Theory of divalent ions in crystals

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.     

Simple variational approach to the thermal properties of ionic crystals

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.     

Repulsion parameters of ions and radicals—Application to perovskite structures

The compressible ion approach to repulsion which has been shown to work well for the alkali halides (J. Phys. Chem. Solids37, 395 (1976) ; Curr. Sci. 46, 359 (1977)) has been extended to other cubic ionic crystals. Repulsion parameters have been refined for a number of ions and radicals viz., Cu⁺, Ag⁺, Tl⁺, Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺, Zn²⁺, Cd²⁺, Hg²⁺, Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, Sm²⁺, Eu²⁺, Yb²⁺, Pb²⁺, H^?, O^2?, S^2?, Se^2?, Te^2?, NH₄⁺, SH^?, SeH^?, BrO₃^?, ClO₃^?, ClO₄^?, CN^?, NH₂^?, NO₃^?, BH₄^?, BF₄^?, SO₄^2?, NH^2?. Using these parameters, calculations have been made on the lattice spacings and compressibilities of a number of perovskite-like crystals of the form A⁺B²⁺C₃^?. The predicted values agree well with experiment. In the case of four crystals viz., LiBaF₃, LiBaH₃, LiEuH₃ and LiSrH₃, there were large discrepancies between the calculated and observed lattice spacings. When these crystals were assumed to be of the inverse perovskite structure, calculations showed good agreement with the experimental data.     

Production ofψ particles in N-N collisions and largeP T phenomenon

We calculate the yield ofψ (3105) particles in N-N collisions in a model which associates the production of heavy particles with largeP _T phenomenon. Our results show thatψ (3105) has a fairly strong coupling to other hadrons. We propose a criterion in the search for charmed particles and a parametrization for the expected yields of such particles.     

An explanation of the beam dump experiment

The production of prompt neutrinos in the beam dump experiment is explained in a cluster model, by postulating the emission of strange clusters in hadron collisions, besides the usual non-strange clusters. The low mass strange clusters can decay only by the weak interaction. The leptonic and semi-leptonic decay modes of these clusters give rise to prompt neutrinos. A prediction of the model is that the ratios <v _e>/π ⁺ at PS energies would be the same as SPS energies.