A Calculation Model of the General Theory of Interaction Potentials for Stoichiometric Lanthanide Type Crystals: Applications to the Cs2KLnCl6 System

Abstract

This article aims to develop a generalized model calculation model to be applicable to the general theory of interaction potentials with reference to the stoichiometric elpasolite type crystals. In this study, we have chosen to report both a theoretical model and a calculation strategy to undertake semi empirical calculations of thermodynamic properties, such as reticular energies and heats of formation for the series of systems such as: Cs2KLnCl6. We have also carried out quite a number of calculations for a variety of systems such as: Cs2NaLnF6, Cs2NaLnCl6, Cs2NaLnBr6, Rb2NaLnF6 and Cs2KLnF6 in the Fm3m space group since we aim to check the strengths and weaknesses of our model calculations. We have analyzed a substantial number of approximate theoretical models and have carried a formidable amount of computing simulations to estimate the reticular energies and the corresponding heat of formation for these type of crystal using a semi empirical model. We made use of the thermodynamic cycles of Born-Haber so as to get a broad view with reference to the accuracy of our semi empirical theoretical models. The problem itself is quite challenging since we have focused our attention upon trivalent lanthanide ions in the first inner transition series of the chemical elements: (Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu). There are a significant amount of outstanding research works published in the literature with reference to structural analysis, one photon spectroscopy, vibrionic intensity model calculations and generalized models to deal with these kind of complex crystals. The calculated energy values associated with these observables seems to be most reasonable, and these follow the expected trends, as may be expected on both theoretical and experimental grounds. Both, the advantages and disadvantages of the current model calculations, have been tested against other previous calculations performed for this type of complex systems. It is of a paramount importance, the results obtained and reported in this article with regards to convergence tests as well as some master equations derived to account for the various contributions to the total energy. The Born-Mayer-Buckingham potential is carefully examined with reference to these lanthanide type crystals Cs2KLnCl6. Finally but not at last, the most likely sources for improvement are carefully discussed in this work. We strongly believe that there is enough room for improvement and have therefore initiated a new research program of activities tackling systems of well-known optical and structural properties.