Thermodynamics and Phase Diagrams of Materials

Abstract

The sections in this article are Introduction Notation Gibbs Energy and Equilibrium Gibbs Energy Chemical Equilibrium Predominance Diagrams Calculation of Predominance Diagrams Ellingham Diagrams as Predominance Diagrams Discussion of Predominance Diagrams Thermodynamics of Solutions Gibbs Energy of Mixing Chemical Potential Tangent Construction Gibbs–Duhem Equation Relative Partial Properties Activity Ideal Raoultian Solutions Excess Properties Activity Coefficient Multicomponent Solutions Binary Phase Diagrams Systems with Complete Solid and Liquid Miscibility Thermodynamic Origin of Phase Diagrams Pressure–Composition Phase Diagrams Minima and Maxima in Two‐Phase Regions Miscibility Gaps Simple Eutectic Systems Regular Solution Theory Thermodynamic Origin of Simple Phase Diagrams Illustrated by Regular Solution Theory Immiscibility–Monotectics Intermediate Phases Limited Mutual Solubility–Ideal Henrian Solutions Geometry of Binary Phase Diagrams Application of Thermodynamics to Phase Diagram Analysis Thermodynamic/Phase Diagram Optimization Polynomial Representation of Excess Properties Least‐Squares Optimization Calculation of Metastable Phase Boundaries Ternary and Multicomponent Phase Diagrams The Ternary Composition Triangle Ternary Space Model Polythermal Projections of Liquidus Surfaces Ternary Isothermal Sections Topology of Ternary Isothermal Sections Ternary Isopleths (Constant Composition Sections) Quasi‐Binary Phase Diagrams Multicomponent Phase Diagrams Nomenclature for Invariant Reactions Reciprocal Ternary Phase Diagrams Phase Diagrams with Potentials as Axes General Phase Diagram Geometry General Geometrical Rules for All True Phase Diagram Sections Zero Phase Fraction Lines Choice of Axes and Constants of True Phase Diagrams Tie‐lines Corresponding Phase Diagrams Theoretical Considerations Other Sets of Conjugate Pairs Solution Models Sublattice Models All Sublattices Except One Occupied by Only One Species Ionic Solutions Interstitial Solutions Ceramic Solutions The Compound Energy Formalism Non‐Stoichiometric Compounds Polymer Solutions Calculation of Limiting Slopes of Phase Boundaries Short‐Range Ordering Long‐Range Ordering Calculation of Ternary Phase Diagrams From Binary Data Minimization of Gibbs Energy Phase Diagram Calculation Bibliography Phase Diagram Compilations Thermodynamic Compilations General Reading

On the effect of oxygen partial pressure on the chromium distribution coefficient in melt-grown ruby crystals

“…as long as the vapour pressure of the condensed phases is low compared to the oxygen pressure, the predominance (Ellingham) diagram of the system (Fig. 1), consisting of plots of the equilibrium oxygen fugacity versus temperature for reactions (2), can be easily computed from tabulated thermodynamic data [23,24]. The diagram area is divided into fields of predominance of a certain oxide, which is the oxide that will be formed because its formation is associated with the reduction of Gibbs energy of the system.…”

“…Available thermodynamic data in the CrO-Cr 2 O 3 -Al 2 O 3 system including those of liquid and solid solutions permit calculation of phase equilibria for arbitrary (T, p O 2 ) conditions using numerical algorithms for Gibbs energy minimization [23,25,26]. In particular, sections of constant oxygen fugacity may be computed (Fig.…”

Glass transition and mixing thermodynamics of a binary eutectic system

“…Alternatively, studies of binary phase diagrams suggest that in the framework of the regular solution model, a negative enthalpy of mixing would decrease liquidus temperature T l , while positive enthalpy of mixing would enhance T l . 75 Thus, the negative enthalpy of mixing immediately leads to a highly reduced glass transition temperature T rg (= T g /T l ), which often serves as an indicator of the glass forming ability of materials. 76 Similarly, the strong impact of enhanced interactions on the glass formation in mixtures is also emphasized in ion-water solutions, where the addition of Li + ions into water is proven to favor the glass formation of aqueous solutions compared with Na + and K + ions due to the stronger ion-water interactions, while the latter two have either moderate or less interactions with water molecules.…”

Thermodynamics of equilibrium and partitionless solidifications in glass forming binary eutectic alloys

“…The phase diagrams of the four binary alloys are shown in Fig.1 together with the compositional dependence of the activity coefficients,  , of the components, which indicate the degree of deviation of the real solution from the ideal mixing ( = 1), and are closely related with the interaction between unlike atoms in the alloys. The two cases of  < 1 and  > 1 mean the attractive and repulsive 4 interactions between unlike atoms, respectively [43]. The values of  of Ag-Cu, Sb-Pb, Au-Si and Ni-Zr alloys respectively are taken from the literature [44][45][46][47].…”