Crystallographic Algorithms and Tables

Definitions, results and algorithms forming the background of the computer package CARAT are outlined. CARAT handles crystallographic space groups up to dimension 6.

A New Approach Towards Measuring Structure Factors and Valence-Electron Distribution in Crystals with Large Unit Cells

By simultaneously observing the intensity oscillations with thickness of many reflections in electron diffraction, the structure factors of reflections at small angles in large-unit-cell crystals are accurately measured. These structure factors are highly sensitive to bonding and charge transfer.

Use of Statistical Information in X-ray Crystallography with Application to the Holographic Method

Bayesian formulas are obtained for processing X-ray diffraction data, for the weighting of observed reflections and for the estimation of missing data. Maximum-entropy reconstruction is introduced into the holographic method.

The Effects of Dynamical Diffraction on the Measurement of Gravitationally Induced Quantum Phase Shifts by Neutron Interferometry

Previous calculations of the corrections to the gravitationally induced phase shift of the neutron in silicon crystal Mach–Zehnder interferometers due to dynamical diffraction are extended to include skew-symmetric interferometers and the C3 detector beam. Gravitationally induced interference effects within each subbeam of the interferometer are discussed.

The Optical Activity of Lysozyme Crystals

All the components of the gyration tensor for a lysozyme crystal were determined using the HAUP method. A strange character of the optical properties of the enzyme is shown. The change of structure of lysozyme in solution and crystalline states is quantitatively established.

Application of Direct Methods to Dynamical Electron Diffraction Data for Solving Bulk Crystal Structures

It is shown that direct methods can be used with dynamical electron diffraction data from bulk crystal structures to restore structural information contained in the function |ψ(r)-1|. The use of dynamical data can lead to enhanced sensitivity to light atoms, which is explained using dynamical theory.

X-ray Diffraction by a One-Dimensional Paracrystal of Limited Size

The features of diffraction by one-dimensional paracrystals, monodisperse and polydisperse, are discussed based on new explicit equations. A practical application to measure the paracrystal size and degree of disorder using single X-ray reflection is given.

The Translation Problem in Molecular Replacement Techniques. I. About the Role of Triplet Invariants

Direct methods are used to solve the translation problem in molecular replacement techniques.

Iterative Low-Pass Filtering for Estimation of the Background in Fiber Diffraction Patterns

A method, based on an iterative application of low-pass filter and deconvolution procedures, was applied to estimate the background and layer-line intensities in X-ray fiber diffraction patterns taken from filamentous bacteriophage samples.

The Genetic Algorithm: Foundations and Apllications in Structure Solution from Powder Diffraction Data

Recently, new methods based on the use of genetic algorithms have been explored and developed for solving crystal structures from powder diffraction data. In this paper, the fundamental concepts underlying genetic algorithms are discussed and the implementation of this approach for structure solution from powder diffraction data is described; opportunities for future developments in the foundations and applications of genetic algorithms in this field are highlighted.

Nonlinear Least-Squares Fitting of Numerical Relativistic Atomic Wave Functions by a Linear Combination of Slater-Type Functions for Atoms with Z = 1–36

New relativistic atomic ground-state wave functions for atoms H through Kr have been fitted by a linear combination of Slater functions. All results are accessible at http://wings.buffalo.edu/~chem9982.

Towards General Diffractometry. I. Normal-Beam Equatorial Geometry

A mathematical description of the normal-beam equatorial goniometer with misaligned axes φ and θ as well as methods for transforming the setting angles between different goniometers and procedures for positioning reflections are described.

Analysis of Single-Crystal Diffuse X-ray Scattering via Automatic Refinement of a Monte Carlo Model

The feasibility is demonstrated of automatic least-squares refinement of a Monte Carlo model of a disordered structure by quantitative comparison of its calculated diffraction pattern with observed diffuse scattering data. The method is applied to the material Fe₃(CO) 12, which shows strong diffuse scattering caused by the fact that the triangular Fe₃ group can occupy a given molecular site, in either of two different orientations.

Stable Desmearing of Slit-Collimated SAXS Patterns by Adequate Numerical Conditioning

Physically reliable conditioning of the experimental data and introduction of a suitable Moore–Penrose pseudoinverse can achieve analytical stability of the desmearing procedure for SAXS patterns. The algorithm remains stable despite large noise contributions.

Polytypism and Related Phenomena in CdBr₂-Doped Dendritic Single Crystals of Cadmium Iodide

Undoped and CdBr₂-doped dendritic crystals of cadmium iodide are grown from vapour and characterized for their polytypism and related phenomena. The effect of doping on polytype formation and associated phenomena is discussed.

X-ray charge densities and chemical bonding by P. Coppens