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.

This article presents a table of the crystal structure of allotropic forms of metallic elements in terms of the Pearson symbol, space group, and prototype of the structure. The temperatures of the phase transformations are listed in degree Celsius and the pressures are in GPa. The lattice parameters of the unit cells are given in nanometers. The compilation of the table is restricted to changes in crystal structure that occur as a result of a change in temperature or pressure.

X-ray diffraction (XRD) is the most extensively used method for identifying and characterizing various aspects of metals related to the arrangements and spacings of their atoms for bulk structural analysis. XRD techniques are also applicable to ceramics, geologic materials, and most inorganic chemical compounds. This article describes the operating principles and types of XRD analyses, along with information about the threshold sensitivity and precision, limitations, sample requirements, and capabilities of related techniques. The necessary instrumentation for XRD analyses include the Debye-Scherrer camera and the X-ray diffractometer. The article also describes the uses of XRD analyses, such as the identification of phases or compounds in metals and ceramics; detection of order and disorder transformation; determination of lattice parameters and changes in lattice parameters due to alloying and temperature effects; measurement of residual stresses; characterization of crystallite size and perfection; characterization of preferred orientations; and determination of single crystal orientations.