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