This article presents the Schmid's law that describes the response of crystal structures to loading. It describes the Taylor model to calculate the uniaxial yield stress of an isotropic face-centered cubic aggregate in terms of critical resolved shear stress. The article discusses the stress-based approach of the Bishop and Hill procedure to directly find stress states that could simultaneously operate at least five independent slip systems. It presents ways to find isostress or lower-bound yield loci for sheets having single-crystal orientation.

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.

This article provides a detailed account of the concepts of single-crystal x-ray diffraction (XRD). It begins with a historical review of XRD methods, followed by a description of the various factors involved in crystal symmetry. The article then focuses on the phase problem in x-ray structural analysis and validation of the structural model. Some of the factors to be considered for performing experimental procedure are provided. The article presents several examples of applications of single-crystal XRD. The following sections cover the crystallographic problem in terms of structural analysis, software programs for crystal structure solution and refinement, and visualization of crystal structures. The article ends with a discussion on various databases available for single-crystal XRD analysis.

This article provides an explanation on how crystal plasticity is implemented within finite element formulations by the use of physical length scales: crystal scale and continuum scale. It provides theoretical formulations for kinematic framework for deforming crystals and polycrystals, elastic and plastic behaviors of single crystals, refinements to the single-crystal constitutive, and crystal-scale finite-element. The article also presents examples that illustrate the capabilities of the formulations at the length scales.

The crystal structure of a material is an important aspect of corrosion and oxidation processes. This article provides a general introduction to the crystal structure of materials, providing information on the crystal systems, lattice dimensions, nomenclature, and solid-solution mechanisms used to characterize structures. It illustrates the unit cells and ion positions for some simple metal crystals, arranged alphabetically according to Pearson symbol. The space lattice and crystal system, space-group notation, and prototype for each crystal are also illustrated.

Crystal structure is the arrangement of atoms or molecules in the solid state that involves consideration of defects, or abnormalities, in idealized atomic/molecular arrangements. The three-dimensional aggregation of unit cells in the crystal forms a space lattice or Bravais lattice. This article provides a brief review of the terms and basic concepts associated with crystal structures. It also discusses some of the significant defects obstructing plastic flow in real crystals, namely point defects, line defects, stacking faults, twins, and cold work. Several tables in the article provide information on the crystal structures and lattice parameters of allotropes of metallic elements.

This article defines crystallographic terms and concepts, including crystal structure, unit cell, structure symbols, lattice, space-group notation, and atom position. It schematically illustrates the atom positions, prototypes, structure symbols, space-group notations, and lattice parameters for some of the simple metallic crystals. A table that lists the crystal structures of various metal elements is presented. The crystal structures are described by the Pearson symbols for crystal system, space lattice, total number of atoms per unit cell, and prototype structure. The article tabulates the assorted structure types of metallurgical interest arranged according to Pearson symbol. It also provides information on crystal defects in all real crystals, explaining some significant ones, such as point defects, line defects, stacking faults, and twins.

This article summarizes a physical model of an interface structure and shows how the model helps in optimizing atomistic modeling studies. It presents the orientation relationship of the interface structure to define the mutual crystallographic position of adjacent crystals. The article describes the model-informed atomistic modeling of the interface structures for interpolating the results of atomistic modeling to predict the properties of interfaces. Theories to predict low-energy orientation relationships are described. The article discusses the use of the localization parameter, such as shear modulus, bonding energy, and transformations, for prediction of interface structures. It provides information on the application of the atomistic modeling of interface structure to predict interface reaction mechanisms.

This article outlines several polycrystal formulations commonly applied for the simulation of plastic deformation and the prediction of deformation texture. It discusses the crystals of cubic and hexagonal symmetry that constitute the majority of the metallic aggregates used in technological applications. The article defines the basic kinematic tensors, reports their relations, and presents expressions for calculating the change in crystallographic orientation associated with plastic deformation. It surveys some of the polycrystal models in terms of the relative strength of the homogeneous effective medium (HEM). The article analyzes the anisotropy predictions of rolled face-centered-cubic and body centered-cubic sheets and presents simulations of the axial deformation of hexagonal-close-packed zirconium. The applications of polycrystal constitutive models to the simulation of complex forming operations, through the use of the finite element method, are also presented.

Self-consistent models are a particular class of models in continuum micromechanics, that is, the field concerned with making predictions of the properties and evolution of aggregates whose single-crystal deformation behavior is known. This article provides information on the measurement and representation of textures as well as prediction of texture evolution in single-phase materials and two-phase aggregates.

This article illustrates the three techniques for producing glassy metals, namely, liquid phase quenching, atomic or molecular deposition, and external action technique. Devitrification of an amorphous alloy can proceed by several routes, including primary crystallization, eutectoid crystallization, and polymorphous crystallization. The article demonstrates a free-energy versus composition diagram that summarizes many of the devitrification routes. It provides a historical review of the corrosion behavior of fully amorphous and partially devitrified metallic glasses. The article describes the general corrosion behavior and localized corrosion behavior of transition metal-metal binary alloys, transition metal-metalloid alloys, and amorphous simple metal-transition metal-rare earth metal alloys. It concludes with a discussion on the environmentally induced fracture of glassy alloys, including hydrogen embrittlement and stress-corrosion cracking.

This article describes the methods of X-ray diffraction analysis, the types of information that can be obtained, and its interpretation. The discussion covers the basic theories of X-rays and various types of diffraction experiments, namely single-crystal methods for polychromatic and monochromatic beams, powder diffraction methods, and the Rietveld method.

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 introduces various techniques commonly used in the characterization of semiconductors, namely single-crystal, polycrystalline, amorphous, oxide, organic, and low-dimensional semiconductors and semiconductor devices. The discussion covers material classification, fabrication methods, sample preparation, bulk/elemental characterization methods, microstructural characterization methods, surface characterization methods, and electronic characterization methods.

This article provides a brief introduction to neutron diffraction as well as its state-of-the-art capabilities. The discussion covers the general principles of the neutron, neutron-scattering theory, generation of neutrons, types of incident radiation, and purposes of single-crystal neutron diffraction, powder diffraction, and pair distribution function analysis. The relationship between detector space and reciprocal space are presented. Various factors involved in sample preparation, calibration, and techniques used for analyzing diffraction data are described. The article also presents application examples and possible future developments in neutron diffraction.

This article discusses the techniques and applications of synchrotron x-ray diffraction, providing information on x-ray generation, monochromation, and crystallography. X-ray diffraction techniques covered include single-crystal and powder diffraction. Some of the factors involved in the construction and development of macromolecular x-ray crystallography are also described.

This article provides crystallographic and engineering data for single oxide ceramics, zirconia, silicates, mullite, spinels, perovskites, borides, carbides, silicon carbide, boron carbide, tungsten carbide, silicon-nitride ceramics, diamond, and graphite. It includes data on crystal structure, density, mechanical properties, physical properties, electrical properties, thermal properties, and magnetic properties.

The electron backscatter diffraction (EBSD) technique has proven to be very useful in the measurement of crystallographic textures, orientation relationships between phases, and both plastic and elastic strains. This article focuses on backscatter diffraction in a scanning electron microscope and describes transmission Kikuchi diffraction. It begins with a discussion on the origins of EBSD and the collection of EBSD patterns. This is followed by sections providing information on EBSD spatial resolution and system operation of EBSD. Various factors pertinent to perform an EBSD experiment are then covered. The article further describes the processes involved in sample preparation that are critical to the success or usefulness of an EBSD experiment. It also discusses the applications of EBSD to bulk samples and the development of EBSD indexing methods.

Heat treatment of depleted uranium (DU) alloys with 4.0 wt% or more molybdenum or equivalent is similar to that of dilute alloys. This article discusses the metallurgical characteristics and processing considerations of DU and its alloys, and describes the control of grain size and orientation using beta treatment. It lists the typical mechanical properties of DU as functions of the amount of cold work and hardness data of uranium rod, and describes the annealing of cold-worked DU. The article also describes the heat treatment of dilute alloys of DU, focusing on the three basic furnace designs used for heating or heat treating of unalloyed uranium: molten salt baths, inert-atmosphere furnaces, and vacuum furnaces. Finally, it presents procedures that are examples of heat treatment used to meet certain specifications of ultimate tensile strength, yield strength, and elongation.

The modeling and simulation of texture evolution for titanium alloys is often tightly coupled to microstructure evolution. This article focuses on a number of problems for titanium alloys in which such coupling is critical in the development of quantitative models. It discusses the phase equilibria, crystallography, and deformation behavior of titanium and titanium alloys. The article describes the modeling and simulation of recrystallization and grain growth of single-phase beta and single-phase alpha titanium. The deformation- and transformation-texture evolution of two-phase (alpha/beta) titanium alloys are also discussed.