This article begins with information on fundamental Laplace transformation rules. Some general theorems concerning operations on transforms are provided. The article also discusses the applications of Laplace transforms. It concludes with a table that lists the values of Laplace transforms.

Eutectoid and peritectoid transformations are classified as solid-state invariant transformations. This article focuses primarily on the structures from eutectoid transformations with emphasis on the classic iron-carbon system of steel. It reviews peritectoid phase equilibria that are very common in several binary systems. The addition of substitutional alloying elements causes the eutectoid composition and temperature to shift in the iron-carbon system. The article graphically illustrates the effect of various substitutional alloying elements on the eutectoid transformation temperature and effective carbon content. The partitioning effect of substitutional alloying elements, such as chromium, manganese, and silicon, in pearlitic steel is also illustrated.

This introductory article provides basic information on the various aspects of solid-state transformation: multiphase microstructures, substructures, and crystallography, which assist in characterizing the morphology of phase transformations. It contains a flowchart that illustrating the classification of transformations by growth processes.

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.

Solid-state transformations from invariant reactions are of three types: eutectoid, peritectoid, and monotectoid transformations. This article focuses on structures from eutectoid transformations with an emphasis on the classic iron-carbon system of steel. It illustrates the morphology of a pearlite nodule and the effect of various substitutional alloy elements on the eutectoid transformation temperature and effective carbon content, respectively. Peritectic and peritectoid phase equilibria are very common in several binary systems. The article reviews structures from peritectoid reactions and details the formation of peritectic structures that can occur by at least three mechanisms: peritectic reaction, peritectic transformation, and direct precipitation of beta from the melt.

Massive transformations are thermally activated phenomena and exhibit nucleation and growth characteristics primarily controlled by the interface between parent and product phases that is generally considered incoherent. This article focuses on the nucleation and growth kinetics involved in massive transformations and illustrates the resulting phases and structures in ferrous and nonferrous metals and alloys.

This article assesses the evolution of martensite modeling in the changing materials engineering environment. It describes the physics of displacive transformations using Ginzburg-Landau theory, microstructure representation, dynamics and simulations, density functional theory, and shuffle transitions. The article reviews the application of the Ginzburg-Landau approach to rigorous solutions for issues in the structure of a martensitic nucleus based on the martensitic nucleation theory. The three basic behavior modes of martensitic growth, such as elastic, elastic/plastic, and fully plastic are discussed. The article also reviews the overall kinetics of martensitic transformations.

The transformation of austenite of cast irons represents a more complex and less studied subject. This article discusses the general features of the decomposition of austenite into bainite. It describes the heat treatment cycles of austempered cast iron microstructure. The article reviews several factors, such as presence of graphite and austenite grain size, which affect the transformation rate of austenite during austempering of free-graphite cast irons.

This article provides a discussion on transformers and reactors for induction heating. It presents information on the initial considerations in the selection process and the demands of power supply and load circuits. The article describes the types of transformers and reactors used in induction heating and maintenance operations. It also provides a discussion on load matching covering the following topics: initial considerations in the load-matching process, understanding the load circuit and the power supply circuit, selecting the desired operating point, adjusting the value of components, and testing the setup.

Solid-state transformations occurring in a weld are highly nonequilibrium in nature and differ distinctly from those experienced during casting, thermomechanical processing, and heat treatment. This article provides a description of the special factors affecting transformation behavior in a weldment. It reviews the heat-affected and fusion zones of single-pass and multi-pass weldments. The article also includes a discussion on the welds in alloy systems, such as stainless steels and aluminum-base, nickel-base, and titanium-base alloys.

This article begins with the one-component, or unary, diagram for magnesium. The diagram shows what phases are present as a function of the temperature and pressure. When two metals are mixed in the liquid state to produce a solution, the resulting alloy is called a binary alloy. The article describes the various types of solid solutions such as interstitial solid solutions and substitutional solid solutions. Free energy is important because it determines whether or not a phase transformation is thermodynamically possible. The article discusses the thermodynamics of phase transformations and free energy, as well as kinetics of phase transformations. It concludes with a description of solid-state phase transformations that occur when one or more parent phases, usually on cooling, produces a phase or phases.

Solid-state transformations occurring in a weld are highly nonequilibrium in nature and differ distinctly from those experienced during casting, thermomechanical processing, and heat treatment. This article focuses on welding metallurgy of fusion welding of steels and highlights the fundamental principles that form the basis of many of the developments in steels and consumables for welding. Examples in the article are largely drawn from the well-known and relatively well-studied case of ferritic steel weldments to illustrate the special physical metallurgical considerations brought about by the weld thermal cycles and by the welding environment. The article provides information on welds in other alloy systems such as stainless steels and aluminum-base, nickel-base, and titanium-base alloys.

This article discusses the stable and metastable three-phase fields in the binary Fe-C phase diagram. It schematically illustrates that austenite decomposition requires accounting for nucleation and growth of ferrite and then nucleation and growth of pearlite in the remaining untransformed volume. The article describes the austenite decomposition to ferrite and pearlite in spheroidal graphite irons and lamellar graphite irons. It provides a discussion on modeling austenite decomposition to ferrite and pearlite.

The processing of steel involves five distinct sets of texture development mechanisms, namely, austenite deformation, austenite recrystallization, gamma-to-alpha transformation, ferrite deformation, and static recrystallization during annealing after cold rolling. This article provides an introduction on crystallographic textures. It discusses the effects of austenite rolling and recrystallization on the texture and transformation behavior of recrystallized austenite and deformed austenite. The article illustrates the overall summary of the rolling and transformation behavior. It details cold-rolling textures, annealing textures, and recrystallization textures of steel samples. The article concludes with a summary of texture development during cold rolling and annealing.

The solidification of hypoeutectic cast iron starts with the nucleation and growth of austenite dendrites, while that of hypereutectic iron starts with the crystallization of primary graphite in the stable system or cementite in the metastable system. This article begins with a discussion on the nucleation and growth of austenite dendrites. It describes the nucleation of lamellar graphite, spheroidal graphite, and austenite-iron carbide eutectic. The article reviews three main graphite morphologies crystallizing from the iron melts during solidification: lamellar (LG), compacted or vermicular (CG), and spheroidal. It discusses the metastable solidification of austenite-iron carbide eutectic and concludes with information on gray-to-white structural transition of cast iron.