International Tables for Crystallography最新文献

{"title":"Transformations of coordinate systems","authors":"H. Wondratschek, M. Aroyo, B. Souvignier, G. Chapuis","doi":"10.1107/97809553602060000923","DOIUrl":"https://doi.org/10.1107/97809553602060000923","url":null,"abstract":"When dealing with descriptions of structures, it is not seldom that we are faced with the problem of comparing identical crystal structures described with respect to different coordinate systems. For example, two descriptions of the same structure can differ by an origin shift or by a different choice of the basis. Different phases of the same compound often differ in their symmetry at various temperatures or pressures. Any detailed comparison of their structures requires the selection of a common basis and consequently the transformation of the original data to a different coordinate system. The purpose of this chapter is to provide the mathematical tools to accomplish these transformations. The method for transforming the crystallographic data following a change of origin or a change of the basis is given and illustrated with some examples. The transformation rules of the metric tensor characterizing both the direct and reciprocal space and of the space-group symmetry operations under coordinate transformations are further derived and discussed. More than 40 different types of coordinate-system transformations representing the most frequently encountered cases are listed and illustrated. Finally, synoptic tables of space (plane) groups show different types of symmetry operations belonging to the same coset with respect to the translation subgroup and a large selection of alternative settings of space (plane) groups and their Hermann–Mauguin symbols covering most practical cases.","PeriodicalId":338076,"journal":{"name":"International Tables for Crystallography","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123502919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Space groups and their descriptions","authors":"B. Souvignier, H. Wondratschek, M. Aroyo, G. Chapuis, A. Glazer","doi":"10.1107/97809553602060000922","DOIUrl":"https://doi.org/10.1107/97809553602060000922","url":null,"abstract":"This chapter provides an introduction to the various crystallographic items used for the presentation of the symmetry data in the space-group tables of this volume. It starts with a detailed introduction to the Hermann–Mauguin symbols for space, plane and crystallographic point groups, and to their Schoenflies symbols. A description is given of the symbols of the symmetry operations applied in the volume, and their listings in the general-position and the symmetry-operations blocks. This is followed by analysis of some specific features of the symmetry-element and general-position graphical representations of space groups. Seitz symbols for crystallographic symmetry operations are discussed and illustrated, along with the so-called additional symmetry operations of space groups, which result from the periodicity of the space groups. The classification of points in direct space into general and special Wyckoff positions, and the study of their site-symmetry groups and Wyckoff multiplicities are presented in detail. In addition, more advanced topics like Wyckoff sets, eigensymmetry groups and non-characteristic orbits are treated. The final sections offer a useful introduction to two-dimensional sections and projections of space groups and their symmetry properties.","PeriodicalId":338076,"journal":{"name":"International Tables for Crystallography","volume":"216 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124248169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Many-body quantum physics in XANES of highly correlated materials, mixed-valence oxides and high-temperature superconductors","authors":"A. Bianconi","doi":"10.1107/s1574870720003535","DOIUrl":"https://doi.org/10.1107/s1574870720003535","url":null,"abstract":"The x-ray absorption near edge structure (XANES), developed in these last 40 years using synchrotron radiation, is a unique tool probing electronic correlations in complex systems via quantum many body final state effects. Multi electron excitations have been observed first in the sixties in x-ray absorption spectra of atoms and later in molecules and solids. The applications of XANES many body final states to probe unique features of electronic correlation in heavy fermions, mixed valence systems, mixed valence oxides and high temperature superconductors are discussed.","PeriodicalId":338076,"journal":{"name":"International Tables for Crystallography","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121314959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A general introduction to groups","authors":"B. Souvignier","doi":"10.1107/97809553602060000919","DOIUrl":"https://doi.org/10.1107/97809553602060000919","url":null,"abstract":"In this chapter, we introduce the fundamental concepts of group theory with the focus on those properties that are of particular importance for crystallography. Among other examples, the symmetry groups of an equilateral triangle and of the square are used throughout to illustrate the various concepts, whereas the actual application to crystallographic space groups will be found in later chapters. Starting from basic principles, we proceed to subgroups and the coset decomposition with respect to a subgroup. A particular type of subgroup is a normal subgroup. These are distinguished by the fact that the cosets with respect to such a subgroup can themselves be regarded as the elements of a group, called a factor group. These concepts have a very natural application to crystallographic space groups, since the translation subgroup is a normal subgroup and the corresponding factor group is precisely the point group of the space group. We then show how groups can be related by introducing homomorphisms, which are mappings between the groups that are compatible with the group operation. An important link between abstract groups and groups of symmetry operations is the notion of a group action. This formalizes the idea that group elements are applied to objects like points in space. In particular, objects that are mapped to each other by a group element are often regarded as equivalent and the subgroup of group elements that fix an object provides an important characterization of this object. Applied to crystallographic space groups acting on points in space, this gives rise to the concept of Wyckoff positions. We finally look at the notion of conjugacy and at normalizers, which provide important information on the intrinsic ambiguity in the symmetry description of crystal structures.","PeriodicalId":338076,"journal":{"name":"International Tables for Crystallography","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131127308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"2.1 Phonons","authors":"G. Eckold","doi":"10.1107/97809553602060000911","DOIUrl":"https://doi.org/10.1107/97809553602060000911","url":null,"abstract":"This chapter is devoted to the implications of lattice symmetry on the form, i.e. on the eigenvectors, of lattice vibrations. It is restricted to the consideration of perfect crystals and harmonic vibrations. In addition, some aspects of anharmonicity are discussed in terms of a quasi-harmonic model, yielding the connection between microscopic dynamics and macroscopic thermodynamic quantities such as thermal expansion. In Section 2.1.2, the fundamentals of lattice dynamics are presented, with special emphasis on the role of the dynamical matrix. Section 2.1.3 deals with the symmetry properties of this matrix along with its eigenvectors and eigenfrequencies. \u0000 \u0000 \u0000Keywords: \u0000 \u0000Debye model; \u0000Debye temperature; \u0000Gruneisen parameter; \u0000Hamiltonian; \u0000Raman spectroscopy; \u0000acoustic branches; \u0000acoustic modes; \u0000anharmonicity; \u0000compatibility relations; \u0000compressibility; \u0000degeneracy; \u0000dispersion curves; \u0000dynamical matrix; \u0000force constants; \u0000harmonic approximation; \u0000heat capacity; \u0000irreducible representations; \u0000lattice dynamics; \u0000normal coordinates; \u0000phonon dispersion; \u0000phonons; \u0000selection rules; \u0000thermal expansion; \u0000time-reversal degeneracy","PeriodicalId":338076,"journal":{"name":"International Tables for Crystallography","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126499281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"1.9 Atomic displacement parameters","authors":"W. Kuhs","doi":"10.1107/97809553602060000908","DOIUrl":"https://doi.org/10.1107/97809553602060000908","url":null,"abstract":"The theory of lattice dynamics shows that the atomic thermal Debye–Waller factor is related to the atomic displacements. In the harmonic approximation, these are fully described by a fully symmetric second-order tensor. Anharmonicity and disorder, however, cause deviations from a Gaussian distribution of the atomic displacements around the atomic position. A generalized description of atomic displacements therefore also involves first-, third-, fourth- and even higher-order displacement terms.The description of the properties of these tensors is the purpose of this chapter. The number of independent tensor coefficients depends on the site symmetry of the atom and are given in tables. The symmetry restrictions according to the site symmetry are tabulated for second- to sixth-rank thermal motion tensors. A selection of representation surfaces of higher-rank tensors showing the distribution of anharmonic deformation densities is given at the end of the chapter. \u0000 \u0000 \u0000Keywords: \u0000 \u0000Gram–Charlier series; \u0000atomic displacement; \u0000cumulants; \u0000invariants; \u0000quasimoments; \u0000representation surface; \u0000site symmetry; \u0000site-symmetry restrictions; \u0000tensor contraction; \u0000tensor expansion","PeriodicalId":338076,"journal":{"name":"International Tables for Crystallography","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133428022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"2.2 Electrons","authors":"K. Schwarz","doi":"10.1107/97809553602060000912","DOIUrl":"https://doi.org/10.1107/97809553602060000912","url":null,"abstract":"The electronic structure of a solid, characterized by its energy band structure, is the fundamental quantity that determines the ground state of the solid and a series of excitations involving electronic states. In the first part of this chapter, several basic concepts are summarized in order to establish the notation used and to repeat essential theorems from group theory and solid-state physics that provide the definitions that are needed in this context (Brillouin zones, symmetry operators, Bloch theorem, space-group symmetry). Next the quantum-mechanical treatment, especially density functional theory, is described and the commonly used methods of band theory are outlined (the linear combination of atomic orbitals, tight binding, pseudo-potential schemes, the augmented plane wave method, the linear augmented plane wave method, the Korringa–Kohn–Rostocker method, the linear combination of muffin-tin orbitals, the Car–Parinello method etc.). The linear augmented plane wave scheme is presented explicitly so that concepts in connection with energy bands can be explained. The electric field gradient is discussed to illustrate a tensorial quantity. In the last section, a few examples illustrate the topics of the chapter. \u0000 \u0000 \u0000Keywords: \u0000 \u0000Bloch function; \u0000Bloch states; \u0000Bloch theorem; \u0000Bravais lattices; \u0000Brillouin zone; \u0000Car–Parrinello method; \u0000Korringa–Kohn–Rostocker method; \u0000Seitz operator; \u0000Sommerfeld model; \u0000atomic orbitals; \u0000augmented plane wave method; \u0000band structure; \u0000chemical bonding; \u0000core electrons; \u0000crystal harmonics; \u0000density functional theory; \u0000density of states; \u0000electric field gradient; \u0000energy bands; \u0000exchange–correlation; \u0000free-electron model; \u0000full-potential methods; \u0000itinerant electrons; \u0000linear combination of atomic orbitals; \u0000linear combination of muffin-tin orbitals; \u0000linearized augmented plane wave method; \u0000local coordinate system; \u0000localized electrons; \u0000muffin-tin approximation; \u0000nuclear quadrupole moment; \u0000partial charges; \u0000periodic boundary conditions; \u0000pseudo-potential; \u0000quantum-mechanical treatment; \u0000reciprocal lattice; \u0000relativistic effects; \u0000representations; \u0000semi-core states; \u0000small representations; \u0000tight binding","PeriodicalId":338076,"journal":{"name":"International Tables for Crystallography","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125817381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"1.10 Tensors in quasiperiodic structures","authors":"T. Janssen","doi":"10.1107/97809553602060000909","DOIUrl":"https://doi.org/10.1107/97809553602060000909","url":null,"abstract":"This chapter is devoted to the symmetry-related physical properties of quasiperiodic crystals. In the first part the symmetry properties are described: point groups, superspace groups and the action of symmetry groups. The second part concerns the properties of tensors in higher-dimensional spaces, with emphasis on the particular cases of the piezoelectric, elastic and electric field gradient tensors. The last section gives tables of characters of some point groups for quasicrystals and of the matrices of the corresponding irreducible representations. \u0000 \u0000 \u0000Keywords: \u0000 \u0000Fourier module; \u0000compensating gauge transformations; \u0000elastic constants; \u0000electric field gradient; \u0000icosahedral quasicrystals; \u0000incommensurate structures; \u0000irreducible representations; \u0000metric tensor; \u0000modulation wavevector; \u0000octagonal quasicrystals; \u0000piezoelectric tensor; \u0000quasicrystals; \u0000quasiperiodic structures; \u0000superspace; \u0000superspace groups; \u0000tensors","PeriodicalId":338076,"journal":{"name":"International Tables for Crystallography","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125122000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"2.4 Brillouin scattering","authors":"R. Vacher, E. Courtens","doi":"10.1107/97809553602060000914","DOIUrl":"https://doi.org/10.1107/97809553602060000914","url":null,"abstract":"Brillouin scattering of light originates from the interaction of an incident radiation with thermal acoustic vibrations in matter and probes the long-wavelength acoustic phonons. In this chapter, calculations of the sound velocities and scattered intensities for the most commonly investigated vibrational modes in bulk condensed matter are presented. Tables list the geometries for longitudinal and transverse acoustic modes in the eleven Laue classes. The current state of the art for Brillouin spectroscopy is also briefly summarized. \u0000 \u0000 \u0000Keywords: \u0000 \u0000Brillouin scattering; \u0000elastic waves; \u0000electro-optic effect; \u0000scattering cross section","PeriodicalId":338076,"journal":{"name":"International Tables for Crystallography","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116443650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"3.4 Domain structures","authors":"V. Janovec, J. Přívratská","doi":"10.1107/97809553602060000918","DOIUrl":"https://doi.org/10.1107/97809553602060000918","url":null,"abstract":"This chapter is devoted to the crystallographic aspects of static ferroic domain structures. The exposition is based on well defined concepts and rigorous relations that follow from the symmetry lowering at the ferroic phase transition. Necessary mathematical tools are explained in Section 3.2.3 and important points are illustrated with simple examples. Synoptic tables provide useful ready-to-use data accessible even without knowledge of deeper theory. Three main concepts needed in a rigorous analysis (both in a continuum and a microscopic description) of any domain structure are thoroughly discussed. (1) Domain states (orientation states or structural variants) representing inner structures of domains are classified according to their characteristic properties (ferroelastic, ferroelectric etc.) and their hierarchy (primary, secondary, principal, basic etc.). A synoptic table is given with all possible symmetry lowerings at ferroic transitions and contains the numbers of ferroic, ferroelectric and ferroelastic domain states, Aizu's classification and the representation characterizing the principal domain states. (2) Relations between domain states (twin laws) determine domain distinction, switching of domain states in external fields and properties of interfaces (domain walls) between coexisting domains. Tables give for each possible transition all independent twin laws and for each twin law the number of equal and distinct tensor components of material tensors up to rank 4 in two coexisting domains of a domain twin. (3) The basic properties of domain twins and domain walls are determined by their symmetry, which is expressed by crystallographic layer groups. The fundamental significance of this description is explained and illustrated. Synoptic tables give for each twin law the possible orientations of compatible domain walls and their symmetries. \u0000 \u0000 \u0000Keywords: \u0000 \u0000Aizu classification; \u0000Dauphine twins; \u0000coherent domain walls; \u0000dichromatic complexes; \u0000domain pairs; \u0000domain states; \u0000domain structures; \u0000domain twins; \u0000domain walls; \u0000ferroelastic domain pairs; \u0000ferroelastic domain states; \u0000ferroelastic domain structures; \u0000ferroelastic domain twins; \u0000ferroelastic domain walls; \u0000ferroelastic single-domain states; \u0000ferroelectric domain states; \u0000ferroelectric domain structures; \u0000ferroic domain states; \u0000ferroic domain structures; \u0000ferroic transitions; \u0000layer groups; \u0000morphic tensor components; \u0000non-ferroelastic domain pairs; \u0000non-ferroelastic domain states; \u0000non-ferroelastic domain structures; \u0000non-ferroelastic domain twins; \u0000non-ferroelastic domain walls; \u0000non-ferroelastic phases; \u0000non-ferroelectric domain states; \u0000non-ferroelectric phases; \u0000parent clamping approximation; \u0000physical property tensors; \u0000stabilizers; \u0000switching; \u0000symmetry descent; \u0000twin laws; \u0000twinning group","PeriodicalId":338076,"journal":{"name":"International Tables for Crystallography","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133031274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}