Search Results (2)

Apatites are very important compounds of mineralogical and biological meaning. Apatites originated from the calcium hydroxy compound 3Ca₃(PO₄)₂·Ca(OH)₂ and potentially might form three series of isomorphic salts, derived from cationic substitutions in the positions of Ca(I) and Ca(II) ions in the core compound; anionic substitutions of phosphates; and substitutions of anions and very simple chemical entities instead of the hydroxyl group in channel locations. The energies coupled with the ion exchanges inside those three locations were studied using our original method resulting from the transformation of Braggs’ law. The energy changes resulting from the ion exchanges were studied in connection with either the ionic radii for the cations or ionic volumes for the anions. The same series were observed when the variabilities of energy were confronted with the variabilities in the sinus of diffraction angle Θ showing changes in momentum transfer. In particular, the relationships between the energy changes and the coupled changes in the universal crystallographic parameter d showed the surprising uniformity of all ion exchanges in the apatites. The incremental change in the Braggs’ d-parameter always demands the same change in the energy, with good approximation, independently of the location of the ion exchange. So, the isomorphism of the apatites is not triple but a uniform one at the energy level. Such an approach enables the estimation of the volume of the ion-□ (□-vacancies) agglomerates. The introduction of ions with greater volumes exerts the phenomenon of swelling of apatite cells, which can be quantitatively estimated. The dependence of diffraction spectra on the temperature allows for the determination of minimal values of crystallographic cell volumes and d parameters at the temperature of 0 K. In sum, the study of energies connected with the change of Bragg dimension d is a new and valuable method of insight into the behaviour of apatite crystals. Full article

The introduction of the notion of energy change resulting from the ion exchange in apatites leads to the question: how can some simple isomorphic series be described using the mentioned idea? We concentrated on the simple isomorphic series of compounds: apatite, bioapatite, calcite, aragonite, celestine, K-, Zn- and Cu-Tutton’s salts. It was demonstrated in all the series, except Tutton’s salts, that the change in energy and the change in the crystal cell volume are, in a simple way, dependent on the change in the ionic radii of the introduced ions. The linear relationships between the variations in energy and in the universal crystallographic dimension d were derived from the earlier equations and proven based on available data. In many cases, except the Tutton’s salts, linear dependence was discovered between the change in energy and the sinus of universal angle Θ, corresponding to the change in momentum transfer. In the same cases, linear dependencies were observed between the energy changes and the changes in the volumes of crystallographic cells, and mutually between changes in the crystallographic cell volume V, crystallographic dimension d, and diffraction angle Θ. Full article