Short-range Order Information Research Articles

Polynomial functions for configurational correlation functions in Gibbs energies of solid solutions using cluster variation method

The cluster expansion – cluster variation methods (CE – CVM) offer a reliable framework to obtain short range order information for the chosen configurational state of a system accurate up to the basic cluster chosen in terms of the microscopic state variables called correlation functions (CFs). The calculation of the CFs involves solving a set of nonlinear equilibrium equations using compute intensive numerical methods. In this paper a method is presented to approximate the equilibrium values of CFs as polynomial functions of composition which eliminate the necessity of solving equilibrium equations. The coefficients of these polynomials are expressed as rational functions of temperature and system specific energy parameters. This method is comparable to standard CALPHAD methods in its ease of application without sacrificing information about short range order in the system.This procedure is applied to an A2–B32 system using tetrahedron approximation for the case of exclusive second neighbour pair interactions. These polynomials yield CFs comparable to those obtained from numerical solutions in the usual ranges of energy parameters and temperatures.

Averaged cluster approach to including chemical short-range order in KKR-CPA

The single-site Korringa-Kohn-Rostoker Coherent Potential Approximation (KKR-CPA) ignores short range ordering present in disordered metallic systems. In this paper, we establish a new technique to fix this shortcoming by embedding an averaged cluster that displays chemical short range order (SRO). The degree of SRO can be tuned by externally defined order parameters. This averaged cluster can be embedded in the single site CPA medium, or a self-consistently obtained effective medium that contains SRO information. The validity of this method is demonstrated by applying it to two alloy systems - the CuZn body centered cubic (BCC) solid solution, and AlCrTiV, a four-element BCC high entropy alloy. A comparison between the non-self-consistent and self-consistent modes is also provided for the two above mentioned systems. We make the code available on the internet. Planned extensions to this work are discussed.

Probing the surface atomic structure of Au/Cr2O3/Pd(111) by photoelectron diffraction

A detailed investigation concerning the surface atomic structure of the Au/Cr2O3 model catalyst deposited on a Pd(111) single crystal surface is presented. The system was prepared by molecular beam epitaxy (MBE) and characterized in situ by low-energy electron diffraction (LEED), X-ray photoelectron spectroscopy (XPS) and X-ray photoelectron diffraction (XPD). The element-specific short-range order information was obtained from XPD experiments supported by a comprehensive multiple scattering calculation diffraction approach. Based on the experiments, we have strong evidence of Au island formation on the Cr2O3 surface. The experiments indicated that the islands are constructed of two Au monolayers and formed by the important structural relaxations in the three outermost atomic layers of the Au/Cr2O3 surface. Such a surface structure could explain the particular catalytic reactivity displayed by catalysts based on Au nanoparticles dispersed on several oxide matrices.

Structural Similarity on Multiple Length Scales and Its Relation to Devitrification Mechanism: A Solid-State NMR Study of Alkali Diborate Glasses and Crystals

The nature of the devitrification process is a fundamental problem in glass science and governs the ultimate stability of glass. It is hypothesized that the devitrification mechanism of a given glass composition is strongly correlated with the extent of structural similarity at the intermediate-range level between the glass and crystal phase to which it transforms. However, relatively little information is available to test this hypothesis because of the lack of long-range periodicity in glass and the absence of effective analysis methods. In this work Li2O−2B2O3 (L2B) and Na2O−2B2O3 (N2B) glasses, which respectively exhibit homogeneous (internal) and heterogeneous (surface) devitrification mechanisms, and corresponding crystals were prepared and comprehensively studied by using multiple solid state NMR techniques. Of those, 11B MAS and MQMAS experiments were applied to reveal short-range order information; 7Li and 23Na spin−echo decay and 11B{6Li} and 11B{23Na} rotational echo double resonance (REDOR) ex...

DAFS and XAFS investigation of structural short-range order of decagonal Al-Co-Ni

Due to the lack of long-range periodic order in quasicrystals there are restrictions concerning a straightforward structure analysis on base of x-ray diffraction data. Computed reflection intensities in x-ray diffraction patterns, which are strongly affected by the shape and occupation of hypothetical atomic surfaces, need to be compared with experimental data. The interatomic short-range correlations as to be determined by means of DAFS and XAFS have to be in agreement with these structural models. The use of linearly polarised x-rays allows for orientation sensitive determination of otherwise averaged short-range order information. Additionally wave vector-selectivity of DAFS can yield short-range order information sensitive to sites occupied by atomic species within the coherently scattering structural units.Structural models of decagonal Al-Co-Ni were applied to compute theoretical DAFS and XAFS functions. Calculation of both, energy-dependent structure factors and pair distribution functions obtained within a hypothetical cluster of app. 81 000 atoms as the basis of computation of DAFS are outlined.Co-K and Ni-K DAFS and XAFS measurements at 3 independent reflections of a decagonal Al70Co9.5Ni20.5 single crystal were performed and the experimental data were subjected to quantitative evaluation. The reflections used involved wave vectors parallel and perpendicular to the periodic direction and in a third inclined direction. In agreement with our simulations DAFS of individual reflections and thereby corresponding shortrange orders exhibited no differences within the error limits. The same was found for the case of polarized Co-K and Ni-K XAFS results.

The Structure of Gallium Phosphate Glasses by High-energy X-ray Diffraction

X-ray diffraction experiments are used to obtain short-range order information of gallium phosphate glasses of meta- and pyrophosphate compositions. Parameters of the first-neighbor peaks, such as coordination numbers and distances, are obtained. A strong decrease of the Ga-O coordination number from 6.0±0.2 to 4.6±0.2 upon Ga2O3 addition is found, which is accompanied by a shortening of the Ga-O distances. Only GaO6 octahedra exist at the metaphosphate composition. Close to the pyrophosphate composition, the majority of Ga atoms occupies already tetrahedral sites. The Ga-O coordination number behaves equivalent with the ratio MTO = n(OT)/n(Ga), thus, with the number n(OT) of terminal oxygen atoms (OT) in phosphorus-OT bonds which are available for the coordination of each Ga atom. Thus, P-OT-Ga bridges are formed for all OT atoms. The GaOn polyhedra neither share OT atoms nor form Ga-O-Ga bridges. With increasing fraction of GaO4 tetrahedra and decreasing lengths of the phosphate chains the network expands.

Overview of the Mössbauer results obtained on silicon-rich iron silicide epitaxial phases on Si

Iron silicide phases, grown on or into single‐crystals of silicon, can be produced by different techniques as reactive and molecular beam epitaxy, and ion implantation followed by recrystallisation processes. Different phases have been obtained depending on the experimental conditions: thickness and substrate temperature for deposited layers, ion implantation fluence, substrate temperature and recrystallisation technique for buried silicides. In most of these investigations, Mossbauer Effect has been used to provide short range order information about the system. We present here a summary of these results, which in some cases are compared with those obtained by other characterisation techniques.

Epitaxial gamma-iron silicide grown on single-crystal Si. A summary of Mössbauer results

Metastable γ-FeSi2 grown on or into single‐crystals of silicon can be produced by different techniques as molecular beam epitaxy, and ion implantation followed by ion beam induced epitaxial crystallisation. In these investigations, Mossbauer effect has been used to provide short range order information about the system. We present here a summary of these results, which will be compared and discussed.

Analysis of short-range order and structural model in the glassy semiconductor Ge 0.20Sb 0.20Se 0.60 by X-ray diffraction

An X-ray radial atomic distribution (RDF) study of the amorphous alloy Ge 0.20Sb 0.20Se 0.60 was performed. Short-range order information was obtained by interpreting the RDF data using a theoretical expression which takes into account the variation of the atomic scattering factors with s, the scattering vector modulus. The existence of tetra- and tri-coordinated germanium atoms, suggested in the literature for glassy alloys containing this element, was found to be compatible with the experimentally obtained structural information. A spatial distribution model was generated according to these two possible coordinations for germanium, using the conveniently modified Metropolis Monte Carlo method. The model exhibits tetrahedral units on germanium atoms, forming a network with triangular pyramids with a germanium atom at some vertices. A comparative analysis of the parameters of this model showed good agreement with the values given in the literature for similar alloys.

Diffraction Anomalous Fine Structure: XAFS with Virtual Photoelectrons

This paper discusses a new x-ray structural technique, Diffraction Anomalous Fine Structure (DAFS) , which combines the long-range order sensitivity of diffraction with the short-range order sensitivity and chemical selectivity of x-ray absorption (XAFS). Because absorption and scattering are related by causality, the absorption information available from XAFS is also accessible from DAFS measurements of the elastic, fixed momentum transfer, Bragg reflection intensities. These DAFS measurements exhibit a fine structure versus photon energy analogous to XAFS. DAFS provides all of the usual information of XAFS: the near neighbor bond lengths, numbers, types and disorders around the specifically excited atoms. In addition, because DAFS unifies all of the capabilities of diffraction and XAFS into a single technique, it provides advantages that neither technique possesses separately: (1) Spatial selectivity. DAFS provides short-range order information about the specific subset of long-range ordered atoms selected by the diffraction condition. (2) Site selectivity. DAFS provides site specific short-range order information for inequivalent sites of a single element. (3) Valence sensitivity. DAFS provides valence specific features in the near edge region.

Germanium coordination hypotheses and spatial atomic distribution in the glassy alloy Ge 0.20Bi 0.06Se 0.74

A radial atomic distribution study of the amorphous alloy Ge 0.20Bi 0.06Se 0.74 was performed from the X-ray diffraction data of the samples obtained by quenching the molten material. Shortrange order information was obtained by interpreting the Radial Distribution Function data, using a theoretical expression which takes into account the variation of the atomic scattering factors with s (the scattering vector module) and approximates them to polynomic functions. The tri- and tetra-coordinated germanium hypotheses, suggested in the literature for glassy alloys containing this element, were found to be compatible with the experimentally obtained structural information. Spatial atomic distribution models were generated, considering the coordination hypotheses suggested for the germanium, using the adequately modified Metropolis-Monte Carlo method. A comparative analysis of the structural parameters of these models showed good agreement with the values given in the literature for similar alloys.

A study of short-range order and atomic arrangement in the glassy semiconductor As 0.20Se 0.40Te 0.40 by X-ray diffraction

An X-ray radial atomic distribution (RDF) study of the amorphous alloy As 0.20Se 0.40Te 0.40 was performed. Short-range order information was obtained by interpreting the RDF data using a theoretical expression which takes into account the variation of the atomic scattering factors with s, the scattering vector modulus. The existence of tetra- and tri-coordinated arsenic atoms, suggested in the literature for glassy alloys containing this element, was found to be compatible with the experimentally obtained structural information. A spatial atomic distribution model was generated according to these two possible coordinations for arsenic, using the conveniently modified Metropolis Monte Carlo method. The model obtained exhibits tetrahedral units on arsenic atoms, forming a network with triangular pyramids with an arsenic atom at some vertices. A comparative analysis of the parameters of this model showed good agreement with the values given in the literature for similar alloys.

On the generation, by a random method, of spatial atomic configurations of some Cu-As-Se system glassy alloys

Atomic structure models of the semiconducting glassy alloys Cu xAs 0.5−xSe 0.5 (x = 0.05, 0.10, 0.20) were generated from shortrange order information, supplied by the corresponding radial distribution functions deduced from the intensities given by x-ray diffraction experiments carried out on samples of these alloys obtained by quenching the molten mixtures of their elements. The Metropolis-Monte Carlo random method was used in the making of the models, conveniently modified and bearing the tetracoordinated copper hypothesis in mind. A comparative analysis of the main structural parameters of these models revealed the good agreement of the same with the values given in the literature for similar alloys.

GeAsTe glassy system. Atomic distribution models

Atomic structure models were generated for the semiconducting glassy alloys Ge x As 0.20Te 0.80− x ( x=0.05, 0.10), from shortrange order information given by the corresponding radial distribution functions, obtained from X-ray diffraction intensities. The Metropolis Monte Carlo random method was used in the building of the models, and the fact that Ge atoms can be four- and three-coordinated has been taken into account. The structural parameters obtained from the models agree with those given in the literature for similar alloys.