Th. Hahn

Nomenclature and generation of three-periodic nets: the vector method

Three-periodic nets are connected graphs which permit embeddings having a threefold periodicity. To many crystal structures such nets can be meaningfully assigned and used to express the topology of the structures. It is shown that such a net can be fully characterized by a finite graph in which the edges are labelled in a suitable way. The reversal of the process of assigning a labelled finite graph to a given net can be used to generate nets of real and hypothetical crystal structures in a systematic fashion.

Statistical descriptors in crystallography: Report of the IUCr Subcommittee on Statistical Descriptors

The Subcommittee has attempted to elucidate the nature of problems encountered in the definition and use of statistical descriptors as applied to crystallography and to propose procedural improvements. The report contains (a) a dictionary of statistical terms established for use by experimentalists; (b) a description of the statistical basis for refinement procedures; (c) sections dealing with defects in the physical model used for refinement, and with the choice and significance of weighting schemes; and (d) recommendations, some of which may be readily implemented, whilst others may require a long-term effort to bring them into general use.

Report of a Subcommittee on the Nomenclature of n-Dimensional Crystallography. I. Symbols for point-group transformations, families, systems and geometric crystal classes

The notation of crystallography in arbitrary dimensions is considered. Recommended symbols for point-group transformations, geometric crystal classes, families and systems are presented.

Structural Phase Transition Nomenclature. Report of an IUCr Working Group on Phase Transition Nomenclature

A compact and intuitive nomenclature is recommended for naming each phase formed by a given material in a sequence of phase transitions as a function of temperature and/or pressure. The most commonly used label for each phase in a sequence, such as [alpha], [beta], ..., I, II, ... etc., is included in the new nomenclature.

The substitution of alkalies in tricalcium silicate

Abstract In tricalcium silicate at 1500°C up to 1.4 % K 2 O, 1.4 % Na 2 O and 1.2 % Li 2 O, respectively, can be incorporated. The following structural substitution types were found: K replaces Ca with valency balance by removal of oxygen; Na replaces Ca and occupies interstitial sites, in addition some oxygen atoms are removed. Li replaces Ca as well as Si and occupies interstitial voids. Only modifications T I and T II are stabilized by alkalies. The decomposition temperature of pure Ca 3 SiO 5 was determined to be 1180 ± 10°C and increases strongly with K 2 O- and slightly with Na 2 O-content.

Nomenclature for crystal families, Bravais-lattice types and arithmetic classes. Report of the International Union of Crystallography Ad-Hoc Committee on the Nomenclature of Symmetry

Standard symbols representing crystal families, two- and three-dimensional Bravais-lattice types and arithmetic classes are recommended for use by the IUCr. The six crystal families are designated by lower-case letters. The family letter in the symbol of each of the 14 lattice types is followed by an upper-case letter to distinguish different lattice types within the family. Arithmetic classes are indicated by modified symbols of the corresponding symmorphic space groups.

Structural and superconducting properties of Bi2−mPbmSr2Ca2Cu3O10−δ with 0 ≤ m ≤ 1

Abstract Substitution of Pb for Bi in polycrystalline “Bi 2− x Pb x Sr 2 Ca 2 Cu 3 O 10−δ ” (2223 phase) has been achieved up to the solubility limit of x Pb = 0.35 ± 0.03 by optimizing the annealing time and annealing temperature of each sample. Addition of Pb beyond its solubility limit results in changes of the liquidus compatibility relations. The microstructure of the samples and the chemical compositions of all phases present were studied by scanning electron microscopy (SEM), energy dispersive X-ray fluorescence (EDX) and electron probe microanalysis (EPMA). The lattice parameters of the 2223 phase determined by X-ray powder diffraction reveals also the incorporation of Pb for Bi. Single-crystal X-ray methods show a superstructure along [010] with an incommensurate modulation of q = 0.115b ∗ for x Pb = 0.36 . In spite of the drastic variations in the chemical composition of the 2223 phase, T c remains constant over the whole observed range with T c = 111.5 ± 1.5 K.

The phonon dispersion and lattice dynamics of alpha -AlPO4: an inelastic neutron scattering study

The low-energy part of the phonon dispersion of the quartz isotype alpha -AlPO4 has been investigated by inelastic neutron scattering. The experimental data are reproduced by different lattice dynamical models. Good quantitative agreement with experimental neutron, Raman and infrared data is achieved even with just a simple five-parameter Born-von Karman model. The results are compared with the lattice dynamics of quartz. As a main result, it is found that the lattice dynamics at low frequencies is essentially determined by the properties of the oxygen framework, irrespective of the specific nature of the central atoms within the oxygen tetrahedra. The dynamical stability of the lattice is discussed with regard to the incommensurate phase transition.

X-Ray Topographic and Polarisation-Optical Study of the Low-Temperature Phase Transitions and Domain Structures of KLiSO4

The transformations between the three polar “low-temperature” phases of KLiSO 4 III (space group P6 3 ), IV (P31c) and V (C1c1 or P112 1 ), were investigated by low-temperature X-ray topography and polarisation optics. The disappearance of the phase-III growth twinning (twin law “m‖[001]”) and the appearance of the phase-IV transformation twins (twin law “2‖ [001]”) during the very sluggish III → IV transition (ca. 225 K, thermal hysteresis ≈ 50 K) was directly observed. In both phases the domain boundaries are parallel (0001), normal to the polar axis [001] (pronounced memory effect). The III → IV transition is strongly promoted by dislocations. The IV-V transition (190 K) shows the formation of three pseudo-hexagonal domains and the local metastable coexistence of phases III, IV and V. The ambiguities of the phase-V symmetry are discussed.

Concentration dependence of the modulation parameter with the lock-in phase transition in the system K2MoxW1−xO4

An improved method for synthesizing the compounds K 2 Mo x W 1-x O 4 has been applied. The phase diagram, both on heating and cooling, is presented. The observed nearly linear character of the concentration dependence of the modulation parameter p at 693 K (both after heating and cooling) indicates the existence of a continuous series of incommensurate structures in the concentration interval 0 ≤ x ≤ 1. Either at x = 0 exactly or close to this value a lock-in phase transition takes place, making the structure commensurately modulated.