Abstract:

The linear programming and the least-squares approximation algorithms for estimating phase proportions in the Phase Mixing Equation (PME), in basis of the mass balance principle, were reviewed in detail by several typical applications, including modal analysis of mineral raw materials and crystalline rocks, estimation of the end members in mineral solid solutions, burden calculations of multi-component silicate ceramics, and calculations of the phase proportions in silicate ceramic products. The data as-resolved are bases for classifying crystalline rocks and industrial rocks, for improving preprocessing techniques of mineral raw materials, and also for thermodynamic analysis of materials processes at high temperatures to approach chemical equilibrium in silicate systems. The accumulated uncertainties in various analytical data must be kept in mind during the Phase Mixing Calculation (PMC) in practice. Both of phase proportions and compositions of mineral solid solutions could be optionally approximated, based upon the principle of mineral crystal chemistry, the law of mineral paragenetic assemblage, and the priority of partitioning of minor components into the solid solution phases.

Key words: mineral materials, silicate, mass balance, phase mixing equation, linear programming, least-squares approximation