Thermodynamic descriptions have become available for a large number of alloy systems and allow the calculation of the phase diagrams of multicomponent alloys. This article begins with a discussion on three laws of thermodynamics: the Law of Conservation of Energy, the Second Law of Thermodynamics, and the Third Law of Thermodynamics. It informs that for transformations that occur at a constant temperature and pressure, the relative stability of the system is determined by its Gibbs free energy. The article describes the Gibbs free energy of a single-component unary system and the Gibbs free energy of a binary solution. It schematically illustrates the structure of a binary solid solution with interatomic bonds and shows how the equilibrium state of an alloy can be obtained from the free-energy curves at a given temperature. The article concludes with information on the construction of eutectic and binary phase diagrams from Gibbs free-energy curves.

This article is a comprehensive collection of the thermodynamic equations and property relations of the first and second laws of thermodynamics that are applicable to closed-system consisting of several homogeneous and heterogeneous phases.

This article discusses the application of thermodynamic in the form of phase diagrams for visually representing the state of a material and for understanding the solidification of alloys. It presents the derivation of the relationship between the Gibbs energy functions and phase diagrams, which forms the basis for the calculation of phase diagrams (CALPHAD) method. The article also discusses the calculation of phase diagrams and solidification by using the Scheil-Gulliver equation.

This article introduces the fundamental concepts of chemical thermodynamics and chemical kinetics in describing presolidification phenomena. For metallurgical systems, the most important thermodynamic variables are enthalpy and Gibbs free energy. A qualitative demonstration of the interrelationship between phase diagrams and thermodynamics is presented. The article discusses processes that generally limit the rates of chemical processes. These include nucleation of the product phase and interphase mass transport. The article provides a discussion on the dissolution of alloy with melting point lower than bath temperature and dissolution of alloy that is solid at bath temperatures.

Alloy phase diagrams are useful for the development, fabrication, design and control of heat treatment procedures that will produce the required mechanical, physical, and chemical properties of new alloys. They are also useful in solving problems that arise in their performance in commercial applications, thus improving product predictability. This article describes different equilibrium phase diagrams (unary, binary, and ternary) and microstructures, description terms, and general principles of reading alloy phase diagrams. Further, the article discusses plotting schemes; areas in a phase diagram; and the position and shapes of the points, lines, surfaces, and intersections, which are controlled by thermodynamic principles and properties of all phases that comprise the system. It also illustrates the application of the stated principles with suitable phase diagrams.

This article presents various equations that are essential for the modeling of both single-phase and multiphase profiles. It includes the fundamental laws of diffusion, along with its equations and solutions. The article provides information on the series of applications that illustrate how various diffusional processes can be modeled.

This article provides a summary of the concepts discussed in the articles under the Section “Fundamentals of Corrosion” in ASM Handbook, Volume 13A: Corrosion: Fundamentals, Testing, and Protection. In this section, the thermodynamic aspects of corrosion are descried first followed by a group of articles discussing the fundamentals of aqueous corrosion kinetics. The fundamentals of gaseous corrosion are addressed next. The fundamental electrochemical reactions of corrosion and their uses are finally described.

This article describes the Schottky defect and the Frenkel defect in oxides. It provides information on the p-type metal-deficit oxides and n-type semiconductor oxides. The article discusses diffusion mechanisms and laws of diffusion proposed by Fick. It explains the oxide texture of amorphous and epitaxy oxide layers and presents equations for various oxidation reaction rates. The article reviews different theories to describe the oxidation mechanism. These include the Cabrera-Mott, Hauffe-IIschner, Grimley-Trapnell, Uhlig, and Wagner theories.

Diffusion is the process by which molecules, atoms, ions, point defects, or other particle types migrate from a region of higher concentration to one of lower concentration. This article focuses on the diffusivity data and modeling of lattice diffusion in solid-state materials, presenting their diffusion equations. It discusses different methods for evaluating the diffusivity of a material, including the measurement of diffusion coefficients, composition profiles, and layer growth widths. The article reviews the various types of direct and indirect diffusion experiments to extract tracer, intrinsic, and chemical diffusivities. It provides information on the applications of single-phase and multiphase diffusion.

Molten salts, in contrast to aqueous solutions in which an electrolyte (acid, base, salt) is dissolved in a molecular solvent, are essentially completely ionic. This article begins with an overview of the thermodynamics of cells and classification of electrodes for molten salts: reference electrodes and indicator electrodes. It explains that corrosion in molten salts can be caused by the solubility of the metal in the salt, particularly if the metal dissolves in its own chloride. The article describes the factors that affect the corrosion of titanium, namely, the titanium chloride content of the magnesium chloride melt, magnesium or sodium content, and oxygen content of the product. It concludes with a discussion on the oxygen activity in the titanium metal product.

This article provides a general introduction to the kinetics of aqueous corrosion with an emphasis on electrochemical principles. It describes the thermodynamic basis for corrosion by determining the equilibrium potentials of electrochemical reactions from the Nernst equation. A corrosion process can be controlled by the electronic conductivity of passive films when the cathodic reaction occurs on the surface of the film and by activation control of corrosion. Passivation becomes thermodynamically possible when the corrosion potential exceeds the potential corresponding to the equilibrium between a metal and one of its oxides/hydroxides. The article schematically illustrates a current-potential or polarization curve for an anodic process.

This article begins with balance equations for mass, momentum, energy, and solute and the necessary boundary conditions for solving problems of interest in casting and solidification. The transport phenomena cover a vast range of length and time scales, from atomic dimensions up to macroscopic casting size and from nanoseconds for interface attachment kinetics to hours for casting solidification. The article describes how to determine which phenomena are most important at the particular length and time scale for the problem. It concludes with several examples of the application of transport phenomena in solidification, focusing on microstructure formation.

This article presents the governing equations for moving a solidification front, based on the balance of mass, momentum, energy, and solute. It reviews how material properties and geometry can be analyzed in the context of the governing equations. The article provides several example problems that illustrate how the hierarchy of time and length scales associated with transport leads to the important features of cast microstructures. It includes equations for estimating microsegregation in cast alloys.

This article describes the changes in structure and properties that occur when cold worked metals and alloys are annealed. Recovery, recrystallization, and grain growth are the three stages of structural change that occur when cold-worked metal is annealed. The driving force and extent of structural or property changes may depend on alloy structure and the degree of prior work.

This article discusses the fundamental aspects of phase-field microstructure modeling. It describes the evolution of microstructure modeling, including nucleation, growth, and coarsening. The article reviews two approaches used in the modeling nucleation of microstructure: the Langevin force approach and explicit nucleation algorithm. Calculation of activation energy and critical nucleus configuration is discussed. The article presents the deterministic phase-field kinetic equations for modeling growth and coarsening of microstructure. It also describes the material-specific model inputs, chemical free energy and kinetic coefficients, for phase-field microstructure modeling. The article provides four examples that illustrate some aspects of phase-field modeling.

One of the key attributes of continuous fiber-reinforced ceramic composites (CFCCs) is their ability to undergo inelastic straining upon mechanical loading. This article reviews the mechanics of inelastic deformation and fracture of CFCCs, as needed for the development of damage-tolerant failure prediction methodologies for use in engineering design. It outlines a general framework for the description of fracture in structural materials in the presence of notches and cracks. The article describes the common classes of fracture behavior of CFCCs and presents the constitutive laws needed to describe crack-tip inelasticity. It demonstrates the effects of inelasticity on crack-tip stress fields and addresses the environmental degradation effects on damage tolerance.

Rapid solidification is a tool for modifying the microstructure of alloys that are obtained by ordinary casting. This article describes the fundamentals of the four microstructural changes, namely, microsegregation, identity of the primary phase, identity of the secondary phase, and the formation of noncrystalline phases. It considers three factors to understand the fundamentals of these changes: heat flow, thermodynamic constraints/conditions at the liquid-solid interfaces, and diffusional kinetics/microsegregation. These factors are described in detail.

This article focuses on the modeling and simulation of diffusion-controlled processes related to both materials processing such as heat treatments, and materials degradation from a practical perspective by using the one-dimensional (1-D) sharp interface approach. It describes various diffusion simulation models, such as one-phase simulations, moving phase-boundary simulations, and dispersed system simulations. The article presents case studies that illustrate some examples where diffusion simulations have been applied to industrial-based problems, with an emphasis on the approaches used and the lessons learned from performing such simulations.

Spinodal transformation is a phase-separation reaction that occurs from kinetic behavior. This article discusses the theory of spinodal decomposition, and outlines the methods used in the characterization of spinodal structures in metal matrices.

This article focuses on the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of a structure. It presents the cellular automaton (CA) and phase field (PF) methods that represent the state of the art for modeling macrostructure and microstructure. The article describes the principles of the PF method and provides information on the applications of the PF method. The CA model is introduced as a computationally efficient method to predict grain structures in castings using the mesoscopic scale of individual grains. The article discusses the coupling of the CA to macroscopic calculation of heat, flow, and mass transfers in castings and applications to realistic casting conditions.