Analysis of Combination Rules for Elastic Constants of Mixed Ionic Crystals

Abstract

Various combination rules, proposed so far, for predicting the elastic constants of mixed ionic crystals are critically examined. The mathematical forms of different combination rules are derived, and the numerical results estimated from them are compared with one another. It is found that although the mathematical forms of the combination rules appear to be different from each other the numerical results obtained from them are closer to each other.Verschiedene bisher vorgeschlagene Kombinationsregeln zur Vorhersage der elastischen Konstanten von Ionenmischkristallen werden kritisch untersucht. Die mathematisohen Formen von verschiedenen Kombinationsregeln werden abgeleitet und die numerischen Ergebnisse, die aus ihnen berechnet werden, werden miteinander verglichen. Es wird gefunden, dalJ, obwohl die mathematischen Formen der Kombinationsregeln unterschiedlich untereinander zu sein scheinen, die erhaltenen numerischen Ergebnisse aus ihnen einander naher sind.(2) Khandari, Agra (U.P.), India. . 132J. SHANKER, R. SINGH, and M. KUMAR It has, however, been pointed out by some workers [a, 91 that the rule given by (1)

Some Aspects of Spinodal Decomposition in Spinel Solid Solutions

“…They are illustrated graphically in Figure 1. The spinodal curves were determined an alytically from (1) and (2) using the elastic constants in Table 2, which have been averaged according to Vegard's law [10], In contrast to our earlier calculations, this time the temperature dependence of the elastic constants and their concomitant effect on the an isotropy has been included [11]. However, the temper ature dependence of the lattice parameter a is ne glected, therefore r] = (öln a/dx)P T is obtained directly from lattice parameter measurements ( Figure 2).…”

“…However, it should be noted that the only well known parameter given in Table 3 is the composition-dependent lattice constant of the spinel solid solution (Figure 1). Furthermore, the resulting strain rj dominates the calculation of Xm owing to the quadratic term in (10). Therefore, the calculation based on the linear theory can explain the experimental results of the early decomposition kinet ics quantitatively.…”