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_κ is the mass of the κth atom in the unit cell): B_κ = α_κ T + 2π²h²/3k TM_κ + γ_κ/M²T³, where T ≲ Θ_D/2 and α_κ and γ_κ are constants, depending on interatomic forces only. It is shown that for temperatures above the Debye temperature Θ_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.