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.     

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.     

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.     

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.     

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.     

Grain coarsening inhibited by solute segregation

It will be shown that grain boundaries are in a metastable thermodynamic equilibrium in the presence of solute atoms and, therefore, grain coarsening is stopped as there is no driving force. This is in contradiction to a generally accepted interpretation, where solute drag, i.e. zero mobility of the boundaries, stops grain coarsening. Based on the empirical relation between terminal solubility of a solute and its grain boundary segregation it can be shown that a two-phase mixture with solute atoms agglomerating in a precipitated phase will be the stable thermodynamic equilibrium state. However, if precipitation is kinetically hindered, the metastable equilibrium with a certain grain boundary area and a zero grain boundary energy is attained. Changes in this grain boundary area or grain size respectively are calculated as a function of temperature and compared with experimental findings.     

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.     

A model for interphase precipitation based on finite interface solute drag theory

A model for interphase precipitation with the ledge mechanism, based on a eutectoid reaction, has been developed and combined with the finite interface solute drag model and a numerical solution of the diffusion equations inside the migrating phase interface. In the model, niobium flows in two directions, i.e. perpendicular to the direction of the ledge migration by eutectoid-like reaction and simultaneously parallel to the direction of the ledge migration inside the ledge interface. The difference between ledge transformation and typical phase transformation is compared using this model and the effects of row spacing, temperature and segregation energy are discussed. The calculation results using the model are compared with experimental results and the critical driving force for interphase precipitation is evaluated. The estimations of the niobium carbide precipitation using this model are in good agreement with experimental results.     

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.     

Measurements of grain boundary mobility during recrystallization of a single-phase aluminium alloy

A combination of in situ annealing and electron backscattered diffraction in the SEM has been used to determine the mobility of high angle grain boundaries in a deformed single-phase Al–Si alloy. It is found that the boundary velocity is directly proportional to the driving pressure and that the activation energy for boundary migration over all the conditions investigated is consistent with control by lattice diffusion of the solute. It is confirmed that tilt boundaries of recrystallized grains misoriented by 40±10° about axes within ±10° of 〈111〉 have an increased mobility compared to other high angle boundaries, whereas the mobilities of 40°〈111〉 twist boundaries are similar to those of general high angle boundaries. The mobility maximum for the 40°〈111〉 tilt boundaries is very broad, which is in contrast to the sharp mobility peaks reported for curvature-driven grain growth, and possible reasons for these differences are discussed.     

Grain-boundary segregation and dynamic solute drag theory—A phase-field approach

We propose a model based on a phase-field approach to study grain-boundary segregation and solute drag. We will show that it is possible to model the dynamics of grain-boundary segregation to a stationary boundary as well as solute drag on a moving boundary with the same phase-field model. We shall achieve this by introducing a concentration dependency in the height of the double-well potential in the Gibbs-energy expression. As the model then will be able to treat the build-up of a concentration spike in the boundary as well as its disappearance we shall term this treatment dynamic solute-drag theory.     

凝固组织对连铸板坯中心偏析的影响

根据钢厂生产实践,从凝固组织入手,从宏观角度阐释了凝固组织对中心偏析及钢液流动的影响:中心偏析是由于凝固界面均一向前推进,溶质元素在中心部位汇聚造成的;柱状晶发达,高溶质钢液停留在柱状晶间的间隙内,可以改善中心偏析;等轴晶凝固界面可以分散汇聚在中心部位的溶质元素,改善偏析;钢液补充凝固收缩的现象发生在等轴晶区内,恶化了中心偏析。     

液态锂锡合金中氚解吸行为的模拟

液态锂锡合金是很有前途的聚变-裂变混合堆(FFHR)包层产氚材料。为完成FFHR包层氘-氚燃料循环系统的概念设计,以金属与氢的作用理论为基础,建立了液态Li25Sn75中氚解吸行为的动力学模型,模拟和分析了合金温度、氚分压、氦流量对解吸气中氚分压的影响以及氚在液态Li25Sn75中的传质系数、解吸率和吸附率。计算结果表明：在673~873 K的温度范围内,氚从液态Li25Sn75到气相的整个解吸过程,虽然包含了氚在熔融合金气泡中的扩散与对流、氚通过与气-液界面相连合金层的扩散、在界面发生的氚原子重组多相反应、氚通过气相边界层的扩散和气相中氚的扩散与对流5个子过程,但起决定作用的是氚在合金内的扩散和气-液界面的多相反应重组     

KINETICS OF LIQUID PENETRATING INTO GRAIN BOUNDARY

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Analysis of refining of aluminum using fractional solidification with forced convection

Segregation of iron atoms during refining of aluminum using the fractional solidification technique has been analyzed. The redistribution of the solute atoms was influenced by the solidification and solid/liquid interface tangential velocities. Aluminum purity increased with decreasing solidification velocity and increasing tangential velocity. The diffusion boundary thickness was inversely proportional to the square root of the tangential velocity in the cylindrical rotating system. Effects of the tangential and solidification velocities on the effective redistribution coefficient were investigated. The calculated refining curves were in good agreement with measured values.     

The phase-field approach and solute drag modeling of the transition to massive γ → α transformation in binary Fe-C alloys

The transition between diffusion controlled and massive transformation γ →α in Fe–C alloys is investigated by means of phase-field simulations and thermodynamic functions assessed by the Calphad technique as well as diffusional mobilities available in the literature. A gradual variation in properties over an incoherent interface, having a thickness around 1 nm, is assumed. The phase-field simulations are compared with a newly developed technique to model solute drag during phase transformations. Both approaches show qualitatively the same behavior and predict a transition to a massive transformation at a critical temperature below the T₀ line and close to the α/α + γ phase boundary. It is concluded that the quantitative difference between the two predictions stems from different assumptions on how the properties vary across the phase interface yielding a lower dissipation of Gibbs energy by diffusion in the phase-field simulations. The need for more detailed information about the actual variation in interfacial properties is emphasized.     

A study of the influence of Mn and Ni on the kinetics of the proeutectoid ferrite reaction in steels

The kinetic transition between partitioned and unpartitioned growth of proeutectoid ferrite has been studied for high-purity Fe–C–Mn and Fe–C–Ni alloys, and for temperatures just above the eutectoid. These results (and certain results of previous investigations) are compared with computed paraequilibrium and equilibrium ternary phase diagrams, and it is shown that the transition occurs well within the paraequilibrium two-phase regions, but significantly outside the limit predicted by the local equilibrium analysis of the ternary precipitation reaction. These observations are interpreted in terms of solute drag theory. It is inferred that both Mn and Ni exert a drag on the moving ferrite/austenite interfaces, and that this drag force is due to substitutional solute diffusion within the moving interface. The equilibrium binding energies of each of the substitutional solutes to the boundary are expected to be of order RT.