Calculation of the Mössbauer Parameters for a Disordered Cubic Crystal Lattice

A theoretical expression is derived for a cubic crystal lattice disordered by the introduction of a vacancy‐interstitial pair. Considering only the nearest neighbour interaction for the interstitial atom, the double‐time Green's function has been formally calculated and the ratio of the Debye‐Waller factor for the disordered lattice to that of the perfect lattice has been obtained. It is found that in the presence of a point defect pair, the exponent ratio of the disordered lattice to that of the perfect lattice becomes [1 + 4 Γ lk , × { u (−2)−( h /2 kT) u (−1)}] where γ t k is a factor, for which the major contribution comes from the position vector of the interstitial atom and u (2 p ) is the 2 p ‐th moment of the frequency spectrum of a cubic lattice.