On the theory of interaction potentials in ionic crystals: An application to the thermodynamics of lanthanide type crystals

A rather complete and informative analysis of the intcrmolecular and intramolecular potentials is put forward with reference to the lanthanide type systems, such as Cs₂NaLnF₆, Cs₂NaLnCl ₆, Cs₂NaLnBr₆, Rb2NaLnF6 and Cs ₂KLnF₆ in the Fm3m space group. The current study is focused to the trivalent lanthanide ions, characterized by atomic numbers in the atomic number interval: 57 ≤, Z ≤,71 . A particular situation occurs in both extreme of the series, say for ₅₇La : [₅₄Xe]5d ¹6s² and ₇₁Lu : [₅₄XeJ ₄f¹⁴5d¹6s² , respectively. The La⁺³ ion, behaves as pseudo noble gas whereas Lu⁺³ shows a fully occupied 4f shell. A different situation occurs for the thirteen trivalent lanthanide ions, moving along the series from Ce⁺³ to Yb⁺³, for these ions the 4f shell is not fully occupied and therefore the physical and chemical properties are indeed, somehow challenging and interesting to examine using structural, spectroscopic and theoretical methods and model calculations. In this current research work, we have elaborated some physical models and carried out a substantial amount of calculations, so as to estimate the reticular energy and also, employing a thermodynamic Born-Haber cycle, we have been able to make some sound predictions and numerical estimate of heat of formations for the above series of lanthanide type crystals. The calculated energy values associated with these observables seems to be most reasonable, and these follow the expected trends, as may be anticipated from theoretical and experimental grounds. Both, the advantages and disadvantages of the current model calculations, have been tested against other previous calculations performed. Some convergence tests as well as some master equatiohs are employed 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. Finally but not at last, the most likely sources for improvement are carefully discussed in this work.