Special features of the phonon spectrum and non-radiative transitions in the Cr³⁺ -doped ionic-covalent crystals

A new model which describes the peculiarities of the phonon spectra of homo- and heterodesmic crystals is developed in the present paper. A salient feature of the model is that the specific properties of the heterodesmic compounds (existence of large covalent groups) are considered explicitly by inclusion of the corresponding terms into the dynamic equations. Numerical calculations of the phonon spectrum for the model heterodesmic crystal show a large gap (more than two orders of magnitude) between the optical and acoustic branches. Large variations of the non-radiative transition probabilities in doped homo- and heterodesmic crystals are explained by the effective lowering of the phonon state density in the latter case. Application of the model developed to the comparative studies of CeSc₃(BO₃)₄:Cr³⁺ and LiSrAlF₆:Cr³⁺ crystals resulted in good agreement with available literature data.