Phase-field study of spinodal decomposition under effect of grain boundary

Grain boundary directed spinodal decomposition has a substantial effect on the microstructure evolution and properties of polycrystalline alloys. The morphological selection mechanism of spinodal decomposition at grain boundaries is a major challenge to reveal, and remains elusive so far. In this work, the effect of grain boundaries on spinodal decomposition is investigated by using the phase-field model. The simulation results indicate that the spinodal morphology at the grain boundary is anisotropic bicontinuous microstructures different from the isotropic continuous microstructures of spinodal decomposition in the bulk phase. Moreover, at grain boundaries with higher energy, the decomposed phases are alternating α/β layers that are parallel to the grain boundary. On the contrary, alternating α/β layers are perpendicular to the grain boundary.     

Significant decrease in interfacial energy of grain boundary through serrated grain boundary transition

The mechanism of serrated grain boundary formation and its effect on liquation behaviour have been studied in a wrought nickel-based superalloy – Alloy 263. It was newly discovered that grain boundaries are considerably serrated in the absence of γ?′-phase or M₂₃C₆ at the grain boundaries. An electron energy-loss spectroscopy study suggests that serration is triggered by the discontinuous segregation of C and Cr atoms at grain boundaries for the purpose of relieving the excessive elastic strain energy. The grain boundaries serrate to have specific segments approaching one {111} low-index plane at a boundary so that the interfacial free energy of the grain boundary can be decreased, which may be responsible for the driving force of the serration. The serrated grain boundaries effectively suppress grain coarsening and are highly resistant to liquation due to their lower wettability resulting from a lower interfacial energy of the grain boundary.     

包含倾斜晶界的双晶ZnO的热输运行为

用嵌入位错线法和重合位置点阵法构建含有小角度和大角度倾斜角的双晶氧化锌纳米结构.用非平衡分子动力学方法模拟双晶氧化锌在不同倾斜角度下的晶界能、卡皮查热阻,并研究了样本长度和温度对卡皮查热阻和热导率的影响.模拟结果表明,晶界能在小角度区域随倾斜角线性增加,而在大角度区域达到稳定,与卡皮查热阻的变化趋势一致.热导率随样本长度的增加而增加,卡皮查热阻表现出相反的趋势.然而随着温度的增加,热导率和卡皮查热阻都减小.通过比较含5.45°和38.94°晶界样本的声子态密度,发现声子光学支对热传导的影响不大,主要由声子声学支贡献,大角度晶界对声子散射作用更强,声学支波峰向低频率移动.     

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.     

Thermodynamics and structural aspects of grain boundary segregation

Physical and chemical properties of solid materials are strongly. influenced by the chemical composition of internal interfaces, One of the crucial parameters affecting interfacial chemistry is the atomic structure of the interface. Due to its importance. a considerable amount of work was done to elucidate the relationship between structure and chemical composition of interfaces. This article reviews the present understanding of an important and fundamental part of this relationship, namely, the structural aspects of grain boundary segregation. After a brief outline of grain boundary structure and geometry. thermodynamic approaches to describe grain boundary segregation are summarized and their application to materials is discussed. covering particular sites at a single grain boundary as well as the role of interfaces in polycrystals. Both the experimental evidence of grain boundary segregation anisotropy and the theoretical results of computer simulations of grain boundary segregation are summarized. Useful methods of predicting grain boundary segregation are presented. Finally, segregation behavior of solutes at grain boundaries is compared with that at free surfaces, and examples of chemical composition of intexphase boundaries are given.     

Effects of boundary inclination and boundary type on shear-driven grain boundary migration

A series of molecular dynamics simulations was performed on a bicrystal to which a fixed shear rate was applied parallel to the boundary plane. Under some conditions, grain boundary motion is coupled to the relative tangential motion of the two grains. In order to investigate the generality of this type of coupled shear/boundary motion, simulations were performed for both special (low Σ) and general (non-Σ) [010] tilt boundaries over a wide range of grain boundary inclinations. The data point to the existence of two critical stresses: one for coupled shear/boundary motion and the other for grain boundary sliding. For the non-Σ boundaries, the critical stress for coupled shear/boundary motion is typically smaller than that for sliding; coupled shear/boundary motion occurs for all inclinations. For Σ5 boundaries, for which the critical stress is smaller and depends on boundary inclination, coupled shear/boundary motion occurs for some, but not all inclinations.     

Dependence of grain boundary character distribution on the initial grain size of 304 austenitic stainless steel

Abstract

In order to study the dependence of the grain boundary character distributions (GBCD) on the grain size, annealing treatment was carried out on 304 austenitic stainless steel with different initial grain sizes. The evolution of the GBCD was analysed by electron backscatter diffraction. The experimental results showed that abnormal grain growth (AGG) occurred when grain size was small. With a smaller initial grain size, the number density of abnormally large grains and the fraction of low-Σ CSL boundaries increased but the size of abnormally large grains decreased and the random boundaries presented a continuous network. With a larger initial grain size, the fraction of low-Σ CSL boundaries also increased as well as the size of abnormally large grains but the number density of abnormally large grains decreased and the connectivity of random boundary network was disrupted by low-Σ CSL boundaries, especially Σ3ⁿ (n = 1, 2, 3) boundaries. However, with a very large initial grain size, normal grain growth (NGG) occurred, which had no effect on the fraction of low-Σ CSL boundaries and the connectivity of random boundary network.     

Grain boundary interdiffusion in the case of concentration-dependent grain boundary diffusion coefficient

The grain boundary diffusion in a binary system which exhibits a grain boundary phase transition is considered in the framework of Fisher's model. The kinetic law of the growth of the grain boundary phase and the distribution of the diffusant near the grain boundary are calculated. The method of determining of the concentration dependence of the grain boundary diffusion coefficient from the experimentally measured penetration profiles of the diffusant along the grain boundaries is suggested. The experimental results on Zn diffusion in Fe(Si) bicrystals, Ni diffusion in Cu bicrystals and grain boundary grooving in Al in the presence of liquid In are discussed in light of the suggested model.     

Heterogeneous ceramics formed by grain boundary engineering

Two examples were selected to emphasize the potential of grain boundary engineering in the performance design of heterogeneous ceramics. Gadolinium-doped ceria-based powders were co-fired with additions of silica, and silica and lanthanum oxide, to test the silica scavenging role of lanthanum. The formation of one ionic conducting secondary phase, instead of an insulating phase, was attempted. The structural, microstructural, and electrical characterization of these samples confirmed the formation of one apatite-type lanthanum silicate-based phase and a significant enhancement of the grain boundary conductivity of these materials. One second approach addressed the formation of one mixed conductor, with electronically conductive grain boundaries, surrounding the grains of one lanthanum gallate-based electrolyte (core-shell type microstructure). Fe-doped grain boundaries were formed by selective Fe-diffusion (thermally assisted) from lanthanum ferrite screen printed layers. Combined microstructural and electrical characterization showed that the adopted solution was also effective.     

Grain boundary misorientation changes during grain growth in pure aluminium

A new method is described for data-logging large amounts of grain boundary misorientation information from channelling patterns in the scanning electron microscope (SEM). The method relies on producing specimens where the grain size is larger than the specimen thickness and where the grain boundary planes are perpendicular to the specimen plane (the so-called columnar structure). Results for grain growth in pure aluminium at 460 and 500°C are presented. There is an increase in the proportion of low angle boundaries at the expense of high angle boundaries during growth times of up to a few hours. The reasons are thought to be partly connected with lower low angle boundary mobility compared with high angle boundaries. However, the growth kinetics appear to be normal over the entire growth time range.     

The effect of segregated transition metal ions on the grain boundary resistivity of gadolinium doped ceria: Alteration of the space charge potential

The effect of segregated transition metals on the grain boundary resistivity of 1 mol% Gd-doped ceria has been investigated. The main focus of interest is whether the space charge potential that causes the blocking effect of the grain boundaries of the ceria can be extrinsically modified. The introduction of a small amount (< 0.5 mol%) of transition metals (Fe, Co, Mn and Cu) to 1 mol% Gd-doped ceria results in significant reductions in only the grain boundary resistivities of the samples attributed to exclusive segregation of the transition metals into the grain boundary core. In the case of Co- and Fe-doped samples, the grain boundary resistivity is lowered by an order of magnitude. EELS line scans across the grain boundaries of the Fe-doped sample have indicated that the grain boundaries are free of a secondary phase of transition metal oxide and that the Fe in the grain boundary likely exists as point defects. These results strongly suggest that it is indeed possible to reduce the excess positive charge in the grain boundary core, and thus the grain boundary resistivity in a ceria electrolyte, extrinsically as initially postulated. A defect chemistry model which explains partial counterbalance to the positive grain boundary core charge has been suggested. The resistivity minimum shown for the samples with different Fe concentration indicates that there is an optimum concentration of transition metal in the grain boundary core of the ceria necessary for such a countbalance.     

Mixed conductivity of gadolinium titanate-based pyrochlore ceramics: The grain boundary effects

In order to reveal the role of grain boundaries on the ionic and electronic conduction processes, the transport properties of Gd_2−xGa_xTi₂O_7−δ (x=0.10–0.14) pyrochlore ceramics, pure and with SiO₂ additions, were studied at 700–950 °C by impedance spectroscopy and faradaic efficiency measurements. The oxygen ion transference numbers of “pure” materials in air vary in the range of 0.95–0.97, increasing when temperature decreases. For silica-containing ceramics having, as expected, highly resistive grain boundaries, the ion transference numbers were considerably lower, 0.76–0.88, and increase with temperature. This behavior suggests that grain boundaries in these oxygen ion-conducting ceramics have a larger limiting effect on ionic transport than on electronic conduction. Increasing boundary resistivity may increase the relative role of electronic conductivity in solid oxide electrolytes, thus preventing their potential use in electrochemical cells at low temperatures. Also, the presence of even small electronic contributions to the total conductivity may lead to significant errors in the grain-boundary resistance values estimated from impedance spectroscopy data. The evaluation of the grain boundary exact contribution should be based on a clear knowledge of the magnitude of transference numbers. Paper prestented at the 9th EuroConference on Ionics, Ixia, Rhodes, Greece, Sept. 15 – 21, 2002.     

Theory and simulation of coupled grain boundary migration and grain rotation in low angle grain boundaries

Abstract

Microstructure evolution due to coupled grain boundary migration and grain rotation in low angle grain boundaries is studied through a combination of molecular dynamics and phase field modeling. We have performed two dimensional molecular dynamics simulations on a bicrystal with a circular grain embedded in a larger grain. Both size and orientation of the embedded grain are observed to evolve with time. The shrinking embedded grain is observed to have two regimes: constant dislocation density on the grain boundary followed by constant rate of increase in dislocation density. Based on these observations from the molecular dynamics simulations, a theoretical formulation of the kinetics of coupled grain rotation is developed. The grain rotation rate is derived for the two regimes of constant dislocation density and constant rate of change of dislocation density on the grain boundary during evolution. The theoretical calculation of the grain rotation rate shows strong dependence on the grain size and compares very well with the molecular dynamics simulations. A multi-order parameter based phase field model with coupled grain rotation is developed using the theoretical formulation to model polycrystalline microstructure evolution.     

Heterogeneities of grain boundary arrangement in polycrystals

Data on mutual arrangements of different types of grain boundaries in polycrystals are presented. The heterogeneity in grain boundary distribution, namely, the effect of gathering low-angle or special tilt grain boundaries is found in pure aluminum thin films, in sheets of Fe-3% Si alloy and in Al₂O₃ doped with MgO or MgO and Y ₂O₃. The local texture, i.e., formation of colonies or clusters of close-oriented grains is considered as a reason of this heterogeneity. The influences of grain boundary gathering on the transport properties of polycrystals and on the crack propagation are discussed. A new concept of effective grain size is suggested to analyze the relationship between material microstructures and material properties.     

Effect of grain boundary on electrical properties of polycrystalline lanthanum nickel oxide thin films

In the present work, lanthanum nickel oxide (LNO) thin films were prepared by the sol-gel method. Microstructures of the films were tailored by changing sol concentration so as to investigate the effect of grain boundary on the transport properties of electrons in the polycrystalline LNO films. Based on the temperature dependence of the resistivity and the magnetic field dependence of the magnetoresistance (MR) at various temperatures, the factors that dominate the transport behavior in the polycrystalline LNO films were explored in terms of weak localization and strong localization. The results show that the grain boundary has a significant influence on the transport behavior of the electrons in LNO films at a low-temperature region, which can be captured by a variable-range hopping (VRH) model. The increase of metal–insulator (M–I) transition temperature is ascribed to Anderson localization in grain boundary. At a high-temperature region, electron–electron scattering and electron–phonon scattering predominates in the films. In this case, the existence of more grain boundary shows a minor effect on the transport behavior of the electrons but elevates the residual resistivity of the films.     

Correlation among grain boundary character,carbide precipitation and deformation in Alloy 690

The correlation among grain boundary character, carbide precipitation and deformation in the grain boundary engineering (GBE) treated Alloy 690 samples with and without pre-deformation aged at 715^oC for 15?h was analysed by scanning electron microscopy and electron backscatter diffraction. The fraction of low Σ coincidence site lattice (CSL) grain boundary was enhanced by GBE treatment. The fraction of Σ3 grain boundary decreased, and most of Σ9 and Σ27 grain boundaries disappeared in the deformed GBE samples. After aging treatment, bigger carbide precipitated at coherent Σ3 grain boundary, however, most of plate-like carbide precipitated at incoherent Σ3 grain boundary disappeared in the pre-deformed GBE samples. The larger carbide precipitated on the random grain boundary in the 5% pre-deformed sample, while smaller carbide can be observed in the 15% pre-deformed sample. During the in situ tensile test of the aged GBE samples, grain boundary carbide migrated with the grain boundary migration. The slip bands go across Σ3 grain boundary directly, but cannot go across other grain boundaries. The high density of carbide plate precipitated near incoherent Σ3 and Σ9 grain boundaries can resist the evolution of slip bands. Compared to the Σ3 and Σ9 grain boundaries, Σ27 and random grain boundaries are more easily to form microcrack during deformation. The initiation of grain boundary microcrack not only related to the character of grain boundary but also related to the character of nearby grain boundaries. The phase interface of carbide and matrix is another region to initiate the microcrack.     

Lattice dynamics studies of grain boundary structures: II. Thermodynamic functions

The change in the atomic vibrational frequency spectrum of an fcc crystal due to the presence of a grain boundary is obtained by lattice dynamics methods. The grain boundary is a 36.9° 〈100〉 symmetric tilt coincidence boundary. An orthorhombic computational cell of 58 atoms containing two such boundaries of opposite rotational sense is employed. The atomic interactions are simulated by a Morse potential developed by Cotterill and Doyama to fit aluminum. From the changes in frequency spectrum the excess thermodynamic functions of the grain boundary are calculated and compared with results from both experiment and the Einstein model. The general shift of frequencies toward lower values is probably due to the weaker binding of many atoms near the boundary, while there are some higher frequency states associated with a few more tightly bound atoms.     

A theoretical and experimental study of non-perfect grain boundary dislocations

The aim of this paper is to discuss the possible appearance of non-perfect grain boundary dislocations in grain boundaries in a variety of materials. To begin with, we survey some of the different theoretical treatments which enable grain boundary dislocations and grain boundary structures to be described. The emphasis is put on more recent ideas, and on illustrating the power of group theory in identifying non-perfect grain boundary dislocations. A derivation of the geometric characteristics of interfacial dislocations is carried out in a simple and tutorial way, in a number of representative examples. It is shown that grain boundary dislocations may be divided into three classes: (1) perfect grain boundary dislocations, (2) imperfect grain boundary dislocations, and (3) partial grain boundary dislocations. Experimental transmission electron microscope evidence is then presented for boundaries in the diamond cubic structure, and it is shown that imperfect and partial grain boundary dislocations play an important role in this system. Finally, a comparison of some grain boundary dislocation types in different materials is given.     

Direct experimental determination of grain boundary excess volume in metals

The grain boundary excess volume, i.e., the grain boundary expansion, e{GB}, was experimentally determined for high-angle grain boundaries in nickel using the direct technique of high-precision difference dilatometry. Values of e{GB}=(0.35±0.04)×10{-10} m and e{GB}=(0.32±0.04)×10{-10} m were obtained by measuring the removal of grain boundary volume upon grain growth for two different types of ultrafine-grained samples. The results are discussed in comparison to values obtained so far from indirect techniques and from computer simulations. It demonstrates the strength of the presented novel, direct approach for grain boundary expansion measurements.     

Quantifying the grain boundary resistance against slip transfer by experimental combination of geometric and stress approach using stage-I-fatigue cracks

In recent studies, many groups have investigated the interaction of dislocations and grain boundaries by bi-crystals and micro-specimen experiments. Partially, these experiments were combined with supplementary simulations by discrete dislocation dynamics, but quantitative data for the grain boundary resistance against slip transfer is still missing. In this feasibility study with first results, we use stage-I-fatigue cracks as highly localised sources for dislocations with well-known Burgers vectors to study the interaction between dislocations in the plastic zone in front of the crack tip and selected grain boundaries. The stress concentration at the grain boundary is calculated with the dislocation-free zone model of fracture using the dislocation density distribution in the plastic zone from slip trace height profile measurements by atomic force microscopy. The grain boundary resistance values calculated from common geometric models are compared to the local stress distribution at the grain boundaries. Hence, it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer to a self-contained concept. As a result, the prediction of the grain boundary resistance effect based on a critical stress concept is possible with knowledge of the geometric parameters of the grain boundary only, namely the orientations of both participating grains and the orientation of the grain boundary plane.