Number Of Coordination Spheres Research Articles

On ordering in solid solutions of Cu-25 at % Au and Cu-75 at % Au

Based on the X-ray diffuse scattering (XRDS) method, a methodology for experimental determination of the parameters of short-range order in disordered polycrystalline solid solutions is developed. The method is based on accounting for static displacements in the corresponding coordination spheres. Static displacements are described by introducing parameter \(\beta = \frac{1} {\nu }\frac{{d\nu }} {{dc}} \), where v is the unit-cell volume, and c is the solid-solution concentration. The short-range order parameters of polycrystalline Cu-25 at % Au and Cu-75 at % Au solid solutions are calculated for a large number of coordination spheres using experimental values of the XRDS intensity and a refined methodology. It is established that the values of the short-range order parameters of a polycrystalline solid solution are close to analogous values for the Cu3Au superstructure, despite the different character of the XRDS intensity. This points to the presence of long-range interatomic interactions in these solid solutions.

PVT Properties of crystalline polymers. Comparison of Theoretical Predictions and Experimental Data

We compare theoretical predictions of the pVT properties of crystalline polymers with experimental data for polyethylene. We took into account the effect of temperature, lattice coordination number, number of coordination spheres, and other parameters on the volume of the polymer crystal. The experimental and theoretical data on the dependence of the volume of crystalline polyethylene at atmospheric pressure are quite consistent with each other.

Structural studies on Si‐N gradient thin layers by grazing incidence X‐ray diffraction

In this paper, the application of combined method – the powerful tool for structure analysis – used for the structure determination of non‐ordered gradient Si‐N thin films is presented. The method is based on the combination of well‐known methods, like radial distribution function (RDF), pair distribution function (PDF) analyses and the Rietveld refinement. The values of radii and number of coordination spheres, obtained from RDF and PDF analyses, were compared to the theoretical values calculated for typical crystalline structures. Then, the most probable model of the hypothetical ‘unit cell’ of the analysed material might be chosen for the Rietveld refinement. In case of the gradient materials and thin films, the structure analysis is more complicated because the experiment has to be prepared in grazing incident X‐ray diffraction geometry. The X‐ray diffraction patterns collected for different angles of the incident beam show different shape, what indicate different kind of order in layers. Finally, it was stated that the Si‐N layers are nonhomogenous, and their structure depends on the penetration depth. Moreover, there was a possibility to create the complete structure model of whole gradient Si‐N thin film. Copyright © 2014 John Wiley & Sons, Ltd.

The equilibrium states of A 1−x B 1+x binary alloys in the hard-sphere and pair-binding model

The equilibrium ordering states of A 1−x B 1+x alloys are investigated analytically and by computer simulation with the hard-sphere and pair-binding model. The alloy energies are calculated for the case where an excess of the B component forms a solid solution or precipitates as pure phase particles. Criteria for pair-binding energies are obtained that define the type of the resulting alloy. The analytical results are presented for an alloy of arbitrary dimensionality and for any number of coordination spheres involved in interatomic interactions. Illustrating examples are given for B2 and L10 superstructures and for a two-dimensional square lattice in view of the atomic interaction in the first two coordination spheres.

Application of moment interaction to the construction of a stable model of graphite crystal lattice

The aim of the present paper is to construct and study a model of pair moment interaction between carbon atoms in the two-dimensional graphite lattice. The carbon atom is modeled by a structure consisting of three rigidly connected mass points located at the vertices of an equilateral triangle. The interaction between mass points is described by a pair force potential, but the total interatomic interaction contains moment components owing to the finite size of the structure modeling the atom. We compute rank 4 tensors characterizing the elastic properties of the graphite crystal lattice constructed on the basis of our model. We determine lattice stability criteria depending on the number of coordination spheres taken into account. We show that this model permits one to ensure stability of the graphite lattice but significantly underestimates the transverse-to-longitudinal interatomic coupling rigidity ratio. We construct a generalized moment potential that permits one to obtain a rigidity ratio consistent with experimental data.

Diamond Lattice in the Space of Coordination Spheres

An algorithm has been developed for calculating radii, direction vectors, and coordination numbers (c.n.) for an arbitrary number of coordination spheres (CS) of the diamond lattice. It is established that the space of CS of the diamond lattice has imaginary CS in addition to real ones. The imaginary CS are defined by a direction vector, one of the components of which is an imaginary value. The coordination numbers of such CS are zero. For a great number of tabulated CS, we have studied the hierarchies of structural groups (motifs), forming in the space of coordination spheres and determining the X-ray spectra of lattice CS, the crystallomorphological growth forms of diamond crystals, and the forms of diamond fragmentation induced by thermal destruction and melting.

Modeling Order–Disorder Phase Transitions. Inclusion of the Range of Action of the Interatomic Interaction Potential

Results of a computer experiment simulating the atomic ordering process in a model alloy of stoichiometric composition AB and accounting for the range of action of the interatomic-interaction potential are analyzed. The effect of the range of action of the interaction potential (influence of the number of coordination spheres included in the interatomic interaction) on the disordering kinetics and on the order–disorder phase transition in the material at temperatures T c between 0 and 1.1 (T c is the temperature at which the atomic long-range order vanishes) is studied. The structure and energy features of atomic ordering are discussed. The objective necessity of accounting for long-range contributions in modeling order–disorder phase transitions and for the kinetics of temperature–induced ordering and disordering processes is examined.

Method of determing the energy of antiphase boundaries in {h0l} planes in a superstructure with an arbitrary primitive cell

An expression obtained previously by the authors for the energy of formation of an antiphase shear boundary for the {001} orientation is generalized to the case of the {h0l } orientation. The given problem is solved by examining primitive cells of an intermetallide crystal in which one face is parallel to the plane of the antiphase boundary. The energy of the defect is given in the form of an analytical expression that can be used for any ordered alloy with an arbitrary primitive cell without restrictions on the number of coordination spheres in the atomic interactions. An example is presented and the results are compared with known data.