Energetic substantiation of the formation of ytterbium dimers in single forsterite crystals

A structural computer simulation of ytterbium-containing forsterite crystals has been carried out. Atomistic simulation is performed using the GULP 4.1 software package (General Utility Lattice Program). Different mechanisms of ytterbium dissolution in forsterite crystals are considered, and the dissolution energies of isolated defects, as well as charged and neutral clusters of various configurations, are calculated. The results of the calculation manifest that the formation of ytterbium clusters with a magnesium vacancy gives a significant gain in the dissolution energy. The formation of neutral clusters (dimers) in the M1 site М1: (Yb$_{\mathrm{Mg1}}\nu_{\mathrm{Mg1}}$Yb$_{\mathrm{Mg1}})^\times$ leads to an energy reduction by 1.7 eV compared with the statistical distribution of defects. As a result of simulation, it is shown the energetic substantiation of the formation of ytterbium dimers in forsterite crystals. A model of the most energetically favorable center in the M1 site is proposed–a dimer, consisting of a pair of trivalent ytterbium ions with a magnesium vacancy between them, forming a chain parallel to the crystallographic axis $c$.