Approximants and Intermediate Stages during Transformation from a Quasicrystalline to a Crystalline Phase in an Al–Mn–Si Alloy

The transformation from a quasicrystalline to a crystalline Al–Mn–Si phase is described in terms of two complementary rhombohedral elements with edges along threefold axes in the icosahedron.

On Integrating Direct Methods and Isomorphous Replacement Techniques. I. A Distribution Function for Quartet Invariants

For two isomorphous structures, the joint probability distribution function of seven pairs of structure factors is derived, from which quartets may be estimated.

On Integrating Direct Methods and Isomorphous Replacement Techniques. II. The Quartet Invariant Estimate

Formulas estimating quartet phases are provided in the absence of prior information and when the heavy-atom structure is known.

A Method of Electron Diffraction Intensity Correction in Combination with High-Resolution Electron Microscopy

An empirical method is proposed for correcting the distortion of electron diffraction intensity caused by Ewald sphere, crystal bend, dynamical scattering etc. The method is based on the combination of electron diffraction and high-resolution electron microscopy.

Detection of a Point Defect in a Silicon Single Crystal by a Subtraction Method using High-Resolution Transmission Electron Microscopy

The contrast of high-resolution transmission electron-micro- scope images and subtracted images are discussed by changing the noise level to examine the possibility for observation and identification of point defects with weak contrast.

A Recursive Algorithm for the Generation of Symmetry-Adapted Functions: Principles and Applications to the Icosahedral Group

A product of spherical harmonic functions can be resolved algebraically into a sum of single functions. This theorem is used to calculate high-order symmetry-adapted functions by a recursive algorithm.

Orientationa Disorder, the Orientational Density Distribution and the Rotational Potential in C₆₀

The anisotropic density distribution and the rotational potential V(ω) is determined from neutron and X-ray diffraction data of C₆₀ single crystals at 295K. V(ω) exhibits two sets of minima, which are fixed by the intrinsic geometry of the Euler-angle space.

Almost Free Rotation of NH₃ Molecules in Crystals: Observation from a Maximum-Entropy Reconstruction of the Proton Density in [Co(NH₃)₆](PF₆)₂

Maximum-entropy reconstruction combined with a preliminary phasing of the absolute values of the observed structure factors by a crystal structure analysis provides for direct observation of the density of ammonia molecules indicating almost free rotation at 295K as well as at 30K.

On the Problem of the Description of the Ordered Structures in Binary Solid Solutions with a Hexagonal Crystal Lattice

All types of thermodynamically stable (Lifshitz) ordered structures arising from the disordered state of binary solid solutions with a hexagonal crystal lattice are established.

Time Relaxation of the Low-Temperature Modulated Structure of Thiourea

A systematic and reducible slow time variation of the diffracted intensities by the incommensurate phase of thiourea at 170K has been detected. The observed kinetic process can be quantitatively explained in terms of a slow relaxation of the soliton density, the structural modulation evolving towards a more sinusoidal regime.

Variable Coherence Microscopy: a Rich Source of Structural Information from Disordered Materials

Speckle statistics in transmission electron microscopy hollow- cone dark-field images provide evidence for medium-range order in annealed amorphous Ge films

Explicit Orthonormal Fixed Bases for Spaces of Functions that are Totally Symmetric Under the Rotational Symmetries of a Platonic Solid

Explicit complete orthonormal fixed bases are computed for subspaces of the space of square-integrable functions on the sphere where the subspaces contain functions that are totally symmetric under the rotational symmetries of a Platonic solid. The case of the icosahedron is important for structural studies of spherical viruses.

Resonant Exchange Scattering: Polarization Dependence and Correlation Function

The X-ray resonant exchange scattering cross section is reformulated to highlight the contribution of the individual components of the magnetic moment. Static correlation functions are also derived.

The Instrumental Broadening Function of the Bartels Five-Crystal X-ray Diffractometer

An analytical description has been given for the instrumental broadening function of the Bartels diffractometer. This result allows determination of specimen rocking-curve widths from measured widths.

Point Groups and Elastic Properties of Two-Dimensional Quasicrystals

Possible point groups and elastic properties are discussed for a solid with two-dimensional quasi-periodic and one-dimensional periodic structure.

Robust Parameterization of Elastic and Absorptive Electron Atomic Scattering Factors

A robust algorithm has been developed and applied for parameterization of elastic and absorptive electron atomic scattering factors.

Five-Dimensional Symmetry Minimum Function and Maximum-Entropy Method for Ab Initio Solution of Decagonal Structures

A combination of the n-dimensional symmetry minimum function with the maximum-entropy method for ab initio solution of decagonal structures is derived and two structure solutions are presented.

The Influence of the Completeness of the Data Set on the Charge Density Obtained with the Maximum-Entropy Method. A Re-examination of the Electron-Density Distribution in Si

In order to examine the influence of the completeness of the data set on the charge densities derived with the maximum-entropy method (MEM), the structure-factor data for Si measured by the Pendellösung method is reanalysed by the MEM. It is found that the fine features in the previous MEM charge density of Si are non-physical artificial modulations caused by the failure of the MEM to extrapolate over the gap of missing data in the case of an incomplete set and that the maxima at the bond midpoint are exaggerated artificially owing to the incompleteness of the data set used for the MEM.

The Phase Problem in the Analysis of X-ray Diffraction Data in Terms of Electron-Density Distributions

An explanation of why multipole refinements of electron-density distributions may lead to ambiguous or even meaningless results for non-centrosymmetric crystal structures is given. Specific examples show how applying constraints on the density models may improve this situation.

Bragg-Case X-ray Interference in Multilayered Structures. Comparison Between Kinematical Approximation and Dynamical Treatment

A kinematical expression is proposed to describe X-ray interference phenomena in the symmetric Bragg case from multi- lamina structures. The formalism is able to represent any desired sequence of crystalline and non-diffracting layers and hence can be applied to a variety of experimental situations. Comparison is made with experimental rocking curves obtained from implanted silicon with embedded amorphous layers.

A Detailed Observation of the Nonprojectiveness of X-ray Moiré-Fringed Diffraction Images

The real state of the unusual spatial oscillation of Moiré fringes on the beam path out of a crystal is investigated with such experimental data as moiré topographs, intensity profiles, plots of the positions and directions of oscillating fringes, and a map of the oscillation amplitude over the whole field of the moiré pattern.

Multiplicity of crystal planes belonging to the point group -4m2. Erratum

Erratum to International Tables for Crystallography, Vol. A, Table 10.2.2. The multiplicity of 00l or 00-l in the point group -4m2 is 2.

Ab initio molecular packing analysis

A method is presented which, given a molecular structure and an intermolecular force field, can predict observed polymorphic crystal structures and molecular clusters without any prior assumption of space symmetry.