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

Abstract

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.

Regular Solution Approach to Modeling the Supercritical Fluid Extraction of Two-Component Solutes from Ground Oilseeds

“…The initial content of each pseudo-component, S 1 and S 2 , of extractable oil compounds per unit volume of the The horizontal axis is the overall mole fraction x 1 of the oil component S 1 in the system. 34 The vertical axis is the overall mole fraction x 2 of the oil component S 2 in the system. The gray triangle covers the overall compositions corresponding to the oil−solvent equilibrium S 1 + S 2 + CO 2 .…”

“…Figure 2. Phase diagram of the three-component system S 1 + S 2 + CO 2 with overall compositions corresponding to three (3), two (2), and single (1) phase equilibria at g i (CO 2 ) = 1.6118, Ω 1 = −Ω 2 = −0.4, and Ω = −1.The horizontal axis is the overall mole fraction x 1 of the oil component S 1 in the system 34. The vertical axis is the overall mole fraction x 2 of the oil component S 2 in the system.…”

Course on the Use of DFT Calculations to Improve Understanding of Phase Diagrams in Solid-State Chemistry

“…A main issue was then to understand the underlying principles of such diagrammatic graphs and to be able to define all possible compositions mathematically in such a diagram. Reading ternary phase diagrams has been treated in several earlier publications in this Journal , , so it seems unnecessary to dwell more deeply into that topic here.…”