Cluster centers in forsterite laser crystals Mg$_2$SiO$_4$ : Cr and Mg$_2$SiO$_4$ : Cr : Li

The structures of chromium-containing cluster centers in forsterite laser crystals Mg$_2$SiO$_4$ : Cr and Mg$_2$SiO$_4$ : Cr : Li have been simulated using the interatomic potential method. A system of position-dependent parameters of interatomic interaction potentials in forsterite has been developed. In the ionic approximation, this system adequately describes the structure, properties, and defects of the crystal with correct representation of the preferred positional arrangement of chromium ions. The preferred mechanisms of chromium dissolution in forsterite crystals have been evaluated from a comparison of the energies of formation of chromium-containing clusters with different configurations. It has been demonstrated that the results of the simulation of interatomic interaction potentials are consistent with the experimental data obtained from electron paramagnetic resonance and optical spectroscopy studies.