MAXWELL-BOLTZMANN DISTRIBUTION OF M2+ . VACANCY PAIRS IN COMPENSATED FCC LATTICE

Coulomb interactions in the face-centered cubic (fcc) lattice are exemplified by the interactions of M2+ impurity ions with their charge compensation vacancies in alkali halides. At low temperatures and high dilution, the canonical ensemble partition function leads to a Maxwell-Boltzmann distribution in the distance of separations of the M2+: vacancy pairs, which can be calculated in terms of the geometric restrictions of the fcc lattice. The most predominant pairs, in the order of their relative importance, are C4v (2,0,0), Cs (2,1,1,), C2v (1,1,0), C2v (2,2,0), Cs (3,1,0), C1 (3,2,1), C3v (2,2,2), and C4v (4,0,0). The calculated distribution is compared with optical Zeeman and spin-resonance spectroscopic observations in the KCl: Sm2+ and KCl: Mn2+ systems. © 1969 The American Physical Society.