A thermokinetic description of nanoscale grain growth: Analysis of the activation energy effect

The inhibition of grain growth by solute segregation in nanoscale materials has often been described using kinetic models (e.g. Acta Mater 1999;47:2143) or thermokinetic models (e.g. Acta Mater 2009;57:1466), in which constant activation energy and a negligible effect of solute segregation on activation energy were assumed. In this paper, an intact thermokinetic model for nanoscale grain growth was developed by incorporating mixed effects of activation energy and grain boundary (GB) energy. By application of the model to nanoscale grain growth in Ni–P, Pb–Zr, Fe–Zr and Ru–Al alloys, the validity of the present model was confirmed, in combination with verification of the initial condition of GB segregation. On this basis, the increase of activation energy and the decrease of GB energy are interrelated and thus the kinetics and the thermodynamics of normal grain growth are linked. Based on a comparison of three characteristic velocities V_TK, V_GE and V_AE of GB derived from the present thermokinetic model, grain boundary energy model and activation energy model, a mechanism of controlled nanoscale grain growth was proposed, which indicated a transition from a kinetic-controlled to a thermodynamic-controlled process.     

Grain boundary segregation,solute drag and abnormal grain growth

By employing a phase-field model, we simulated the grain boundary (GB) kinetics in terms of GB segregation of solute atoms for an isolated grain embedded in a matrix and demonstrated that the phase-field simulation could describe the GB movement under conditions of GB segregation in a quantitatively correct way. We then modeled grain growth in association with GB segregation in two-dimensional polycrystalline systems, and clarified that similarity between the Cottrell effect and the solute drag effect holds even on the macroscopic scale, that is, abnormal grain growth (AGG) can be induced by the solute drag effect. This AGG can take place spontaneously in homogeneous systems without any texture, anisotropy of GB mobility and/or energy, pinning particles and grain size advantage. The basic characteristics of this AGG and the effects of the solute diffusivity and the average grain size were investigated in detail.     

Solute segregation transition and drag force on grain boundaries

We investigate solute segregation and transition at grain boundaries and the corresponding drag effect on grain boundary migration. A continuum model of grain boundary segregation based on gradient thermodynamics and its discrete counterpart (discrete lattice model) are formulated. The model differs from much previous work because it takes into account several physically distinctive terms, including concentration gradient, spatial variation of gradient-energy coefficient and concentration dependence of solute–grain boundary interactions. Their effects on the equilibrium and steady-state solute concentration profiles across the grain boundary, the segregation transition temperature and the corresponding drag forces are characterized for a prototype planar grain boundary in a regular solution. It is found that omission of these terms could result in a significant overestimate or underestimate (depending on the boundary velocity) of the enhancement of solute segregation and drag force for systems of a positive mixing energy. Without considering these terms, much higher transition temperatures are predicted and the critical point is displaced towards much higher bulk solute concentration and temperature. The model predicts a sharp transition of grain boundary mobility as a function of temperature, which is related to the sharp transition of solute concentration of grain boundary as a function of temperature. The transition temperatures obtained during heating and cooling are different from each other, leading to a hysteresis loop in both the concentration–temperature plot and the mobility–temperature plot. These predictions agree well with experimental observations.     

Modelling the influence of grain-size-dependent solute drag on the kinetics of grain growth in nanocrystalline materials

The large relative change in total grain-boundary area that accompanies grain growth in a nanocrystalline material has a potentially strong influence on the kinetics of grain growth whenever grain-boundary migration is controlled by solute (impurity) drag. As the grain-boundary area decreases, the concentration of solute or impurity atoms segregated to the boundaries is expected to increase rapidly, introducing a grain-size dependence to the retarding force on boundary migration. We have modified the Burke equation—which assumes the drag force to be independent of the average grain size—to take into account a linear dependence of grain-boundary pinning on grain size. The form of the resulting grain-growth curve is surprisingly similar to Burke's solution; in fact, a constant rescaling of the boundary mobility parameter is sufficient to map one solution approximately onto the other. The activation energies for grain-boundary motion calculated from the temperature dependence of the mobility parameter are therefore identical for both models. This fact provides an explanation for the success of Burke's solution in fitting grain-growth data obtained in systems, such as nanocrystalline materials, for which the assumption of grain-size-independent solute drag is incorrect.     

Phase field modeling of grain boundary migration with solute drag

The grain boundary (GB) motion in the presence of GB segregation is investigated by means of phase field simulations. It is found that the solute concentration at the moving GB may increase with increasing velocity and becomes larger than the equilibrium value, which is unexpected according to the solute drag theory proposed by Cahn, but has been observed in some experiments. A non-linear relation between the driving force (curvature) and the GB velocity is found in two cases: (1) the GB motion undergoes a transition from the low-velocity extreme to the high-velocity extreme; (2) the GB migrates slowly in a strongly segregating system. The first case is consistent with the solute drag theory of Cahn. As for the second case, which is unexpected according to solute drag theory, the non-linear relation between the GB velocity and curvature comes from two sources: the non-linear relation of the solute drag force with GB velocity, and the variation in GB energy with curvature. It is also found that, when the diffusivity is spatially inhomogeneous, the kinetics of GB motion is different from that with a constant diffusivity.     

纳米晶体材料热稳定性的研究进展

纳米晶体材料独特的结构特征使其具有不同于传统多晶材料的优异性能,如何提高纳米晶体材料的热稳定性,避免其过度粗化,是近年来材料领域研究的热点课题。本文综述了国内外对纳米晶体材料热稳定性的研究进展,简要介绍了纳米晶体材料的微观结构特点,着重分析了溶质原子、第二相颗粒和微观应力等因素对纳米晶体材料晶粒长大的影响规律,介绍了纳米晶体材料的热力学和动力学稳定机制。     

Thermodynamic effects on the kinetics of vacancy-generating processes

The inhibiting effect of vacancies on the very process in which they are generated is considered from a thermodynamic viewpoint. Examples of such processes treated here in some detail are grain growth and pore dissolution. It is shown that these processes are inhibited due to vacancy generation. A particular scenario discussed implies intermittent “locking”. After a period of uninhibited kinetics the process comes to a halt due to a thermodynamic back force “locking” it. It can only re-start once the vacancies produced are removed by diffusion. This repetitive cycle leads to an overall reduction in the rate of the kinetic process in question. Specific predictions with regard to grain growth in fine-grained (particularly nanocrystalline) materials and void dissolution kinetics in sintering are made. A third example considered is vacancy drag on a moving individual grain boundary. The magnitude of the drag is re-assessed by taking into account the Gibbs free energy of the vacancies generated.     

Application of the maximal entropy production principle to rapid solidification: A sharp interface model

A maximal entropy production principle (MEPP) for chemical reactions was proposed to develop a sharp interface model for rapid solidification. In the modeling, the transport theorem was applied to distinguish the Gibbs energy dissipated by the interface and by the bulk phases from the total Gibbs energy. The bulk and the interface kinetics were described simultaneously and the effect of diffusion in the growing phase on the interface kinetics was incorporated. To obtain a general model, both the interface and the bulk phases were allowed to be under local non-equilibrium conditions. It was found that the model with solute drag is consistent with MEPP, in contrast with the model without solute drag. The model was applied to describe steady-state planar solidification of Si-9at.% As alloy, and a relatively good agreement between the model predictions and the experimental results was obtained. To show the solute drag effect, a partial solute drag model was proposed. Since an unreasonably large interface diffusion velocity results from negligible solute drag effect, the solute drag effect should be significant in solidification.     

考虑热力学和动力学相关性的二元合金凝固界面动力学建模

在同时考虑碰撞限制生长模式和短程扩散限制生长模式的情况下,提出一个更加完善且具有可变动力学前因子的二元合金固?液界面动力学模型.与上述两种生长模式相耦合,提出4种潜在的热力学和动力学相关性,并将其应用于平界面迁移和枝晶凝固.其中,有效热力学驱动力与有效动力学能垒间的线性相关性更符合物理实际.基于此线性热力学和动力学相关...     

KINETICS OF LIQUID PENETRATING INTO GRAIN BOUNDARY

ＫＩＮＥＴＩＣＳＯＦＬＩＱＵＩＤＰＥＮＥＴＲＡＴＩＮＧＩＮＴＯＧＲＡＩＮＢＯＵＮＤＡＲＹ￥Ｃｈｅｎ，Ｋａｎｇｈｕａ；Ｈｕａｎｇ，Ｂａｉｙｕｎ（ＰｏｗｄｅｒＭｅｔａｌｌｕｒｇｙＲｅｓｅａｒｃｈｉｎｓｔｉｔｕｔｅ，ＣｅｎｔｒａｌＳｏｕｔｈＵｎｉｖｅｒｓｉ...     

Research Progresses on Thermal Stabilization of Metal Nanocrystalline Alloys

纳米晶体材料由于内部存在高的晶界分数,晶粒长大的驱动力较高,导致常温及高温下的热稳定性较差,给这类材料的加工和使用带来了障碍。本文从热力学与动力学两方面介绍了现阶段二元纳米晶合金热稳定性研究领域的主要进展,分别介绍了热力学稳定研究中的Trelewicz/Schuh（TS）模型、Wynblatt/Ku（WK）模型,Koch等人所用的方法,以及动力学稳定基本理论等主要模型,并对各模型进行了对比分析及客观总结。     

Modeling of solute drag in the massive phase transformation

The role of solute drag in the massive phase transformation is evaluated through the dissipation of Gibbs energy by diffusion. As an introduction, the solute drag in grain boundary migration is first examined using the wedge-shaped energy function considered by Cahn and by Lücke and Stüwe. The effect of a diffusivity varying from a low value in the bulk to a high value in the center of the boundary is examined. It decreases the solute drag drastically. For the massive phase transformation it is demonstrated how the solute drag increases by the tendency for segregation and by a high diffusivity in the interface but it decreases if the diffusivity is lower than in the parent phase. The most important contribution to solute drag comes from the spike of solute atoms in the parent phase being pushed forward by the advancing interface. The spike is thus an obstacle for growth that must be broken through in order for diffusion-controlled growth to turn partitionless. The possibility of dynamic nucleation is also discussed.     

Effect of interstitial carbon on the mechanical properties of electrodeposited bulk nanocrystalline Ni

Solid solution strengthening by carbon and sulfur in bulk nanocrystalline Ni was studied by electrodeposition and first-principles calculations. Bulk nanocrystalline Ni with a carbon content of 30–1600 ppm and a sulfur content of 140–1200 ppm was prepared using a sulfamate bath with different complexing agents and gloss agents. The hardness values of the bulk nanocrystalline Ni were scattered as the grain size decreased to ～12 nm with increasing carbon and sulfur content. It was found that the scatter could be explained by considering the effect of impurities such as solute atoms on the hardness of electrodeposited Ni, in addition to the Hall–Petch relationship. Thus, to determine the structure of Ni–C and Ni–S solid solutions and estimate the contribution of impurities to hardness, the enthalpy of solution and misfit strain were calculated by first-principles calculations. The results indicate that carbon exists as an interstitial solute atom in the Ni matrix, producing large misfit strains, and sulfur exists as a substitutional solute atom, inducing no significant changes. A model of solid solution strengthening due to interstitial solute atoms was developed by considering the interaction between mobile dislocations and solute atoms. This study has effectively divided the observed solid solution effect from the grain refinement effect in electrodeposited nanocrystalline Ni. The results of this study point to the origin of high-strength electrodeposited bulk nanocrystalline Ni.     

Solute drag effects during the dynamic recrystallization of nickel

Solute drag effects during dynamic recrystallization were studied using five different nickel–sulfur alloys. The steady state stress for dynamic recrystallization, measured using hot compression tests, depends on the sulfur concentration. The experimental results are analyzed using a model that relates the steady state stress to the grain boundary mobility. At the lower temperatures, the mobilities are strongly reduced by a solute drag effect; above a transition temperature, the drag effect becomes negligible. The extent of sulfur segregation at grain boundaries during recrystallization was assessed using cryogenic tensile tests of microsamples removed from the hot compressed specimens. The fracture surfaces exhibit the characteristics of intergranular brittleness when hot compression is carried out within the “grain boundary segregation” temperature range; above the transition temperature, the fracture surfaces are purely ductile.     

Relating Initial Texture to Deformation Behavior During Cold Rolling and Static Recrystallization Upon Subsequent Annealing of an Extruded WE43 Alloy

Deformation behaviors during cold rolling and static recrystallization behaviors upon subsequent annealing of an extruded WE43 alloys with different initial textures were investigated in this study. Three types of differently textured WE43 initial alloys were labeled as samples Ⅰ, Ⅱ and Ⅲ. The results showed that multiple twinning modes and basal slip dominated the deformation of samples during cold rolling. Cold-rolled sample Ⅰ activated the larger number of double twins with high strain energy...     

Phase field crystal model of solute drag

The atomic scale interaction of solute with a migrating grain boundary has been studied using a binary phase field crystal (PFC) model. This model bridges between atomistic and continuum simulation techniques as it operates on diffusive timescales but at atomistic length scales. For this study, a two-dimensional channel containing two grains separated by a flat grain boundary has been constructed that allows for a channel length on the order of one micrometer. A new formalism has been developed to allow for the application of an external driving pressure for the growth of one grain. These simulations account for solute/grain boundary interactions, resulting in a solute drag effect on the grain boundary motion. The PFC simulations show good agreement with classical solute drag theory, though deviations due to the atomic scale nature of the interface exist.     

表面机械研磨处理制备纳米晶Ni的晶粒生长动力学

利用表面机械研磨处理(SMAT)技术在纯Ni上制备一定厚度的纳米晶表层,利用X射线衍射(XRD)和透射电镜(TEM)研究了纳米晶Ni的晶粒生长动力学,计算了描述晶粒生长动力学的时间指数n和晶粒生长激活能Q.研究表明,纳米晶Ni在423～723 K退火时的时间指数n约为0.14.当纳米晶Ni在423 ～523 K退火时,其晶粒生长激活能Q为32.1 kJ/mol,表明在这一温度区间内晶粒生长由晶界和亚晶界的微结构重新排列所控制;当纳米晶Ni在523～723 K退火时,晶粒生长激活能Q为121.3 kJ/mol,表明在这一温度区间内晶粒生长由晶界扩散所控制.TEM观察表明纳米晶Ni在较高温度下退火时出现异常的晶粒长大现象.     

On the Thermodynamic Aspect of Interaction Between Dislocations and Highly Mobile Interstitial Solute:With Special Focus on Recent Progress in Pd–H System:A Review

It is well known that, in kinetics, the interaction between dislocations and interstitial solute normally exerts strong solute drag effect on dislocations, leading to strong solution hardening of the metals. However, due to the low mobility of interstitial solute in many metals, thermodynamic aspect of the interaction between dislocations and interstitial solute is often unobservable and omitted. It will be shown in this article by reviewing the H-induced behaviors in metal–H systems, especially the recent progress in Pd–H system that, when the interstitial solute atoms are highly mobile and able to collect in the vicinity of mobile dislocations easily, the scenario will be remarkably different. The interaction between dislocations and these highly mobile interstitial solute atoms, in thermodynamics, will reduce the line energy of dislocations and will facilitate the generation of dislocations, leading to an increase in dislocation density and an enhanced strain hardening of metals upon plastic deformation.