Grain boundary curvature and grain growth kinetics with particle pinning

Second-phase particles are used extensively in design of polycrystalline materials to control the grain size. According to Zener’s theory, a distribution of particles creates a pinning pressure on a moving grain boundary. As a result, a limiting grain size is observed, but the effect of pinning on the detail of grain growth kinetics is less known. The influence of the particles on the microstructure occurs in multiple length scales, established by particle radius and the grain size. In this article, we use a meso-scale phase-field model that simulates grain growth in the presence of a uniform pinning pressure. The curvature of the grain boundary network is measured to determine the driving pressure of grain growth in 2D and 3D systems. It was observed that the grain growth continues, even under conditions where the average driving pressure is smaller than the pinning pressure. The limiting grain size is reached when the maximum of driving pressure distribution in the structure is equal to the pinning pressure. This results in a limiting grain size, larger than the one predicted by conventional models, and further analysis shows consistency with experimental observations. A physical model is proposed for the kinetics of grain growth using parameters based on the curvature analysis of the grain boundaries. This model can describe the simulated grain growth kinetics.     

冷却速率对温敏聚N-异丙基丙烯酰胺胶体结晶过程的影响

冷却速率对结晶过程具有重要的影响. 本文采用温敏poly-N-isopropylacrylamide (PNIPAM) 胶体晶体体系实时观察了冷却速率对结晶晶粒尺寸的影响. 通过高倍透射明场观察和Bragg衍射观察研究连续冷却下的晶粒形核和生长实时演化过程, 发现随着冷却速率的增加, PNIPAM胶体晶体晶粒尺寸不断减少. 晶粒尺寸与冷却速率符合幂指数关系, 与金属体系具有相似的演化规律.     

温度梯度对晶粒生长行为影响的相场模拟

利用相场法建立了一个可应用于研究温度梯度影响下的晶粒生长行为的二维模型,模拟了多晶材料退火过程中由温度梯度引起的非均匀晶粒生长和定向晶粒生长行为.结果表明:退火过程中,在静态温度梯度的影响下,体系的晶粒呈现不均匀生长,且从晶粒生长指数来看,不同程度地偏离了正常晶粒生长;在动态温度梯度的影响下,体系内部常出现柱状晶粒生长,柱状晶粒前端持续生长至温度最高位置;柱状晶粒生长与动态热源的移动速率密切相关,只有当动态热源的移动速率处于最小和最大晶粒生长速率之间时,柱状晶粒才会出现. 关键词： 晶粒生长 相场法 晶界迁移率 局部退火     

Modeling of temperature and rate dependence of the flow stress and evolution of a deformation defect medium in dispersion-hardened materials

The influence of characteristics of the second phase, strain rate and temperature, and initial defect state of a material on the curves of deformation hardening and the kinetics of components of the defect sub-system is investigated using a mathematical model of the plastic deformation for dispersion-hardened materials with an incoherent hardening phase.     

Nonuniform growth of embedded silicon nanocrystals in an amorphous matrix

The phase transformation of a metastable system occurs when islands of a second stable phase form and grow. The growth velocity of the islands controls the kinetics of the phase transformation. In this work we consider the amorphous-to-crystalline transformation in silicon as the prototype of a solid-to-solid transformation. The results of atomistic simulations are fit using an analytic model for the growth of [100]-oriented nanosized crystalline fibers embedded into an amorphous matrix. We demonstrate that the radius of the island does not grow, in general, at constant velocity. On the contrary, we identify a decelerated motion that is due to anisotropic effects of the crystal grain. Such a nonuniform growth should be taken into account in the modeling of solid-to-solid crystallization.     

Peculiarities of the growth kinetics of silicon-germanium alloy layers from silane and germane with an additional heated element in the vacuum chamber

To study the disintegration of the molecules of hydrides at the surface of the growing layer and their influence on the rate of the epitaxial process a model of the growth kinetics of Si_1?x Ge_x alloy layers from silane and germane by the molecular beam epitaxy method with SiH₄ and GeH₄ gas sources is considered. Through comparison of numerical simulation data and experimental relationships, the steady-state growth kinetics has been studied and a comparative analysis carried out of the efficiency of entry of Ge(Si) atoms into the growing layer both in the presence of Si and Ge atomic flows in the reactor (the so-called hot-wire method) and in their absence. The growth rates obtained with this method of epitaxial growth and with one of its modifications where the use is made of a sublimating silicon bar as an additional heated element have been compared. Peculiarities in the behavior of the dependence of the layer growth rate on its composition have been revealed and explained.     

Reduced Mobility of Triple Nodes and Lines on Grain Growth in Two and Three Dimensions

Vertex dynamics models in two and three dimensions are applied to study grain growth including a limited mobility of triple points (two dimensions) and triple lines (three dimensions). A recent experiment on a triple node is used to validate the proposed model. The reduced triple node/line mobility in the case of a polycrystalline sample is shown to influence both, the grain growth kinetics and the grain size distribution function.     

Microkinetics of the first- and second-order phase transitions

A model of the phase transition in a lattice of interacting nodes, in which each node is a statistical system with internal structure, is introduced. Configuration entropy of microscopic states of the node is defined as a basic parameter of the model. In the frame of the model the first- and second-order phase transitions are considered in details. The distinction between them on the microscopic level is analyzed. Phase diagrams have been calculated in the mean-field approximation. Changes of the phase diagrams and modifications of phase transitions under external pressure and irradiation are investigated in the frame of the microkinetic approach. Results are referred to real systems.     

Beyond modified mean field: a case for a stochastic grain growth model

ABSTRACT

We address the basic mechanism of grain growth in two and three dimensions in single phase metallic systems. It is argued, a comprehensive grain growth model is best based on a stochastic process described by a Fokker Planck equation. This concept is sufficient to determine almost all features of grain growth in general terms. The existence of the von Neumann law and its counterpart in three dimensions enables us to provide an explicit form of the Fokker Planck equation and thus determine many features of grain growth in great detail. Finally, we illustrate this model by determining the salient features of grain growth in three dimensions in the long time limit, and comparing them with experimental and computational results.     

两相钛合金再结晶退火组织与织构演变的蒙特卡罗模拟

蒙特卡罗(MC)方法被广泛应用于模拟金属材料在退火过程中的静态再结晶行为. 在已有两相材料晶粒长大MC模型基础上, 引入形核阶段, 综合考虑再结晶晶粒吞并形变晶粒和再结晶晶粒竞争长大两种情况, 建立了退火时两相合金再结晶MC模型.结合电子背散射衍射所测 初始晶粒形貌、相成分、晶体学取向及应变储能相对值, 该模型被应用于TC11钛合金退火过程中的微观组织及织构演变模拟.结果表明, 所建模型能够较好体现退火过程中两相晶粒的形核及晶粒长大行为. 与β相相比较, α相具有较低的再结晶速率和较高的晶粒长大速率, 前者主要归结于α相较低的初始应变储能, 后者则体现了该条件下初始组织形貌、分布及两相比例对晶粒长大具有重要影响; 由于非均匀形核的影响, 模拟得到的再结晶速率变化与 假设均匀形核的Johnson-Mehl-Avrami-Kolmogorov 再结晶方程存在明显差异.同时, 两相的基本织构特征在退火过程中无明显变化, 但织构强度增加. 关键词： 两相钛合金 再结晶 蒙特卡罗方法 织构     

Solid-phase wetting at grain boundaries in the Zr-Nb system

The microstructure of Zr-Nb polycrystalline alloys with niobium concentrations of 1, 2.5, 4, and 8 wt % is investigated in the temperature interval of 620–840°C. It is revealed that the second solid phase β-Nb forms either a chain of separate lens-like precipitates or continuous homogeneous layers at grain boundaries in zirconium, depending on the annealing temperature and the energy of the Zr/Zr grain boundary. It is shown that the greater the quantity of the second solid phase, the lower is the temperature of the termination of grain-boundary wetting. A model is constructed that explains the dependence of the temperature of grain boundary wetting on the amount of wetting phase. It is found that the complete wetting of all grain boundaries in zirconium by the second solid phase does not occur in Zr-Nb alloys.     

Microstructures and electrical conductivity of nanocrystalline ceria-based thin films

Ceria-based thin films are potential materials for use as gas-sensing layers and electrolytes in micro-solid oxide fuel cells. Since the average grain sizes of these films are on the nanocrystalline scale (< 150 nm), it is of fundamental interest whether the electrical conductivity might differ from microcrystalline ceria-based ceramics. In this study, CeO₂ and Ce_0.8Gd_0.2O_1.9−x thin films have been fabrication by spray pyrolysis and pulsed laser deposition, and the influence of the ambient average grain size on the total DC conductivity is investigated. Dense and crack-free CeO₂ and Ce_0.8Gd_0.2O_1.9−x thin films were produced that withstand annealing up to temperatures of 1100 °C. The dopant concentration and annealing temperature affect highly the grain growth kinetics of ceria-based thin films. Large concentrations of dopant exert Zener drag on grain growth and result in retarded grain growth. An increased total DC conductivity and decreased activation energy was observed when the average grain size of a CeO₂ or Ce_0.8Gd_0.2O_1.9−x thin film was decreased.     

Crystallization and grain growth characteristics of yttria-stabilized zirconia thin films grown by pulsed laser deposition

Knowledge about the crystallization and grain growth characteristics of metal oxide thin films is essential for effective microstructural engineering by thermal post-annealing and the integration to Si-based miniaturized electroceramic devices. Finite size and interface effects may cause fundamentally different behavior compared to three dimensional macroscopic systems. This work presents a comprehensive investigation of the crystallization kinetics and microstructural evolution upon thermal post-annealing of amorphous 200 nm and 1.2 μm thin films of 8 mol% yttria-stabilized zirconia grown by pulsed laser deposition (PLD) using ex- and in-situ X-ray diffraction, Raman spectroscopy, and electron microscopy techniques. The layers exhibit a remarkably low crystallization temperature of 200-250 °C while exposure to energetic electrons induces the formation of randomly dispersed ~ 20 nm sized crystallites already at ambient temperature. The isothermal amorphous to crystalline phase transformation kinetics can be described quantitatively by the Johnson-Mehl-Avrami-Kolmogorov model. They reveal characteristics of a three dimensional growth under cation bulk diffusion control with heterogeneous nucleation that changes from continuous to instantaneous initial seeding at temperatures above 300 °C. Large (> 100 nm) equiaxed grains are formed rapidly without a stabilization of transient nanocrystals during the thermally induced phase transformation. A stagnation of normal grain growth resulting in a logarithmic normal size distribution is observed once the average grain dimensions approach the film thickness. The results on the crystallization and grain growth of the PLD-grown YSZ films are evaluated with regards to the fabrication of YSZ solid electrolyte membranes for Si-supported micro solid oxide fuel cells and gas sensors.     

Influence of the mode of deformation on recrystallisation kinetics in Nickel through experiments,theory and phase field model

Abstract

In this paper, we report the influence of the mode of deformation on recrystallisation kinetics through experiments, theory and a phase field model. Ni samples of 99.6% purity are subjected to torsion and rolling at two equivalent plastic strains and the recrystallisation kinetics and microstructure are compared experimentally. Due to significant differences in the distributions of the nuclei and stored energy for the same equivalent strain, large differences are observed in the recrystallisation kinetics of rolled and torsion-tested samples. Next, a multi-phase field model is developed in order to understand and predict the kinetics and microstructural evolution. The coarse-grained free energy parameters of the phase field model are taken to be a function of the stored energy. In order to account for the observed differences in recrystallisation kinetics, the phase field mobility parameter is a required constitutive input. The mobility is calculated by developing a mean field model of the recrystallisation process assuming that the strain free nuclei grow in a uniform stored energy field. The activation energy calculated from the mobilities obtained from the mean field calculation compares very well with the activation energy obtained from the kinetics of recrystallisation. The recrystallisation kinetics and microstructure as characterised by grain size distribution obtained from the phase field simulations match the experimental results to good accord. The novel combination of experiments, phase field simulations and mean field model facilitates a quantitative prediction of the microstructural evolution and kinetics.     

Grain growth and static recrystallization kinetics in Co–20Cr–15W–10Ni (L-605) cobalt-base superalloy

The grain size evolution of cold-rolled L-605 cobalt-base superalloy during ultra-rapid annealing is investigated in this paper. Cold-worked specimens undergo static recrystallization, leading to grain refinement or grain coarsening depending on the annealing time and temperature. The kinetics of grain growth is found to be independent of the initial deformation. The evolution of grain size can be simply described by a grain growth model for high temperatures and long annealing times, and the mobility of interfaces is estimated by modelling. Fast annealing treatment process is a very promising technique to customize grain size and enhance mechanical strength. In particular, the reduction of annealing time is an efficient method to produce a refined microstructure through static recrystallization.     

Coarsening in Sintering: Grain Shape Distribution,Grain Size Distribution,and Grain Growth Kinetics in Solid-Pore Systems

Sintering occurs when packed particles are heated to a temperature where there is sufficient atomic motion to grow bonds between the particles. The conditions that induce sintering depend on the material, its melting temperature, particle size, and a host of processing variables. It is common for sintering to produce a dimensional change, typically shrinkage, where the powder compact densifies, leading to significant strengthening. Microstructure coarsening is inherent to sintering, most evident as grain growth, but it is common for pore growth to occur as density increases. During coarsening, the grain structure converges to a self-similar character seen in both the grain shape distribution and grain size distribution. Coarsening behavior during sintering conforms to classic grain growth kinetics, modified to reflect the evolving microstructure. These modifications involve the grain boundary coverage due to pores, liquid films, or second phases and the altered grain boundary mobility due to these phases. The mass transport rates associated with each of these interfaces are different, with different temperature and composition dependencies. Hence, the coarsening rate during sintering is not constant, but changes with the evolving microstructure. Core aspects treated in this review include models for coarsening, grain shape, grain size distribution, and how pores, liquids, dispersoids, and other phases determine microstructure coarsening during sintering.     

Kinetic crossover of coalescence conditions in a supersaturated homogeneous solution

Coalescence conditions under which the asymptotic behavior of the distribution function differs substantially from the Lifshitz-Slezov (LS) classical distribution are found in terms of an approach that includes the finiteness of the grain size during phase transitions. If the grain growth kinetics is controlled by monomer diffusion and grain dissolution, an intermediate asymptotic regime of coalescence may arise that eventually changes to LS-like diffusion. The change in the prevailing grain growth mechanism shows up in the crossover effect for scaling indices that describe the time dependence of the grain size.     

Dynamical role of the degree of intraspecific cooperation: A simple model for prebiotic replicators and ecosystems

We present a simple mean field model to analyze the dynamics of competition between two populations of replicators in terms of the degree of intraspecific cooperation (i.e., autocatalysis) in one of these populations. The first population can only replicate with Malthusian kinetics while the second one can reproduce with Malthusian or autocatalytic replication or with a combination of both reproducing strategies. The model consists of two coupled, nonlinear, autonomous ordinary differential equations. We investigate analytically and numerically the phase plane dynamics and the bifurcation scenarios of this ecologically coupled system, focusing on the outcome of competition for several degrees of intraspecific cooperation, σ, in the second population of replicators. We demonstrate that the dynamics of both populations can not be governed by a limit cycle, and also that once cooperation is considered, the topology of phase space does not allow for coexistence. Even for low values of the degree of intraspecific cooperation, for large enough autocatalytic replication rates, the second population of replicators is able to outcompete the first one, having a wide basin of attraction in state space. We characterize the same power law dependence between the outcompetition extinction times, τ, and the degree of intraspecific cooperation for both populations, given by τ∼c_iσ⁻¹. Our results suggest that, under some kinetic conditions, the appearance of autocatalysis might be favorable in a population of replicators growing with Malthusian kinetics competing with another population also reproducing exponentially.