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.

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 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 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.

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 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.

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.

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.

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.

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, to develop an understanding of the underlying mechanisms governing deformation at elevated temperatures, discusses the phenomenological effects resulting from temperature-induced thermodynamic and kinetic changes. It describes the deformation behavior of engineering materials using expressions known as constitutive equations that relate the dependence of stress, temperature, and microstructure on deformation. The article reviews the characteristics of creep deformation and mechanisms of creep, such as power-law creep, low temperature creep, power-law breakdown, diffusional creep, twinning during creep deformation, and deformation mechanism maps. It discusses the creep-strengthening mechanisms for most structural engineering components. The article provides a description of the microstructural modeling of creep in engineering alloys.

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.

This article reviews the types of passivity and presents tactics that employ passivity to control corrosion. Thermodynamics provides a guide to the conditions under which passivation becomes possible. A valuable guide to thermodynamics is the potential-pH diagram and the Pourbaix diagram. The article presents a potential-pH diagram for the iron-water system and an illustration of an idealized anodic polarization curve for a metal surface, which serves as a basis for describing the kinetics of passivation. It discusses five properties of passive films: thickness, composition, structure, electronic properties, and mechanical properties. The article outlines three possible processes that can form passive films: direct film formation, dissolution precipitation, and anodic oxidation of metal ions in solution. It describes the breakdown of the passive film using various models and highlighting the effect of alloy composition and structure.

Modeling of structure formation in casting of alloys involves several length scales, ranging from the atomic level to macroscopic scale. Intermediate length scales are used to define the microstructure of the growing phases and the grain structure. This article discusses the principles and applications of the phase field method and the cellular automaton method for modeling the direct evolution of structure at the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of the structure that involves nucleation and growth.

Metals can react chemically with oxygen when exposed to air. Essential to an understanding of the gaseous corrosion of a metal are the crystal structure and the molar volume of the metal on which the oxide builds, both of which may affect growth stresses in the oxide. This article presents crystal structures and thermal properties of pure metals and oxides in a tabular form. The free energy of reaction, which describes the oxidation process of a pure divalent metal, is presented. The article illustrates the Richardson-Jeffes diagram, which is used in the determination of the standard Gibbs energy change of formation of oxides and the corresponding dissociation pressures of the oxides as a function of temperature. It demonstrates the Kellogg diagram which shows stability range in more complicated multioxidant systems. The article explains the determination of partial pressures of gas mixtures and partial pressures of volatile oxidation products.

This article reviews the solubilities of the common gases present in ferrous metals, such as cast irons, and nonferrous metals, such as aluminum, copper, magnesium, and their alloys. The kinetics of the relevant reactions, reactions during solidification, and possible methods of control or removal of the dissolved gases are discussed. The most common method for removing hydrogen from aluminum, copper, and magnesium is inert gas flushing. The article provides information on techniques to overcome gas porosity in ferrous and nonferrous metals.

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.

Recovery, recrystallization, and grain growth are the stages that a cold worked metal undergoes when it is annealed. This article describes the changes in the structure and properties that occur on annealing a cold-worked metal. It summarizes the experimental recrystallization studies by Burke and Turnbull with six laws of recrystallization. Applications of these laws of recrystallization are discussed in detail with examples. The article reviews the classification of grain growth according to the growth behavior of grains, namely, normal or continuous grain growth and abnormal or discontinuous grain growth. The latter has also been termed exaggerated grain growth, coarsening, or secondary recrystallization.

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.