IONIC MODULI: A NEW SEMI-EMPIRICAL MODEL FOR THE ELASTICITY OF CRYSTALLINE IONIC COMPOUNDS

Compressibility is a fundamental parameter governing the behavior of materials at non-ambient conditions, and modelling this behavior for volumetrically abundant mineral phases is critically important to our understanding of planetary interiors. However, there currently exists no quantitative model explaining the bulk modulus of a material in terms of simpler parameters.

In the spirit of Roebling medalist Nancy Ross’s many contributions to fundamental crystal chemistry at high P-T conditions, this work presents a new semi-empirical model which quantitatively predicts the bulk modulus of crystalline ionic compounds in terms of the compression of constituent ions. The model assumes that ions are elastic spheres which compress reproducibly and independently of their environment, according to a simple first order equation of state with a single parameter, the ionic modulus. These ionic moduli (defined analogously to the bulk modulus) are then combined via a Reuss-style limit to give the bulk modulus of the material. Testing preliminary versions of this model against P-V compression data for the alkali halides reveals that the model correctly predicts the bulk moduli of strongly ionic compounds within 10% error, much better than expected by random statistics (given the number of model parameters). It is also demonstrated that the compressibility of most alkali metal and halide ions are a simple linear function of the zero-pressure ionic radius. The results indicate that electron clouds compress in a largely reproducible fashion according to a simple physical law relating to the radial distribution of electrons.

The model’s differing rates of change in ionic radius as a function of pressure for different ions, combined with Pauling’s radius ratio limits, also enable the prediction of pressure thresholds for increases in coordination number. Thus, the ionic modulus model provides the first ab initio predictions of P-T phase diagrams. Once further developed, this approach may prove invaluable for explaining the systematics of planetary interiors as a function of size and bulk composition.