Crystallographic Texture and Group Representations


Book Description

This book starts with an introduction to quantitative texture analysis (QTA), which adopts conventions (active rotations, definition of Euler angles, Wigner D-functions) that conform to those of the present-day mathematics and physics literature. Basic concepts (e.g., orientation; orientation distribution function (ODF), orientation density function, and their relationship) are made precise through their mathematical definition. Parts II and III delve deeper into the mathematical foundations of QTA, where the important role played by group representations is emphasized. Part II includes one chapter on generalized QTA based on the orthogonal group, and Part III one on tensorial Fourier expansion of the ODF and tensorial texture coefficients. This work will appeal to students and practitioners who appreciate a precise presentation of QTA through a unifying mathematical language, and to researchers who are interested in applications of group representations to texture analysis. Previously published in the Journal of Elasticity, Volume 149, issues 1-2, April, 2022




Representation of Crystallographic Space Groups


Book Description

This new edition of Kovalev's renowned text (first English edition, 1965) presents all the irreducible representations (IRs) and irreducible corepresentations (ICRs) for the 230 crystallographic space groups. In order to give readers the opportunity of representing generally the entire crystallographic symmetry, the method of inducing an IR of the local groups is presented first, and then complete lists of induced representations (InRs) which allow the calculation of the microstructure of any crystal (already known or not yet discovered, but geometrically not forbidden) in any physical question. For research students and researchers in theoretical aspects of solid state physics, crystallography, and space group theory. Translated from the second Russian edition of 1987. Annotation copyright by Book News, Inc., Portland, OR




Crystallographic Texture of Materials


Book Description

Providing a comprehensive and invaluable overview of the basics of crystallographic textures and their industrial applications, this book covers a broad range of both structural and functional materials. It introduces the existing methods of representation in an accessible manner and presents a thorough overview of existing knowledge on texture of metallic materials. Texture analysis has widespread use in many industries, and provides crucial input towards the development of new materials and products. There has been rapid growth in the science and art of texture analysis in the last few decades. Other topics addressed within this book include recent research on texture in thin films and non-metals, and the dependence of material properties on texture, and texture control in some engineering materials. This book constitutes an invaluable reference text for researchers and professionals working on texture analysis in metallurgy, materials science and engineering, physics and geology. By using content selectively, it is also highly accessible to undergraduate students.




Crystal Symmetries


Book Description

Crystal Symmetries is a timely account of the progress in the most diverse fields of crystallography. It presents a broad overview of the theory of symmetry and contains state of the art reports of its modern directions and applications to crystal physics and crystal properties. Geometry takes a special place in this treatise. Structural aspects of phase transitions, correlation of structure and properties, polytypism, modulated structures, and other topics are discussed. Applications of important techniques, such as X-ray crystallography, biophysical studies, EPR spectroscopy, crystal optics, and nuclear solid state physics, are represented. Contains 30 research and review papers.




Probabilistic Models of Cosmic Backgrounds


Book Description

Combining research methods from various areas of mathematics and physics, Probabilistic Models of Cosmic Backgrounds describes the isotropic random sections of certain fibre bundles and their applications to creating rigorous mathematical models of both discovered and hypothetical cosmic backgrounds. Previously scattered and hard-to-find mathematical and physical theories have been assembled from numerous textbooks, monographs, and research papers, and explained from different or even unexpected points of view. This consists of both classical and newly discovered results necessary for understanding a sophisticated problem of modelling cosmic backgrounds. The book contains a comprehensive description of mathematical and physical aspects of cosmic backgrounds with a clear focus on examples and explicit calculations. Its reader will bridge the gap of misunderstanding between the specialists in various theoretical and applied areas who speak different scientific languages. The audience of the book consists of scholars, students, and professional researchers. A scholar will find basic material for starting their own research. A student will use the book as supplementary material for various courses and modules. A professional mathematician will find a description of several physical phenomena at the rigorous mathematical level. A professional physicist will discover mathematical foundations for well-known physical theories.




Electron Backscatter Diffraction in Materials Science


Book Description

Crystallographic texture or preferred orientation has long been known to strongly influence material properties. Historically, the means of obtaining such texture data has been though the use of x-ray or neutron diffraction for bulk texture measurements, or transmission electron microscopy or electron channeling for local crystallographic information. In recent years, we have seen the emergence of a new characterization technique for probing the microtexture of materials. This advance has come about primarily through the automated indexing of electron backscatter diffraction (EBSD) patterns. The first commercially available system was introduced in 1994, and since then of sales worldwide has been dramatic. This has accompanied widening the growth applicability in materials scienceproblems such as microtexture, phase identification, grain boundary character distribution, deformation microstructures, etc. and is evidence that this technique can, in some cases, replace more time-consuming transmission electron microscope (TEM) or x-ray diffraction investigations. The benefits lie in the fact that the spatial resolution on new field emission scanning electron microscopes (SEM) can approach 50 nm, but spatial extent can be as large a centimeter or greater with a computer controlled stage and montagingofthe images. Additional benefits include the relative ease and low costofattaching EBSD hardware to new or existing SEMs. Electron backscatter diffraction is also known as backscatter Kikuchi diffraction (BKD), or electron backscatter pattern technique (EBSP). Commercial names for the automation include Orientation Imaging Microscopy (OIMTM) and Automated Crystal Orientation Mapping (ACOM).




Crystallographic Groups


Book Description




Introduction to Texture Analysis


Book Description

Reflecting emerging methods and the evolution of the field, Introduction to Texture Analysis: Macrotexture, Microtexture, and Orientation Mapping keeps mathematics to a minimum in covering both traditional macrotexture analysis and more advanced electron-microscopy-based microtexture analysis. The authors integrate the two techniques and address the subsequent need for a more detailed explanation of philosophy, practice, and analysis associated with texture analysis. The book illustrates approaches to orientation measurement and interpretation and elucidates the fundamental principles on which measurements are based. Thoroughly updated, this Third Edition of a best-seller is a rare introductory-level guide to texture analysis. Discusses terminology associated with orientations, texture, and their representation, as well as the diffraction of radiation, a phenomenon that is the basis for almost all texture analysis Covers data acquisition, as well as representation and evaluation related to the well-established methods of macrotexture analysis Updated to include experimental details of the latest transmission or scanning electron microscope-based techniques for microstructure analysis, including electron backscatter diffraction (EBSD) Describes how microtexture data are evaluated and represented and emphasizes the advances in orientation microscopy and mapping, and advanced issues concerning crystallographic aspects of interfaces and connectivity Offers new and innovative grain boundary descriptions and examples This book is an ideal tool to help readers in the materials sciences develop a working understanding of the practice and applications of texture.




Quantitative Texture Analysis


Book Description