Theory of atomic ordering in copper-platinum alloys

An expression is obtained for the energy of a binary system with an hcp lattice using a many-particle model. This expression is used for calculating regions of relative stability of modifications of the copper-platinum alloy. The effect of a many-particle interatomic interaction on the order-disorder phase equilibrium diagram and on order parameters is studied. Agreement between theory and experiment has been achieved for the first time for the phase diagram as well as for short-range order parameters in the two spheres of copper-platinum alloy. It is shown, within the framework of the model used, that such a comprehensive agreement between theory and experiment is possible only if many-particle interaction and the trigonal character of L1₁ phase are taken into account. Calculations were performed with the help of the multicluster version of the Kikuchi method in the tetrahedron + triangle approximation. Results obtained clarify significantly the Understanding of the interatomic interaction in copper-platinum alloy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 46–53, March, 1984.     

Point-defect properties in HCP rare earth metals with analytic modified embedded atom potentials

The analytic embedded atom method (EAM) type many-body potentials of hcp rare earth metals (Dy, Er, Gd, Ho, Nd, Pr, and Tb) have been constructed. The hcp lattice is shown to be energetically most stable when compared with the fcc and bcc structure, and the hcp lattice with ideal c/a. The mechanical stability of the corresponding hcp lattice with respect to large change of density and c/a ratio is examined. The phonon spectra, stacking fault and surface energy are calculated. The activation energy for vacancy diffusion in these metals has been calculated and the most possible diffusion paths are predicted. Finally, the self-interstitial atom (SIA) formation energy and volume have been evaluated for eight possible sites. This calculation suggests that the crowdion and basal split are the most stable configurations. The SIA formation energy increases linearly with the increase of the melting temperature.Received: 26 March 2003, Published online: 9 September 2003PACS: 34.20.Cf Interatomic potentials and forces - 66.30.Fq Self-diffusion in metals, semimetals, and alloys - 61.72.Ji Point defects (vacancies, interstitials, color centers, etc.) and defect clusters - 61.72.Bb Theories and models of crystal defects     

Influence of the size and shape of free nanoparticles on the local changes in the lattice parameter and on the structural stability of body-centered cubic zirconium and iron

The influence of the shape and size of nanocrystals on the lattice relaxation of body-centered cubic metals (zirconium, iron) at a constant temperature has been investigated using the molecular dynamics method with the many-body interatomic interaction potential obtained in terms of the embedded-atom model. The calculations have been performed for isolated clusters with sizes ranging from 2.5 to 17 nm for zirconium and from 2 to 14 nm for iron. It has been demonstrated that, in free zirconium and iron particles, the relaxation of the lattice constant along the [100], [010], and [001] directions has an oscillatory character. Irrespective of the size of the zirconium and iron particles, the equilibrium distances between atoms at the center of cubic clusters are minimum compared to those observed in near-surface layers and the equilibrium value of the lattice parameter for the bulk sample. In spherical clusters, the region of a maximum contraction corresponds to a depth approximately equal to 0.2 particle diameter from the surface. An increase in the size of both cubic and spherical clusters leads to a decrease in the deviation of the local lattice parameter from the equilibrium value for the bulk sample. It has been established that the size and shape of the cluster substantially affect the temperature and mechanism of the structural transformation from the body-centered cubic phase into the hexagonal close-packed phase.     

The effect of crystal equilibrium condition on the lattice dynamical model parameters of a body centred cubic metal

Using barium, for which results that compare favourably with experiment have been obtained, the effect on the lattice dynamical model parameters of a body centred cubic metal of explicitly imposing the crystal equilibrium condition on various ion-ion coupling schemes when used with the modified electron-ion interaction scheme of Bhatia has been studied. When the equilibrium condition is not used, the calculated model parameters lose their physical significance with the result that at equilibrium, the sum of the ionic and electronic pressures is not zero. This inconsistency is removed when the equilibrium condition is explicitly imposed on the models. It is not meaningful to compare the two results with and without the equilibrium condition imposed, not only because the imposition of the equilibrium condition reduces the number of independent parameters of the models by one, but also because the results apply to different states of the crystal. Also the comparison of calculated model parameters and measured quantities such as phonon frequencies make sense only when both are determined for the same state of the crystal. This condition is satisfied only when the equilibrium condition, which has unfortunately been ignored in most lattice dynamical studies, is explicitly imposed on lattice dynamical models.     

Calculation of Vacancy Induced Properties in FCC Metals Using an Alternative Lattice Dynamical Model

Combining the conventional Kanzaki's lattice statics method with an alternative lattice dynamical model called decoupling transformation, a new approach is proposed to calculate the vacancy induced properties in FCC metals. This approach has the advantage over the traditional least-square fit approach in the way that all the model parameters are linearly independent and so it can avoid the problem of non-uniqueness in dynamical model parameters when interactions with more distant atoms are taken into account by fitting to the experimental phonon frequencies only. Numerical results on the lattice dynamical properties such as phonon dispersion curves and interatomic interaction force constants and the vacancy induced properties such as the atomic displacements, lattice relaxation energy, divacancy interaction energy and relaxation volume are obtained specifically for two similar FCC metals, to wit, Cu and Ni and are compared with previous calculations. It is concluded that the interatomic interactions up to the fourth nearest neighbours are already good enough for describing both the lattice vibrational and vacancy induced properties for both metals.     

Internal equilibrium and crystal dynamics of tantalum

A lattice dynamical model for bcc metals, which satisfies the internal force equilibrium condition of the lattice is proposed. The present model combines a linearized Thomas-Fermi Theory for the electron-ion interaction and the central pair potential for ion-ion interaction. as an application, the computed phonon dispersion, vibrational spectrum, and lattice specific heat of tantalum show fairly good agreement with experiments.     

Calculations of the thermodynamic properties for binary hcp alloys with simple embedded atom method model

The simple embedded atom method model for hcp metals developed by Johnson has been applied to calculate the thermodynamic properties of all binary alloy systems for the eleven transition hcp metals. It has been shown that the agreement with the calculation results from Miedema thermodynamic theory and with the available experimental data is general good, but the agreement with the experimental data for the formation energy of Co-Y alloys is weak, which implies that a more better model for hcp metals is needed.Project supported by the National Natural Science Fundation     

Model for lattice dynamics in metals

A lattice dynamical model for cubic metals, which satisfies the internal force equilibrium condition of the lattice, is proposed. The present model combines a linearized Thomas Fermi theory for the electron-ion interaction and the axially symmetric model for the ion-ion interaction. The computed frequencies of copper and sodium are in good agreement with the experimental data.     

Phase stabilities of fcc Ti nanocrystals

A model for the equilibrium transition size and temperature between hcp and fcc structure of nanocrystals Ti has been established in terms of the effect of surface stress on the internal pressure of nanocrystals. It was found that as size and temperature decreased, the relative stability of fcc structure in comparison with hcp structure increased. The obtained result is consistent with other theoretical and experimental data.     

Structural and thermodynamic properties of AlB2 compound

We employ a first-principles plane wave method with the relativistic analytic pseudopotential of Hartwigsen, Goedecker and Hutter (HGH) scheme in the frame of DFT to calculate the equilibrium lattice parameters and the thermodynamic properties of AlB₂ compound with hcp structure. The obtained lattice parameters are in good agreement with the available experimental data and those calculated by others. Through the quasi-harmonic Debye model, obtained successfully are the dependences of the normalized lattice parameters a/a₀ and c/c₀ on pressure P, the normalized primitive cell volume V/V₀ on pressure P, the variation of the thermal expansion α with pressure P and temperature T, as well as the Debye temperature \Theta_D and the heat capacity C_V on pressure P and temperature T.     

Phonon anomalies and superconductivity in the hcp metals,Tc, Re,and Ru

The phonon dispersion curves have been measured for the hcp metals, Tc, Re, and Ru in the [001] direction at room temperature. A pronounced phonon anomaly has been observed for the LO mode in Tc and Re which is absent in Ru. A low temperature study of Tc revealed a strong temperature dependence of the anomaly. It is suggested that the magnitude of the phonon anomaly is correlated with the strength of the electron-phonon interaction in these metals.     

高温高压下钼的结构稳定性研究

以钼为代表的一系列过渡金属,在高温高压的相变及结构稳定性研究是实验和理论研究的热点.钼在常温常压下是bcc结构,但是在高温高压下可能的相结构一直未能确定.本文首先预测了几种高压下的结构,并计算了其自由能及力学性质.针对可能的hcp结构,我们通过新近发展的自洽晶格动力学方法,充分考虑声子间相互作用,成功获得了hcp结构高温高压声子色散曲线,结果表明hcp相在热力学及动力学上都是能够稳定存在的结构,是一种可能的高压相.     

Monte Carlo study of the Quartet Ising model consistent with selfduality

The transition temperature obtained from recent Monte Carlo calculations for the Quartet Ising model on the fcc lattice deviated by 17% from the exact transition temperatureT _c ^SD required by selfduality which we have proven afterwards. Here we use Monte Carlo results of the internal energy, which agree well with low- and high temperature series, to determine entropy and free energy and obtain aT _c in excellent agreement (±0.1%) with the exact value. The Quartet model on the hcp lattice is shown to be selfdual too; the rapidly converging series for the fcc and the hcp lattice differ only in higher order.Guest stay     

Formation,structure, and magnetic changes at annealing of films deposited by laser sputtering of Ni and Pd

The electron microscopy investigations of Pd, Ni, and Ni-Pd alloy films are carried out. The films were produced by laser sputtering of one- and two-element targets. It is shown that, in the case of alternate deposition of nickel and palladium, polycrystalline films with a metastable hcp lattice are formed. The hcp lattice parameters increase monotonically with increasing palladium content in the film. As a result of the annealing, Ni and Ni-Pd alloy films acquire an equilibrium fcc structure. A positive deviation from Vegard’s law occurs for the dependence of the lattice parameter of the solid solution on the Pd concentration. The as-prepared Ni and Ni-Pd alloy films with the hcp structure are characterized by the absence of a magnetic moment. The transition into the ferromagnetic state occurs after annealing, and hysteresis is observed upon magnetization reversal.     

Calculation of the surface energy of hcp-metals with the empirical electron theory

A brief introduction of the surface model based on the empirical electron theory (EET) and the dangling bond analysis method (DBAM) is presented in this paper. The anisotropy of spatial distribution of covalent bonds of hexagonal close-packed (hcp) metals such as Be, Mg, Sc, Ti, Co, Zn, Y, Zr, Tc, Cd, Hf, and Re, has been analyzed. And under the first-order approximation, the calculated surface energy values for low index surfaces of these hcp-metals are in agreement with experimental and other theoretical values. Correlated analysis showed that the anisotropy of surface energy of hcp-metals was related with the ratio of lattice constants (c/a). The calculation method for the research of surface energy provides a good basis for models of surface science phenomena, and the model may be extended to the surface energy estimation of more metals, alloys, ceramics, and so on, since abundant information about the valence electronic structure (VES) is generated from EET.     

Crystal structure analysis in (3+d) dimensions

Inelastic neutron scattering on in situ grown bcc single crystals of the group 4 metals Ti, Zr and Hf show a band of low energy and strongly damped phonons. Geometrical considerations show how these damped lattice vibrations achieve the displacements necessary for the two martensitic phase transitions from bcc to ω (under pressure) and from bcc to hcp (upon lowering the temperature). The low energy and temperature dependent phonons are precursor fluctuations of the hcp or ω phase within the bcc phase.     

On the bond forces in metals. II

For a number of metals with a cubic crystal lattice an estimate has been made of the pair interaction energy as part of the metallic bond energy obtained in [1] by a statistical method.     

Thermal expansion behaviors of hcp and fcc Co nanowire arrays

The lattice parameters of as-prepared and annealed Co nanowires with hcp and fcc structures have been measured using the in situ high-temperature x-ray diffraction method. The hcp and fcc Co nanowires have been fabricated within the porous anodic alumina membranes by a direct-current electrodeposition technique. The results indicate that the variational quantity of the interplanar spacing for hcp Co nanowire arrays is bigger than that for fcc Co nanowire arrays in spite of as-prepared and annealed samples. The structural difference between hcp and fcc Co nanowires results in the different thermal expansion behaviors.     

Diffusion fronts and gradient percolation: A survey

Twenty years ago, Bernard Sapoval suggested that the solders obtained by inter-diffusion of two metals, could have a fractal structure. He, then, initiated simulation calculations based on a lattice gas model, describing the diffusion of non-interacting particles on a square lattice. These ideas are nowadays a mainstream field of research, developing in various domains including topics as different as fractal etching, imbibition experiments, fractal structures of polymer interfaces, image treatment, fracture surfaces, urban growth, predatory–prey interaction, etc.