Analysis of vacancies produced at non-equilibrium concentrations by interdiffusion

In this paper, we address the fundamental problem of chemical interdiffusion in binary alloys for the case where vacancies at non-equilibrium concentrations may be generated during the interdiffusion process. We take a very general phenomenological approach to interdiffusion but develop it in a new way. Both high vacancy and low vacancy concentrations are dealt with. For the commonly encountered small vacancy concentration case our strategy centres on directing the information about the driving force associated with the non-equilibrium vacancies (which is effectively not measurable) onto the velocity of inert marker(s) in the diffusion zone. Assuming access to independent knowledge of the two tracer diffusivities we derive expressions for the transport coefficient (for the case of non-equilibrium vacancies) using an analysis along Boltzmann–Matano lines. Using the random alloy model we show that in principle it is possible to measure the relative concentration of non-equilibrium vacancies produced during interdiffusion.     

Equilibrium vacancy concentration in disordered binary alloys

The equilibrium vacancy concentration in disordered binary alloy is calculated in this paper. The calculations are performed in the configuration approximation, explicitly taking into account various types of vacant site neighborhoods. The self-diffusion coefficient is determined as a function of alloy composition.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 79–83, May, 1972.     

Electromigration revisited: competition between Kirkendall shift and backstress in pure metals and two-phase alloys

The simple phenomenological model and analytical approach of electromigration in the two-phase alloy (solder) under combined influence of the Kirkendall effect, backstress and sedimentation is presented. It is compared with electromigration in pure metal under condition of quasi-equilibrium vacancies (unlimited power of vacancy sinks-sources) and electromigration in pure metal with account of nonequilibrium vacancies.     

Spinodal method of vacancy diffusion study in ionic mixed crystals at room temperature

Some aspects of the spinodal method of deducing diffusion coefficients are considered. The decomposition kinetics yield the interdiffusion coefficient which is, however, not an intrinsic property of ionic crystals at low temperatures since it depends on the nonequilibrium vacancy concentration. Comparing, though, the spinodal kinetics in crystals doped with aliovalent impurity and undoped crystals enables one to obtain the vacancy diffusion coefficient which is an intrinsic property. The spinodal decomposition has been studied in nominally pure and Ca²⁺-doped mixed crystals of NaCl-KCl by the thermal gradient method and the cation vacancy diffusion coefficient D_v = 2 × 10⁻¹²cm²s⁻¹ at room temperature.     

Modeling phase decomposition and patterning in binary alloy systems subjected to neutron irradiation

We study processes of phase decomposition and patterning in a model of a binary alloy system subjected to sustained irradiation. We exploit the reaction rate theory and generalize the Darken approach of vacancy diffusion to describe generation, recombination, annihilation and spatial interaction of point defects. It is shown that an increase in the defect production rate phase, decomposition processes are replaced by disordering and patterning with vacancy clusters' formation. At elevated damage rates, both phase separation and patterning are accompanied by pattern selection processes. In the framework of numerical simulations, dynamics of phase decomposition and vacancy clusters formation is studied in detail. A change in the morphology of vacancy clusters during irradiation and their statistical properties are discussed.     

Shrinking kinetics by vacancy diffusion of a pure element hollow nanosphere

In this paper, shrinking via the vacancy mechanism of a hollow mono-atomic nanosphere is described. Using Gibbs–Thomson boundary conditions, an exact solution is obtained for the kinetic equation in quasi steady-state at the linear approximation. Collapse time as a function of the geometrical size of a hollow nanosphere is found. An extension to hollow binary alloy nanospheres is also made. Previous Monte Carlo simulations of this problem are discussed.     

替位杂质对贵金属(111)表面稳定性影响的分子动力学研究

采用嵌入原子方法的原子间相互作用势，通过分子动力学方法研究了过渡族金属Cu，Ag，Au，Ni，Pd，Pt(111)表面的相互替位掺杂对表面稳定性的影响，计算了替位掺杂体系的表面能与表面空位形成能，探讨了影响表面稳定性的因素及其变化规律. 计算表明：替位杂质对表面能变化的影响主要是替位杂质的凝聚能和原子半径，而影响空位形成能变化的原因除凝聚能和原子半径外，合金溶解热具有重要的作用. 此外，通过替位杂质导致的体系表面能变化对合金体系的偏析行为进行了预测，理论预测与实验结果符合很好. 关键词： 替位杂质 贵金属 表面能 表面空位形成能     

Effect of triangle vacancy on thermal transport in boron nitride nanoribbons

Recently, triangle vacancy in hexagonal boron nitride is observed experimentally. Using nonequilibrium Green’s function method, we investigate thermal transport properties of boron nitride nanoribbons (BNNRs) with a triangle vacancy. The effect of triangle vacancy on the phonon transmission of zigzag-edged BNNRs (Z-BNNRs) is different from that of armchair-edged BNNRs (A-BNNRs). The triangle vacancy induces antiresonant dips in the spectrum of Z-BNNRs. Moreover, the boron-terminated triangle vacancy causes antiresonant zero-transmission dip and the number of the zero-transmission dip increases with the geometrical size of triangle vacancy. For the A-BNNRs with triangle vacancy, except some antiresonant dips, a resonant peak is found in the transmission. The antiresonant and resonant phenomena are explained by analyzing local density of states and local thermal currents. Although the antiresonant dip and the resonant peak are both originated from quasibound states, their distributions of local thermal currents are distinct, which leads to the transport discrepancy. In addition, the thermal conductance of BNNRs decreases linearly with increasing the vacancy size.     

Possible mechanisms of atomic disorder in binary alloys

Possible mechanisms of atomic disorder are analyzed. Equilibrium configurations of a binary alloy of stoichiometric composition AB are obtained in a computer experiment to simulate the process of atomic ordering of an alloy from the completely disordered state to the equilibrium state through a chain of successive nonequilibrium configurations. Fiz. Tverd. Tela (St. Petersburg) 39, 1456–1460 (August 1997)     

A density-corrected quantum Boltzmann equation

Binary correlations are a recognized part of the pair density operator, but the influence of binary correlations on the singlet density operator is usually not emphasized. Here free motion and binary correlations are taken as independent building blocks for the structure of the nonequilibrium singlet and pair density operators. Binary correlations are assumed to arise from the collision of twofree particles. Together with the first BBGKY equation and a retention of all terms that are second order in gas density, a generalization of the Boltzmann equation is obtained. This is an equation for thefree particle density operator rather than for the (full) singlet density operator. The form for the pressure tensor calculated from this equation reduces at equilibrium to give the correct (Beth-Uhlenbeck) second virial coefficient, in contrast to a previous quantum Boltzmann equation, which gave only part of the quantum second virial coefficient. Generalizations to include higher-order correlations and collision types are indicated.     

Effect of Ni and vacancy concentration on initial formation of Cu precipitate in Fe–Cu–Ni ternary alloys by molecular dynamics simulation

In the present work, the effects of Ni atoms and vacancy concentrations(0.1%, 0.5%, 1.0%) on the formation process of Cu solute clusters are investigated for Fe–1.24%Cu–0.62%Ni alloys by molecular dynamics(MD) simulations. The presence of Ni is beneficial to the nucleation of Cu precipitates and has little effect on coarsening rate in the later stage of aging. This result is caused by reducing the diffusion coefficient of Cu clusters and the dynamic migration of Ni atoms. Additionally, there are little effects of Ni on Cu precipitates as the vacancy concentration reaches up to 1.0%,thereby explaining the embrittlement for reactor pressure vessel(RPV) steel. As a result, the findings can hopefully provide the important information about the essential mechanism of Cu cluster formation and a better understanding of ageing phenomenon of RPV steel. Furthermore, these original results are analyzed with a simple model of Cu diffusion, which suggests that the same behavior could be observed in Cu-containing alloys.     

Atomistic simulation of the vacancy diffusion in (0 0 1) surface of MoTa alloy

The formation and diffusion of a single Mo or Ta vacancy in the (0 0 1) surface of the B₂-type MoTa alloy have been investigated by using modified analytical embedded-atom method (MAEAM). The results show that the effect of the surface on the vacancy is only down to the sixth layer. It is easier for the vacancy to form in the first layer. Comparing the migration energy of the vacancy migrating in the intra-layer, to the upper layer and to the nether layer via 2NN jump, we find that the vacancy in the first or second layer is preferred to migrate in intra-layer, and that in the third or fourth layer is favorable to migrate to the upper layer. Although 1NN jump will result in an anti-site so that a disorder in the order alloy, it may also occur due to the much lower migration energy especially for the vacancy in the second and third layer to migrate to the first and second layer, respectively.     

Effects of Cr on H and He trapping and vacancy complexes in V in a fusion environment: a first-principles study

First-principles density functional theory was used to investigate the interaction between hydrogen (H) and helium (He) in V–Cr alloy, which is a potential structural material for use in fusion reactors. When vacancies are present in the V–Cr alloy, a single He atom prefers to occupy the octahedral site near the Cr atom rather than vacancy centre, which differs from the cases of iron and tungsten. Because of the decrease of the electron density around the He atom, there was a strong interaction between He and H. In the vicinity of He-vac complexes, H atoms tend to stay in the tetrahedral site rather than occupy the octahedral-interstitial site. A single He-vac complex can trap as many as six H atoms, which is more than can be trapped by an empty vacancy in the V–Cr alloy because of the electronic density redistribution of vacancy vicinity. This strong attraction explains the enhanced retention of H and He observed near the surface of V and V-based alloys under both sequential and simultaneous bombardments. The results provide useful insight into the application of the V-based alloys as candidate structural materials in fusion Tokamaks.     

Electronic and transport properties of V-shaped defect zigzag MoS_2 nanoribbons

Based on the nonequilibrium Green＇s function （NEGF） in combination with density functional theory （DFT） calcu- lations, we study the electronic structures and transport properties of zigzag MoS2 nanoribbons （ZMNRs） with V-shaped vacancy defects on the edge. The vacancy formation energy results show that the zigzag vacancy is easier to create on the edge of ZMNR than the armchair vacancy. Both of the defects can make the electronic band structures of ZMNRs change from metal to semiconductor. The calculations of electronic transport properties depict that the currents drop off clearly and rectification ratios increase in the defected systems. These effects would open up possibilities for their applications in novel nanoelectronic devices.     

Thermodynamic basis for a variational model for crystal growth

Variational models provide an alternative approach to standard sharp interface models for calculating the motion of phase boundaries during solidification. We present a correspondence between objective functions used in variational simulations and specific thermodynamic functions. We demonstrate that variational models with the proposed identification of variables are consistent with nonequilibrium thermodynamics. Variational models are derived for solidification of a pure material and then generalized to obtain a model for solidification of a binary alloy. Conservation laws for internal energy and chemical species and the law of local entropy production are expressed in integral form and used to develop variational principles in which a "free energy," which includes an interfacial contribution, is shown to be a decreasing function of time. This free energy takes on its minimum value over any short time interval, subject to the laws of conservation of internal energy and chemical species. A variational simulation based on this model is described, and shown for small time intervals to provide the Gibbs-Thomson boundary condition at the solid-liquid interface.     

Modeling microstructure evolution of binary systems subjected to irradiation and mechanical loading

We study a change in mechanical properties of binary systems subjected to irradiation influence described by ballistic flux of atomic mixing having regular and stochastic contributions. By using numerical modeling based on the phase field approach we study dynamics of deformation fields in a previously irradiated system and in the binary system deformed during irradiation. An influence of both deterministic and stochastic components of ballistic flux onto both yield strength and ultimate strength is studied. We have found that degradation of mechanical properties relates to the formation of percolating clusters of shear bands. Considering a hardening coefficient we analyze stages of plastic deformation of both initially irradiated alloy and alloy subjected to sustained irradiation. Stability of binary alloy under mechanical loading in the form of shear strain with a constant rate and cyclic deformation is discussed.     

AES studies of surface composition of AgCu alloys

The influence of pretreatments like sputtering, annealing and cleaving on the surface composition is important in quantitative Auger electron spectroscopy. The present paper deals with this influence for the binary alloy system AgCu with 100, 95, 80, 60, 50, 40, 20, 5, and 0 at% Ag. Sputtering causes an enrichment of Cu on the surface due to the higher sputter coefficient of Ag. In contrast cleaving yields an enrichment of Ag due to the lower tensile strength of Ag. The surface composition obtained by scribing is used as standard for the bulk composition because this technique is independent of parameters like sputter coefficient or tensile strength. The results are compared with previous measurements of homogeneous alloy systems.     

Spinodal decomposition of an ABv model alloy: Patterns at unstable surfaces

We develop mean-field kinetic equations for a lattice gas model of a binary alloy with vacancies (ABv model) in which diffusion takes place by a vacancy mechanism. These equations are applied to the study of phase separation of finite portions of an unstable mixture immersed in a stable vapor. Due to a larger mobility of surface atoms, the most unstable modes of spinodal decomposition are localized at the vapor-mixture interface. Simulations show checkerboard-like structures at the surface or surface-directed spinodal waves. We determine the growth rates of bulk and surface modes by a linear stability analysis and deduce the relation between the parameters of the model and the structure and length scale of the surface patterns. The thickness of the surface patterns is related to the concentration fluctuations in the initial state. Received 28 October 1998