X-ray investigation of lateral hetero-structures of inversion domains in LiNbO₃, KTiOPO₄ and KTiOAsO₄

Periodically-poled ferroelectric crystals are studied by observing their superlattice (grating) diffraction profiles with high-resolution X-ray diffraction. In order to successfully model the data, the effects of strain, and sample and beam coherence, must be taken into account.

Symmetry of semi-reduced lattices

The characterization of Bravais types is extended according to metrical, algebraic and geometric properties onto a wide class of primitive lattices (including Buerger-reduced and a substantial part of Delaunay-reduced) related to low-restricted semi-reduced descriptions. There are excellent theoretical and practical reasons for looking at crystal lattice symmetry from an entirely new point of view – the combinatorial set of 960 matrices, their semi-reduced lattice context and their geometric properties.

Structure factor for an icosahedral quasicrystal within a statistical approach

A structure factor for an icosahedral quasicrystal with an arbitrary decoration scheme based on a primitive icosahedral tiling model and a statistical approach is derived. The average unit cell concept is used as an alternative to the commonly used higher-dimensional description.

Absolute refinement of crystal structures by X-ray phase measurements

The application of X-ray phase measurements for absolute identification and improvement of atomic model structures is described.

Icosahedral symmetry breaking: C₆₀ to C₈₄, C₁₀₈ and to related nanotubes

The structure of a particular type of hollow-cage higher fullerene (C_60+N24) is described and their construction explained from a symmetry-breaking mechanism starting from perfect icosahedral symmetry of C₆₀ to specific subgroups A₁ × A₁. This mechanism expands and completes previous results describing the existence of other groups of fullerenes (C_60+N10, C_60+N18) based on the breaking of icosahedral symmetry of C₆₀ to the subgroups H₂ and A₂. The mechanism is extended to describe the cases that generate carbon nanotubes.

Unique atom hyper-kagome order in Na₄Ir₃O₈ and in low-symmetry spinel modifications

Group-theoretical and thermodynamic methods of the Landau theory of phase transitions are used to investigate the hyper-kagome atomic order in structures of ordered spinels and a spinel-like Na₄Ir₃O₈ crystal. The existence of hyper-kagome lattices in six types of ordered spinel structures is predicted theoretically.

Determination of small crystal structures from a minimum set of diffraction intensities by homotopy continuation

A method from numerical algebraic geometry, called homotopy continuation, is used to determine small crystal structures of four or fewer atoms directly from a minimum set of diffraction intensities.

Magnetic structure determination from the magnetic pair distribution function (mPDF): ground state of MnO

Combined atomic and magnetic pair distribution function (PDF) refinements have been performed against neutron scattering data from MnO, recovering the expected long-range-ordered antiferromagnetic state and supporting a scenario of monoclinic symmetry on a local length scale of ∼100 Å. This represents the first experimental application of the magnetic PDF method.

More statistics on intermetallic compounds – ternary phases

Ternary intermetallics – 13 026 compounds contained in the database Pearson's Crystal Data – are discussed with respect to their components, structure types and stoichiometries.

Axial point groups: rank 1, 2, 3 and 4 property tensor tables

Physical property tensors of materials such as nanotubes or polymers are determined by the material's axial point group. Rank 1, 2, 3 and 4 property tensors are given for a wide variety of tensor types invariant under each point group in all 31 infinite series of axial point groups.