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.

Superconductivity has been found in a wide range of materials, including pure metals, alloys, compounds, oxides, and organic materials. Providing information on the basic principles, this article discusses the theoretical background, types of superconductors, and critical parameters of superconductivity. It discusses the magnetic properties of selected superconductors and types of stabilization, including cryogenic stability, adiabatic stability, and dynamic stability. The article also focuses on alternating current losses in superconductors, including hysteresis loss, penetration loss, eddy current loss, and radio frequency loss. Furthermore, the article describes the flux pinning phenomenon and Josephson effects.

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.

This article focuses on the industrial applications of phase diagrams. It presents examples to illustrate how a multicomponent phase diagram calculation can be readily useful for industrial applications. The article demonstrates how the integration of a phase diagram calculation with kinetic and microstructural evolution models greatly enhances the power of the CALPHAD approach in materials design and processing development. It also discusses the limitations of the CALPHAD approach.

This article focuses on the modeling of microstructure evolution during thermomechanical processing in the two-phase field for alpha/beta and beta titanium alloys. It also discusses the mechanisms of spheroidization, the coarsening, particle growth, and phase decomposition in titanium alloys, with their corresponding equations.

This article describes the integration of thermodynamic modeling, mobility database, and phase-transformation crystallography into phase-field modeling and its combination with transformation texture modeling to predict phase equilibrium, phase transformation, microstructure evolution, and transformation texture development during heat treatment of multicomponent alpha/beta and beta titanium alloys. It includes quantitative description of Burgers orientation relationship and path, discussion of lattice correspondence between the alpha and beta phases, and determination of the total number of Burgers correspondence variants and orientation variants. The article also includes calculation of the transformation strain with contributions from defect structures developed at alpha/beta interfaces as a precipitates grow in size. In the CALculation of PHAse Diagram (CALPHAD) framework, the Gibbs free energies and atomic mobilities are established as functions of temperature, pressure, and composition and serve directly as key inputs of any microstructure modeling. The article presents examples of the integrated computation tool set in simulating microstructural evolution.