The possibility of writing the repulsive energy in the Born model of binary ionic crystals as a sum of two separate contributions from the two ions has been investigated. Such an approach leads to two identities, one connecting the lattice spacings of a family of ionic crystals and the other connecting their compressibilities. These identities have been tested on the alkali halide crystals over a range of pressures. The agreement is found to be quite satisfactory. Some further predictions with respect to crystals which exist as two polymorphs have also been tested. In all cases, the deviations of the experimental values from the exact identities can be traced to the fact that second neighbour repulsions in the crystals have been neglected. It is hence concluded that individual compressive energies for ions in ionic crystals is a very attractive possibility.

Ionic radii and compressibilities have been calculated for a number of monovalent and divalent ions and radicals on the basis of the compressible ion theory. In this theory, the compression energy of an ion is given as a two-parameter function of its radius,A exp (−r/p), the radius and compressibility of the ion being monotonically decreasing functions of the compressing force acting on it. Choosing a standard force reflecting the average environment in the alkali halides, univalent radii and compressibilities have been calculated. This is the first theory to estimate ionic compressibilities. The values show systematic trends among groups of related ions. Anions are found to be significantly more compressible than cations (e.g., the compressibilities of Ca⁺⁺, K⁺, Cl⁻ and S^{− −} are respectively 0.8530, 1.342, 2.952 and 5.150 × 10⁻¹² cm²/ dyne). Multivalent or ‘crystal’ radii and compressibilities have also been calculated by scaling the standard force by the square of the ionic charge. The calculated ionic radii are closer to experimental values than the classical empirical radii.

The problem of the relative stability of ionic structures is still unsolved current semi-empirical theories wrongly predict the caesium halides to have the NaCl structure. We point out here that these theories also predict some of the other alkali halides to occur in cubic ZnS structure. To understand these discrepancies, we study the effect of various interactions (such as second neighbour repulsion, van der Waals interaction and differences in ionic compressibilities) on the relative stability of simple structures. The results throw into question the radius ratio approach. It is suggested that one could allow for the presence of three-body interactions by relaxing the requirement that the repulsion interaction should be strictly proportional to the number of neighbours. Such an approach might explain the relative stability of simple ionic structures.

Ions in ionic crystals are considered to exist in compressible space-filling polyhedral cells analogous to the Wigner-Seitz cell in metals. Repulsion arises from the compression energy of the ions written as a surface integral over the ionic cells. Two adjustable parameters are introduced per ion with the provision that the same parameters can be used in any crystal of any structure in which the ion occurs. The 18 parameters for the 5 alkali and 4 halogen ions have been determined from PV data on the 20 alkali halides. The important successes of the theory are: (i) All the twenty alkali halides are correctly predicted to occur in their observed structures (ii) The thermal transition in CsCl is explained (iii) The pressure transitions in the alkali halides are predicted well (iv) The calculated values of the variation of transition pressures with temperature agree well with experiment. These results are much better than those obtained by earlier theories.

A simple theory is developed which shows that the regions of stability of the CsCl, NaCl and ZnS structures can be demarcated in a two-dimensional plot of the radius ratio versus the strength of the van der Waals interaction. There is good agreement with experiment. The effect of pressure on these structures is explained qualitatively. The increased occurrence of the ZnS structure and the decreased stability of the CsCl structure in the A²⁺ B²⁻ crystals compared to the A⁺B⁻ crystals is also explained. Finally it is shown that the radius ratio and the polarizabilities of the ions are the important factors that determine the structures of AB₂ crystals.

It is suggested that the radio astronomical technique of image reconstruction calledclean could be profitably used in crystallography to improve sharpened Patterson maps andE-maps. The method is here generalized to handle the symmetries which arise in crystallographic maps. Simulations on model one and two dimensional structure are presented to illustrate the power of the method.

The thermal properties of ionic crystals are analysed using the variational principle of classical statistical mechanics. The Einstein and Debye pictures of the lattice vibrations are adopted as trial Hamiltonians. No explicit calculation of the lattice spectrum is needed. The variational result for the thermal expansion in the Einstein picture is identical to that recently derived by Narayan and Ramaseshan by a physically motivated thermal force picture. The agreement with experimental values in the alkali halide family of crystals is surprisingly good, the root mean square error being about 14%. The parameters in the interionic potential used are obtained from the lattice spacings and compressibilities of the crystals and not from anharmonic properties. The Debye picture gives about equally good results for the thermal expansion, but better results for the thermal vibration amplitudes of the ions. It differs from the Einstein picture in incorporating correlated vibrations of atoms and in having an explicit Coulomb contribution to the thermal properties. It is suggested that the theory given in this paper has a useful role to play in studies of thermal expansion and phase stability for large families of ionic crystals when combined with semi-empirical theories.

The divalent ions in alkaline earth chalcogenides are viewed as compressible objects and are treated within a purely ionic model. As in earlier studies on the alkali and ammonium halides, the ions are taken to be in the form of space-filling polyhedral cells and the compression energy, which is the source of repulsion, is written as a surface integral over the cell faces. A simple method of computing the repulsion energy in any crystal lattice of arbitrary symmetry is proposed and the repulsion parametersB andσ are refined for the divalent ions under study. The theory explains the predominant occurrence of the NaCl structure in the alkaline earth chalcogenides. Hard sphere radii are estimated for the tetravalent cations Ti⁴⁺, Sn⁴⁺ and Pb⁴⁺ using the repulsion parameters of O²⁻ ion and the data on the corresponding rutile structure oxides. These radii are seen to be consistent with the measured interionic distances in several compounds occurring in the perovskite structure. The free transfer of repulsion parameters among several structures, which is a key feature of the present approach to repulsion, is confirmed to be valid by the present study.