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The article discusses the use of t-distributions in a probability plot to model real data more realistically. It defines probability plots as a tool in crystallography used to verify how the distribution of errors in a set of observed values visually compares with a general presumed error distribution. It suggests that the use of a Student's t-distribution in analyzing errors by means of a probability plot improves error modeling.

The article discusses the problem of a minimum tetrahedron in a three-dimensional lattice and its solution by lowering the number of bodies admitted by the minimum condition. It points to tetrahedron as the simplest three-dimensional body determined by the smallest possible number of quite arbitrary points. It provides a formula that suggests the possibility of thrice ambiguous minitetrahedra.

The article discusses the relationship of the properties of the hyperspherical harmonics with the analysis of crystallographic orientation information and the orientation distribution functions (ODF). It provides an addition theorem for the hyperspherical harmonics and an exact expressions for the matrices that determine the effect of rotations on the hyperspherical harmonics. It indicates a possible increase in the use of the hypersherical harmonic expansion for the crystallography community and the materials science community as a whole.

In this article, a number of the results relevant to the concept of sublattices of a basic crystallographic lattice are reviewed, emphasizing particularly previously unpublished work on the algebraic aspects. A three-dimensional geometric lattice L can be considered as an infinite Abelian group under addition. A sublattice S of L, which is also three-dimensional, is a subgroup of L such that the finite quotient group, is an Abelian group of order the index of S in L. The sublattice itself in its standard form is represented by an upper triangular matrix. The index of the sublattice is given by the determinant of this matrix. It is first noted that a sublattice described by an arbitrary basis set in L may be converted to this standard form. Next the sublattice is expressed as the intersection of a set of sublattices of individual index a power of a distinct prime, i.e. where p1, p2 etc. are prime numbers and is the Euclidean factorization of n. This decomposition is important because it corresponds to the Sylow decomposition of the corresponding quotient group It is also useful to be able to carry out two commutative binary operations on sublattices of L; these are to find their common sublattice of lowest index in L, which is their intersection and their common superlattice of highest index in L, given by where <> indicates the span of the sublattices. [ABSTRACT FROM AUTHOR]

Quartz aggregates that formed by coalescence of quartz crystals in the magma or in hydrothermal solution are considered. If the individuals have rhombohedral faces in contact, there will be two special cases: parallel intergrowths and intergrowths that agree in orientation and contact plane with Esterel twins grown from a twinned nucleus. For all other known cases, i.e. when the relative orientation satisfies the Japan, Sardinian, Tiflis, Zyndel-A or Samshvildo law, both individuals have exactly coinciding short symmetry translations in only one direction in the contact plane (monoperiodic twins). If a rhombohedral face is in contact with a prism face, monoperiodic twins will occur if the relative orientation satisfies the Zinnwald, Disentis or a proposed hypothetic law. The orientation of the two lattices can be expressed by a 180° rotation about an axis with low indices independent of c/ a in the case of the Esterel, Japan and Sardinian laws. The same is true for the Tiflis and Zyndel-A laws only if they are redefined, and not at all in the case of the Samshvildo, Zinnwald, Disentis and hypothetic laws. When the two individuals have rhombohedral faces in contact, there will even be exact two-dimensional coincidence (multiplicity σ) in the contact plane and exact three-dimensional coincidence (multiplicity Σ) in space if the square of the axial ratio c/ a is rational. Indications are found that (despite their high values) these multiplicities may be related to the frequency of occurrence of intergrowths in low- and high-quartz. [ABSTRACT FROM AUTHOR]

The structure of the coincidence symmetry group of an arbitrary -dimensional lattice in the -dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry subgroup (the subgroup formed by those coincidence symmetries that are elements of the orthogonal group). Conditions under which the coincidence isometry group can be generated by reflections defined by vectors of the lattice are discussed and an algorithm to decompose an arbitrary element of the coincidence isometry group in terms of reflections defined by vectors of the lattice is given. [ABSTRACT FROM AUTHOR]

The Bilbao Crystallographic Server is a web site with crystallographic programs and databases freely available on-line ( ). The server gives access to general information related to crystallographic symmetry groups (generators, general and special positions, maximal subgroups, Brillouin zones etc.). Apart from the simple tools for retrieving the stored data, there are programs for the analysis of group–subgroup relations between space groups (subgroups and supergroups, Wyckoff-position splitting schemes etc.). There are also software packages studying specific problems of solid-state physics, structural chemistry and crystallography. This article reports on the programs treating representations of point and space groups. There are tools for the construction of irreducible representations, for the study of the correlations between representations of group–subgroup pairs of space groups and for the decompositions of Kronecker products of representations. [ABSTRACT FROM AUTHOR]

This article is a roadmap to a systematic calculation and tabulation of tensorial covariants for the point groups of material physics. The following are the essential steps in the described approach to tensor calculus. (i) An exact specification of the considered point groups by their embellished Hermann–Mauguin and Schoenflies symbols. (ii) Introduction of oriented Laue classes of magnetic point groups. (iii) An exact specification of matrix ireps (irreducible representations). (iv) Introduction of so-called typical (standard) bases and variables – typical invariants, relative invariants or components of the typical covariants. (v) Introduction of Clebsch–Gordan products of the typical variables. (vi) Calculation of tensorial covariants of ascending ranks with consecutive use of tables of Clebsch–Gordan products. (vii) Opechowski's magic relations between tensorial decompositions. These steps are illustrated for groups of the tetragonal oriented Laue class D4 z− 4 z2 x2 xy of magnetic point groups and for tensors up to fourth rank. [ABSTRACT FROM AUTHOR]

The system of Hermann–Mauguin symbols for space and subperiodic Euclidean groups in two and three dimensions is extended to groups with continuous and semicontinuous translation subgroups (lattices). An interpretation of these symbols is proposed in which each symbol defines a quite specific Euclidean group with reference to a crystallographic basis, including the location of the group in space. Symbols of subperiodic (layer and rod) groups are strongly correlated with symbols of decomposable space groups on the basis of the factorization theorem. Introduction of groups with continuous and semicon­tinuous lattices is connected with a proposal for several new terms that describe the properties of these groups and with a proposal to amend the meaning of space groups and of crystallographic groups. Charts of plane, layer and space groups describe variants of these groups with the same reducible point group but various types of lattices. Examples of such charts are given for plane, layer and space groups to illustrate the unification principle for groups with decomposable lattices. [ABSTRACT FROM AUTHOR]

The theory of domain states is reviewed as a prerequisite for consideration of tensorial distinction of domain states. It is then shown that the parameters of the first domain in a ferroic phase transition from a set of isomorphic groups of the same oriented Laue class can be systematically and suitably represented in terms of typical variables. On replacing these variables by actual tensor components according to the previous paper [Kopský (2006), Acta Cryst. A 62, ], we can reveal the tensorial parameters associated with each particular symmetry descent. Parameters are distinguished by the ireps to which they belong and this can be used to determine which of them are the principal parameters that distinguish all domain states, in contrast to secondary parameters which are common to several domain states. In general, the parameters are expressed as the covariant components of the tensors. A general procedure is described which is designed to transform the results to Cartesian components. It consists of two parts: the first, called the labelling of covariants, and its inverse, called the conversion equations. Transformation of parameters from the first domain state to other states is now reduced to irreducible subspaces whose maximal dimension is three in contrast with higher dimensions of tensor spaces. With this method, we can explicitly calculate tensor parameters for all domain states. To find the distinction of pairs of domain states, it is suitable to use the concept of the twinning group which is briefly described. [ABSTRACT FROM AUTHOR]

Tables of crystallographic properties of the magnetic subperiodic groups, i.e. the 31 magnetic frieze-group types, the 394 magnetic rod-group types and the 528 magnetic layer-group types are presented. The content and format is similar to that of non-magnetic subperiodic groups and space groups given in International Tables for Crystallography. Additional content for each group type includes a diagram of general positions with corresponding general magnetic moments, Seitz notation used as a second notation for symmetry operations, and general and special positions listed with the components of the corresponding magnetic moments allowed by symmetry. [ABSTRACT FROM AUTHOR]

Presents the 2003 Executive Committee Report on meetings of the International Union of Crystallography. World Directory of Crystalography; List of publications; Work of the Commissions.

For a small and ideally imperfect crystal, a method for calculating n-beam X-ray diffraction intensities has been developed on the basis of macroscopic intensity exchanges among the beams. This kinematical formulation results in a set of simultaneous equations that can be solved by numerical calculation. To validate the macroscopic formulae, the Darwin intensity transfer equations, which describe microscopic interactions by both diffraction and absorption, are integrated on a spherical crystal. With the hypotheses that one beam contributes to other beams as proportional to its observed intensity, the macroscopic and microscopic formulations are proved to be equivalent; quantitative evaluation of the n-beam effect thereby becomes available for practical experiments using a specimen with finite cross section of X-ray absorption. Examples of the &PSI;-scan simulation on Si 111 and 222 are presented to characterize the present method, demonstrating the reasonable behaviour of the observed diffraction intensity while the linear absorption coefficient and the specimen size are varied. [ABSTRACT FROM AUTHOR]

The problem of coincidences of planar lattices is analyzed using Clifford algebra. It is shown that an arbitrary coincidence isometry can be decomposed as a product of coincidence reflections and this allows planar coincidence lattices to be characterized algebraically. The cases of square, rectangular and rhombic lattices are worked out in detail. One of the aims of this work is to show the potential usefulness of Clifford algebra in crystallography. The power of Clifford algebra for expressing geometric ideas is exploited here and the procedure presented can be generalized to higher dimensions. [ABSTRACT FROM AUTHOR]

Spectra of parametric X-radiation (PXR) in the range of anomalous dispersion of atoms of a crystallographic unit cell are theoretically analyzed. Characteristics of PXR are calculated for both ultrarelativistic (E ≥ 50 MeV) and non-relativistic (E ... 100 keV) electrons interacting with complex organic crystals. The analysis of the PXR angular distribution is shown to permit the realization of the anomalous scattering method for the direct measurement of structure amplitude phases. [ABSTRACT FROM AUTHOR]

Comparative X-ray diffraction studies at different temperatures are used to complement the information usually extracted from 'single-point' charge-density studies. The response of soft bonds against (temperature driven) changes of the crystalline environment might be indicative of some intramolecular mode associated with an incipient bonding. This is in fact confirmed for the anion [FeCo(CO)8]- in the [(Ph3P)2N]+ salt. In contrast, the [Crk2H(CO)10]- anion, whose conformation is known to strongly depend on the counterion, is actually insensitive to T variations in the [K(C18H36N2O6)]+ salt. [ABSTRACT FROM AUTHOR]

The article determines the crystallography of a new metastable phase in Zr-N alloy. Selected-area and convergent-beam electron diffraction were used to determine the lattice, point and space groups of the metastable phase. This phase is body-centered tetragonal with a space-group symmetry of I4/mmm. The thinned specimen was examined in transmission electron microscope at 200 kV. The specimen was tilted along different Kikuchi bands to reach several low-index zone axes and the corresponding selected-area diffraction patterns were then recorded.

The article proposes a procedure for phase extension in crystallography using the iterative Fienup-Gerchberg -Saxton algorithm and Hilbert transforms. Based on an incomplete set of phases, the magnitudes of many non-Bragg reflections with fractional indices can be calculated with high accuracy using equations derived from the Shannon sampling theorem and the Hilbert transform. Constraints play a very important role in the iterative algorithm. Constraints in reciprocal and real space are the key points that drive the iterations toward a unique solution. In this way, it is shown that the iterative algorithm conventionally used for phasing diffuse scattering from non-periodic objects can also be applied to problems in conventional crystallography to find the phase of high-order beams from a known set of low-order phases.

The article studies the fine structure of X-ray diffuse scattering in the vicinity of high-angle superlattice Bragg reflections. The resonant features of X-ray diffuse scattering from the AlAs/GaAs superlattice was observed when the incoming or outgoing angle is nearly equal to the Bragg angle of the wide-angle reflections from the superlattice or substrate. The degree of denomination in intensity of the incoming feature over the outgoing one was shown to indicate the decay rate of the coherent X-ray field through the diffuse-scattering channel.

Presents information on the International Union of Crystallography Nineteenth General Assembly and International Congress of Crystallography held in Geneva, Switzerland, from August 6-15, 2002. Information is provided on delegates, events and different sessions of the meeting.

Presents a report of a subcommittee on the nomenclature of dimensional crystallography. Recommended symbols for point-group transformations, geometric crystal classes, families and systems; Mathematical formulation of the theory of space groups.

Discusses a feasible set approach to the crystallographic phase problem. Methods in solving the crystallographic phase problem; Basic elements required to solve an image recovery problem; Difference between the crystallographic phase and the image recovery problems.

The article discusses the contribution and impact regarding the research on novel materials wherein it is considered as among the fastest growing fields of scientific activity. It mentions that the quest for novel materials possess tremendous technological and social impact and added that it has boosted the development of novel techniques for improving material fabrication. Moreover, it also provides an overview of the workshop on structural transitions in solids.

Provides information on subscription rates and prices for crystallography journals. "Acta Crystallographica Section A: Foundations of Crystallography"; "Acta Crystallographica Section B: Structural Science"; "Acta Crystallographica Section C: Crystal Structure Communications."

Discusses the charge density (CD) of a chemical compound, the most information-rich observable that is available for the system Information contained in the CE on the chemical bonding as well as on physical and chemical properties; Diffraction experiments at short wavelength and low temperature; Capability of CD to define the electronic ground state of a system.