Segregation of impurities and vacancies on phase and antiphase boundaries in alloys

The equilibrium distribution of low-concentration impurities or vacancies is investigated in the region of a coherent phase boundary or antiphase boundary in a binary alloy. A general expression for the free energy of an inhomogeneous multicomponent alloy, which generalizes the expression previously derived for a binary alloy, is presented. Explicit formulas for the impurity concentration profile c _im(x) in terms of the distribution of the principal components of the alloy near a boundary are obtained from this expression in the mean-field and pair-cluster approximations. The shape of this profile is determined by a “preference potential” P, which characterizes the attraction of an impurity to one of the alloy components, as well as by the temperature T and the phase transition temperature T c. At small values of P/T impurities segregate on a phase boundary, and the degree of this segregation, i.e, the height of the maximum of c _im(x), in the region of the boundary increases exponentially as the ratio T _c/T increases. For P ≠ 0 the c _im(x) profile near a phase boundary is asymmetric, and as P/T increases, it takes on the form of a “worn step.” The maximum on the c _im(x) curve then decreases, and at a certain |P|≳T _c it vanishes. Segregation on an antiphase boundary is investigated in the case of CuZn ordering in a bcc alloy. The form of c _im(x) near an antiphase boundary depends significantly both on the form of the potential P and on the stoichiometry of the alloy. At small P impurities segregate on an antiphase boundary, and at fairly large P “antisegregation,” i.e., a decrease in the impurity concentration on the antiphase boundary in comparison with the value within the antiphase domains, is also possible. Zh. éksp. Teor. Fiz. 112, 714–728 (August 1997)     

杂质对镁合金耐蚀性影响的电子理论研究

利用大角重位点阵模型建立了Mg合金［0001］对称倾斜晶界模型，应用实空间的连分数方法计算了杂质在晶界的偏聚能，杂质原子间相互作用能和不同体系的费米能级，讨论了杂质在晶界的偏聚行为，杂质间的相互作用与有序化的关系及杂质对镁合金腐蚀性能影响的物理本质. 计算结果表明，杂质原子偏聚于晶界，且主要偏聚于晶界的压缩区；杂质原子间相互排斥，因此在晶界区形成有序相；费米能级与材料的腐蚀电位存在这样的关系：材料的费米能级越高，其腐蚀电位就越低，容易被腐蚀，相反费米能级低，其腐蚀电位就高，不容易腐蚀. 体系中成分不同区域的费米能级差导致电子从费米能级高的区域流向费米能级低的区域，正是费米能级差构成了镁合金电化学腐蚀的电动势. 关键词： 电子理论 晶界偏聚 镁合金 腐蚀机理     

Interaction of Solute Impurity with Grain Boundary: The Impurity Drag Effect

An equation of grain boundary motion in a binary polycrystal is derived. The derivation is based on minimization of free energy of the total systems. The equation takes into account an impurity segregation at the grain boundary, grain boundary curvature and energy.As an example, we apply this equation to the analysis of the impurity drag effect problem. It is shown, that the sign of the impurity effect on grain boundary velocity (delay or acceleration) does not depend on kinetic coefficients. The sign of the effect is determined by a thermodynamic function which combines the grain boundary segregation coefficient, the derivative of grain boundary energy with respect to absorbed impurity concentration, and the derivative of bulk free energy with respect to bulk impurity concentration.     

Segregation Effects at a High-Angle Twist Boundary in ZnO

Ab initio density functional plane-wave pseudopotential calculations were performed for a = 7 ( = 21.79°) [0001] twist boundary in ZnO with and without the presence of Sb impurities. The segregation energies revealed a significant driving force for segregation and it was shown that the formation of an Sb monolayer was favoured. Decreased coordination in the boundary core suggested a trend towards the formation of an intergranular phase. The impurity states caused by the monolayer were located within the band gap and higher in energy relative to the state produced by a single impurity. Charge transfer to the Sb monolayer was observed indicating a possible enhancement of the grain boundary potential barrier.     

An interfacial complex in ZnO and its influence on charge transport

The segregation of native defects and Bi impurities to a high-angle grain boundary in ZnO is studied by first-principles calculations. It is found that the presence of Bi(Zn) increases the concentration of native defects of acceptor type in the grain boundary. This leads to the formation of a Bi(Zn)+V(Zn)+O(i) interfacial complex under O-rich conditions and exhibits a localized acceptor state. This state, which is different from that of the isolated impurity, gives the grain boundary p-type character and when embedded between n-type ZnO grains is consistent with the double Schottky barrier model for Bi-doped ZnO varistors.     

Pb2+ Defects in perovskite-like KMgF3 crystals

Abstract

The physical properties of Pb²⁺ impurities in the perovskite-like lattice of KMgF₃ are very similar to those of (ns)² ions in alkali halides. The impurity inhomogeneous distribution leads to high dopant levels in the bottom region of the crystals, with a segregation coefficient equal to 0. 020. The optical features of the 336 nm emission support its attribution to luminescence of Pb²⁺ ions from the relaxed excited B state.     

Co-Segregation Effects on Boundary Migration

We analyze the effect of co-segregation on the mobility of grain boundaries within the framework of the impurity drag theory originally proposed by Cahn and Lücke and Stüwe for an ideal solution. The new derivation extends this model to the case where there are two types of impurities (or three components in the alloy). Since the resultant expression for the boundary mobility is complicated, numerical solutions were obtained for several cases to show how co-segregation affects the boundary mobility. Depending on the relative diffusivities of the two impurities which are both attracted to the boundary, the mobility may either increase or decrease with increasing concentration of one of the impurities. When one of the impurities is attracted to the boundary and the other repelled from the boundary, increasing the concentration of the attractive impurity can lead to a sharp decrease in the boundary mobility.     

Impurity effects on adhesive energies

Some simple arguments are made about the effect of impurities on adhesive interactions at solid junctions. A universal adhesive force relation is derived for brittle adhesion. The adhesive binding energy, ΔE, is an important parameter in brittle adhesion forces. ΔE has also been shown by others to be important when there is plastic flow. We found that impurity effects on ΔE are determined by the segregation energies to the junction and to the free surfaces. At low temperatures, if it is energetically more favorable for impurities to segregate to the surfaces than to the junction, then the impurities will decrease ΔE. The converse is also true. For example, for self junctions which are in registry, ΔE is decreased if surface segregation is exothermic and increased if it is endothermic. These segregation energy relationships are consistent with the results of a number of experiments on the effects of impurities on adhesion forces and grain boundary embrittlement.     

Role of anisotropy of the coupling constant in a superconductor model with singularities near the Fermi surface

The role of anisotropy of the coupling constant in the influence of nonmagnetic impurities on the behavior of the superconducting transition temperature T _c is investigated in the high-temperature superconductor (HTSC) model, where high values of T _c result from an increase in the density of states near the Fermi surface. It is shown that this model is more sensitive to impurities than the BCS model; Anderson compensation does not occur in the HTSC model, even for identical distributions of the densities of states in the superconducting and impurity channels, and the impurity contributions are no longer linear with respect to the impurity concentration in the vicinity of T _c. Anisotropy of the superconducting gap Δ and the possibility of its disappearance at certain points on the Fermi surface due to various types of pairing are manifested in the stability of the superconducting phase against the influence of impurities. Fiz. Tverd. Tela (St. Petersburg) 39, 1940–1942 (November 1997)     

Theoretical study of defect formation processes in metals

Abstract

The equilibrium solute atmosphere around a straight edge dislocation in interstitial solid solutions has been investigated. A long-range deformation interaction among impurities is accounted for. Quantitative estimations have been given for the example of carbonaceous martensite. The impurity concentrations in an atmosphere around the dislocation core are calculated for a given temperature in dependence on its mean value in the specimen. For a dislocation with an impurity atmosphere stationary fluxes of interstitial atoms and vacancies on the dislocation are calculated; a concentration dependence of impurity parameters indicating a dislocation capture efficiency of the self-interstitial atoms and vacancies and the parameter of dislocation preference B are received; a radiation-induced deformation rate (swelling and creep) is determined.     

Observation of a new gettering mechanism in (Hg,Cd)Te

A new gettering mechanism is proposed for substitutional impurities which diffuse by an interstitial process. In this mechanism, an externally imposed gradient of self interstitials generates a gradient in impurity interstitials leading to the segregation of fast diffusing impurities to low interstitials, high vacancy regions. Data are presented to support this model in (Hg, Cd)Te alloys, as well as explicitly rule out gettering by dislocations, by segregation to precipitates, or by enhanced solubility arising from the interaction of the impurity with a varying Fermi level.     

Effect of phonon scattering from neutral and charged impurity centers on the lattice heat conductivity of PbTe:(Tl, Na)

Experimental data on the effect of thallium and sodium impurities on the lattice heat conductivity of PbTe at room temperature are reported. Because the lattice of lead chalcogenides is strongly polarized near charged impurities, the effect of impurities on the lattice heat conductivity depends substantially on their charge state. This property of the material has been used to determine the charge state of the thallium impurity in PbTe. The results obtained argue for a model of quasi-local thallium-impurity states which assumes low electron-correlation energy at an impurity center. Fiz. Tverd. Tela (St. Petersburg) 40, 1206–1208 (July 1998)     

Interactions between Surface Impurities and the Electron–Hole System of a Semiconductor Crystal

The effects of creation and annihilation of impurities on the surface of a highly doped semiconductor under changes in the surface concentration n of dopant atoms constituting impurities are predicted theoretically. The effects are determined by electrostatic interactions of charged surface impurity species with charge carriers and semiconductor ions. The effects are observed in a certain range of n, provided the surface impurities exhibit donor (acceptor) properties, and the semiconductor is doped with an acceptor (donor) impurity.     

High-speed superplasticity of microcrystalline alloys under conditions of local grain boundary melting

A model is proposed for the high-speed superplasticity of materials under conditions of local grain boundary melting at temperatures close to solidus. It is shown that the local melting of grain boundaries containing segregations of impurity atoms, results in the formation of a structure consisting of liquid-phase regions and solid intergranular bridges which provide cohesion of the grains during the deformation process. The equilibrium concentration, dimensions, and activation energy for the formation of solid bridges are determined as a function of the temperature, initial impurity concentration in the boundary, and the boundary thickness. A mechanism is proposed for grain-boundary slip under conditions of local grain boundary at anomalously high strain rates. Zh. Tekh. Fiz. 68, 38–42 (December 1998)     

Statistical description of the motion of dislocation kinks in a random field of impurities adsorbed by a dislocation

A model has been proposed for describing the influence of impurities adsorbed by dislocation cores on the mobility of dislocation kinks in materials with a high crystalline relief (Peierls barriers). The delay time spectrum of kinks at statistical fluctuations of the impurity density has been calculated for a sufficiently high energy of interaction between impurities and dislocations when the migration potential is not reduced to a random Gaussian potential. It has been shown that fluctuations in the impurity distribution substantially change the character of the migration of dislocation kinks due to the slow decrease in the probability of long delay times. The dependences of the position of the boundary of the dynamic phase transition to a sublinear drift of kinks x ∝ t^δ (δ σ 1) and the characteristics of the anomalous mobility on the physical parameters (stress, impurity concentration, experimental temperature, etc.) have been calculated.     

The Formation of Defect Complexes in a ZnO Grain Boundary

The microscopic properties a ZnO grain boundary containing extrinsic point defects are studied using a density functional computational approach. The results show that the grain boundary acts as a sink for native defects, such as the zinc vacancy and the oxygen interstitial, and also for bismuth substitutional impurities. The defects tend to accumulate at under-coordinated sites in the boundary core and prefer to form small clusters. In particular the segregation of Bi promotes the formation of the other native defects by lowering their formation energies in the boundary. Individually, the native defects and the Bi impurity do not produce deep interface states in the band gap which are electrically active. However, when the defects cluster to form a Bi_Zn-V_Zn-O_i complex, new gap states are created of acceptor type. It is suggested that these new states are caused by defect interactions which compensate one another resulting in the depletion of an occupied impurity state and new bond formation. The results are discussed in terms of the Schottky barrier model commonly used to describe the electrical characteristics of ZnO varistors.     

An atomistic study of grain boundary segregation and cracking

A Monte Carlo model is applied to study a Σ = 5 (310) fcc tilt boundary structure and impurity segregation to this boundary. The Johnson-type potential functions are used to express atomic interactions for two binary alloys of NiCu and CuSb systems. Through atomic relaxation near absolute zero, the basic structural unit of the Σ = 5 CSL boundary is found to dissociate into two subunits. For the NiCu system, copper segregation to the boundary follows the Gibbsian equilibrium segregation behavior in which the segregation is localized on a few atomic layers, its amount increases with increase in the bulk concentration but decreases with increase in temperature. For the CuSb system, an assumption of the CuCu bond weakening due to the strong, adjacent CuSb bonds is also incorporated to realize the embrittling effect of Sb atoms. The preferential site for the large Sb atoms is the vertex of a pentagonal bipyramid in the Σ = 5 grain boundary. Without bond weakening, the Sb-segregated grain boundary maintains a structure combined with a distorted pentagonal bipyramid and a capped trigonal prism. However, with bond weakening some bonds of the trigonal prisms are disrupted in order to form new pentagonal bipyramids. When a uniaxial strain is applied in the direction perpendicular to the grain boundary plane, the weakened copper bonds become the source of microcracks thus enhancing brittle fracture along the Sb-segregated grain boundary.     

Effect of Coulomb correlations in a variable-valence impurity system and phonon drag on the thermoelectric constants in two-dimensional systems

The temperature behavior of the longitudinal Nernst-Ettingshausen coefficient in 2D systems is studied theoretically taking account of phonon drag and Coulomb correlations in a system of mixed-valence impurities at low temperatures. It is shown that the effect changes sign at the transition from entrainment to scattering by a correlated system of impurity centers. A sign change does not occur in the case of scattering by randomly distributed impurity centers. This temperature behavior of the Nernst-Ettingshausen coefficient is due to the radical rearrangement of the impurity system as a result of strong Coulomb correlations present in a system of impurities with mixed valence. As a result, the character of the scattering of charge carriers by the correlated system of charge centers changes substantially. Fiz. Tverd. Tela (St. Petersburg) 40, 553–556 (March 1998)     

Mobility of electrons upon scattering by a multicomponent correlated system of impurity centers

A system that contains two sorts of impurity centers spatially distributed in a random way is considered. Not all impurities of the first sort are ionized, and all the impurities of the second sort are ionized. Spatial correlations in the system of impurity ions of the first sort are investigated under conditions when the correlation radius of an impurity ion is limited from above due to a deficit of neutral impurities. The influence of randomly spatially arranged small-sized donors (impurities of the second sort) on correlations in the system of impurity ions is analyzed. The equations for describing the effect of small-sized donors on correlations in the system of impurity ions are obtained. The electron mobility at zero temperature is calculated by the example of HgSe: Fe (the correlated system of impurity centers consists of iron atoms and small-sized donors whose concentration is higher than the Mott concentration).     

Two magnetic impurities with arbitrary spins in open boundary t-J model

From the open boundary t-J model an impurity model is constructed in which magnetic impurities of arbitrary spins are coupled to the edges of the strongly correlated electron system. The boundary R matrices are given explicitly. The interaction parameters between magnetic impurities and electrons are related to the potentials of the impurities to preserve the integrability of the system. The Hamiltonian of the impurity model is diagonalized exactly. The integral equations of the ground state are derived and the ground state properties are discussed in detail. We discuss also the string solutions of the Bethe ansatz equations, which describe the bound states of the charges and spins. By minimizing the thermodynamic potential we get the thermodynamic Bethe ansatz equations. The finite size correction of the free energy contributed by the magnetic impurities is obtained explicitly. The properties of the system at some special limits are discussed and the boundary bound states are obtained.