Chapter 1: Thermodynamics & Phase Diagrams

Thermodynamics & Phase Diagrams begins by defining key thermodynamic functions such as enthalpy and entropy, explaining how their interplay determines phase stability under varying conditions of temperature and pressure, distinguishing between stable and metastable states. The discussion extends to single-component systems, analyzing how free energy varies with temperature to determine melting points and how pressure shifts equilibrium temperatures via the Clausius-Clapeyron relationship. A significant portion of the text is dedicated to binary solutions, differentiating between ideal solutions, where mixing is driven solely by configurational entropy, and regular solutions, which incorporate enthalpy of mixing based on the quasi-chemical model of interatomic bond energies. The summary details the mathematical derivation of chemical potential and activity, using the common tangent construction to locate equilibrium compositions in heterogeneous systems and introducing the lever rule for phase fraction calculations. These concepts are applied to construct various binary phase diagrams from free energy curves, explaining phenomena such as miscibility gaps, long-range ordering, and the formation of intermediate phases and intermetallic compounds. The chapter also explores the Gibbs Phase Rule for determining degrees of freedom and analyzes the temperature dependence of solid solubility and equilibrium vacancy concentrations using Arrhenius-type exponential functions. Furthermore, the influence of interfaces is examined through the Gibbs-Thomson effect, showing how surface curvature and interfacial energy alter solubility limits and melting temperatures for small particles. The complexity increases with an introduction to ternary equilibrium, utilizing Gibbs triangles and free energy surfaces to visualize tie-lines, tie-triangles, and solidification paths in three-component systems. Finally, the distinction between thermodynamics and kinetics is clarified, introducing the concept of thermal activation, transition states, and the Arrhenius rate equation to describe the rate at which phase transformations occur.