Creating and destroying vacancies in solids and non-equilibrium grain-boundary segregation

Determining how the vacancies in excess of equilibrium concentration are created and destroyed in solids is crucial for understanding many of their physical characteristics and processes. Grain boundaries are known to be sources and sinks for bulk vacancies, but the exchange that will occur between the grain boundary and the bulk under a stress is still obscure. In the present paper, we show that grain boundaries will work as sources to emit vacancies when a compressive stress is exerted on them and as sinks to absorb vacancies when a tensile stress is exerted. At the same time, this physical process will produce solute non-equilibrium grain-boundary segregation and dilution. A set of kinetic equations is established to describe this physical process. Additionally an attempt has been made to simulate the experimental data with the kinetic equations to justify the physical process.     

The effect of surface contact conditions on grain boundary interdiffusion in a semi-infinite bicrystal

The Kirkendall effect is conditioned by active diffusion as well as by active sources and sinks for vacancies. In the case of grain boundaries under the condition of negligible bulk diffusion, the Kirkendall effect is highly localized and responsible for the formation of an extra material wedge in the grain boundary, which may lead to high stress concentrations. The Kirkendall effect in grain boundaries of a binary system is described by a set of partial differential equations for the mole fraction of one of the diffusing components and for the stress component normal to the grain boundary completed with the respective initial and boundary conditions. The contact conditions of the grain boundary with the surface layer acting as source of one of the diffusing components can be considered as equilibrium ones ensuring the continuity of generalized chemical potentials of both diffusing components. Thus, the boundary conditions are determined by the difference in chemistry (i.e. how the thermodynamic parameters depend on chemical composition) of the grain boundaries and of the surface layer. The simulations based on the present model indicate a drastic influence of the chemistry on the grain boundary interdiffusion and Kirkendall effect.     

Thermodynamic stability of binary nanocrystalline alloys: analysis of solute and excess vacancy

Regarding that the excess volume in grain boundaries (GBs) is released as the vacancies which are accommodated by the crystal bulk during grain growth, a free-energy function for binary nanocrystalline solid solution is proposed, based on the pairwise nearest-neighbor interactions. The model, for the given composition and temperature, predicts an equilibrium grain size, subjected to a mixed effect due to solute segregation and due to excess vacancies. Furthermore, excess-vacancy-inhibited grain coarsening can be attained, which plays a minor role in holding the thermal stability of nanocrystalline alloys, as compared to the effect of solute segregation.     

Grain-boundary dislocations and enhanced diffusion in nanocrystalline bulk materials and films

A theoretical model is suggested which describes the transformations of grain-boundary dislocation walls and their influence on diffusion processes in nanocrystalline materials fabricated under highly non-equilibrium conditions. It is shown that the decay of boundary dislocation walls of finite extent, occurring via the climb of boundary dislocations and the corresponding emission of vacancies, is capable of highly enhancing the grain-boundary diffusion in nanocrystalline materials. The enhanced diffusion, in turn, strongly affects the deformation behaviour of nanocrystalline materials. In the case of nanocrystalline films deposited on to substrates, the effects of misfit stresses on the transformations of boundary dislocation walls and the diffusion are analysed. It is demonstrated that the mean diffusion coefficient in a nanocrystalline film may increase by approximately several orders of magnitude owing to misfit stresses.     

Atomistic simulations of interactions between the 1 / 2⟨111⟩ edge dislocation and symmetric tilt grain boundaries in tungsten

The strength of polycrystals is largely controlled by the interaction between lattice dislocations and grain boundaries. The atomistic details of these interactions are difficult to discern even by advanced high-resolution microscopy methods. In this paper we present results of atomistic simulations of interactions between an edge dislocation and three symmetric tilt grain boundaries in body-centred cubic tungsten. Our simulations reveal that the outcome of the dislocation–grain-boundary interaction depends sensitively on the grain boundary structure, the geometry of the slip systems in neighbouring grains, and the precise location of the interaction within the grain boundary. A detailed analysis of the evolution of the grain boundary structures and local stress fields during dislocation absorption and transmission is provided.     

Finite element modelling of creep cavity filling by solute diffusion

In recently discovered self healing creep steels, open-volume creep cavities are filled by the precipitation of supersaturated solute. These creep cavities form on the grain boundaries oriented perpendicular to the applied stress. The presence of a free surface triggers a flux of solute from the matrix, over the grain boundaries towards the creep cavities. We studied the creep cavity filling by finite element modelling and found that the filling time critically depends on (i) the ratio of diffusivities in the grain boundary and the bulk, and (ii) on the ratio of the intercavity distance and the cavity size. For a relatively large intercavity spacing 3D transport is observed when the grain boundary and volume diffusivities are of a similar order of magnitude, while a 2D behaviour is observed when the grain boundary diffusivity is dominant. Instead when the intercavity distance is small, the transport behaviour tends to a 1D behaviour in all cases, as the amount of solute available in the grain boundary is insufficient. A phase diagram with the transition lines is constructed.     

Structure,energy and solute segregation behaviour of [110] symmetric tilt grain boundaries in yttria-stabilized cubic zirconia

Yttria-stabilized cubic zirconia bicrystals with [110] symmetric tilt grain boundaries are systematically fabricated by the diffusion bonding method. It is revealed that the grain-boundary atomistic structures, excess energies and solute segregation behaviours are strongly dependent on the macroscopic geometries of the boundaries. High-resolution transmission electron microscopy combined with lattice statics calculations suggests that the grain-boundary structures are characterized by the accumulation of coordination-deficient cation sites at their cores, whose densities have a clear correlation with excess energies and amounts of solute segregation. The orientation dependence of grain-boundary properties in cubic zirconia can thus be linked and understood via local grain-boundary atomistic structures with the characteristic miscoordinated cation sites.     

Defect chemistry of grain boundaries in proton-conducting solid oxides

The defect chemistry of charged grain boundaries in an acceptor-doped oxide in equilibrium with water vapour is examined theoretically. The basis of the theoretical approach is that the formation of charged grain boundaries and attendant space-charge zones is governed by differences in the standard chemical potentials of oxygen vacancies and hydroxide ions between bulk and grain-boundary core, that is, by the thermodynamic driving energies for defect redistribution. A one-dimensional continuum treatment is used to predict the space-charge potential and defect concentrations in the grain-boundary core as a function of water partial pressure, temperature and acceptor dopant concentration for various values of the two thermodynamic driving energies. The results are discussed with respect to experimental data in the literature for acceptor-doped perovskite oxides (e.g. BaZrO₃) and fluorite oxides (e.g. CeO₂).     

Grain boundary migration initiated by diffusion

A review is presented of work related to two new processes which arise in crystalline materials when impurities diffuse along grain boundaries from the surface of the material: diffusion-initiated grain boundary migration and recrystallization. We analyze the conditions under which DIGM occurs, the kinetics of the process, its driving forces, and also the changes in the grain fine structure and the near-grain regions, as well as the nucleation of new grains on the migrating boundaries, caused by an uncompensated impurity atom flux. We consider the mechanisms for DIGM. It is shown that not one of the mechanisms proposed to describe DIGM is capable of explaining all the experimentally observed properties of grain boundary migration under DIGM conditions. We note that changes in the grain boundary structure caused by the impurity atoms diffusing along it are due to diverse grain-boundary processes, which have important technological implications.V. D. Kuznetsov Physicotechnical Institute, Tomsk State University, Siberia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 34–57, May, 1992.     

Analysis of creep due to grain-boundary diffusion in hexagonal microstructures

For steady-state deformation caused by grain-boundary diffusion in hexagonal microstructures, the stress distribution on grain boundaries and the macroscopic strain rates are analysed by taking the effects of viscous grain-boundary sliding into account. The maximum normal stress and the extent of stress concentration are shown to decrease as the grain-boundary viscosity increases. For infinite viscosity and/or extremely small grain sizes, the distribution of the normal stress becomes uniform on grain boundaries. The strain rates are predicted by both the stress analysis and the energy balance method, and the two strain rates are consistent with each other. The predicted strain rates also decrease as the grain-boundary viscosity increases. The present analysis reveals that the grain-size exponent is dependent on the grain size and the grain-boundary viscosity: the exponent becomes unity for small grain sizes and/or high viscosity, while it is three for large grain sizes and/or low viscosity. Recent experimental observations that the strain rates of nano-sized grain are much lower than those predicted by grain-boundary diffusion are explained by the increasing contribution of viscous grain-boundary sliding with decreasing grain size.     

高自旋极化氧化物材料的颗粒边界磁电阻效应

颗粒边界磁电阻是高自旋极化氧化物颗粒体系中由于颗粒边界的存在而导致显著的磁电阻效应。本文将这种磁电阻效应定义为颗粒边界磁电阻效应。这里所说的颗粒边界,包括各种自然和人工晶界、粉末颗粒表面、复合材料中的颗粒界面等多种情况;所涉及的材料包括高自旋极化氧化物多晶、压缩粉末和各种复合材料等。对颗粒边界磁电阻效应的研究,不仅有助于人们进一步理解高自旋极化氧化物磁输运性质的基本机制,并为寻求具有高磁电阻效应的新型自旋电子学器件提供理论基础。本文综述了高自旋极化氧化物颗粒边界磁电阻研究的主要背景和发展现状,介绍了该领域中主要的实验发现和理论模型,展望了未来的发展。     

Conductivity of single-crystal and polycrystalline bilayer metal films under the conditions of interdiffusion

The electrical conductivity of a bilayer film with a single-crystal or polycrystalline structure is theoretically investigated under the conditions of metal interdiffusion at an arbitrary ratio between the thickness of layers and the mean free path of electrons in the layers. It is shown that analysis of the changes in the electrical conductivity of the bilayer film due to diffusion annealing allows one to elucidate the nature of the processes of bulk and grain-boundary diffusion, to determine the effective depth of penetration of impurity atoms into the bulk and grain boundaries of the sample, and to obtain information on the bulk and grain-boundary diffusion coefficient.     

Changes in the diffusion properties of nonequilibrium grain boundaries upon recrystallization and superplastic deformation of submicrocrystalline metals and alloys

The effect of an increase in the coefficient of the grain-boundary diffusion upon recrystallization and superplastic deformation of submicrocrystalline (SMC) materials prepared by severe plastic deformation has been studied. It is shown that the coefficient of the grain-boundary diffusion of the SMC materials is dependent on the intensity of the lattice dislocation flow whose value is proportional to the rate of the grain boundary migration upon annealing of SMC metals or the rate of the intragrain deformation under conditions of superplastic deformation of SMC alloys. It is found that, at a high rate of grain boundary migrations and high rates of superplastic deformation, the intensity of the lattice dislocation flow bombarding grain boundaries of SMC materials is higher than the intensity of their diffusion accommodation, which leads to an increase in the coefficient of the grain-boundary diffusion and a decrease in the activation energy. The results of the numerical calculations agree well with the experimental data.     

Grain Boundary Kinetics in Oxide Ceramics with the Cubic Fluorite Crystal Structure and its Derivatives

Kinetics of grain boundaries in oxides with the cubic fluorite structure and its derivatives has been investigated using fine grain ceramics that are fully dense. Grain growth measurements in these materials have provided information on grain boundary diffusivity over a diffusion distance of the order of the initial grain size. With the addition of solute cations, grain boundary mobility can be varied over many orders of magnitude, often with very different activation energies. This is caused by the variation of defect population and the defect-solute association. Definitive evidence for solute drag has also been observed in some cases, but solute drag can not be confirmed as a general mechanism in solid solutions. Lastly, while grain boundary at low temperature may continue to serve as a fast diffusion path, it may not be able to migrate because of additional pinning mechanisms such as those exerted by grain boundary nodal points or lines. This means that sintering without grain growth is possible, opening up an avenue for obtaining ultrafine ceramics by pressureless sintering.     

The relationship between grain-boundary structure and segregation in a rapidly solidified Fe-P alloy

It is well known that the amount of solute segregation can vary from one grain boundary to another. Though it is accepted that this variation is due to differences in boundary structure and crystallography, direct correlation between the degree of segregation and specific boundary structural characteristics is not well documented. In the present paper, P grain-boundary segregation in rapidly solidified Fe was studied by X-ray mapping (XRM) in a scanning transmission electron microscope (STEM). The boundary structure was characterized by convergent beam electron diffraction (CBED). To explore the relationship between the degree of segregation and boundary structure, a parameter?β?is introduced, which describes how well the two crystal planes on either side of a grain boundary match each other in a manner similar to the long-established plane matching theory. The introduction of this parameter enables us to relate the degree of segregation to boundary structure in a consistent way, e.g., both small-angle and low?Σ?symmetric boundaries correspond to low angle of β, leads to a low degree of segregation.     

Atomistic sliding mechanisms of the Σ=5 symmetric tilt grain boundary in bcc iron

Atomistic computer simulations were performed to investigate the mechanisms of grain-boundary sliding in bcc Fe using molecular statics and molecular dynamics with embedded-atom method interatomic potentials. For this study we have chosen the Σ?=?5, (310)[001] symmetrical tilt boundary with tilt angle θ?=?36.9°. Sliding was determined to be governed by grain-boundary dislocation activity with Burgers vectors belonging to the displacement shift complete lattice. The sliding process was found to occur through the nucleation and glide of partial grain-boundary dislocations, with a secondary grain-boundary structure playing an important role in the sliding process. Interstitial impurities and vacancies were introduced into the grain boundary to study their role as nucleation sites for the grain-boundary dislocations. While vacancies and H interstitials act as preferred nucleation sites, C interstitials to not.     

Nanocrack nucleation in polycrystalline silicon during grain-boundary sliding

A theoretical model is proposed to describe nanocrack nucleation in polycrystalline silicon. In terms of this model, nanocrack nucleation is stimulated by grain-boundary sliding, which creates sources of local stresses in triple junctions of grain boundaries. The relaxation of these local stresses is the main driving force of nanocrack nucleation near triple junctions in polycrystalline silicon, in which grain-boundary sliding contributes substantially to plastic deformation under cyclic loading at room temperature. The model is used to calculate the critical external stress required for nanocrack nucleation in polycrystalline silicon.     

Solute-atom segregation/structure relations at high-angle (002) twist boundaries in dilute Ni−Pt alloys

Monte Carlo simulations, utilizing embedded atom method (EAM) potentials, are employed to investigate in detail solute-atom segregation behavior at high-angle symmetrical (002) twist boundaries, at T=850 K, in Pt-3 at.% Ni and Ni-3 at.% Pt alloys. Solute enhancement in those alloys occurs on both sides of the phase diagram, although it is considerably higher on the Ni-rich side. The distributions of solute concentrations within the first and the second planes are very inhomogeneous, with the sites highly enhanced in solute being in the minority. The remaining sites exhibit little or no enhancement. The highest level of solute concentrations at individual sites continues to increase with the value of the rotations angle, , until saturation occurs at about the =5 misorientation. The large differences in concentrations between different types of sites suggest the possibility of an ordered grain-boundary phase. The correlation between the structure and solute species concentrations in most cases follows the trends observed for low-angle boundaries: Pt as a solute prefers the structural units of the perfect crystal type, while Ni as a solute tends to segregate at the filler units associated with the cores of the primary grain boundary dislocations. A strong correlation is observed between the position of a site in the first or second (002) plane and the plane of the interface. Rigid-body translations are detected for two boundaries on the Pt-rich side of the phase diagram. Roughening and possible structural multiplicity occur in the =5 boundary on the Ni-rich side. The same boundary on the Pt-rich side of the phase diagram exhibits a considerable amount of structural and chemical disorder.     

Application of automated crystallography for transmission electron microscopy in the study of grain-boundary segregation

Analytical Electron Microscopy (AEM) has brought significant progress in the study of grain-boundary segregation. Using X-ray energy-dispersive spectrometry (XEDS) in the AEM, elemental segregation information can be related to the crystallographic character of the same boundary via conventional Transmission Electron Microscope (TEM) diffraction techniques. While significant efforts have been made to improve XEDS analysis of sub-nanometer segregation layers, the methods for crystallographic characterization of grain boundaries have remained the same for several decades and labor-intensive processes. Recently, a method termed Automated Crystallography for TEM (ACT) was developed, which automates crystallographic characterization of grains under TEM observation. In the present work, we combine ACT and X-ray mapping via EDS in AEM for the study of Sb grain-boundary segregation in a rapidly solidified Cu-0.08 wt % Sb alloy. In contrast with previous reports, a large degree of anisotropy in Sb segregation level between different boundaries is found. ACT results suggest that one of the several grain boundaries observed with no detectable Sb segregation is very close to a Sigma 3 coincidence-site lattice structure. The reason for the observed anisotropy in the present alloy is discussed, based upon McLean's theory of segregation.