Acta Crystallographica Section A

Foundations of Crystallography

Volume 52, Part 2 (March 1996)

Cover illustration: Indicatrix of the inverse of Young's modulus for ADP, a tetragonal crystal. Courtesy of A. Authier, Laboratoire de Minéralogie-Cristallographie, Université Pierre et Marie Curie, Paris, France.

• research papers
• short communications

research papers

Acta Cryst. (1996). A52, 125-132    [doi:10.1107/S010876739501169X]

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

V. Hansen and J. Gjønnes

Synopsis: 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.

Acta Cryst. (1996). A52, 133-142    [doi:10.1107/S0108767395012116]

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

C. Giacovazzo and D. Siliqi

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

Acta Cryst. (1996). A52, 143-151    [doi:10.1107/S0108767395012189]

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

C. Giacovazzo and D. Siliqi

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

Acta Cryst. (1996). A52, 152-157    [doi:10.1107/S0108767395012682]

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

D. X. Huang, W. Liu, Y. X. Gu, J. W. Xiong, H. F. Fan and F. H. Li

Synopsis: 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.

Acta Cryst. (1996). A52, 158-170    [doi:10.1107/S0108767395012657]

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

M. Awaji and H. Hashimoto

Synopsis: 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.

Acta Cryst. (1996). A52, 171-175    [doi:10.1107/S0108767395012578]

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

W. Prandl, P. Schiebel and K. Wulf

Synopsis: 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.

Acta Cryst. (1996). A52, 176-188    [doi:10.1107/S0108767395012566]

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

P. Schiebel, K. Wulf, W. Prandl, G. Heger, R. Papoular and W. Paulus

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

Acta Cryst. (1996). A52, 189-197    [doi:10.1107/S0108767395011433]

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

P. Schiebel, W. Prandl, R. Papoular and W. Paulus

Synopsis: 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.

Acta Cryst. (1996). A52, 198-202    [doi:10.1107/S0108767395012761]

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

V. N. Bugaev and R. V. Chepul'skii

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

Acta Cryst. (1996). A52, 203-211    [doi:10.1107/S0108767395012864]

Time Relaxation of the Low-Temperature Modulated Structure of Thiourea

I. Aramburu, G. Madariaga, J. M. Pérez-Mato and T. Breczewski

Synopsis: 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.

Acta Cryst. (1996). A52, 212-220    [doi:10.1107/S0108767395012876]

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

M. M. J. Treacy and J. M. Gibson

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

Acta Cryst. (1996). A52, 221-235    [doi:10.1107/S0108767395012888]

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

Y. Zheng and P. C. Doerschuk

Synopsis: 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.

Acta Cryst. (1996). A52, 236-244    [doi:10.1107/S0108767395012670]

X-ray Resonant Exchange Scattering: Polariztaion Dependence and Correlation Function

J. P. Hill and D. F. McMorrow

Synopsis: 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.

Acta Cryst. (1996). A52, 245-250    [doi:10.1107/S0108767395013742]

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

P. D. Healey and J. E. Ayers

Synopsis: 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.

Acta Cryst. (1996). A52, 251-256    [doi:10.1107/S0108767395014036]

Point Groups and Elastic Properties of Two-Dimensional Quasicrystals

C. Hu, R. Wang, W. Yang and D. Ding

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

Acta Cryst. (1996). A52, 257-276    [doi:10.1107/S0108767395014371]

Robust Parameterization of Elastic and Absorptive Electron Atomic Scattering Factors

L.-M. Peng, G. Ren, S. L. Dudarev and M. J. Whelan

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

Acta Cryst. (1996). A52, 277-286    [doi:10.1107/S010876739501422X]

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

T. Haibach and W. Steurer

Synopsis: 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.

Acta Cryst. (1996). A52, 287-290    [doi:10.1107/S0108767395014917]

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

M. Takata and M. Sakata

Synopsis: 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.

Acta Cryst. (1996). A52, 291-301    [doi:10.1107/S0108767395014942]

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

A. El Haouzi, N. K. Hansen, C. Le Hénaff and J. Protas

Synopsis: 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.

Acta Cryst. (1996). A52, 302-311    [doi:10.1107/S0108767395015546]

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

A. Parisini, S. Milita and M. Servidori

Synopsis: 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.

Acta Cryst. (1996). A52, 312-325    [doi:10.1107/S0108767395015571]

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

J. Yoshimura

Synopsis: 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.

short communications

Acta Cryst. (1996). A52, 326    [doi:10.1107/S0108767395015364]

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

I.-H. Suh

Synopsis: 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.

Acta Cryst. (1996). A52, 326-328    [doi:10.1107/S0108767395016679]

Ab initio molecular packing analysis

D. E. Williams

Synopsis: 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.

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