Formation of interference fringes in the Bragg–(Bragg)^m–Laue mode

The origin of X-ray interference fringes observed in the beams diffracted from a lateral surface of a thin plane-parallel Ge crystal is shown to be the interference between the beams in the Bragg–Laue and the Bragg–Bragg–Laue cases.

The relationship of the hyperspherical harmonics to SO(3), SO(4) and orientation distribution functions

Several mathematical results pertaining to the representation of texture information in the axis–angle parameterization by the hyperspherical harmonic expansion are provided. In particular, an addition formula for the basis functions of this expansion and an alternative form of the matrix by which a rotation of the sample affects the basis functions are presented.

Investigations of the bond-selective response in a piezoelectric Li₂SO₄·H₂O crystal to an applied external electric field

Piezoelectric lithium sulfate monohydrate, Li₂SO₄·H₂O, was analyzed with respect to the relationship between the static structural properties of the crystal and its response to an external electric field. The distortions of the cation–anion bond lengths in the LiO₄, LiO₃(H₂O) and SO₄ tetrahedra were evaluated and were found to reflect the electron-density-related properties of the Li—O and S—O bonds.

On a minimum tetrahedron in a three-dimensional lattice. Part I. Lattices with a shortest basis fulfilling b · c ≥ 0, a · c ≥ 0, a · b ≥ 0

The possibility of using a tetrahedron instead of a cell (i.e. a parallelepiped) as a representative body of a lattice is examined. Necessary and sufficient conditions for its uniqueness are found for lattices having a shortest basis with a · b ≥ 0, a · c ≥ 0, b · c ≥ 0.

MAD techniques applied to powder data: finding the structure given the substructure

The joint probability distribution function method is combined with MAD techniques to solve the phase problem from powder data.

Towards the best model for H atoms in experimental charge-density refinement

Discussion of the consequences of different treatments of H atoms in experimental charge-density studies of model complexes of DMAN leads to the best model for H atoms in experimental charge-density refinement.

Determination of molecular envelopes from solvent contrast variation data

An algorithm for reconstructing macromolecular envelopes from solvent contrast variation data is described and illustrated by simulations.

Probability plots based on Student's t-distribution

The use of Student's t-distribution in a probability plot is discussed.

Concise intensity statistics of Friedel opposites and classification of the reflections

Previous results on intensity statistics of Friedel opposites, for general and special reflections, are concisely re-examined and confirmed by purely statistical methods. A complete classification of the reflections, based on the above, is presented.

Three new types of interpenetrating sphere packings

Three new types of interpenetrating homogeneous sphere packings with symmetries Ccce and Fddd are described.