A mathematical model of scandium ore deposit formation in liquating magmatic melts

Solidification of liquating silicate magmatic melts may lead to formation of rare earth mineral deposits. By the example of quasi-binary system SiO2–Sc2O3, the processes of cooling and directional solidification of the melt in an intrusive chamber have been studied, and velocities of the phase fronts and the width of the phase separation field have been calculated. Using the fluctuation approach, the physical and mathematical model of the formation and growth of dispersed phase in the continuous cooling of liquating melt was developed, and the conditions of incorporating the dispersed inclusions by solidified matrix phase were determined. The proposed model allows obtaining quantitative estimates of the size and number of inclusions per unit of hardened rock, depending on the solidification conditions and the initial chemical composition of the melt.