International Tables for Crystallography Volume F is an expert guide to macromolecular crystallography for the structural biologist. It was commissioned by the International Union of Crystallography in recognition of the extraordinary contributions that knowledge of macromolecular structure has made, and will make, to the analysis of biological systems, from enzyme catalysis to the workings of a whole cell. The volume covers all stages of a crystallographic analysis from the preparation of recombinant proteins, through crystallization, diffraction data collection, phase determination, structure validation and structure analysis. Although the volume is written for experienced scientists, it is recognized that the reader is more likely to be a biologist interested in structure than a classical crystallographer interested in biology. Thus, there are chapters on the fundamentals, history and current perspectives of macromolecular crystallography, as well as on useful programs and databases such as the Protein Data Bank. Each chapter is written by one or more internationally recognized experts.This second edition features 19 new articles and many articles from the first edition have been revised. The new articles cover topics such as standard definitions for quality indicators, expression of membrane proteins, protein engineering, high-throughput crystallography, radiation damage, merohedral twinning, low-resolution ab initio phasing, robotic crystal loading, whole-cell X-ray diffraction imaging and halogen interactions in biological crystal structures. There are also new articles on relevant software, including software for electron microscopy. These enhancements will ensure that Volume F continues to be a key reference for macromolecular crystallographers and structural biologists.More information on the series can be found at: http://it.iucr.org

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.Volume A1, an extension of and supplement to Volume A, presents a systematic treatment of the maximal subgroups and minimal supergroups of the crystallographic plane groups and space groups. The volume is divided into 3 parts:Part 1: An introduction to the theory of space groups at various levels and with many examples.Part 2: A complete listing of all maximal subgroups and minimal supergroups for each plane group and space group. Graphs that illustrate the group-subgroup relations are also presented.Part 3: Lists the relations between the Wyckoff positions of every maximal subgroup of every space group, including the cell transformations and coordinate transformations.New to the second edition of Volume A1:A new chapter on building trees of group-subgroup relations for crystal structures that can be derived from a high-symmetry structure type (aristotype).A new chapter on the Bilbao Crystallographic Server, describing the databases and computer programs that are related to the subjects of the volume.A detailed discussion of the listed supergroup data and a description of a procedure for the complete derivation of the minimal supergroups from the listed (complete) data on maximal subgroups.This volume is invaluable for the study of group-subgroup relations, and is therefore essential for those interested in phase transitions, the systematic compilation of crystal structures, twinning phenomena and related fields of crystallographic research.More information on the series can be found at: http://it.iucr.org

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science. Each of the eight volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching.Volume E covers the standard nomenclature and representations for the 7 crystallographic frieze-group types, the 75 crystallographic rod-group types and the 80 crystallographic layer-group types. The information tabulated for these groups is identical in format and content to that given for the 230 space groups in Volume A, and is essential for the analysis of the structure and physical properties of crystalline materials that contain linear or planar substructures. In addition, scanning tables are given for each of the 230 space groups, designed for use in the analysis of interfaces.This second edition of Volume E has been revised and includes additional information in the comparison tables of notations for the subperiodic group types to improve ease of use. The Seitz notation of each symmetry operation has also been included.More information on the series can be found at: http://it.iucr.org

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.Each of the volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching.Volume G deals with methods and tools for organizing, archiving and retrieving crystallographic data. The volume describes the Crystallographic Information File (CIF), the standard data exchange and archival file format used throughout crystallography.The volume is divided into five parts:Part 1 – An introduction to the development of CIF.Part 2 – Details concepts and specifications of the files and languages.Part 3 – Discusses general considerations when defining a CIF data item and the classification and use of data.Part 4 - Defines all the data names for the core and other dictionaries.Part 5 - Describes CIF applications, including general advice and considerations for programmers.The accompanying software includes the CIF dictionaries in machine-readable form and a collection of libraries and utility programs.Volume G is an essential guide for programmers and data managers handling crystal-structure information, and provides in-depth information vital for recording or using single-crystal or powder diffraction data in small-molecule, inorganic and biological macromolecular structure science.More information on the series can be found at: http://it.iucr.org

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.Each of the volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching.Volume C provides the mathematical, physical and chemical information needed for experimental studies in structural crystallography. This volume covers all aspects of experimental techniques, using all three principal radiation types (X-ray, electron and neutron), from the selection and mounting of crystals and production of radiation, through data collection and analysis, to interpretation of results. Each chapter is supported by a substantial collection of references, and the volume ends with a section on precautions against radiation injury.Eleven chapters have been revised, corrected or updated for the third edition of Volume C.More information on the series can be found at: http://it.iucr.org

This sixth edition of what was previously known as the Brief Teaching Edition of Volume A provides an introduction to the basic crystallographic data for space groups found in Volume A, for symmetry relations between space groups in Volume A1 and for subperiodic groups in Volume E of International Tables for Crystallography, to magnetic space groups and to the symmetry database that forms part of International Tables Online at https://it.iucr.org. It is designed for graduate students and young researchers who are new to the field of crystallographic symmetry, and includes many illustrative examples to help readers to understand and use these different kinds of information. Selected tables of symmetry data from the full volumes in the series are also included, making this a handy aid for classroom teaching. References are also provided to further specialized sources for those who need to go deeper into the subject and to textbooks for those who need more background information.

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science. Volume A of the series, Space-group symmetry, contains diagrams and tables of data for the 17 plane groups, the 230 space groups and the 32 crystallographic point groups.This new edition is edited by M. I. Aroyo and has been extensively updated and revised.Part 1 of the volume provides an introduction to space-group symmetry. It includes chapters on groups, crystallographic and space-group symmetry, descriptions of space groups, coordinate-system transformations and methods of space-group determination. The final chapter provides a useful introduction to topics treated in more depth in Volumes A1 and E of the series. The chapters in this part have been written with teaching in mind, and will prove invaluable for undergraduates or graduates wishing to learn about symmetry in crystallography, while providing a clear introduction to the topic for researchers from other disciplines.Part 2 of the volume presents the diagrams and tables of plane- and space-group data. The layout of the tables of data, the symbols used in the diagrams and the classification of the space groups are explained in a useful guide. Together these form an essential resource not only for professional crystallographers, but also for chemists, physicists, mineralogists, biologists and material scientists who employ crystallographic methods and who are concerned with the structure and the properties of crystalline materials.Part 3 treats more advanced topics on space-group symmetry, and covers crystal lattices, point groups and crystal classes, space-group symbols and their use, lattice complexes, normalizers of space groups, and magnetic subperiodic groups and magnetic space groups.There are eight new chapters in this 6th edition of Volume A, and five chapters have been revised. The layout of the space-group tables has been simplified as the sub- and supergroup data are now available in Volume A1, and there are new general-position diagrams for the cubic space groups.Additional diagrams showing tilted, perspective views of some of the more complex cubic space groups are also provided.More information on the series can be found at: http://it.iucr.org

Powder diffraction is the mostly widely used crystallographic method, with applications spanning all aspects of structural science. This new volume of International Tables for Crystallography covers all aspects of the technique with over 50 chapters written by experts in the field. Consisting of seven parts, this volume: Provides an overview of the principles of powder diffraction.Discusses the radiation sources used for powder-diffraction studies, instrumentation, the use of different sample environments and methods of sample preparation.Covers methodology, including data processing, indexing and reduction, whole-pattern modelling and quantitative analysis. An overview of the relevant crystallographic databases is also provided.Focuses on structure determination (including real- and reciprocal-space methods and the maximum-entropy method), structure refinement and structure validation.Discusses defects, texture and microstructure, including stress and strain, domain size and thin films.Reviews the available software for powder diffraction.Describes applications to many areas of industrial and academic importance, including macromolecules, minerals and mining, pharmaceuticals, ceramics, cement, superconductors, pigments, forensic science, archaeology, energy storage, petrochemicals and aluminium production.Volume H is the key reference for all powder diffractionists from beginners to advanced practitioners and has been designed to be a practical volume without sacrificing rigour. Many examples of the powder-diffraction method are discussed in detail, and in several cases the data used in the examples are available for the reader to download.More information on the series can be found at: https://it.iucr.org.

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.Each of the volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching.Volume D is concerned with the influence of symmetry on the physical and tensor properties of crystals and on their structural phase transitions. This role is very important in many different disciplines of the science of materials such as crystallography, elasticity, solid-state physics, magnetism, optics, ferroelectricity and mineralogy, and Volume D deals with all these aspects in a unified way.The volume is divided into 3 parts:Part 1: Introduces the mathematical properties of tensors and group representations and gives their independent components for each of the crystallographic groups.Part 2: Devoted to the symmetry aspects of excitations in reciprocal space: phonons, electrons, Raman scattering and Brillouin scattering.Part 3: Deals with the symmetry aspects of structural phase transitions and twinning. A prominent feature is the joint description of twinning and domain structures, which are usually presented in completely separate ways in handbooks of physics and mineralogy.Supplementary software is provided to support and enhance Chapters 1.1 and 1.2 for the determination of irreducible group representations and tensor components, and Part 3 on structural phase transitions.New to this edition:This second edition of Volume D features a new chapter (Chapter 1.11) on the tensorial properties of local crystal susceptibilities, by V. E. Dmitrienko, A. Kirfel and E. N. Ovchinnikova. This chapter describes the symmetry and physical phenomena that allow and restrict forbidden reflections excited at radiation energies close to the X-ray absorption edges of atoms. Reflections caused by magnetic scattering are also discussed.In Part 1, Chapters 1.1 (an introduction to the properties of tensors), 1.2 (on representations of crystallographic groups), 1.3 (elastic properties), 1.5 (magnetic properties) and 1.10 (on tensors in quasiperiodic structures) have been revised. In particular, Chapter 1.5 features a new section on multiferroics by M. Kenzelmann.Chapter 3.3 on twinning of crystals has been updated and new sections on the effect of twinning in reciprocal space and on the relations between twinning and domain structure have been added. Chapter 3.4 on domain structures has also been updated.More information on the series can be found at: http://it.iucr.org/

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.Volume B presents accounts of the numerous aspects of reciprocal space in crystallographic research. This volume is a vital addition to the library of scientists engaged in crystal structure determination, crystallographic computing, crystal physics and other fields of crystallographic research. Graduate students specializing in crystallography will find much material suitable for self-study and a rich source of references to the relevantliterature.New to this edition:A new chapter on modern extensions of the Ewald method for Coulomb interactions in crystals.Three new sections on electron diffraction and electron microscopy in structure determination, describing point-group and space-group determination by convergent-beam electron diffraction, three-dimensional reconstruction, and single-particle reconstruction. Substantial revisions to the chapters on space-group representations in reciprocal space, direct methods, Patterson and molecular replacement techniques, and disorder diffuse scatteringMore information on the series can be found at: http://it.iucr.org

X-ray absorption spectroscopy and X-ray emission spectroscopy are complementary to crystallographic methods, particularly for materials science and the study of nanostructure and systems with partial disorder and partial local order, including solutions, gases, liquids, glasses and powders.This new volume of International Tables for Crystallography has nine parts and over 150 chapters contributed by a wide range of international experts. Part 1 provides a brief overview and introduction to the background of X-ray absorption spectroscopy (XAS) and experimental facilities.Part 2 discusses the quantum theory of XAS and related approaches.Part 3 describes both standard and advanced experimental methods used in XAS, X-ray emission spectroscopy (XES) and related techniques.Part 4 covers both standard and more advanced pre-processing of data.Part 5 gives an extensive overview of the analysis of experimental data.Part 6 provides details of the major software packages for data collection, reduction and analysis.Part 7 outlines the importance in science, reporting and hypothesis testing of the exchange of input and processed output data, and data deposition. It also presents excerpts of tables of data and supplementary material for XAS, pre-edge studies, X-ray absorption near-edge spectroscopy (XANES) and X-ray absorption fine structure (XAFS) studies. These tables are also available in full as online supporting information.Part 8 explores a wide range of applications of XAS in fields including materials science, physics, chemistry, biology, earth sciences, catalysis and cultural heritage.Part 9 presents definitions of the terms and quantities used, as developed by the International Union of Crystallography's Commission on XAFS.The volume has been written for the worldwide XAS community of thousands of practitioners, beamline scientists, experts and academics, and for the novice user who wishes to know what XAS and XES can do for them and how they may use these techniques for their particular purposes. The volume is therefore intended to be a self-contained, authoritative reference work that can also be used for training, learning or teaching, providing practical guidance for readers of all levels of experience.More information on the volumes in the series International Tables for Crystallography can be found at https://it.iucr.org.

International Tables for Crystallography Volume F is an expert guide to macromolecular crystallography for the structural biologist. It was commissioned by the International Union of Crystallography in recognition of the extraordinary contributions that knowledge of macromolecular structure has made, and will make, to the analysis of biological systems, from enzyme catalysis to the workings of a whole cell. The volume covers all stages of a crystallographic analysis from the preparation of recombinant proteins, through crystallization, diffraction data collection, phase determination, structure validation and structure analysis. Although the volume is written for experienced scientists, it is recognized that the reader is more likely to be a biologist interested in structure than a classical crystallographer interested in biology. Thus, there are chapters on the fundamentals, history and current perspectives of macromolecular crystallography, as well as on useful programs and databases such as the Protein Data Bank. Each chapter is written by one or more internationally recognized experts.This second edition features 19 new articles and many articles from the first edition have been revised. The new articles cover topics such as standard definitions for quality indicators, expression of membrane proteins, protein engineering, high-throughput crystallography, radiation damage, merohedral twinning, low-resolution ab initio phasing, robotic crystal loading, whole-cell X-ray diffraction imaging and halogen interactions in biological crystal structures. There are also new articles on relevant software, including software for electron microscopy. These enhancements will ensure that Volume F continues to be a key reference for macromolecular crystallographers and structural biologists.More information on the series can be found at: http://it.iucr.org

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.Volume A1, an extension of and supplement to Volume A, presents a systematic treatment of the maximal subgroups and minimal supergroups of the crystallographic plane groups and space groups. The volume is divided into 3 parts:Part 1: An introduction to the theory of space groups at various levels and with many examples.Part 2: A complete listing of all maximal subgroups and minimal supergroups for each plane group and space group. Graphs that illustrate the group-subgroup relations are also presented.Part 3: Lists the relations between the Wyckoff positions of every maximal subgroup of every space group, including the cell transformations and coordinate transformations.New to the second edition of Volume A1:A new chapter on building trees of group-subgroup relations for crystal structures that can be derived from a high-symmetry structure type (aristotype).A new chapter on the Bilbao Crystallographic Server, describing the databases and computer programs that are related to the subjects of the volume.A detailed discussion of the listed supergroup data and a description of a procedure for the complete derivation of the minimal supergroups from the listed (complete) data on maximal subgroups.This volume is invaluable for the study of group-subgroup relations, and is therefore essential for those interested in phase transitions, the systematic compilation of crystal structures, twinning phenomena and related fields of crystallographic research.More information on the series can be found at: http://it.iucr.org

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science. Each of the eight volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching.Volume E covers the standard nomenclature and representations for the 7 crystallographic frieze-group types, the 75 crystallographic rod-group types and the 80 crystallographic layer-group types. The information tabulated for these groups is identical in format and content to that given for the 230 space groups in Volume A, and is essential for the analysis of the structure and physical properties of crystalline materials that contain linear or planar substructures. In addition, scanning tables are given for each of the 230 space groups, designed for use in the analysis of interfaces.This second edition of Volume E has been revised and includes additional information in the comparison tables of notations for the subperiodic group types to improve ease of use. The Seitz notation of each symmetry operation has also been included.More information on the series can be found at: http://it.iucr.org

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.Each of the volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching.Volume G deals with methods and tools for organizing, archiving and retrieving crystallographic data. The volume describes the Crystallographic Information File (CIF), the standard data exchange and archival file format used throughout crystallography.The volume is divided into five parts:Part 1 – An introduction to the development of CIF.Part 2 – Details concepts and specifications of the files and languages.Part 3 – Discusses general considerations when defining a CIF data item and the classification and use of data.Part 4 - Defines all the data names for the core and other dictionaries.Part 5 - Describes CIF applications, including general advice and considerations for programmers.The accompanying software includes the CIF dictionaries in machine-readable form and a collection of libraries and utility programs.Volume G is an essential guide for programmers and data managers handling crystal-structure information, and provides in-depth information vital for recording or using single-crystal or powder diffraction data in small-molecule, inorganic and biological macromolecular structure science.More information on the series can be found at: http://it.iucr.org

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.Each of the volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching.Volume C provides the mathematical, physical and chemical information needed for experimental studies in structural crystallography. This volume covers all aspects of experimental techniques, using all three principal radiation types (X-ray, electron and neutron), from the selection and mounting of crystals and production of radiation, through data collection and analysis, to interpretation of results. Each chapter is supported by a substantial collection of references, and the volume ends with a section on precautions against radiation injury.Eleven chapters have been revised, corrected or updated for the third edition of Volume C.More information on the series can be found at: http://it.iucr.org

This sixth edition of what was previously known as the Brief Teaching Edition of Volume A provides an introduction to the basic crystallographic data for space groups found in Volume A, for symmetry relations between space groups in Volume A1 and for subperiodic groups in Volume E of International Tables for Crystallography, to magnetic space groups and to the symmetry database that forms part of International Tables Online at https://it.iucr.org. It is designed for graduate students and young researchers who are new to the field of crystallographic symmetry, and includes many illustrative examples to help readers to understand and use these different kinds of information. Selected tables of symmetry data from the full volumes in the series are also included, making this a handy aid for classroom teaching. References are also provided to further specialized sources for those who need to go deeper into the subject and to textbooks for those who need more background information.

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science. Volume A of the series, Space-group symmetry, contains diagrams and tables of data for the 17 plane groups, the 230 space groups and the 32 crystallographic point groups.This new edition is edited by M. I. Aroyo and has been extensively updated and revised.Part 1 of the volume provides an introduction to space-group symmetry. It includes chapters on groups, crystallographic and space-group symmetry, descriptions of space groups, coordinate-system transformations and methods of space-group determination. The final chapter provides a useful introduction to topics treated in more depth in Volumes A1 and E of the series. The chapters in this part have been written with teaching in mind, and will prove invaluable for undergraduates or graduates wishing to learn about symmetry in crystallography, while providing a clear introduction to the topic for researchers from other disciplines.Part 2 of the volume presents the diagrams and tables of plane- and space-group data. The layout of the tables of data, the symbols used in the diagrams and the classification of the space groups are explained in a useful guide. Together these form an essential resource not only for professional crystallographers, but also for chemists, physicists, mineralogists, biologists and material scientists who employ crystallographic methods and who are concerned with the structure and the properties of crystalline materials.Part 3 treats more advanced topics on space-group symmetry, and covers crystal lattices, point groups and crystal classes, space-group symbols and their use, lattice complexes, normalizers of space groups, and magnetic subperiodic groups and magnetic space groups.There are eight new chapters in this 6th edition of Volume A, and five chapters have been revised. The layout of the space-group tables has been simplified as the sub- and supergroup data are now available in Volume A1, and there are new general-position diagrams for the cubic space groups.Additional diagrams showing tilted, perspective views of some of the more complex cubic space groups are also provided.More information on the series can be found at: http://it.iucr.org

Powder diffraction is the mostly widely used crystallographic method, with applications spanning all aspects of structural science. This new volume of International Tables for Crystallography covers all aspects of the technique with over 50 chapters written by experts in the field. Consisting of seven parts, this volume: Provides an overview of the principles of powder diffraction.Discusses the radiation sources used for powder-diffraction studies, instrumentation, the use of different sample environments and methods of sample preparation.Covers methodology, including data processing, indexing and reduction, whole-pattern modelling and quantitative analysis. An overview of the relevant crystallographic databases is also provided.Focuses on structure determination (including real- and reciprocal-space methods and the maximum-entropy method), structure refinement and structure validation.Discusses defects, texture and microstructure, including stress and strain, domain size and thin films.Reviews the available software for powder diffraction.Describes applications to many areas of industrial and academic importance, including macromolecules, minerals and mining, pharmaceuticals, ceramics, cement, superconductors, pigments, forensic science, archaeology, energy storage, petrochemicals and aluminium production.Volume H is the key reference for all powder diffractionists from beginners to advanced practitioners and has been designed to be a practical volume without sacrificing rigour. Many examples of the powder-diffraction method are discussed in detail, and in several cases the data used in the examples are available for the reader to download.More information on the series can be found at: https://it.iucr.org.

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.Each of the volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching.Volume D is concerned with the influence of symmetry on the physical and tensor properties of crystals and on their structural phase transitions. This role is very important in many different disciplines of the science of materials such as crystallography, elasticity, solid-state physics, magnetism, optics, ferroelectricity and mineralogy, and Volume D deals with all these aspects in a unified way.The volume is divided into 3 parts:Part 1: Introduces the mathematical properties of tensors and group representations and gives their independent components for each of the crystallographic groups.Part 2: Devoted to the symmetry aspects of excitations in reciprocal space: phonons, electrons, Raman scattering and Brillouin scattering.Part 3: Deals with the symmetry aspects of structural phase transitions and twinning. A prominent feature is the joint description of twinning and domain structures, which are usually presented in completely separate ways in handbooks of physics and mineralogy.Supplementary software is provided to support and enhance Chapters 1.1 and 1.2 for the determination of irreducible group representations and tensor components, and Part 3 on structural phase transitions.New to this edition:This second edition of Volume D features a new chapter (Chapter 1.11) on the tensorial properties of local crystal susceptibilities, by V. E. Dmitrienko, A. Kirfel and E. N. Ovchinnikova. This chapter describes the symmetry and physical phenomena that allow and restrict forbidden reflections excited at radiation energies close to the X-ray absorption edges of atoms. Reflections caused by magnetic scattering are also discussed.In Part 1, Chapters 1.1 (an introduction to the properties of tensors), 1.2 (on representations of crystallographic groups), 1.3 (elastic properties), 1.5 (magnetic properties) and 1.10 (on tensors in quasiperiodic structures) have been revised. In particular, Chapter 1.5 features a new section on multiferroics by M. Kenzelmann.Chapter 3.3 on twinning of crystals has been updated and new sections on the effect of twinning in reciprocal space and on the relations between twinning and domain structure have been added. Chapter 3.4 on domain structures has also been updated.More information on the series can be found at: http://it.iucr.org/

International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.Volume B presents accounts of the numerous aspects of reciprocal space in crystallographic research. This volume is a vital addition to the library of scientists engaged in crystal structure determination, crystallographic computing, crystal physics and other fields of crystallographic research. Graduate students specializing in crystallography will find much material suitable for self-study and a rich source of references to the relevantliterature.New to this edition:A new chapter on modern extensions of the Ewald method for Coulomb interactions in crystals.Three new sections on electron diffraction and electron microscopy in structure determination, describing point-group and space-group determination by convergent-beam electron diffraction, three-dimensional reconstruction, and single-particle reconstruction. Substantial revisions to the chapters on space-group representations in reciprocal space, direct methods, Patterson and molecular replacement techniques, and disorder diffuse scatteringMore information on the series can be found at: http://it.iucr.org

X-ray absorption spectroscopy and X-ray emission spectroscopy are complementary to crystallographic methods, particularly for materials science and the study of nanostructure and systems with partial disorder and partial local order, including solutions, gases, liquids, glasses and powders.This new volume of International Tables for Crystallography has nine parts and over 150 chapters contributed by a wide range of international experts. Part 1 provides a brief overview and introduction to the background of X-ray absorption spectroscopy (XAS) and experimental facilities.Part 2 discusses the quantum theory of XAS and related approaches.Part 3 describes both standard and advanced experimental methods used in XAS, X-ray emission spectroscopy (XES) and related techniques.Part 4 covers both standard and more advanced pre-processing of data.Part 5 gives an extensive overview of the analysis of experimental data.Part 6 provides details of the major software packages for data collection, reduction and analysis.Part 7 outlines the importance in science, reporting and hypothesis testing of the exchange of input and processed output data, and data deposition. It also presents excerpts of tables of data and supplementary material for XAS, pre-edge studies, X-ray absorption near-edge spectroscopy (XANES) and X-ray absorption fine structure (XAFS) studies. These tables are also available in full as online supporting information.Part 8 explores a wide range of applications of XAS in fields including materials science, physics, chemistry, biology, earth sciences, catalysis and cultural heritage.Part 9 presents definitions of the terms and quantities used, as developed by the International Union of Crystallography's Commission on XAFS.The volume has been written for the worldwide XAS community of thousands of practitioners, beamline scientists, experts and academics, and for the novice user who wishes to know what XAS and XES can do for them and how they may use these techniques for their particular purposes. The volume is therefore intended to be a self-contained, authoritative reference work that can also be used for training, learning or teaching, providing practical guidance for readers of all levels of experience.More information on the volumes in the series International Tables for Crystallography can be found at https://it.iucr.org.