Beyond Space Groups: the Arithmetic Symmetry of Deformable Multilattices

This paper presents an arithmetic approach to the symmetry of complex crystalline structures (multilattices). This generalizes the one classically used for simple lattices and gives a finer description of multilattice symmetry than that obtained through space groups.

Geometrical Model of the Phase Transformation of Decagonal Al–Co–Ni to its Periodic Approximant

A geometrical model of the quasicrystal-to-crystal transformation based on small atomic displacements including phason flips is discussed using the example of decagonal Al–Co–Ni.

Obtaining the Crystal Potential by Inversion from Electron Scattering Intensities

A method to obtain the crystal potential from the intensities of diffracted beams in high-energy electron diffraction is proposed.

The Background: from Observation to a `Non-Event' in Single-Crystal Diffractometry

Background intensities are summarized in a model defining an accurate reference level upon which the coherent Bragg intensities are superimposed. The background model reduces the random errors on I net eliminating the background as an error component.

Dynamical Three-Beam Diffraction in a Quasicrystal

A three-beam diffraction experiment is described in which circularly polarized X-rays are used. Different azimuthal plots are observed when the helicity of the incident beam is switched, in accordance with a noncentrosymmetric structure.

Symmetrical X-ray Diffraction in a Perfect Rectangular × l Crystal. Extinction and Absorption

The Takagi–Taupin equations for two beams are analysed using the boundary-value Green function technique for the case of symmetrical diffraction in a perfect rectangular × l crystal. Analytical and numerical results are presented for the extinction and absorption factors.

Crystallogeometrical Approach to Stacking-Fault Analysis in Ordered Alloys

The analytical expression for the energy of an unrelaxed stacking fault in a n-dimensional ordered alloy is given in terms of the pair-potential functions.

The Ab Initio Solution of Structures from Powder Diffraction Data: the Use of Maximum Entropy and Likelihood to Determine the Relative Amplitudes of Overlapped Reflections Using the Pseudophase Concept

The maximum-entropy–likelihood method of solving crystal structures from powder diffraction data is extended to include the estimation of the individual intensities of the overlapping reflections using Duncan's statistical procedure combined with likelihood estimation.

Calculation of Thermodynamic Properties of Solids from Accurate Diffraction Data: Isotope Separation Factor in Systems Containing Crystalline Phase

A method of calculation of the thermodynamic functions from accurate X-ray diffraction data has been developed. The isotope-reduced partition-function ratio β D/H for the LiH (LiD) crystal and the separation factor α D/H for the isotope exchange in the solid–gas Li(H,D)–(H₂,D₂) system have been calculated.

A Two-Dimensional Bloch-Wave Method for Dynamical RHEED Calculations

A new two-dimensional Bloch-wave method is developed for dynamical RHEED calculations.

The `Frozen-Lattice' Approach for Incoherent Phonon Excitation in Electron Scattering. How Accurate Is It?

For electron dynamic thermal diffuse scattering, it is proved for the first time that the calculation based on the `frozen lattice' model gives an identical result to the quantum inelastic phonon excitation theory if the incoherence between different orders of diffuse scattering is considered. This conclusion holds for both high- and low-energy electrons and it establishes the quantum-mechanical basis of many existing theories.

Relevance of Charge-Density Measurements for High-Precision Calculations

The re-analysis of high-precision photon diffraction data in beryllium, diamond, silicon, copper and germanium is carried out for an accurate comparison with local density approximation calculations.

Electron Scattering Factors of Ions and their Parameterization

Elastic electron scattering factors of 106 ions are represented in a parameterized form and it is shown that for most transmission electron diffraction applications the effect of crystal ionicity on the absorptive electron scattering may be neglected.

On the Relation of Modulated Structures with the Automorphisms of the d-Dimensional Tori Created by the Compaction of the (3+d)-Dimensional Space

A hypothesis is put forward concerning the existence of the general relation between aperiodic crystal structures and the invariants of the group of the automorphisms of the d-dimensional torus. A relation is proved between the one-dimensional and two-dimensional displacive modulations and the rationality of some invariants of the group of automorphisms of both the circle S¹ and the torus T².

On the Prediction of Crystal Morphology. I. The Hartman–Perdok Theory Revisited

The Hartman–Perdok theory for the prediction of crystal morphology is reformulated on the basis of F faces having a roughening temperature higher than 0 K. The presence of multiple connected nets for a single orientation can give rise to symmetry roughening and high growth rates.

On the Prediction of Crystal Morphology. II. Symmetry Roughening of Pairs of Connected Nets

All cases where symmetry may lead to symmetric roughening for pairs of connected nets of the crystal structure are derived. Symmetry roughening has severe implications for crystal morphology.

An exact analytical expression for the primary extinction factor for a perfect spherical crystal in the limit θ _oh → π/2

An analytical formula is derived for the primary extinction factor in the Bragg limit in the case of a perfect spherical crystal. The result is compared with the corresponding Laue limit.

Compilation of temperature factors of hexagonal close packed elements

A compilation of temperature factors for 14 h.c.p. elements is presented.

The equations of the statistical dynamical theory of X-ray diffraction for deformed crystals. Erratum

Erratum to Acta Cryst. (1998), A54, 214–218.

Simulations for solid state physics. An interactive teaching resource for students and teachers edited by R. H. Silsbee and J. Dräger

Quantum dynamics of simple systems edited by G.-L. Oppo, S. M. Barnett, E. Riis and M. Wilkinson

Dynamics of crystal surfaces and interfaces edited by P. M. Duxbury and T. J. Pence