Reconstruction of an object from its symmetry-averaged diffraction pattern

An object can be reconstructed from its diffraction pattern incoherently averaged with respect to a discrete group of symmetries under conditions on the shape of the object and the order of the group.

Higher-dimensional point groups in superspace crystallography

The (n,d)-dimensional superspace crystallography is extended to include n-dimensional crystallographic point groups and not only those isomorphic to finite subgroups of the orthogonal group O(d), with d the physical dimension.

Solving the crystal structures of zeolites using electron diffraction data. I. The use of potential-density histograms

The maximum-entropy method for solving zeolite structures from electron diffraction data is supplemented with potential-density histograms.

Solving the crystal structures of zeolites using electron diffraction data. II. Density-building functions

The maximum-entropy method for solving structures from electron diffraction data is modified to use potential density-building functions and used successfully to solve eight zeolite and related structures.

Crystallography without crystals. I. The common-line method for assembling a three-dimensional diffraction volume from single-particle scattering

The capabilities and limitations are demonstrated and discussed of a common-line method of assembling a three-dimensional oversampled diffraction data volume suitable for structure solution from diffraction patterns of randomly oriented protein molecules obtained with a fourth-generation X-ray source. The method requires a detected photon count of 10 per pulse/pixel, about three orders of magnitude greater than anticipated for a 500 kDa protein.

Ferroic classifications extended to ferrotoroidic crystals

Ferromagnetic, ferroelectric and ferroelastic classifications of multiferroic crystals are extended to include ferrotoroidic crystals.

Precise determination of anomalous scattering factors of Ge by using X-ray resonant scattering

A method for the determination of the anomalous scattering factor very near an absorption edge is proposed based on the fact that phase change of the real part of the atomic scattering factor is large and affects the peak position of the rocking curve. As an example, the anomalous scattering factor of Ge is determined with accuracy better than 1%.

Minimally resolution biased electron-density maps

Algorithms for calculating minimally resolution biased electron-density maps are described.

A note on Bragg-case Pendellösung and dispersion surface

Bragg-case Pendellösung involves wavefields belonging to the same branch of the dispersion surface if the dispersion surface is considered in an infinite medium but wavefields belonging to different branches if the actual dispersion surface is considered in the semi-infinite medium where they are generated by the incident wave.

Why phase errors affect the electron function more than amplitude errors

Images generated using the phases from structure A and the amplitudes from structure B look recognizably like A. This paper quantifies that similarity by calculating statistics such as the correlation coefficient between the true and phase-swapped structures.

Magnetic group maximal subgroups of index ≤4

The maximal subgroups of index ≤4 of the one-, two- and three-dimensional magnetic space groups and the two- and three-dimensional magnetic subperiodic groups are tabulated.

Theories and techniques of crystal structure determination

J. D. Bernal. The sage of science

Ewald Prize Award

Notes for authors 2008