Emulation of short-range ordering within the Compound Energy Formalism: Application to the calcite-magnesite solid solution

Abstract

Modern thermodynamic assessment studies of multicomponent systems typically employ the Compound Energy Formalism (CEF) to describe phases of variable composition, which may show effects of chemical ordering. In CEF, the ordering is described by splitting a crystallographic site in which several components can substitute for each other into subsites (sublattices) and by allowing fractional occupancies of these subsites to vary. This type of component redistribution over subsites (sublattices) is classified in solid solution theories as long-range order (LRO). A well-known shortcoming of CEF is the absence of a direct description of the effects of short-range order (SRO), which do not involve a redistribution of components between sublattices, but reveal themselves in various modes of clustering. Here we show that SRO can be taken into account within CEF as an additional (fictive) LRO effect driven by an extra negative excess enthalpy term. We argue that the mathematical form of this term should be constrained such that it ensures its vanishing both in low- and high-temperature limits. Including such a term into CEF allows a significant improvement in the description of phase relations in the system of calcite-magnesite, CaCO3-MgCO3. The modified CEF model with SRO emulation is made available in the GEM-Selektor software.