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The crystalline structure and Fe local environment in a Co-doped Ni–Fe–Ga Heusler alloy, prepared by the melt-spinning technique, were investigated by X-ray diffraction (XRD) and EXAFS at room and low temperatures. The characteristic temperatures of the austenite–martensite phase transitions were determined by differential scanning calorimetry via cooling and heating cycles of the alloy ribbons. As shown by room-temperature XRD, the austenitic phase of the alloy has the chemically ordered L21 Heusler structure. This was confirmed by EXAFS, although this technique was not able to conclusively distinguish between the L21 and B2 structures of the austenite for the analyzed alloy. The low-temperature martensitic phase and its structural evolution towards austenite with increasing temperature were studied by high-energy X-ray diffraction, which evinced the martensite modulation. However, the Fe environment could be fitted by EXAFS with the tetragonal L10 structure of the non-modulated martensite. This proves that the martensite modulation has structural effects on a long-range scale, without significant changes in the short-range order around the atoms. The changes in the local structure around iron on martensitic transformation were correlated with changes in the electronic structure, described by XANES spectroscopy at the Fe K edge.

The results of Roth et al. [IUCrJ (2020). 7, 673–680] provide a clear picture of occupational correlations in half-Heusler compounds.

Samples of Cu47.5Zr47.5Al5metallic glass were prepared at different cooling rate,R. The dependence of the X-ray diffraction patterns onRwas analysed by comparing them with corresponding patterns of computer-simulated models generated at different cooling rates as well. The observed changes in the experimental diffraction patterns are reproduced by the simulations, showing an increasing fraction of icosahedral clusters with decreasing cooling rate. The difference of the fractions of icosahedrally coordinated atoms in mould-cast and rapidly quenched Cu47.5Zr47.5Al5averages to 3 (1)%. Different frozen-in thermal displacements and different density are ruled out as a possible origin for the experimental observations.

The generalized multicomponent short-range order (GM-SRO) parameter has been adapted for the characterization of short-range order within the highly chemically and spatially resolved three-dimensional atomistic images provided by the microscopy technique of atom-probe tomography (APT). It is demonstrated that, despite the experimental limitations of APT, in many cases the GM-SRO results derived from APT data can provide a highly representative description of the atomic scale chemical arrangement in the original specimen. Further, based upon a target set of the GM-SRO parameters, measured from APT experiments, a Monte Carlo algorithm was utilized to simulate statistically equivalent atomistic systems which, unlike APT data, are complete and lattice based. The simulations replicate solute structures that are statistically consistent with other correlation measures such as solute cluster distributions, enable more quantitative characterization of nanostructural phenomena in the original specimen and, significantly, can be incorporated directly into other models and simulations.

Oral presentation fgiven at the 24th Congress and General Assembly of the International Union of Crystallography (IUCR2017), held in Hyderabad (India) on August 21-28th, 2017.

The structures of Li3V6O13 and Li3+δV6O13, δ ≃ 0.3, have been determined by single-crystal X-ray diffraction. Both compounds have the space group C2/m, with very similar cell parameters. In Li3V6O13, the Li atoms are found in the Wyckoff positions 4(i) and 2(b) with multiplicities of four and two, respectively. Since Li3V6O13 exhibits no superstructure reflections, it is concluded that Li3V6O13 contains one disordered lithium ion in an otherwise ordered centrosymmetric structure. On inserting more lithium into the structure, the Li3+δV6O13 phase is formed with the homogeneity range 0 3V6O13. A mechanism for this behaviour and for the further formation of the Li6V6O13 end-phase in the Li x V6O13 system is proposed.

The concept of dynamic Delauney systems and dynamic Voronoi–Dirichlet polyhedra is introduced. By means of this concept, the connection between the topology of systems with many particles with the presence or absence of short-range or long-range order is investigated. A number of topological criteria for the presence or absence of short-range order in model systems of `gas' or `liquid' type are proposed and tested. The features of the topology of crystal lattices of chemical substances and model multiregular systems of points, caused by the presence of long-range order in the arrangement of particles, are investigated.

A full reciprocal-space volume of diffuse scattering data from a single-crystal of the mineral mullite, Al2(Al2 + 2x Si2 − 2x )O10 − x , x = 0.4, was collected. These data were analysed using least-squares techniques by writing an equation for the diffuse scattering that involves only the local order between vacancies on specific oxygen sites in the material. The effect of the large, but predictable, cation shifts on the diffuse intensity is taken account of in the coefficients of the oxygen-vacancy short-range-order intensities. This analysis shows that the vacancies are negatively correlated at the near-neighbour ½ 〈110〉, [110], 〈001〉 and 〈011〉 interatomic vectors and positively correlated along the 〈010〉, 〈101〉, ½ 〈112〉 and ½ 〈310〉 vectors. Subsequent Monte Carlo modelling of the structure based on these local-order parameters demonstrates that the structure of mullite is dominated by effective near-neighbour vacancy–vacancy repulsive interactions. A real-space model of mullite is presented that is approximately consistent with the measured local-order parameters.

Two models of icosahedral quasicrystals are compared and connected. These are canonical-cell ordering (CCO) over medium-length scales (about 10 A and more) and dodecahedral local ordering (DLO), which describes interatomic arrangements. In the DLO model, each atom is surrounded by closest neighbours positioned at several vertices of a regular pentagon-dodecahedron; of the 20 vertices of any dodecahedron, only a few can be occupied simultaneously without conflict (eight at most). Some icosahedral quasicrystals and their crystalline approximants exhibit DLO as the main structure motif at atomic scales. DLO networks are formally described using an unconventional projection of a six-dimensional lattice. It is shown that most DLO configurations (but not all of them!) can be constructed from small atomic size canonical cells that are a factor of τ3 smaller than the original ones. Two of the small canonical cells have the forms of distorted tetrahedra. It is also shown that DLO produces naturally the two most popular decorations of the Ammann rhombohedra: the edge decoration and the vertex-face decoration. Moreover, both decorations can be identified inside the same approximant. For medium-range distances, DLO leads to CCO with special decorations of the canonical cells. Therefore, the ordering in quasicrystals and in their approximants can be constructed as a hierarchy of dodecahedral ordering (or a hierarchy of canonical cells). It is shown that within the DLO model there may be an additional ordering of closest neighbours that leads to the transition between quasicrystals with primitive and face-centred lattices. The DLO-based duality between α-AlMnSi and Al5Li3Cu approximants is demonstrated. Possible physical reasons for DLO are considered. Some intrinsic features and difficulties of the DLO and CCO models (frustrations, disorder etc.) are discussed.

Local molecular arrangements have been generated with the help of Monte Carlo computer simulation using experimentally measured short-range-order parameters in two isostructural (monoclinic) isomers of dibromodimethyldiethylbenzene. The computer program was based on the GC concept of Gehlen & Cohen [Phys. Rev. A (1965), 139, 844-855] modified for use with molecular crystals. It is seen that the atomic contact distances play an important role and the first nine short-range-order parameters were required to obtain a reliable picture of the structure of the disordered molecular crystal. Microstructures for the two isomers were found to be very similar.

In-plane local arrangements of Ag atoms in the stage-2 intercalation compound Ag 0.15 TiS 2 are visualized by the Monte Carlo simulation technique with the use of two-dimensional short-range order parameters Microregions of the 3 1/2 x 3 1/2 R30° in-plane ordered arrangement become more numerous with decreasing temperature, while the numbers of the other possible ordered arrangements do not depend on temperature.

In the crystal structure analysis of disordered structures consisting of randomly distributed polar lattice cells, additional information on the range of order can be obtained by introducing thegparameter in the structure-factor equationF(h) =A(h) +igB(h). In the case of perfect disorder, the parametergtends to zero; however, in the case of local order, the crystal structure contains small polar clusters and thegparameter becomes greater than zero (0

Powder FTIR spectra of the solid solution series vertical bar(Ca2-xEux)(4)(OH)(8)vertical bar[(Al2+xSi1-x)(4)O-24]-SOD, 0

The 'transition' state in binary f.c.c. based systems is assumed to be characterized by the repetition of interpenetrating polyhedral clusters of atoms occupying lattice sites and having the macroscopic composition. Its mathematical formulation leads to relations between the short-range order (SRO) coefficients, which in turn impose conditions on the distribution in reciprocal space of the diffuse intensity as observed in electron diffraction patterns. It follows that for a given cluster type the diffuse intensity can only differ from zero along certain surfaces or curves. The effect of deviations from the ideal composition of the clusters is briefly discussed. The theory allows an explanation of available diffraction data on certain binary alloys in the initial stages of ordering i.e. in the 'transition' state between the SRO state and the long-range order (LRO) state.

Ternary oxides AMO2, A2MO3 and A5MO6 with monovalent A and tri-, tetra- or hepta-valent M metals can exhibit order/disorder transitions with about 20 superstructures of the NaC1 lattice. Some structures can be related to AM, A2M and A5M alloys with a larger distortion of the lattice due to stronger interactions between metal atoms. In ternary oxides about 30 short-range order configurations are selected for the first, second and third shell of metal atoms in applying Pauling's electrovalence rule. Stable configurations are characterized by the strength of Coulomb interactions and by a high point symmetry of the M atoms. Mainly disordered ternary oxides can vary stoichiometrically with a frequent occurrence of vacancies or with partial occupation of tetrahedral interstices by A atoms.

Diffuse X-ray scattering has been measured in the orientationally disordered phase of C2C16 at 453 K. A model structure, which was generated in a Monte Carlo program, reproduces the dominant single-molecule part of the diffuse scattering. In addition the existence of a one-dimensional orientational order along the body diagonals of the cubic lattice is demonstrated. The related planes of diffuse scattering are calculated in terms of the Naya model [Naya (1974). J. Phys. Soc. Jpn, 37, 340-347].

An X-ray partial diffuse intensity equation has been explicitly expressed as a function of ordering energies between different atomic species by referring to the description of the interatomic correlation function of de Fontaine [J. Phys. Chem. Solids (1973), 34, 1285–1304]. The expression suggests the appearance of a negative partial intensity. As an interesting example of its application, the calculation of the partial intensity for the disordered Cu2NiZn ternary alloy by means of the derived equation in terms of the ordering energies obtained theoretically by de Rooy, van Royen, Bronsveld & de Hosson [Acta Metall. (1980), 28, 1339–1347] is shown to lead to a distribution of diffuse scattering very similar to that given by experimental observations [Hashimoto, Iwasaki, Ohshima, Harada, Sakata & Terauchi (1985). J. Phys. Soc. Jpn, 54, 3796–3807].

Determination des valeurs des coefficients de correlation intermoleculaire definissant l'ordre local d'orientation des molecules

A three-dimensional X-ray diffuse scattering investigation of the short-range order in a-phase Cu-AI alloys, and its dependence on alloy composition, quenching temperature and isothermal annealing at 250°C, has been carried out. The Cowley-Warren order coefficients were determined after separation of the size effects using a procedure based on the Boric-Sparks quadratic approximation of atomic displacements. These short-range-order coefficients were analyzed in terms of the complete spectrum of nearest-neighbor atomic configurations, without the necessity of invoking a specific model for the characteristic feature(s) of the localorder structure. Although in the composition range investigated the equilibrium condition is a short-rangeordered structure, the nearest-neighbor configurations bear a marked resemblance to the long-period antiphase-shift structures which have been found in alloys with more AI. Because essentially all of the most highly ordered configurations were found to exist isolated from each other in a 9.13 at.% A1 alloy, it is concluded that they represent inherently stable, spatial arrangements of the atoms. In alloys containing 13.56 and 14.76 at.% AI, connected ordered configurations, or small ordered domains, were detected, and this effect increases markedly with increasing A1 content. Isothermal annealing at 250°C of a Cu-14.76 at.% A1 alloy quenched from 650°C results in a net disordering process; however, superimposed on this, in the early stages of annealing, is an enhancement of the population density of an atomic configuration confined to planes of the { 111 } type. This is interpreted as evidence for occurrence of the Suzuki mechanism. It is argued that the body of published experimental observations on this alloy system is better understood if one recognizes the existence of stacking faults, and their interaction with the matrix, in addition to that of short-range order.

Experimental measurements were performed on a 48.4 at. % Ni/51.6 at. % Pt alloy. The order parameter S in equilibrium was measured as a function of temperature T by means of X-ray diffraction. Up to 592±3°C the sample is a single-phase ordered alloy with an order parameter above 0.98. Between 592 and 625±3°C there exists a two-phase region in which the ordered and disordered phases are in equilibrium. Above 625±3°C a disordered f.c.c. structure exists. Diffuse X-ray intensity measurements were performed at T = 1.1 Tc and both the short-range parameters αi and the size-effect parameters βi were calculated. From the αi parameters so derived three ordering energies νi were determined. It was found that these energies were consistent with the symmetry of the ordered phase below the critical temperature.

In order to determine short-range order in a solid solution from diffuse X-ray or neutron diffraction experiments the separation of atomic size effects from the experimental data is a crucial problem. It is demonstrated by a model calculation that a clear improvement of the separation method proposed by Borie & Sparks is obtained if the range of measurement is extended to include the first Brillouin zone.

High-resolution electron-microscope images of the (1½0) special-point short-range-ordering alloys NiaMo, Au4Cr, AuaV and muaFe are compared, and the extent to which optical diffractograms from local regions of such micrographs can be interpreted is discussed. For Au4Cr and Ni4Mo, the observed state or order can be interpreted as being due to the presence of microdomains of the D022 structure and elements of the Dla structure, extending sometimes several unit cells along the c direction, but being quite often only one or a small number of unit cells wide. For Au4V and Au4Fe, the observed diffuse intensity is probably too weak to allow decisive conclusions. It is argued that the 'microdomain' model and the 'concentration-wave' model are two descriptions of the same physical reality which are revealed by different imaging modes. A reinterpretation of some results obtained by X-ray diffraction on NiaMo by Chakravarti, Starke, Sparks & Williams [J. Phys. Chem. Solids (1974), 35, 1317-1326] confirm the proposed model.

Etude experimentale de la decomposition de l'alliage par diffusion de rayons X, microscopie electronique, en transmission et mesures de la conductivite electrique. Analyse de l'ordre a courte distance dans l'alliage homogeneise et trempe a partir de 1323 K. Determination du mecanisme de separation par un processus de nucleation et croissance

The study of the scattering outside the Bragg reflexions shows no local order in the ordered phase I of alloys such as Au (50 at. %) Cu (46 at. %) Ni (4 at. %) even for the smallest degree of long range order. The modulation of the scattering appears only with the presence of short range order in the disordered α phase. There is evidence of a two-phase region on the equilibrium diagram at the AuCu3 stoichiometric composition.

The local atomic arrangements in an Au-40 at.% Pd alloy were investigated by measuring the X-ray diffuse scattering from a single crystal. A computer simulation of the short-range structure was used in the interpretation of the diffuse scattering results. The interpretation indicated a tendency toward the formation of a tetragonal AB long period superlattice which has not previously been observed to occur. The static displacements of the atoms from their average positions were shown to be very small in this alloy.

The short-range-order diffuse scattering from disordered Cu-Pd and Cu-Pt alloys has been studied by electron diffraction using thin foils prepared from bulk specimens. Twofold and fourfold splittings of diffuse scattering are observed at 100, 110 and equivalent positions in the composition ranges from about 13 to 60 at.% Pd in the Cu-Pd system and up to about 45 at.% Pt in the Cu-Pt system. The separation of the split maxima increases with Pd or Pt content. A close investigation has revealed that the split maxima correspond to the intersections of slightly curved diffuse streaks around the 100 and 110 positions. These results can be interpreted well using the Fermi-surface-imaging theory proposed by Krivoglaz, indicating that the interaction potential in these alloys mainly originates from conduction electrons, and that the diffuse scattering reflects the form of the Fermi surface, i.e. the flatness normal to the (110) directions.