Phase Equilibria, Phase Diagrams, and Phase Modeling

Abstract

Phase diagrams, phase equilibria data in graphical form, are a standard tool of materials scientists and engineers. Such compilations of data can be indispensable when, for example, there are questions about the thermodynamic stability of a phase under a given set of working conditions, or in a particular operating environment (e.g., materials compatibility issues). The easiest way for a metallurgical engineer to determine whether an aluminum or tungsten vessel would be the best choice as a container for molten zinc is to consult the Al-Zn and W-Zn phase diagrams. In this particular case, the phase diagrams would show that Al-Zn alloy formation would be expected to occur since zinc exhibits an increasing solid solubility in aluminum with temperature, whereas tungsten is much more resistant to corrosion by molten zinc.The solid-state chemist interested in preparing new materials also finds phase diagrams valuable. Strictly speaking, phase diagrams describe the phase relationships within single-component or multicomponent systems in stable thermodynamic equilibrium. Hence, the phase diagram tells us if a given phase in that system will be accessible under those equilibrium conditions (although metastable phases certainly may be obtainable under appropriate circumstances). Even when a stable phase is accessible, control of the stoichiometry may be difficult to achieve due to complex phase equilibria. For example, many transition metals have a propensity to adjust their oxidation state depending on the temperature and oxygen partial pressure, which can result in a multiphase product (impurities) and/or one with mixed valency.It is imperative that one be able to properly interpret phase diagrams. In the first part of this chapter, we review some underlying concepts from thermodynamics necessary for understanding phase equilibria. The interpretation of phase diagrams is subsequently taken up. Afterwards, the reader is introduced to the calculation of phase diagrams (CALPHAD) method, in which phase equilibria predictions are made on high-order systems by extrapolation of thermochemical data from the Principles of Inorganic Materials Design