Acta Crystallographica Section A

Foundations of Crystallography

Volume 68, Part 2 (March 2012)


	Cover illustration: The sequence of constructing the cartwheel pattern of the first-level hierarchy of the quasi-periodic pattern on the interior walls of the courtyard of the Madrasa of al-'Attarin (1323), Fez, Morocco [Al Ajlouni (2012). Acta Cryst. A68, 235-243].

research papers
short communications
obituaries
international union of crystallography

research papers

Acta Cryst. (2012). A68, 167-180 [ doi:10.1107/S0108767311049853 ]

Quantitative crystal structure descriptors from multiplicative congruential generators

Synopsis: Certain number-theoretic relations, known as multiplicative congruential generators, are developed into quantitative crystal structure descriptors, facilitating a linearization procedure that eventually allows for a concise, fully reconstructable representation of structural information. Potential applications are related to the computational storage, retrieval and analysis of crystal structures, their algorithmic generation in the first place, and their combinatorial enumeration and classification.

Online 12 January 2012

Acta Cryst. (2012). A68, 181-187 [ doi:10.1107/S010876731105598X ]

Lattice refinement strategies

J. K. Edmiston, J. V. Bernier, N. R. Barton and G. C. Johnson

Synopsis: This article quantitatively reconciles crystallographic and mechanics approaches to lattice refinement as part of X-ray diffraction procedures. It also derives finite deformation relations of reciprocal-lattice vectors, and demonstrates infinitesimal strain descriptions, commonly employed in stress analysis, to be correct with an error at quadratic order in strain. This error may be important to consider for high-precision or high-strain studies.

Online 27 January 2012

Acta Cryst. (2012). A68, 188-195 [ doi:10.1107/S0108767311044990 ]

New consistency tests for high-accuracy measurements of X-ray mass attenuation coefficients by the X-ray extended-range technique

C. T. Chantler, M. T. Islam, N. A. Rae, C. Q. Tran, J. L. Glover and Z. Barnea

Synopsis: A new method - the multiple independent foil technique - provides data consistency tests and extends the X-ray extended-range technique for measuring X-ray mass attenuation coefficients and X-ray absorption spectroscopy.

Online 5 January 2012

Acta Cryst. (2012). A68, 196-207 [ doi:10.1107/S0108767311051592 ]

Image formation in the scanning transmission electron microscope using object-conjugate detectors

C. Dwyer, S. Lazar, L. Y. Chang and J. Etheridge

Synopsis: The use of object-conjugate detectors in STEM encompasses the three-dimensional imaging technique of SCEM and the recently developed atomic resolution technique of R-STEM. Image formation in this optical geometry is analysed using geometric optics and wave optics, and the relationship between these theories is examined using Wigner distributions. It is shown that geometric optics accurately describes R-STEM and is also applicable to SCEM in a restricted sense.

Online 12 January 2012

Acta Cryst. (2012). A68, 208-221 [ doi:10.1107/S010876731105118X ]

Mathematical aspects of molecular replacement. II. Geometry of motion spaces

G. S. Chirikjian and Y. Yan

Synopsis: The geometric structure of fundamental domains and coset spaces constructed from the continuous group of rigid-body motions and any chiral space group are explored. Almost-uniform sampling methods for these spaces are developed for use in the molecular-replacement method.

Online 7 February 2012

Acta Cryst. (2012). A68, 222-234 [ doi:10.1107/S0108767311046241 ]

The superstructure determination of displacive distortions via symmetry-mode analysis

S. Kerman, B. J. Campbell, K. K. Satyavarapu, H. T. Stokes, F. Perselli and J. S. O. Evans

Synopsis: A structural parameter set consisting of group-theoretically derived symmetry modes facilitates an unbiased determination of a displacively distorted structure. The space-group symmetry is identified from the active symmetry modes rather than being assumed.

Online 5 January 2012

Acta Cryst. (2012). A68, 235-243 [ doi:10.1107/S010876731104774X ]

The global long-range order of quasi-periodic patterns in Islamic architecture

R. A. Al Ajlouni

Synopsis: The first global structural model for describing the long-range translational and orientational order of quasi-crystalline formations in Islamic architecture is presented. It is shown that ancient designers, using simple consecutive geometry, have resolved the complicated long-range principles of quasi-periodic formations.

Online 5 January 2012

Acta Cryst. (2012). A68, 244-255 [ doi:10.1107/S0108767311053281 ]

Covariance and correlation estimation in electron-density maps

A. Altomare, C. Cuocci, C. Giacovazzo, A. Moliterni and R. Rizzi

Synopsis: The covariance between two points of an electron-density map has been calculated, no matter the correlation between the model and target structures.

Online 25 January 2012

Acta Cryst. (2012). A68, 256-265 [ doi:10.1107/S0108767311053815 ]

Phase retrieval in protein crystallography

Z.-C. Liu, R. Xu and Y.-H. Dong

Synopsis: An oversampling method based on the hybrid input-output algorithm is proposed to retrieve the phases of reflections in crystallography from the low-resolution envelopes of the proteins.

Online 7 February 2012

Acta Cryst. (2012). A68, 266-277 [ doi:10.1107/S0108767312001705 ]

Higher-dimensional crystallography of N-fold quasiperiodic tilings

S. Deloudi and W. Steurer

Synopsis: Crystallography and periodic average structures of two-dimensional quasiperiodic tilings with N-fold symmetry (N = 7, 8, 9, 10, 11, 12, 13, 15) were studied using the higher-dimensional approach.

Online 8 February 2012

Acta Cryst. (2012). A68, 278-285 [ doi:10.1107/S010876731104788X ]

Computation of small-angle scattering profiles with three-dimensional Zernike polynomials

H. Liu, R. J. Morris, A. Hexemer, S. Grandison and P. H. Zwart

Synopsis: Three-dimensional Zernike polynomials are employed to efficiently compute small-angle X-ray scattering (SAXS) profiles. Three-dimensional Zernike polynomials faithfully reproduce three-dimensional objects with complex surfaces, including surface-bound solvent. The resulting SAXS profiles are in good agreement with existing computational procedures.

Online 9 February 2012

Acta Cryst. (2012). A68, 286-294 [ doi:10.1107/S0108767312000062 ]

Totally unimodular nets

J.-G. Eon, D. M. Proserpio and V. A. Blatov

Synopsis: A method for generating a special class of nets from finite graphs is described.

Online 16 February 2012

short communications

Acta Cryst. (2012). A68, 295-297 [ doi:10.1107/S0108767311052263 ]

Frequency distribution of the reduced unit cells of centred lattices from the Protein Data Bank

K. Swaminathan

Synopsis: This study presents the frequency distribution of the reduced unit cells of all centred lattice entries of the Protein Data Bank in four unit-cell-dimension-based groups and seven interaxial-angle-based subgroups.

Online 12 January 2012

Acta Cryst. (2012). A68, 298-300 [ doi:10.1107/S0108767311052561 ]

A novel iterative solution to the phase problem

J. Feng

Synopsis: An iterative phase solution based on the global minimization is proposed.

Online 12 January 2012

Acta Cryst. (2012). A68, 301-303 [ doi:10.1107/S0108767312003066 ]

On the significance of Bragg reflections

M. R. V. Jørgensen, H. Svendsen, M. S. Schmøkel, J. Overgaard and B. B. Iversen

Synopsis: The statistical descriptor, W, recently introduced by Henn & Meindl [Acta Cryst. (2010), A66, 676-684] is modified to include the scale factors introduced in data processing, and the effects of using empirical error models on the final significance distribution are discussed.

Online 16 February 2012

Acta Cryst. (2012). A68, 304 [ doi:10.1107/S010876731200325X ]

Response to On the significance of Bragg reflections by Jørgensen et al.

J. Henn and K. Meindl

Synopsis: A response is given to the article On the significance of Bragg reflections by Jørgensen et al. [Acta Cryst. (2012). A68, 301-303].

Online 16 February 2012