Chapter 7: Phase Equilibrium in One-Component Systems

Phase Equilibrium in One-Component Systems initiates the application of fundamental thermodynamic laws and concepts to materials systems, concentrating on establishing phase equilibrium in systems containing a single component. A phase is rigorously defined as a physically distinct homogeneous region separated by an interphase interface, distinguished by its state of aggregation, crystal structure, and composition. Equilibrium is fundamentally established at finite temperatures when the Gibbs free energy (G) of the system reaches its minimum value, ensuring stability against macroscopic change. Conditions for equilibrium mandate the elimination of driving forces, specifically requiring uniformity in temperature (thermal equilibrium), pressure (mechanical equilibrium), and chemical potential across all phases. Analysis of the variation of molar G with temperature (at constant pressure) shows that its slope equals the negative of the molar entropy (S); since entropy is positive, the G-T curve must always possess a negative slope. Phase stability is governed by the phase exhibiting the lowest Gibbs free energy. The intersection of G-T curves defines the equilibrium melting temperature (Tm), where G of the solid and liquid are equal. Melting is identified as a first-order phase transformation because primary derivatives of the Gibbs free energy, specifically molar entropy, volume, and enthalpy, display a definitive discontinuity at the transition temperature. Furthermore, the relationship between changes in pressure and temperature necessary to maintain two-phase equilibrium is quantified by the Clapeyron equation, which states that the rate of change of pressure with respect to temperature is proportional to the ratio of the enthalpy change of the transformation to the product of the temperature and the volume change. When this is applied to condensed phase-vapor systems, and assuming ideal vapor behavior, it simplifies to the Clausius-Clapeyron equation, which demonstrates that saturated vapor pressure increases exponentially with rising temperature. These equilibrium conditions are represented graphically in P-T phase diagrams, which project the intersections of the G-T-P surfaces onto a two-dimensional plot; curves represent two-phase equilibrium and the triple point is the invariant state where three phases coexist. The Gibbs Equilibrium Phase Rule for a single component, which states that F equals 3 minus phi (F = 3 - ϕ), defines the number of thermodynamic degrees of freedom (F) available when phi phases are simultaneously in equilibrium. Finally, the chapter examines phenomena such as allotropy and polymorphism in solid-solid equilibria, using examples like iron to illustrate how contributions from factors such as spin entropy influence phase stability at varying temperatures, and how external influences, like an applied magnetic field, stabilize phases with higher magnetic susceptibility.