Phase Relations in Ternary Systems in the Subsolidus Region: Methods to Formulate Solid Solution Equations and to Find Particular Compositions

A good understanding of ternary phase diagrams is required to advance and/or to reproduce experimental research in solid-state and materials chemistry. The aim of this paper is to describe the solutions to problems that appear when studying or determining ternary phase diagrams. A brief description of the principal features shown in phase diagrams of ternary systems in the subsolidus region is included. We present a systematic procedure to obtain specific compositions of particular interest as well as to calculate binary and ternary ratios of compounds inside the Gibbs triangle and a step-by-step methodology to formulate solid solution equations in binary, ternary, or higher-composition compounds. Specific problems and their solutions are presented as a practical guide, linking the learned concepts with their applications in ceramics and solid-state chemistry research. In addition, ready-to-go exercises with worked-out solutions are included for practice. The procedures described herein may be helpful to those interested in phase diagram interpretation, preparation, and analysis.