The Estimation of Elastic Properties from Analogue Compounds

Summary The concept of isostructural compounds as elastic analogues is extended to include some new correlations involving the bulk modulus, K, the shear modulus, p, and their pressure derivatives, K and p', and these are combined here with some previously demonstrated correlations. For many simple compounds, K correlates with the mole atomic volume, V, according to the well-known relation KV" = C,, where C1 is a constant characteristic of crystal structure, and n is usually about 1. An analogous relation, pV" = Cz, is shown here to be an equally accurate approximation. C2 is again characteristic of crystal structure and m is usually about $. Some exceptions are related to the presence of transition metal ions, and possibly to magneto-elastic coupling and non-stoichiometry. These relations are poorer approximations for more complex compounds. Much of the irregularity can be attributed either to the presence of more than one dominant bond type or to the presence of transition metal ions and associated effects. For complex compounds, an alternative correlation, previously demonstrated, is updated and refined using the above insights into simple compound properties: the ratios of elastic velocities and density of a compound to those of its isochemical mixture of simple compounds are characteristic of the crystal structure of the compound. The behaviour of the dimensionless derivatives (8 In K/8 In P)~ = K' and (8 In p/ula In P)~ = Kp'/p is examined. Kp'/p decreases rapidly with increasing cation size in isostructural series, and increases with increasing co-ordination number. K' is remarkably constant for alkali halides, but irregularly variable for oxides and silicates. Much of this irregularity may be due to experimental inaccuracies.