Grain boundary crystallography in polycrystalline yttria-stabilised cubic zirconia

Properties of grain boundaries such as grain boundary energy, mobility and diffusion are reported to depend strongly on their crystallography. While studies on ceramic bicrystals with low Σ misorientations have shown highly ordered structures and low energies, studies on dense polycrystalline ceramics often show the significance of grain boundary planes. In the present study, grain boundary plane distributions were studied for yttria-stabilised cubic zirconia with varying grain sizes using Electron Back Scattered Diffraction technique combined with a stereological approach. Despite nearly isotropic grain boundary plane distributions, a highly anisotropic grain boundary character distribution is observed for specific misorientations. Certain low-energy symmetric tilts such as Σ3 and Σ11 are found to occur with high frequencies across the grain size range studied, leading to an inverse correlation between GB energy and frequency of occurrence, consistent with other ceramics studied in literature.     

Theory of grain boundary motion during high-temperature DIGM

A theory of diffusion induced grain boundary migration (DIGM) is presented for high temperatures where volume diffusion of solute atoms out of the grain boundary is important. It is shown that due to the presence of a gradient term in the expression for the free energy of solid solution, even a relatively small discontinuity in the solute distribution across the gain boundary provides enough driving force for grain boundary migration. From the expression obtained for the grain boundary velocity the coefficient for the Ni diffusion across the grain boundaries in a Cu(Ni) polycrystal has been estimated.     

Strain induced grain boundary premelting in bulk copper bicrystals

In bulk bicrystals strain induced grain boundary premelting (SIGBPM) occurs when heavy screw dislocation pileup can be held up to a certain high temperature, approximately 0.6T _M, where T _M is the melting point of bulk material in Kelvin. SIGBPM occurs at grain boundaries to which new twist component is added due to the rotation of both component crystals toward opposite direction about the axis perpendicular to the grain boundary plane. At the original grain boundary, grain boundary sliding takes place due to this relative rotation. In f.c.c. metals with relatively low stacking fault energies such as copper, nickel, brass(30Zn) and silver, dislocations dissociate into partials. Therefore high density tangled dislocations introduced during plastic deformation hardly loose. If these dislocations can be held to high temperatures, SIGBPM is promoted. Formation of static or dynamic recrystallized grains suppresses SIGBPM itself and the propagation of grain boundary cracks formed by SIGBPM.     

Coercivity enhancement of sintered Nd-Fe-B magnets by grain boundary diffusion with Pr80-xAlxCu20 alloys

A grain boundary diffusion (GBD) process with Pr_80-xAl_xCu₂₀ (x = 0, 10, 15, 20) low melting point alloys was applied to commercial 42M sintered Nd-Fe-B magnets. The best coercivity enhancement of a diffused magnet was for the Pr₆₅Al₁₅Cu₂₀ GBD magnet, from 16.38 kOe to 22.38 kOe. Microstructural investigations indicated that increase in the Al content in the diffusion source can form a continuous grain boundary (GB) phase, optimizing the microstructure to enhance the coercivity. The coercivity enhancement is mainly due to the formation of a continuous GB phase to separate the main phase grains. Exchange decoupling between the adjacent main phase grains is enhanced after the GBD process. Meanwhile, the introduction of Al can effectively promote the infiltration of Pr into the magnet, which increases the diffusion rate of rare-earth elements within a certain range. This work provides a feasible method to enhance coercivity and reduce the use of rare-earth resources by partial replacement of rare-earth elements with non-rare-earth elements in the diffusion source.     

利用Pr_(70)Cu_(30)晶界扩散改善烧结钕铁硼废料矫顽力的研究

钕铁硼磁体制备过程中出现的部分块体废料由于矫顽力较低,性能难以满足使用要求.本文主要通过晶界扩散技术来提高废料磁体的矫顽力.采用Pr_(70)Cu_(30)合金作为扩散介质,对烧结钕铁硼废料磁体进行了晶界扩散处理,研究了扩散温度、扩散时间和回火时间对扩散后的磁体性能的影响.结果显示,800℃下扩散3 h,磁体的矫顽力从原来的7.88 kOe(1 Oe=79.5775 A/m)提升至11.55 kOe,提升幅度为46.6%,同时剩磁没有明显降低.扩散后回火对矫顽力的提升有一定的作用.800℃下扩散4h后的磁体在500℃回火3h后,最高矫顽力可达11.97 kOe,比原磁体废料提高了51.9%,接近成品磁体的水平.显微组织分析证实了晶界扩散的作用.扩散处理后的磁体中,主相晶粒间形成了连续晶间相,起到有效的磁隔离作用,有利于矫顽力的提高.研究还发现,Pr_(70)Cu_(30)晶界扩散虽然可以使磁体腐蚀电位上升,但也会增加腐蚀电流密度,不利于磁体抗腐蚀性的改善.本文工作对于提高材料的成品率具有重要意义.     

An atomic scale characterization of coupled grain boundary motion in silicon bicrystals

The mechanical response of symmetric tilt grain boundaries (GBs) in silicon bicrystals under shear loading are characterized using molecular dynamics simulations. It is seen that under shear, high-angle GBs namely Σ5 and Σ13 having a rotation axis [0 0 1] demonstrate coupled GB motion, such that the displacement of grains parallel to the GB interface is accompanied by normal GB motion. An atomic-scale characterization revealed that concerted rotations of silicon tetrahedra within the GB are the primary mechanisms leading to the coupled GB motion. Interestingly, so far, this phenomenon has only been examined in detail for metallic systems. A distinguishing feature of the coupled GB motion observed for the silicon symmetric tilt bicrystals as compared to metallic bicrystals is the fact that in the absence of shear, spontaneous coupled motion is not observed at high temperatures.     

Deformation study of bicrystalline and nano-polycrystalline structures using phase field crystal method

Deformation behaviors of bicrystalline and nano-polycrystalline structures of various tilt angles and inclination angles in two dimensions are investigated in detail using a two-mode phase field crystal model.The interaction between grain boundary(GB)and dislocation is also examined in bicrystals and nano-polycrystals that both contain asymmetric and symmetric tilt GBs,with energy analysis being carried out to analyze these processes.During deformation simulations,we assume the volume of each simulation cell at every time step is coincident with that of the initial state just before deformation.Our simulation results show that the behaviors of symmetric and asymmetric GBs in bicrystals and nano-polycrystals differ from each other depending on tilt angle and inclination angle.A new dislocation emission mechanism of interest is observed in bicrystals which contain low angle symmetric tilt GBs.Low angle GB has a higher mobility relative to high angle GB in both bicrystalline and nano-polycrystalline structures,as does asymmetric GB to symmetric GB.The generation,motion,pileup and annihilation of dislocations,grain rotation and grain coalescence are observed,which is consistent with the simulation results obtained by molecular dynamics.These simulation results can provide strong guidelines for experimentation.     

界面旋转角对双晶镁力学性质影响的分子动力学模拟

采用分子动力学模拟方法,研究了在拉伸载荷下晶界对双晶镁变形机制的影响,对不同旋转角度的模型以及对称与非对称结构的模型进行了研究.模拟结果表明:应变加载方向与晶向所成角度对双晶镁塑形变形阶段的流动应力能够产生明显的影响;对称结构的双晶镁模型的塑性性质明显优于非对称结构模型.研究结果还发现,由于晶界区域不同的位错成核及发射等运动,大角度双晶模型的塑性响应明显优于对应小角度模型的塑性响应.     

Surface exchange reactions and fast grain boundary diffusion in polycrystalline materials: Application of a spherical grain model

Laplace transforms of the solution functions to the diffusion equations for surface exchange reactions and fast grain boundary diffusion in polycrystalline materials of finite thickness have been derived by applying a spherical grain model. Diffusion profiles have been calculated for semi-infinite diffusion systems as well as thin films by application of numerical Laplace inversion. The surface exchange reaction at the surface of the sample (e.g. oxide ceramics) in contact with the constant diffusion source (e.g. gas phase) is assumed to be fairly slow such that the diffusion source is not in equilibrium with the surface during the diffusion anneal. Two limiting cases for the surface conditions are taken into account, viz. fast surface diffusion and a uniform ratio of the surface exchange coefficient/diffusion coefficient. The calculated profiles refer to Harrison's type-A diffusion kinetics. Apart from expressions for the effective diffusion coefficient, analogous relations for the effective surface exchange coefficient are proposed. Relaxation curves for the total amount of diffusant exchanged with the diffusion source are discussed in terms of the diameter of the spherical grains (average grain size), surface exchange coefficient, bulk and grain boundary diffusion coefficient, respectively.     

Grain boundary diffusion patterns under nonequilibrium and migration of grain boundaries in nanoctructure materials

In this work, the model of grain boundary diffusion from a permanent source along nonequilibrium migratory grain boundaries is considered. Grain boundary nonequilibrium is characterized by a value of boundary excess energy up to which relaxation goes. It is shown increasing excess energy and migration velocity of nonequilibrium boundaries lead to increasing diffusant volume penetrating into a sample during annealing time.     

The stability of triple junctions during the grain boundary diffusion process

The grain boundary diffusion in a system with triple junctions is considered in such a geometry, in which the flows of diffusing atoms meet at the triple line. The solutions of the diffusion equation is given in the frameworks of Fisher's model and under the assumption of quasi-stationary distribution of the diffusing atoms along the grain boundaries. The change of the mechanical equilibrium at the triple junction due to the increase of the concentration of solute atoms is considered. It is shown that under some circumstances the triple junction looses its stability with respect to migration in the direction to the diffusion source. The stability diagrams in the segregation-diffusivity parameter space are plotted.     

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.     

Internal friction in Al bicrystals with ⟨111⟩ tilt and twist grain boundaries

Internal friction measurements were performed on various ?111? tilt and twist grain boundaries in high-purity Al bicrystals. The temperature dependence of the grain boundary internal friction peak was determined, and the activation parameters of grain boundary relaxation were obtained. These parameters were found to change in a wide range depending on boundary geometry. The activation enthalpy of boundary relaxation and the pre-exponential factor of the relaxation time are related according to the compensation effect. The results are discussed in terms of the model of correlated relaxations. Bicrystals with vicinal Σ3 boundaries were observed to behave like single crystals, i.e. an internal friction peak did not appear. This evidences that both coherent and incoherent (60° ?111? tilt) twins possess a high mechanical resistance.     

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.     

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.     

Effect of High-Temperature Structure and Diffusion on Grain-Boundary Diffusion Creep in fcc Metals

Molecular dynamics simulations of high-energy twist and tilt bicrystals of fcc palladium reveal a universal, liquid-like, isotropic high-temperature diffusion mechanism, characterized by a rather low self-diffusion activation energy that is independent of the boundary type or misorientation. Medium-energy grain boundaries exhibit the same behavior at the highest temperatures; however, at lower temperatures the diffusion mechanism becomes anisotropic, with a higher, misorientation-dependent activation energy. Our simulations demonstrate that the lower activation energy at elevated temperatures is caused by a structural transition, from a solid boundary structure at low temperatures to a liquid-like structure at high temperatures. We demonstrate that the existence of such a transition has important consequences for diffusion creep in nanocrystalline fcc metals. In particular, our simulations reveal that in the absence of grain growth, nanocrystalline microstructures containing only high-energy grain boundaries exhibit steady-state diffusion creep with a creep rate that agrees quantitatively with that given by the Coble-creep formula. Remarkably, the activation energy for the high-temperature creep rate is the same as that characterizing the universal high-temperature diffusion in high-energy energy bicrystalline grain boundaries.     

Diffusion along the Grain Boundaries in Crystals with Dislocations

A generalization of the Fisher model of the grain boundary diffusion is suggested, which takes into account the diffusion along short circuit diffusion paths (i.e., dislocations) in the bulk of crystalline grains. For the B-regime of the grain boundary diffusion, three different penetration modes have been found: at the short times the penetration depth of the element diffusing along the grain boundary is given by the Whipple solution of the Fisher model, but with the pipe diffusion coefficients along the dislocation cores instead of the volume diffusivities; at the intermediate times the penetration depth is a weak function of time, and at the large times the penetration depth again increases with time according to the Whipple solution, however, the rate of this increase is much smaller than in the initial period of time. The applications of the model for diffusion in nanomaterials are discussed.     

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.     

晶粒生长演变相场法模拟界面表达的物理模型

讨论了当前固态组织演变过程的相场法模拟模型,论证了相场法中界面的概念以及模型中界面的各种处理方法,以AZ31镁合金再结晶系统为例,研究了模型参数取值对界面特征的影响,提出了晶界作用域的概念,阐述了晶界作用域就是相场模型中界面处有序化变量的变化范围,其物理意义是界面能量的分布范围,并对应于成分界面偏析的范围.模拟得出,晶界作用域宽度主要由梯度项系数决定,晶界能则由梯度项系数和耦合项系数共同决定.对于AZ31镁合金,模拟研究了晶界作用域宽度取值的合理性和对显微组织影响的关系,得出取值为1.18 μm时,模拟符 关键词： 相场法 界面 计算机模拟 显微组织