Hard-sphere random-packing model for an ionic glass: Yttrium iron garnet

A computer model for amorphous yttrium iron garnet has been constructed using a modification of a method pioneered by Bennett involving the sequential addition of hard spheres. The method is embellished to allow for the presence of local electrostatic forces which are assumed to keep neighboring ions of like charge as far apart as the basic building algorithm will allow. This distance (between ion centers), for amorphous YIG, is $d=2.4$ {}. The electric-field-gradient distribution at the iron sites is calculated in a point-charge approximation and provides an excellent interpretation of the observed M\"ossbauer quadrupole line shape in the paramagnetic phase. Ion-pair correlation densities out to a range of 10 {} have been computed for all combinations of the constituent species. Finally the distribution of iron-oxygen-iron bond angles is computed and from this, via superexchange theory, a qualitative knowledge of the exchange distribution is obtained. This suggests that the magnetic properties of vitreous YIG may resemble those of a dilute antiferromagnet near its critical concentration.