Solution of the crystallographic phase problem by iterated projections

A new method of ab initio phase determination is demonstrated which does not rely on reciprocal-space formulations of atomicity.

Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6

Classification levels for crystallographic groups are reconsidered and for each level enantiomorphism is discussed. Explicit results are given for dimensions up to 6.

X-ray scattering amplitude of an atom in a permanent external electric field

The X-ray scattering by a many-electron atom in a permanent external electric field is developed. It was found that field-induced atomic shell deformations can be neglected during the structure analysis of a crystal in an electric field.

Multiparametric scaling of diffraction intensities

A novel method of scaling diffraction intensities is presented.

X-ray Takagi–Taupin dynamical theory generalized to n-beam diffraction cases

A new X-ray dynamical diffraction theory that can deal with n-beam cases comprehensively (n ∈ {3, 4, 6, 8, 12}) has been derived based on the Takagi–Taupin dynamical theory.

Ab initio protein phasing at 1.4 Å resolution

A new phasing approach able to solve ab initio protein structures via diffraction data at 1.4 Å resolution is described and tested.

The phase problem in neutron crystallography

The phase problem of neutron crystallography is formulated as a problem in constrained global minimization, the solution of which, by means of a modified Shake-and-Bake algorithm (Neutron Shake-and-Bake), exploits the property of the neutron density function that it takes negative as well as positive values. The applications show that the positivity of the density function is not only not required for the solution of the phase problem but that positivity is actually a hindrance.

Solving non-periodic structures using direct methods: phasing diffuse scattering

The reconstruction of the charge density of an isolated non-periodic object from X-ray scattering is simulated using direct methods. The ability to phase diffuse scattering is relevant to the imaging of inorganic nanoparticles.

The estimate of the protein phases for the SAD case: a simplified formula

A simple probabilistic formula is derived to estimate protein phases in the single-wavelength diffraction (SAD) case.

Relations between the zinc-blende and the NaCl structure type

A new transition mechanism is proposed for the transformation from the zinc-blende to the NaCl type. It is described by means of a deformation of a heterogeneous sphere packing in space group P3₂.

Local squaring functions for non-spherical templates

Local squaring functions for individual atoms are effective phase refinement and automatic model building tools. The generalization to multiatom fragments is developed.

Variations in abundance of known crystalline compounds as a function of lattice constants

Preliminary plots of the abundance of inorganic compounds as a function of their crystallographic parameters disclosed sharp peaks which in some cases corresponded to specific sphere packing or structure types.

C₇₂ to C₁₀₀ fullerenes: combinatorial types and symmetries

The symmetry point-group statistics for all combinatorially different C₇₂ to C₁₀₀ fullerenes with free 5-gonal facets only are suggested for the first time. The shapes with automorphism group orders not less than 3 are drawn in Schlegel diagrams.

Structure, odd lines and topological entropy of disorder of amorphous silicon. Correction

Erratum to Acta Cryst. (2002), A58, 346–351.