Pairwise Interaction Model Research Articles

Derivation of the Model Hamiltonian for HCP and FCC Structures from the Pairwise Interaction Model and Low Temperature Analysis of the Model Hamiltonian

The model Hamiltonians for several common stacked crystals are well described by introducing the position vector and Ising spin in the previous paper. From the pairwise interaction model the model Hamiltonian for the hcp and the fcc structures is derived. Interactions of second neighboring atom pairs along the stacking sequence contribute mainly to construction of the hcp and the fcc structures. Physical meanings of the coupling constant J between Ising spins and that V between the position vectors are made clear. The behavior of the model Hamiltonian at low temperatures is analyzed on the basis of a systematic series expansion procedure. The structural phase transition from the fcc to the hcp structures with increasing temperature occurs in case where J is positive.

Effective elastic moduli of two-phase composites containing randomly dispersed spherical inhomogeneities

Based on the general micromechanical framework proposed in a companion paper, effective elastic moduli of two-phase composites containing randomly dispersedspherical inhomogeneities are investigated in this paper. At variance with existing micromechanical pairwise interaction models (accurate up to the second-order in particle volume fraction ϕ), the proposed approximate, probabilistic pairwise particle interaction formulationcoupled with the general ensemble-volume averaged field equations leads to a novel, higher-order (in ϕ), and accurate method for the prediction of effective elastic moduli of two-phase composites containing randomly located spherical particles. The relevant ensemble integrals in the proposed formulation are absolutely convergent due to a “renormalization” procedure employed in a companion paper. In accordance with the analogy between the effective shear modulus of an incompressible elastic composite with randomly dispersed rigid spheres and the effective shear viscosity of a colloidal dispersion with randomly dispersed rigid spheres (at high shear rates), the proposed ensemble-micromechanical approach is extended to predict effective shear viscosities of colloidal dispersions at the high-shear limit. Comparisons with experimental data, classical variational bounds, improved three-point bounds, the second-order particle interaction model, and other micromechanical models are also presented. It is observed that significant improvement in predictive capability for two-phase composites with randomly dispersed spheres can be achieved by using the proposed method.

Phonon anomalies and martensitic transitions in bcc materials

The general systematics of phonon spectral anomalies are considered for materials with bcc and B2 structures. In a model of central pair-wise interactions, it is shown that anomalies on the TA2 branch at κ=1/3 (211), the LA phonon branch at κ=2/3 (111), and on the TA branch at κ=1/2 (111) arise simultaneously with the softening of the shear elastic moduli C' and C44. The TA phonon anomaly at κ=1/3 (110) is not due to softening of the elastic moduli, but rather is due to the long range nature of the pair-wise or multiparticle interaction. A model is proposed for the nucleation of the martensitic phase for B2 compounds, the distinctive feature of which is a consideration of the “softening” of the shear moduli, which is modulated by lattice relaxation around ordering defects, along with the possibility of additional defect ordering near the transition.

The Ratio of Dicentrics to Centric Rings Produced in Human Lymphocytes by Acute Low-LET Radiation

Chromosome aberrations produced by ionizing radiation are assumed to develop from DNA double-strand breaks (DSBs) which interact pairwise, in an exchange event. Dicentrics and centric rings are aberrations that exemplify inter- and intrachromosomal exchanges, respectively. We show from a survey of published data that for acute low-LET irradiation of resting human lymphocytes the observed ratio of dicentrics to centric rings is approximately five times smaller than predicted by a pairwise interaction model which assumes complete randomness. Such a low ratio can be interpreted as evidence for a proximity effect, favoring exchanges of an intrachromosomal type. That is, since DSBs induced close together have an above-average chance of pairwise interaction, the observed excess of centric rings indicates that at the time of irradiation there is some degree of spatial confinement for the two arms of a single chromosome. Assuming the excess of centric rings is indeed due to proximity effects, the data are used to estimate that the volume of a domain, within which any one lymphocyte chromosome is localized at one instant during the G0/G1 phase, is at most approximately 20% of the nuclear volume.

Surface segregation and bulk phase separation in segregating alloys

Surface segregation in segregating alloys with a surface has been investigated on the basis of the pairwise interaction model. The theoretical treatment has been carried out within the framework of the Bragg-Williams approximation. Each layer parallel to the surface has been found to undergo a transition between two phases with different layer concentrations. With decreasing temperature, the transitions occur successively above the bulk phase separation temperature. We discuss the mechanism of bulk phase separation with focus on the successive phase transitions of the layers.

Orientation and linear dichroism of Mastigocladus laminosus phycocyanin trimer and Nostoc sp. phycocyanin dodecamer in stretched poly(vinyl alcohol) films

The linear dichroism (LD) spectra of the C-phycocyanin (C-PC) trimer disks oriented in poly(vinyl alcohol) films (PVA) at room temperature and at 95 K were determined. Utilizing the known atomic coordinates of the chromophores (Schirmer, T., Bode, W. and Huber, R. (1987) J. Mol. Biol. 196, 677-695) and theoretical estimates of the orientations of the transition dipole moments relative to the molecular framework, the LD spectra were simulated using the pairwise exciton interaction model of Sauer and Scheer (Biochim. Biophys. Acta 936 (1988) 157-170); in this model, the alpha 84 and beta 84 transition moments are coupled by an exciton mechanism, while the beta 155 chromophore remains uncoupled. Linear dichroism spectra calculated using this exciton model, as well as an uncoupled chromophore (molecular) model, were compared with experimental LD spectra. Satisfactory qualitative agreement can be obtained in both the exciton and molecular models using somewhat different relative values of the theoretically estimated magnitudes of the beta 155 oscillator strength. Because the relative contributions of each of the chromophores (and thus exciton components) to the overall absorption of the C-PC trimer are not known exactly, it is difficult to differentiate successfully between the molecular and exciton models at this time. The linear dichroism spectra of PC dodecamers derived from phycobilisomes of Nostoc sp. oriented in stretched PVA films closely resemble those of the C-PC trimers from Mastigocladus laminosus, suggesting that the phycocyanin chromophores are oriented in a similar manner in both cases, and that neither linker polypeptides nor the state of aggregation have a significant influence on these orientations and linear dichroism spectra. The LD spectra of oriented phycocyanins in stretched PVA films at low temperatures (95 K) appear to be of similar quality and magnitude as the LD spectra of single C-PC crystals (Schirmer, T. and Vincent, M.G. (1987) Biochim. Biophys. Acta 893, 379-385).

Frequency-dependent selection: the high potential for permanent genetic variation in the diallelic, pairwise interaction model.

A detailed analytic and numerical study is made of the potential for permanent genetic variation in frequency-dependent models based on pairwise interactions among genotypes at a single diallelic locus. The full equilibrium structure and qualitative gene-frequency dynamics are derived analytically for a symmetric model, in which pairwise fitnesses are chiefly determined by the genetic similarity of the individuals involved. This is supplemented by an extensive numerical investigation of the general model, the symmetric model, and nine other special cases. Together the results show that there is a high potential for permanent genetic diversity in the pairwise interaction model, and provide insight into the extent to which various forms of genotypic interactions enhance or reduce this potential. Technically, although two stable polymorphic equilibria are possible, the increased likelihood of maintaining both alleles, and the poor performance of protected polymorphism conditions as a measure of this likelihood, are primarily due to a greater variety and frequency of equilibrium patterns with one stable polymorphic equilibrium, in conjunction with a disproportionately large domain of attraction for stable internal equilibria.

Anisotropic surface energy reduction of Zr by chemisorption

The anisotropy of the surface free energy reduction of Zr due to gas adsorption was studied by calculating the surface energies of crystal planes at solid-vapour interfaces. The Langmuir adsorption isotherm was adopted for the calculation, whereby the anisotropy was introduced from the nearest-bond energy approximation based on a pairwise interaction model. The (101̄0) plane was found to have the lowest relative surface energy in the unembrittled state, that of the (0001) plane being slightly higher. Gas adsorption, however, influences the energy state significantly, and the effective surface free energy after adsorption becomes lowest for the (0001) plane, followed by the ( 10 1 ̄ 1 ) plane family. This tendency became more pronounced as the coverage increased. Energy maxima occurred in the planes that were inclined about 30–50° and 70–75°, respectively, to the basal plane. The mode of spatial distribution of the surface energies at 350°C on stereographic triangles was sensitive to a coverage higher than 0.5; the effect of temperature in the range of 250–450°C, however, was relatively insignificant.

Theory of Mixture for III-V Semiconductor Solid Solutions: Short-Range Clustering/Ordering and Spinodal Decomposition

A theory describing mixing phenomena in III-V semiconductor solid solutions is presented with particular emphasis on clarification of the relationship between short-range clustering/ordering and spinodal decomposition. It is pointed out that some problems are involved in the conventional treatment of the mixing phenomena, which is based on the pairwise interaction model. A systematic treatment of the mixing phenomena is developed on the basis of the recently proposed bond model.

Kinetics of 1 × 1 → 1 × 5 surface reconstrucrtion on Ir(100)

The dynamics of the 1 × 1 → 1 × 5 reconstruction process on Ir(100) are studied on the basis of two-level rate equations. The surface energy as a function of the atomic displacement during the reconstruction is obtained by means of a simple pairwise interaction model. The effect of the statistical distribution of the two energy minima, corresponding to the 1 × 1 and 1 × 5 structures, on the time evolution of the reconstruction is investigated. It is shown that the inhomogeneity of the surface suppresses the development of the reconstruction and yields a nonexponential time dependence, as observed experimentally.

Effective binding potentials for the description of metal-metal interaction

The properties of a new type of e,pirical/semi-empirical binding potentials are investigated. Since the influence of the neighbouring atoms on the pair contributions to the potential is appropriately incorporated, molecules, clusters, surfaces, and solids can be treated on equal footing by one set of parameters. Though the number of adjustable parameters needed is essentially not larger than in commonly uses pairwise-interaction models, the description of binding is clearly improved. This is demonstrated by calculations on molecules, small copper clusters and surfaces.

Concentration wave approach to the pairwise interaction model for predicting the atomic structure of ceramics, II

The concentration wave approach is applied to Ti and V oxides with noninteger variable valences. This approach enables both the composition and the structure of the homologous series of Magneli phases Ti n O 2 n−1 and V n O 2 n−1 to be predicted in the composition range between Ti 2O 3 and TiO 2.

The concentration wave approach to the pairwise interaction model for predicting the crystal structures of ceramics, I

The structures of chemical compounds are predicted on the basis of energy calculations with the help of the concentration wave approach. The method predicts both the structures of the most stable oxides with fixed valencies and the structures of the so-called homologous series of Magnéli phases. To exemplify the procedure, the atomic structures of the Ti and V oxides are considered. The rutile and α-PbO 2 structures are shown to be the most stable ones for tetravalent cations while the corundum structure is most stable for trivalent cations.

ON COMPARISONS BETWEEN COMPUTED AND OBSERVED GRAIN BOUNDARY STRUCTURES AND PROPERTIES IN METALS

A detailed assessment is given of the extent to which agreement has been obtained between experimentally observed and calculated structures and/or properties of grain boundaries in metals. All of the calculations employed pair-wise interaction models. Published work as well as new results obtained by the authors are cited. Topics include: boundary width; primary and secondary relaxations (i.e., grain boundary dislocations); magnitude of the boundary energy; lattice translations across the boundary and atomic positions in the boundary core; and fast diffusion in boundaries. It is concluded in general that the pair-potential modeling has been a valuable tool in grain boundary research and has often produced detailed results which are in at least semi-quantitative agreement with observations. However, in some cases the agreement is poor and as might be expected, it is clear that the technique is not capable of producing realistic results in all cases. Various problems are pointed out and discussed.

A pair-wise interaction model of the sigma phase II— configurational characteristics

A simple pair-wise interaction model developed to describe the composition dependence of the thermodynamic properties of sigma phases is used to derive the distribution of atomic species among the five sublattices of these structures. The general dependence of configurational tendencies on relative bond energies is examined. Experimental structural information is reviewed and observed and predicted sublattice occupancies are compared.

A pair-wise interaction model of the sigma phase III — a general approach

The pair-wise interaction model of the sigma phase developed and tested in two orevious papers (1,2) is extended in such a way that the compositions of the five sublattices can vary freely, without the artificial constraints employed earlier (1,2). Two further extensions are described: the first of these allows a variation in the length and nature of the counted bonds and the second permits the treatment of systems with more than two components. These extensions should enable this approach to be applied to a wide variety of closely packed alloy phases. Finally this general approach is reapplied to the sigma phase and the results compared with those of the constrained calculations (1,2).

A pair-wise interaction model of the sigma phase I—thermodynamic properties

The composition dependence of the thermodynamic properties of binary sigma phases is examined on the basis of a simple pair-wise interaction model. The structure is considered in terms of its five sublattices, characterised by sites identified with Kasper-Frank surrounding co-ordinated polyhedra of 12, 12, 14, 14 and 15 respectively. It is assumed that the smallest (CN12) and the largest (CN15) sites are each preferentially occupied by different single alloy components while the intermediate size (CN14) sites are subject to random occupation. The numbers of substitutional defects on the ordered sub-lattices are defined by two independent disorder parameters and the variation of defect concentration and thermodynamic properties with composition is computed. Application of the model is illustrated by reference to thermodynamic and structural data for sigma phases in the V-Fe, V-Co, Cr-Fe, Cr-Co and Mo-Co alloy systems.

The partial excess thermodynamic properties of hydrogen in palladium

New measurements of the hydrogen chemical potential and the partial enthalpy of hydrogen in Pd-H alloys are reported. These results are combined with information available in the literature to obtain a consistent set of values for the partial excess enthalpy and entropy of hydrogen as a function of composition. The partial excess entropy of hydrogen varies from negative values at low hydrogen concentrations to positive values at high hydrogen concentrations and it is demonstrated that the principal contribution to this excess entropy is configurational. Problems associated with trying to interpret these properties in terms of pairwise interaction models are discussed.

Twist boundary energies for metals with long-ranged pairwise interatomic potentials

The recent calculation of Devlin (1982) predicting that the energy of rigid (001) twist boundaries in a central force pairwise interaction model with a long-ranged potential increases linearly with Sigma (for 5<or= Sigma <or=37) is considered. By use of a general argument based on the 'geometry of numbers' it is shown that this linear increase of the energy is too strong to be physically reasonable. Instead, the energy approaches a constant asymptotic value in this range, and any variations can be represented by a higher order term which varies as Sigma -34/.

Susceptibility of mixed magnetic systems and spin glasses in the presence of chemical short range order

Abstract The paramagnetic susceptibility of a magnetic system diluted with non-magnetic atoms is considered. While for the ideal case of random mixing the paramagnetic Curie temperature θ (cB) varies linearly with concentration cB of magnetic atoms, already small amounts of chemical short range order lead to pronounced deviations from linearity for cB → 0. Model calculations of θ (cB) are presented both for the case of mixed systems with an unmixing and with superstructure ordering transition, calculating the respective Cowley short range order parameters by Monte Carlo methods from pairwise interaction models.