Surface order in body-centered cubic alloys

Free (100)-surfaces of body-centered cubic binary alloys are studied in a parameter range where the bulk turns from the ordered B2-phase to the disordered A2-phase. A model is chosen that describes iron-aluminium alloys in a fairly realistic way. Mean field treatments and Monte Carlo investigations both show that under certain circumstances the surface remains ordered far above the bulk disordering temperatureT _c, though the surface order parameter and the surface susceptibility exhibit a singularity atT _c with critical exponents characteristic for the ordinary transition. One finds, that if the surface is nonstoechiometric and different layers are not equivalent with respect to perfect bulk ordering, this induces an effective ordering field at the surface. Finally surface potentials are introduced into the model. Realistic values are determined by mean field considerations from experimental data and their effect on the surface is discussed.     

Dispersion laws in body-centered rhombic crystals

Group-theory methods are used to study the dispersion laws near symmetric points of the Brillouin zone for body-centered rhombic crystals with an account of time inversion and the spin-orbit interaction. The effects of changes in the lattice constant on the qualitative features of the energy spectrum are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 4, pp. 30–38, April, 1969.     

Uniaxial deformation of nanotwinned nanotubes in body-centered cubic tungsten

We perform large-scale molecular dynamics simulations to delve into tensile and compressive loading of nanotubes containing {112} nanoscale twins in body-centered cubic tungsten, as a function of wall thickness, twin boundary spacing, and strain rate. Solid nanopillars without the interior hollow and/or nanotubes without the nanoscale twins are also investigated as references. Our findings demonstrate that both stress-strain response and deformation behavior of nanotwinned nanotubes and nanopillars exhibit a strong tension-compression asymmetry. The yielding of the nanotwinned nanotubes with thick walls is governed by dislocation nucleation from the twin boundary/surface intersections. With a small wall thickness, however, the failure of the nanotwinned nanotubes is dominated by crack formation and buckling under tensile and compressive loading, respectively. In addition, the strain rate effect, which is more pronounced in compressive loading than in tensile loading, increases with a decreasing twin boundary spacing.     

Theory of surface force-constant changes in body-centered cubic lattices

A calculation has been made of force-constant changes at the (100) and (110) surfaces of body-centered cubic crystals. A model consisting of first, second and third-neighbor Lennard-Jones interactions together with harmonic angle-bending interactions is employed. The parameters characterizing the interactions are chosen to fit the equilibrium lattice spacing, the elastic constants, and certain phonon frequencies at high symmetry points in the Brillouin zone. The procedure consists of first calculating the static displacements produced by the creation of the surface and then calculating the change in force constants produced by the cubic and quartic anharmonic terms in the potential energy. Specific results have been obtained for chromium, iron, tungsten, and molybdenum.     

Statistical theory of slip channels in body-centered cubic metals

Received: 26 July 1996/Accepted: 7 October 1996     

Twinning propensity in nanocrystalline face-centered cubic,body-centered cubic,and hexagonal close-packed metals

The nanotwinned structures in metals exhibit the unique combination of physical properties. The unifying approach is developed that can be applied to nanocrystalline (nc) materials with different crystal structures. It is used to make a bridge between microscopical mechanisms of twin nucleation and macroscopic characteristics of the twinning and calculate them. The grain size range of the nanotwinning propensity, the grain size of its peak, and the requisite external twinning stress are calculated for the nc face-centered cubic metals Al, Cu, Ni, Pd, Au, Ag, for nc body-centered cubic metals Ta, Fe, Nb, Mo, and for hexagonal close-packed nc metals Co, Zr, Mg, Ti.     

Mixtures of hard spherocylinders and hard spheres

Monte Carlo simulations have been performed for equimolar mixtures of hard prolate spherocylinders of length: breadth ratio 2:1 and hard spheres, in the fluid region. Two systems have been studied. In the first the breadth of the spherocylinder was equal to the hard sphere diameter, and in the second system both components were of equal molecular volume.

The compressibility factor, PV/NkT, has been obtained for both mixtures at four reduced densities (packing fractions) from 0·20 to 0·45. The results have been compared with the predictions of several analytical equations appropriate to mixtures of hard convex molecules, and an equation due to Pavlicek et al. was found to be very accurate. The results have been used to calculate the excess volumes of mixing at constant pressure, in an attempt to establish the relative importance of the effects of differences in molecular volume and shape on the thermodynamic properties.

The structural properties of the mixtures have also been investigated by calculating pair distribution functions for the three types of pair interactions present in these mixtures.     

Phase transition in a lattice gas of hard spheres with second-neighbor exclusions on the simple cubic lattice

Using reflection positivity and the Peierls argument, we prove the existence of an ordered phase at sufficiently high activity for a lattice gas of hard spheres on the simple cubic lattice with first- and second-neighbor exclusions.     

Thermo-physical properties of body-centered cubic iron-magnesium alloys under extreme conditions

Using density functional theory formulated within the framework of the exact muffin-tin orbitals method, we investigate the thermo-physical properties of body-centered cubic (bcc) iron-magnesium alloys, containing 5 and 10 atomic % Mg, under extreme conditions, at high pressure and high temperature. The temperature effect is taken into account via the Fermi-Dirac distribution of the electrons. We find that at high pressures pure bcc iron is dynamically unstable at any temperature, having a negative tetragonal shear modulus (C^′). Magnesium alloying significantly increases C^′ of Fe, and bcc Fe-Mg alloys become dynamically stable at high temperature. The electronic structure origin of the stabilization effect of Mg is discussed in detail. We show that the thermo-physical properties of a bcc Fe-Mg alloy with 5% Mg agree well with those of the Earth’s inner core as provided by seismic observations.     

Theory of ordering in binary substitution alloy with body-centered cubic lattice

With the framework of a second order approximation of the Kirkwood, a study has been made of ordering in binary substitution alloys with B2 structure. Interatomic interactions in the first and second coordination spheres have been taken into account. It has been shown that an order—disorder phase transformation can be of the first or second kind, depending on the ratio of the ordering energies in the first and second coordination spheres (w and ) and their composition. The calculated configurational thermal capacity in the region of the Kurnakov point agree well with experimental data for /w=0.25.S. M. Kirov Ural Polytechnical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 93–96, September, 1993.     

Dislocation nucleation from symmetric tilt grain boundaries in body-centered cubic vanadium

We perform molecular dynamics (MD) simulations with two interatomic potentials to study dislocation nucleation from six symmetric tilt grain boundaries (GB) using bicrystal models in body-centered cubic vanadium. The influences of the misorientation angle are explored in the context of activated slip systems, critical resolved shear stress (CRSS), and GB energy. It is found that for four GBs, the activated slip systems are not those with the highest Schmid factor, i.e., the Schmid law breaks down. For all misorientation angles, the bicrystal is associated with a lower CRSS than their single crystalline counterparts. Moreover, the GB energy decreases in compressive loading at the yield point with respect to the undeformed configuration, in contrast to tensile loading.     

Kinetic theory of hard spheres

Kinetic equations for the hard-sphere system are derived by diagrammatic techniques. A linear equation is obtained for the one-particle-one particle equilibrium time correlation function and a nonlinear equation for the one-particle distribution function in nonequilibrium. Both equations are nonlocal, noninstantaneous, and extremely complicated. They are valid for general density, since statistical correlations are taken into account systematically. This method derives several known and new results from a unified point of view. Simple approximations lead to the Boltzmann equation for low densities and to a modified form of the Enskog equation for higher densities.     

Colour conductivity of hard spheres

We present an analytic solution for the d-dimensional (d > 1) hard-sphere free flight trajectories in a thermostatted colour field. The solution shows that particles can only reach a finite distance in the direction perpendicular to the field in the absence of collisions. Using a numerical algorithm we designed to simulate many-body hard-sphere systems with curved trajectories, we study the onset of the instability leading to phase separation in the two-dimensional case for a range of field strengths and three densities. For the two fluid densities we find that phase separation occurs for sufficiently strong fields regardless of the initial configuration, and that the phase-separated state eventually becomes a collisionless, non-ergodic steady state. For solid densities the phase-separated configuration is stable and conducting, but is not an attractor for other charge distributions because of the impossibility of particle rearrangement.     

Dissipative dynamics for hard spheres

The dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation. The Liouville operator(s) and associated binary scattering operators are defined as the generators for time evolution in phase space. The BBGKY hierarchy for reduced distribution functions is given, and an approximate kinetic equation is obtained that extends the revised Enskog theory to dissipative dynamics. A Monte Carlo simulation method to solve this equation is described, extending the Bird method to the dense, dissipative hard-sphere system. A practical kinetic model for theoretical analysis of this equation also is proposed. As an illustration of these results, the kinetic theory and the Monte Carlo simulations are applied to the homogeneous cooling state of rapid granular flow.     

Equilibrium fluid-solid coexistence of hard spheres

We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibbs' free energies depending on several crystalline order parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-solid interfaces). We are able to extrapolate to infinite volume the coexistence pressure [p(co)=11.5727(10)k(B)T/σ(3)] and the interfacial free energy [γ({100})=0.636(11)k(B)T/σ(2)].