Interdiffusion in condensed solutions

Expressions for the coefficient of interdiffusion of components in a binary condensed vacancy-free alloy and a diffusion coefficient matrix for the same alloy with equilibrium and nonequilibrium vacancies are studied. In the first alloy, metastable states may appear if the mixing energy is positive. In the case of the second alloy, closed spinodals may arise under certain conditions. In binary systems with a constant concentration of particles having close atomic volumes, a vacancy stationary nonequilibrium distribution is observed, which may generate vacancy “channels” through which atoms diffuse much more rapidly than in the regular lattice.     

Elucidating hydrogen assisting vacancy formation in metals: Mo and Nb as examples

Impurity H is inclined to be trapped by some defects with more space such as vacancy and grain boundary when it dissolves in a metal. Inversely, H can also enhance formation of large amount of vacancies even if there are few vacancies in intrinsic metals initially. Using first-principles simulation combined with statistical model, Mo and Nb as examples, we quantitatively calculate the concentration of vacancies including pure vacancy and H _n -vacancy (H _n V) complexes. The concentrations of vacancies in the form of H _n V notably increase due to the decrease of effective formation energy of vacancy from H stimulation. Our finding solves a long-standing puzzle on the atomistic mechanism underlying H assisting vacancy formation in some metals.     

The cooperative effect of electromigration and non-equilibrium vacancies on reactive phase growth

Phase formation under a direct current was analysed for a binary system with non-equilibrium vacancy distribution. It was shown that the non-equilibrium vacancy distribution diminishes the effect of electromigration on the phase formation process: if the electric current augments the phase growth, the resulting vacancy concentration gradient delays it; if the current opposes phase growth, the vacancy concentration gradient maintains it. A comparative analysis is presented involving the results obtained within Gösele and Tu theory (taking into consideration the finiteness of the reaction rate at interfaces).     

锐钛矿(TiO2)半导体的氧空位浓度对导电性能影响的第一性原理计算

基于低温重氧空位锐钛矿半导体的态密度计算，在同等条件下研究取不同大小模型的锐钛矿做适量浓度的氧空位存在，分别对进入导带的相对平均电子数和氧空位类杂质的散射迁移率进行计算，之后对电导率进行类比，发现锐钛矿半导体的导电性能对适量浓度低的氧空位有利可行得到了证明.同时，低温重氧空位的条件下，锐钛矿半导体的电导率不仅与氧空位浓度有关，而且和进入导带的平均电子数有关，和氧空位散射的电子迁移率有关的正确结论.     

锐钛矿(TiO2)半导体的氧空位浓度对导电性能影响的第一性原理计算

基于低温重氧空位锐钛矿半导体的态密度计算,在同等条件下研究取不同大小模型的锐钛矿做适量浓度的氧空位存在,分别对进入导带的相对平均电子数和氧空位类杂质的散射迁移率进行计算,之后对电导率进行类比,发现锐钛矿半导体的导电性能对适量浓度低的氧空位有利可行得到了证明.同时,低温重氧空位的条件下,锐钛矿半导体的电导率不仅与氧空位浓度有关,而且和进入导带的平均电子数有关,和氧空位散射的电子迁移率有关的正确结论. 关键词： 锐钛矿半导体 氧空位浓度 电导率 第一性原理计算     

Analysis of interdiffusion via vacancy-pairs in strongly ionic solids

In this paper, we analyse chemical interdiffusion via Schottky vacancy-pairs in strongly ionic crystals for diffusion couples (AY–BY), where A and B take the same valence. We derive a sum-rule relating the phenomenological coefficients that is based on an earlier sum-rule derived by Moleko and Allnatt (Phil. Mag. A, 58 () 677) for diffusion in the multicomponent random alloy via the agency of isolated vacancies. With this sum-rule and other relationships derived by us, we show that the ratio of the intrinsic diffusivities can be expressed in exactly the same simple form as the case for diffusion via isolated vacancies. The functional form for the interdiffusion coefficient when expressed in terms of atom-vacancy exchange frequencies for diffusion is found to be essentially the same as that for isolated vacancies. The difference centres only on the relative differences of the local jump coordination of the vacancies in each case.     

Analysis of the demixing of yttria-stabilized zirconia in an electric field for different diffusion mechanisms

Steady-state demixing of the cations in yttria-stabilized zirconia in an electric field is analyzed for diffusion via independent vacancies, by vacancy pairs and by vacancy triplets. We analyze two conditions, one (open system) where the vacancies are everywhere close to an internal surface, which allows the Schottky defect reaction to permit the equilibration of the concentration of the vacancies, the other (closed system) where such equilibration is only possible at the external surface. For diffusion via independent vacancies and vacancy pairs, critical values of the ratio of the yttrium to zirconium vacancy exchange frequencies causing yttrium enrichment at the cathode are determined. It is also shown that diffusion via the vacancy-triplet mechanism always leads to yttrium enrichment at the anode end. Using Monte Carlo simulation, we also verify the analysis of the situation where demixing occurs by independent cation vacancies in a closed system.     

空位所引起的晶体弹性常数的改变

认为具有少量空位的晶体是一个均匀的晶体,把完整与不完整晶体的区别,归结为势函数的修改。应用Morse函数推导出弹性常数c₁₁和c₁₂的变化率与空位浓度的关系。因为空位邻近的原子有松弛,考虑了由松弛而改变了的相互作用对弹性常数的影响。首先求得铝中空位的第一和第二最近邻的位移百分率各为1.61和-0.32,这里的正号和负号各表示向空位移进和移出。其次,进行了具体的计算,在铜晶体中,估计1％的空位浓度使弹性常数减小1.3—1.4％。然而,铝晶体中的空位对弹性常数的影响     

Theory of oxidation/reduction-induced valence transformations of metal ion dopants in oxide crystals mediated by oxide-vacancy diffusion: II. Kinetic analysis

We consider theoretically valence transformations of doping metal ions in oxide crystals induced by oxidation and reduction obtained by changes in the ambient oxygen partial pressure. Three types of oxygen vacancies are assumed to mediate transformations: neutral, singly ionized, and doubly ionized. In the companion part I paper we provide thermodynamic analyses yielding concentration relations among the oxygen vacancy, metal ions, holes and electrons, as functions of the ambient oxygen pressure. In the present companion part II paper we provide time dependent concentration profiles of the various species and reaction rate profiles. The diffusion exhibits a complex behavior; under some conditions, it may be described by a constant diffusivity, and is symmetric with respect to oxidation and reduction. However, under a wide range of conditions, the ionic state changes are highly asymmetric with respect to oxidation and reduction. For example, in the case of a neutral vacancy, a very narrow reaction front may establish during reduction. In the inverse (oxidation) process, however, the different species' profiles are quite smooth.     

高氧空位浓度对锐钛矿TiO2莫特相变和光谱红移及电子寿命影响的第一性原理研究

基于密度泛函理论的第一性原理研究,通过对锐钛矿TiO₂高氧空位浓度、态密度图及吸收光谱图的分析,发现锐钛矿TiO₂高氧空位浓度的条件下,高氧空位浓度对禁带变窄、吸收光谱红移和电子寿命都有很大的影响,从理论上进一步解释了高氧空位浓度对禁带变窄的原因.同时,锐钛矿半导体在高氧空位浓度时发生莫特相变和锐钛矿氧空位在等离子体中吸收光谱红移实验进行比较,发现锐钛矿TiO₂应适量控制高氧空位浓度对吸收光谱红移好于前者.适量控制高氧空位浓度的锐钛矿TiO 关键词： 锐钛矿 高氧空位浓度 吸收光谱红移 第一性原理     

Grain-boundary anelastic relaxation and non-equilibrium dilution induced by compressive stress and its kinetic simulation

Grain boundaries are known to be sources and sinks for bulk vacancies, but the exchange that occurs between the grain boundary and the bulk under a low stress is still obscure. In the present paper, it is shown that grain boundaries may act as sources to emit vacancies when an anelastic deformation occurs under a compressive stress. These emitted supersaturated vacancies are combined with solute atoms to form complexes. Solute non-equilibrium grain-boundary dilution may be induced by the diffusion of complexes away from the boundary. An equation of solute concentration at grain boundary is derived under stress equilibrium during its anelastic relaxation. Furthermore, kinetic equations are also established to describe the non-equilibrium grain-boundary dilution. Additionally, an attempt is made to simulate experimental data to justify the present model.     

Interdiffusion in two-layer Pd/Ag films I. The effects of interphase boundaries

Interdiffusion processes in epitaxial single-crystal Pd/Ag thin films within the temperature range 20°–500°C are studied by transmission electron microscopy, electron diffraction and electrical resistance methods. Homogenization is investigated both during deposition and during annealing.The mass transfer kinetics is found to depend significantly on the original structure of the interphase boundary (dislocations present or not) and on its reconstruction due to interdiffusion. Regular networks of misfit dislocations at the interface can retard interdiffusion, while network failures lead to acceleration of homogenization process. The vacancy flows play a decisive role in these processes. The effects of interphase dislocations on the DIGM, DIR and RID processes are discussed.The numerical study of electrical resistance variations during annealing is carried out. The concentration profiles are plotted for a nontrivial dependence of interdiffusion coefficient on concentration. The numerical results are compared with the experimental data.     

Point-defect concentrations in B2 NiAl alloys under pressure

The pressure dependence of point-defect concentrations is calculated on the basis of two recently published models. It is demonstrated that the effective formation volume of vacancies shows asymmetrical character about stoichiometry. For Ni-rich and stoichiometric compositions, the concentration of Ni vacancies versus pressure can be described by a simple exponential function. The concentration of Ni antisite defects is independent of pressure. For Al-rich compositions, the concentration of Ni vacancies shows a more complex behaviour. At low pressures the vacancy concentration is independent of pressure, the effective formation volume is zero, while above a critical pressure the vacancy concentration becomes pressure dependent. This can be explained by the annihilation reaction of Ni vacancies. The pressure of complete replacement depends on the stoichiometry and has proved to be very sensitive to the input parameters used in the different models. The changes expected in diffusion activation energy and activation volume with composition are discussed on the basis of calculated temperature and pressure dependence of Ni vacancy concentration, assuming vacancy-mediated diffusion. The pressure effect on the boundary that separates regions in which triple defects or interbranch defects dominate was also investigated. It was observed that pressure expands the region in which Al interbranch defects dominate.     

Excitonic instabilities,vacancies, and reconstruction of covalent surfaces

Two possibilities for explaining the superlattices of (111) surfaces of Si(7 × 7) and Ge(2 × 8) are considered. The equilibrium concentration of surface vacancies is related to the ratio of metallic and directional contributions to vacancy energies. The macroscopic thermo-dynamic explanation based on vacancy concentrations is preferred to an alternate microscopic one based on excitonic instabilities. A relation between anisotropy of surface energies and vacancy concentrations is proposed that predicts new superlattices for Si (100) 2 × 1, (110) 2 × 1, 5 × 1 and 4 × 5.     

Determination of the nonequilibrium concentration of vacancies in silicon crystals by measuring the concentration of nickel atoms at lattice sites

A method is proposed for determining the nonequilibrium concentration of vacancies and vacancy complexes in silicon crystals by measuring the concentration of electrically active nickel atoms at the sites of the silicon lattice, [Ni _s ], after the diffusion of nickel at temperatures from 550 to 650°C. It is shown experimentally that, after the diffusion of nickel from the surface into silicon samples with different initial nonequilibrium concentrations of vacancy complexes, [V]_init, formed during crystal growth, the concentration [Ni _s ] in the bulk of a sample to a good degree of accuracy corresponds to the vacancy concentration [V]_init determined by a standard method based on the analysis of the concentration profiles of [Au _s ] after the diffusion of gold from the surface. This method for determining the concentration of vacancies is much simpler than the standard method and allows one to use lower temperatures and a lower thermal budget.     

Erbium-induced interdiffusion of gallium and aluminum in GaAs/AlGaAs quantum-well structures

Incorporation of erbium into GaAs/AlGaAs quantum-well structures in the course of their MBE growth has been shown experimentally to initiate effective Ga and Al interdiffusion and Er diffusion due to the erbium-induced enhanced vacancy formation. A mechanism for the formation of cation vacancies is proposed, which is based on the generation of local strains by the incorporating erbium. It is shown that erbium interacts with aluminum to produce in AlGaAs aluminum-enriched, erbium-containing clusters. Fiz. Tverd. Tela (St. Petersburg) 41, 540–544 (March 1999)     

Generalized equilibrium concentration of polyvacancy: case study for trivacancy in hard-sphere crystals

The equilibrium concentration of polyvacancy in crystal is formulated by modifying the grand canonical ensemble. The generalized equation can be applied to obtain the concentration of vacancy in any order and shape in crystal. In this work, a Widom-like particle insertion method is adopted implemented with molecular dynamics simulation to obtain individual formation free energies for constituent vacancies in polyvacancy. As a case study, equilibrium concentrations and formation free energies were obtained of four and nine trivacancies identified in face-centred-cubic (FCC) and hexagonal-close-packed (HCP) hard-sphere crystals, respectively. The result is in excellent agreement with literature data available for the FCC. Further, stabilities of equilateral triangular trivacancies are elucidated and their relative stabilities in FCC and HCP hard-sphere crystals are reported. Overall trivacancy concentration is higher in the HCP HS crystal.     

Equilibrium concentration of point defects in crystalline4He at O K

We calculate the concentrations of vacancies and intersitials in the ground state of a Bose solid which models⁴He. Because ground-state boson wave functions are nodeless, their probability densities correspond to classical Boltzmann factors, and properties of Bose solids, such as the concentration of vacancies and interstitials, can be calculated using classical statistical mechanics. We model the ground-state wave function of⁴He with the product (Jastrow) form that corresponds to a classical 1/r ^b pair potential, and use a quasiharmonic approximation to calculate the concentrations of vacancies and interstitials in an fcc lattice with this potential. We find that the fractional concentration of vacancies at the melting point is 1.60×10^–5 for 1/r ⁹ and 6.36×10^–6 for 1/r ⁶, while the interstitial fractional concentrations are 1.32×10^–3 and 1.08×10^–5, respectively; the defect concentrations decrease by 7–16 orders of magnitude when the crystal density increases by 50%. At the same density, and with the same 1/r ⁹ potential, the concentration of vacancies in an hcp lattice is essentially the same as in an fcc lattice, but the interstitial concentration is much lower, apparently because the fcc lattice contains a more favorable split-interstitial site than does hcp. Therefore, our fcc vacancy results should be directly relevant for (hcp)⁴He, providing what we think is a lower bound on the vacancy concentration, while the interstitial concentration in⁴He is probably much lower than our results.     

He,Au离子辐照AuCu_3致元素表面偏析

采用磁控溅射方法在单晶硅(111)衬底上制备了AuCu_3薄膜,用2 MeV He离子和1 MeV Au离子对薄膜进行辐照,用卢瑟福背散射对He,Au离子辐照前后AuCu_3薄膜近表面的成分变化进行了分析,对不同离子辐照导致的表面元素偏析行为进行了研究.结果表明:当2 MeV He离子辐照时,随着辐照剂量增大,观察到样品近表面Au元素偏析的趋势;当1 MeV Au离子辐照时,随着辐照剂量增大,观察到样品近表面Cu元素偏析的趋势,与He离子辐照相反.通过对He,Au离子在样品中产生的靶原子空位及其分布分析,发现靶原子空位浓度分布的梯度是导致两种不同表面元素偏析趋势的原因,空位扩散是其中的主要机理.