Mössbauer Effect in Some Polyatomic Crystals

Abstract

AbstractExpressions are obtained for the probability of the Mössbauer effect and the thermal shift in the energy of a γ‐photon for binary crystalline compounds ABr−1. These compounds include crystals of the type NaCl or CsCl, crystals of completely ordered alloys (AuCu3, AlFe3 etc.), and monatomic crystals with isolated impurity atoms. It is assumed that the force constants depend only on the differences of the position vectors of the atoms. The treatment includes the two cases in which nucleus A or nucleus B is resonant. The case in which atom A (mass M0) and atom B (mass M) differ considerably in mass is analysed in greater detail. For M0/M ≪ 1 or M0/M ≫ 1 the fraction e of recoilless emissions (or absorptions) of γ‐rays by atom A and the thermal shift δE0 are independent of M0/M for given interatomic forces. Values of these quantities are hence determined by the appropriate limiting expressions (M0 = const, M → ∞ or M → 0). Thus the finite Mössbauer effect for an atoms surrounded by light atoms is independent of the mass of the latter. In addition there exists a limit to the gain in the probability of the Mössbauer effect and in the thermal shift for an atom which can be obtained by surrounding it with increasingly heavier atoms. It is also shown that the probability of the effect and the thermal shift for the atoms A, for the given interactions, are essentially independent of r. The quasiclassical expansions of Zj and δEj, for the j‐th atom in a unit cell, are obtained for more complicated compounds of the type A A … A (r1 + r2 + … rn = r) by the method of moments.