximates Debye-Waller B values by a sum of three terms is derived from the theory of lattice dynamics in the harmonic approximation. For cubic crystals (M is the mass of the th atom in the unit cell): B = T + 22h2/3k TM + /M2T3, where T D/2 and and are constants, depending on interatomic forces only. It is shown that for temperatures above the Debye temperature D of the lattice, the second and third terms in the above expression can be neglected. From this, it follows that above the Debye temperature Debye-Waller B values become independent of the atomic masses. Consequently, the heavier atoms in a lattice do not necessarily have the smaller B values.