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.     

Solute distribution in nanocrystalline Ni–W alloys examined through atom probe tomography

Atom probe tomography is used to observe the solute distribution in electrodeposited nanocrystalline Ni–W alloys with three different grain sizes (3, 10 and 20?nm) and the results are compared with atomistic computer simulations. The presence of grain boundary segregation is confirmed by detailed analysis of composition fluctuations in both experimental and simulated structures, and its extent quantified by a frequency distribution analysis. In contrast to other nanocrystalline alloys previously examined by atom probe tomography, such as Ni–P, the present nanocrystalline Ni–W alloys exhibit only a subtle amount of solute segregation to the intergranular regions.     

Theoretical aspects of solute segregation to high-angle grain boundaries

A high-angle grain boundary is modeled as a planar defect characterized by its thickness and atomic density. We successively examine the elastic and electronic contributions to the solute/grain boundary binding energy. We deduce the effect of the grain boundary physical parameters on its propensity for segregation. The thickness of high-angle grain boundaries is not a fundamental parameter for segregation. The atomic density in the grain boundary controls the electronic binding energy. The rate of change of elastic constants with the density is the important factor in the elastic contribution to segregation. We conclude that segregation to boundaries with small excess volumes is not precluded.     

W-In体系溶质晶界偏聚行为的第一性原理计算

基于第一性原理构建了钨基合金体系的溶质偏聚模型,以W-In体系为例研究了不同浓度下溶质的晶界偏聚行为和成键特征,从电子结构层面揭示了W-In体系的键合作用,预测了W-In体系界面稳定性随溶质浓度的变化规律.结合键布居、电荷密度、差分电荷密度和态密度等电子结构分析,发现了W-In体系中溶质原子在偏聚过程中的键性转变特征,阐明了W-In键由晶粒内部的离子键过渡为晶界区域强共价键的微观机理.模型计算首次得到了W-In体系中溶质本征偏聚能随In浓度的非单调变化规律,结合键合作用和能量分析揭示了溶质浓度对本征偏聚能的影响机制.计算预测了W-In体系达到高热稳定性所需的最佳溶质浓度范围和应避开的溶质浓度范围.本研究为具有高温稳定性的钨基合金材料的设计与制备提供了理论基础和定量化指导.     

Criteria for the Occurrence of the Diffusion-Induced Grain Boundary Migration

Recent experimental data on diffusion-induced grain boundary migration (DIGM) are reviewed. For the case of the coherency strain driving force, quantitative criteria for the occurrence of DIGM are suggested, which establish the relationship between the net driving force for grain boundary migration, the diffusivity in the vicinity of the grain boundary, the enthalpy of the grain boundary segregation, the misfit parameter for the solute atoms in the matrix and the solubility of the diffusing element in the matrix. It is shown that an upper limit for the grain boundary velocity during DIGM exists due to the solute drag effect.     

Free volumes in bulk nanocrystalline metals studied by the complementary techniques of positron annihilation and dilatometry

Free-volume type defects, such as vacancies, vacancy-agglomerates, dislocations, and grain boundaries represent a key parameter in the properties of ultrafine-grained and nanocrystalline materials. Such free-volume type defects are introduced in high excess concentration during the processes of structural refinement by severe plastic deformation. The direct method of time-differential dilatometry is applied in the present work to determine the total amount and the kinetics of free volume by measuring the irreversible length change upon annealing of bulk nanocrystalline metals (Fe, Cu, Ni) prepared by high-pressure torsion (HPT). In the case of HPT-deformed Ni and Cu, distinct substages of the length change upon linear heating occur due to the loss of grain boundaries in the wake of crystallite growth. The data on dilatometric length change can be directly related to the fast annealing of free-volume type defects studied by in situ Doppler broadening measurements performed at the high-intensity positron beam of the FRM II (Garching, Munich, Germany).     

Microdeformation behaviour of Al–SiC metal matrix composites

The satisfactory performance of metal matrix composites depends critically on their integrity, the heart of which is the quality of the matrix-reinforcement interface. The nature of the interface depends in turn on the processing of the MMC component. At the micro-level, the development of local concentration gradients around the reinforcement can be very different according to the nominal conditions. These concentration gradients are due to the metal matrix attempting to deform during processing. This plays a crucial role in the micro-structural events of segregation and precipitation at the matrix-reinforcement interface. Equilibrium segregation occurs as a result of impurity atoms relaxing in disordered sites found at interfaces, such as grain boundaries, whereas non-equilibrium segregation arises because of imbalances in point defect concentrations set up around interfaces during non-equilibrium heat treatment processing. The amount and width of segregation depend very much on (a) the heat treatment temperature and the cooling rate, (b) the concentration of solute atoms and (c) the binding energy between solute atoms and vacancies. An aluminium–silicon–magnesium alloy matrix reinforced with varying amounts of silicon carbide particles was used in this study. A method of calculation has been applied to predict the interfacial fracture strength of aluminium, in the presence of magnesium segregation at metal matrix interface. Preliminary results show that the model succeeds in predicting the trends in relation to segregation and intergranular fracture strength behaviour in these materials. Microhardness profiles of reinforced and un-reinforced aluminium alloys are reported. The presence of precipitates at alloy-reinforcement interface identified by Nano-SEM.     

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.     

SmCo7纳米晶合金晶粒组织热稳定性的热力学分析与计算机模拟

推导出了单相纳米晶合金的晶界过剩体积与晶粒尺寸之间的定量关系, 建立了纳米晶合金的晶界热力学性质随温度和晶粒尺寸发生变化的确定性函数. 针对SmCo₇纳米晶合金, 通过纳米晶界热力学函数计算和分析, 研究了单相纳米晶合金的晶粒组织热稳定性. 研究表明, 当纳米晶合金的晶粒尺寸小于对应于体系中晶界自由能最大值的临界晶粒尺寸时, 纳米晶组织处于相对稳定的热力学状态; 当纳米晶粒尺寸达到和超过临界尺寸时, 纳米晶组织将发生热力学失稳, 导致不连续的快速晶粒长大. 利用纳米晶合金热力学理论与元胞自动机算法相耦合的模型对SmCo₇纳米晶合金在升温过程中的晶粒长大行为进行了计算机模拟, 模拟结果与纳米晶合金热力学模型的计算预测结果一致, 由此证实了关于纳米晶合金晶粒组织热稳定性的研究结论. 关键词： 纳米晶合金热力学 7纳米晶合金')" href="#">SmCo₇纳米晶合金 热稳定性 计算机模拟     

The Harrison diffusion kinetics regimes in solute grain boundary diffusion

Knowledge of the limits of the principal Harrison kinetics regimes (Types A, B and C) for grain boundary diffusion is very important for the correct analysis of depth profiles in a tracer diffusion experiment. These regimes for self‐diffusion have been extensively studied in the past by making use of the phenomenological lattice Monte Carlo (LMC) method with the result that the limits are now well established. However, the relationship of these self‐diffusion limits to the corresponding ones for solute diffusion in the presence of solute segregation to the grain boundaries remains unclear. In the present study, the influence of solute segregation on the limits was investigated with the LMC method for the well‐known parallel grain boundary slab model by showing the equivalence of two diffusion models. It is shown which diffusion parameters are useful for identifying the limits of the Harrison kinetics regimes for solute grain boundary diffusion. It is also shown how the measured segregation factor from the diffusion experiment in the Harrison Type‐B kinetics regime may differ from the global segregation factor.     

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.     

The effect of grain refining on the microsegregation of aluminium–magnesium alloy 5182

Aluminium alloy 5182 (AA5182) contains approximately 4.5% Mg as its principal alloying addition, and is most commonly used to make the lid of the aluminium can. With a view to the possible future development of a micro-macro model to describe the casting of this alloy, the effect of grain refinement on the microsegregation of magnesium in industrial rolling ingots of AA5182 has been investigated at three different depths beneath the edge of the ingot (and hence three different cooling rates)—60, 140 and 600 mm. The accuracy with which published microsegregation models are able to predict the solute distribution profile is assessed. It has been found that the magnesium segregation range (C_max–C_min) of the grain refined samples actually increases as cooling rate decreases. The range of the non grain refined samples is independent of cooling rate. The solute concentration profiles of the theoretical microsegregation models examined do not correlate well with the experimentally measured profiles. It is concluded that this poor correlation is due to either the effect of post solidification homogenisation or the influence of macroscopic variables during the cast. A more accurate model of post solidification homogenisation is required to assess the relative contribution of each of these factors to the poor correlation. In addition, it is concluded that the measurement of segregation is best done using a combination of EDX mapping and point analysis techniques to locate and quantify the areas of maximum and minimum solute concentration.     

Effective diffusivity of solute in multiphase materials with segregation

The effective diffusion coefficient D_eff for solute in a multiphase microstructure in which solute segregation can occur is related to D_eff for an isomorphic microstructure in which no segregation occurs. This permits analytical expressions (approximations, bounds, etc.) and methods of numerical calculation for D_eff that neglect solute segregation to be applied to systems that exhibit segregation. As an example, exact results are obtained for solute diffusion and segregation to grain boundaries in an idealized polycrystalline microstructure.     

Grain boundary compositions in stoichiometric and off-stoichiometric Y1Ba2Cu3O7−x

The grain boundary segregation behavior of stoichiometric and off-stoichiometric YBa₂Cu₃O_7−x has been studied with analytical electron microscopy (AEM) to complement previous results obtained with Auger electron spectroscopy (AES). It was observed that the grain boundary segregation levels varied from boundary to boundary. In stoichiometry material, excess copper and deficient oxygen were observed at the grain boundaries. In materials containing excess barium, excess yttrium and deficient copper levels were observed at the grain boundaries. The grain boundary segregation levels in the materials containing excess barium can be related to the resistivity and critical current density results. Preferential segregation to specific sites in grain boundaries was observed by AEM. The effect of grain boundary segregation on the superconducting properties of these materials is discussed in terms of the weak link behavior and a possible percolative mechanism in order to maintain a continuous current path.     

Solute-atom segregation at symmetric twist and tilt boundaries in binary metallic alloys on an atomic-scale

Monte Carlo and overlapping distributions Monte Carlo (ODMC) techniques are employed to simulate grain boundary (GB) segregation in a number of single-phase binary metallic alloys—the Au-Pt, Cu-Ni, Ni-Pd, and Ni-Pt systems. For a series of symmetric [001] twist and [001] tilt boundaries, with coincident site lattice (CSL) structures, we demonstrate that the Gibbsian interfacial excess of solute is a systematic function of the misorientation angle. We also explore in detail whether the GB solid solution behavior is ideal or nonideal by comparing the results of Monte Carlo and ODMC simulations. The range of binding free energies of specific atomic sites at GBs for solute atoms is also studied. The simulational results obtained demonstrate that the thermodynamic and statistical thermodynamic models commonly used to explain GB segregation are too simple to account for the microscopic segregation patterns observed, and that it is extremely difficult. If not impossible, to extract the observed microscopic information employing macroscopic models.     

Computer simulation of solute segregation to a Σ = 5 tilt boundary in Au,Cu and Ni

A Lattice Energy Function that combines a Mie type interatomic potential and a free electron gas volume dependence has been applied to the study of grain boundary energy and structure of a Σ = 5 tilt boundary in Au, Cu and Ni and of solute segregation to the same. Interatomic potentials and volume dependencies of the solvent and solute were adjusted to fit the relative partial molar enthalpy and volume at infinite dilution order to construct a AB type potential and volume dependence. This AB interaction is then applied to calculate the binding energies of solute to various grain boundary sites and the resulting change in grain boundary energy. A relationship between the binding energy and change in grain boundary is derived. The relative values of the grain boundary energy are in agreement with experimental values of the average grain boundary energies. The relative binding energies of the tested solvent-solute systems are in agreemnet with expectations that certain systems should have larger binding energies than others. The behavior of solute binding energies and local relaxations are in agreement with other studies of grain boundary segregation which use different Lattice Energy Functions and relaxation algorithms. The change in grain boundary energy is shown to be directly proportional to the binding energy.     

Diffusion, Solute Segregations and Interfacial Energies in Some Material: An Overview

We have shown a connection among the three important properties of interfaces, namely, the free energy, diffusion and solute segregation through the conjecture that the interface free energy is the difference between those responsible for diffusion in the lattice and the interface itself. The interface energy is known to decrease upon solute additions. We discuss the methodology and the thermodynamical analysis of the diffusion parameters which enable extraction of the interfacial energies and illustrate them by results obtained in a wide variety of materials. Investigations carried out in pure polycrystalline metals have yielded grain boundary energies comparable to those directly measured. Furthermore, we discuss the role of solute segregation at grain boundaries in alloys in altering diffusion. From the perturbations caused, the solute segregation parameters—the enthalpy and the entropy of binding—have been extracted and levels of solute concentrations estimated. It is shown that similar analyses when applied to complex materials, e.g. the Pb–Sn eutectic alloy, several intermetallic compounds, and oxide systems, also result in acceptable values of interface energies and segregation factors. Finally, some ad-hoc guidelines are provided to alter diffusion in interfaces through solute additions in order to achieve some end use engineering objectives.     

Three-dimensional atomic scale analysis of nanostructured materials

The 3-dimensional atom probe (3DAP) has been used to provide atomic-scale microcharacterisation of a number of nanostructured materials. Grain boundary segregation has been investigated in electrodeposited nanocrystalline nickel and Ni-P. In the nanocrystalline nickel, there was no observable grain boundary segregation in the as-deposited condition. After annealing, carbon and sulphur contamination was found at the boundary of an abnormally-grown grain. In the as-deposited Ni-P alloy, only limited grain boundary segregation of P is seen, but annealing produces significant segregation and the formation of Ni₃P precipitates at grain boundaries. The phase chemistry in a melt-spun amorphous Fe-Si-Cu-Nb-B-Al (FINEMET-type) alloy has also been studied, and the hetereogeneous nucleation of Fe-Si nanocrystals at Cu precipitates shown conclusively. It is found that at early stages of crystallisation, there is only limited partitioning of the Si between the nanocrystals and the amorphous matrix. Atom probe studies of thin layered films have historically been limited by specimen preparation problems, but recent advances have now yielded data on metallic multilayer films. This has allowed atomic-scale measurements of interface chemistry in these films for the first time.     

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.     

Focused ion beam preparation of atom probe specimens containing a single crystallographically well-defined grain boundary

Needle-shaped atom probe specimens containing a single grain boundary were produced using the focused ion beam (FIB) of a two-beam FIB/SEM (scanning electron microscope) system. The presented specimen preparation approach allows the unprecedented study of a grain boundary which is well characterised in its crystallographic orientation by means of the field ion microscope (FIM) and the tomographic atom probe (TAP). The analysis of such specimens allows in particular the determination of solute excess atoms at this specific grain boundary and hence the investigation of the segregation behaviour. The crucial preparation steps are discussed in detail in the present study for the Sigma 19 a {331} 110 grain boundary of a 40 at.ppm-Bi doped Cu bi-crystal. Transmission electron microscope (TEM) images and TAP analyses of the atom probe tips demonstrate unambiguously the presence of the selectively prepared grain boundary in the apex region of some of the specimens.