Ground-State Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal-Field

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/ zJ-longitudinal crystal D / zJ field plane. We find that there are the first order-order phase transitions in a very small range of D /zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions,

Unifying the crystallization behavior of hexagonal and square crystals with the phase-field-crystal model

By employing the phase-field-crystal models, the atomic crystallization process of hexagonal and square crystals is investigated with the emphasis on the growth mechanism and morphological change. A unified regime describing the crystallization behavior of both crystals is obtained with the thermodynamic driving force varying. By increasing the driving force,, both crystals （in the steady-state） transform from a faceted polygon to an apex-bulged polygon, and then into a symmetric dendrite. For the faceted polygon, the interface advances by a layer-by-layer （LL） mode while for the apex-bulged polygonal and the deridritic crystals, it first adopts the LL mode and then transits into the multi-layer （ML） mode in the later stage. In particular, a shift of the nucleation sites from the face center to the area around the crystal tips is detected in the early growth stage of both crystals and is rationalized in terms of the relation between the crystal size and the driving force distribution. Finally, a parameter characterizing the complex shape change of square crystal is introduced.

Elastic strain response in the modified phase-field-crystal model

To understand and develop new nanostructure materials with specific mechanical properties, a good knowledge of the elastic strain response is mandatory. Here we investigate the linear elasticity response in the modified phase-field-crystal（MPFC） model. The results show that two different propagation modes control the elastic interaction length and time, which determine whether the density waves can propagate or not. By quantitatively calculating the strain field, we find that the strain distribution is indeed extremely uniform in case of elasticity. Further, we present a detailed theoretical analysis for the orientation dependence and temperature dependence of shear modulus. The simulation results show that the shear modulus reveals strong anisotropy and the one-mode analysis provides a good guideline for determining elastic shear constants until the system temperature falls below a certain value.

Numerical Simulation of Two-Dimensional Dendritic Growth Using Phase-Field Model

In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes the physics of dendritic growth in any material during the process of under cooling. The numerical procedure in this work is based on finite difference scheme for space and the 4th-order Runge-Kutta method for time discretization. The effect of each physical parameter on the shape and growth of dendritic crystal is studied and visualized in detail.

Phase Transition for a Mixed Spin-1／2 and Spin-sB System with a Transverse CrystalField

The critical behaviors of a mixed spin-1/2 and spin-sB Ising system with a transverse crystal field are studiedby use of the effective-field theory with correlations. The effect of the transverse crystal field on transition temperaturesis investigated numerically for the honeycomb (z = 3) and square (z = 4) lattices. The results show that there is notricritical point for the system.

Phase field crystal simulation of grain boundary movement and dislocation reaction

The phase field crystal （PFC） model is used to simulate the premelting dislocation movement of the symmetric tilt grain boundary （STGB） under strain action when the system temperature is at far from the melting point and close to the melting point, respectively. The results show a local premelting occurs surrounding the dislocations as the premelting temperature is approached to from below temperature. The premelting dislocations of the STGB can glide under strain action, and the premelting region is a companion for dislocation gliding. The process of STGB decay is very similar at the two high temperature conditions. As premelting presents, it diminishes the gliding resistance for the dislocations and leads to a faster movement of dislocations, and also brings about more energy reduction of the system during the decay process of STGB. In spite of applying strain to these premelting samples in whole decay processes of STGB, the premelting dislocation region does not obviously develop and extend. This indicates that the external strain action does not promote the premelting at the high temperature, and cannot induce more premelting dislocation, which can be owed to the premelting phase around the dislocation exhibit fluid-like properties and to the premelting dislocation easily gliding and relaxing the strain energy; this is in agreement with the results of experiments and molecular dynamics.

Two finite difference schemes for the phase field crystal equation

The phase field crystal(PFC) model is a nonlinear evolutionary equation that is of sixth order in space.In the first part of this work,we derive a three level linearized difference scheme,which is then proved to be energy stable,uniquely solvable and second order convergent in L_2 norm by the energy method combining with the inductive method.In the second part of the work,we analyze the unique solvability and convergence of a two level nonlinear difference scheme,which was developed by Zhang et al.in 2013.Some numerical results with comparisons are provided.

Phase Field Models Versus Parametric Front Tracking Methods: Are They Accurate and Computationally Efficient?

We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification.Here we focus on Stefan problems,and their quasi-static variants,with applications to crystal growth.New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.

韧性材料的微裂纹扩展和连通的晶体相场模拟

采用晶体相场模型研究韧性单晶材料在双轴拉伸条件下微裂纹扩展和连通的演化过程,分析应变、初始裂口处原子密度等因素对裂纹扩展和分叉的影响。结果表明:初始裂口处原子密度对裂纹扩展有明显的影响;对于双轴拉伸作用,当应变较小时,裂纹扩展不分叉;当应变较大时,裂纹扩展才能出现分叉。在裂纹扩展过程中,体系能量不断降低;当裂纹出现分叉时,体系能量降低更快,这表明裂纹扩展过程中弹性应变能的释放比表面能的增加要快。裂纹在扩展过程中,在分叉处会出现与主裂纹断开的孤立的微小空洞。这些微小空洞将成为新的裂纹萌生之地,它们在应力的作用下不断长大,连成一线,形成新的裂纹分支。同一条直线上的两条初始裂纹在扩展过程中,当裂纹尖端靠近时,尖端相互吸引,裂纹相互连通。本研究所得结果与相关模拟结果和实验结果吻合。

直拉单晶硅生长时空洞演化的相场模拟

为研究大直径直拉硅生长时空洞的演化规律,建立了与有限元模型所模拟的晶体生长温度场相结合的空洞演化相场模型,并应用该模型模拟研究了空洞形貌及其分布状态的变化过程以及不同初始点缺陷浓度对空洞演化的影响规律。结果表明:直拉硅单晶生长过程中,空洞的演化经历了孕育-形核-长大-稳定四个阶段,其形貌和分布状态亦由孤立的球形向偏聚的串珠形转变;与较低的点缺陷浓度相比,初始点缺陷浓度较高时,空洞的数目、平均尺寸、面积分数普遍较大,孕育阶段缩短、形核和长大阶段延长;空洞的偏聚及合并、长大的现象显著;当温度低于980 K时,大直径的空洞数目不再增加。

晶体相场法模拟小角度晶界的位错结构及其演化

采用晶体相场模型模拟小角度晶界结构和在外加应力作用下晶界、位错的演化过程,从位错的运动形式、体系自由能与应变关系等角度,讨论晶界位错运动和湮没过程。结果表明:在稳定的小角度晶界中,位错间距与位向差成反比。位错和晶界区域具有较高的能量密度;外加应力会导致一个位错组脱离晶界而分解成两个位错组,且有诱发晶界湮没的趋势;晶界湮没过程可以出现4个阶段或2个阶段,且存在敏感位向差角,位向差稍高于5.85°时晶界湮没过程呈4个阶段,位向差稍低于5.85°时晶界湮没过程呈2个阶段;位向差越小,晶界湮没过程越简单快捷。

不同温度晶界位错湮没过程的晶体相场模拟

【目的】针对不同温度的晶界位错湮没过程进行研究。【方法】采用晶体相场模型模拟中等角度对称倾侧晶界结构在不同温度下的晶界位错演化湮没过程,从位错的运动形式和体系自由能的变化,分析晶界的消失过程和位错的相互作用。【结果】具有二维三角晶格原子点阵结构形成的对称倾侧晶界是由配对的位错对按直线规则排列构成,可以看成由2套位错Burgers矢量组成。晶界湮没主要有如下几方面的特征过程:首先晶界位错攀移,然后发生位错分解,晶界发射位错,位错由攀移运动转化为作滑移运动;接着滑移位错穿过晶粒内部,直到在对面晶界上湮没;剩余的晶界位错继续作攀移运动,然后又出现位错分解,晶界再次发射位错,使得位错转为作滑移运动,与其它作滑移运动的位错在晶内相遇湮没消失。【结论】在低温情况,位错是一对一对地按照一定的顺序发生湮没,而高温情况,位错湮没可以同时出现几对位错一起发生湮没。最后,所有晶界和位错全部消失。

晶体相场模拟取向角对晶界湮没过程的影响

【目的】研究大角晶界的位错运动和相互作用,揭示晶界发射位错的内在原因。【方法】采用晶体相场模型模拟不同取向角的晶界位错湮没过程。【结果】晶界湮没有如下主要过程:开始时位错沿晶界攀移,随后晶界发生位错发射,位错运动方式由攀移转化为滑移;位错滑移穿过晶粒内部,在到达对面晶界处发生湮没;其余的晶界位错仍作攀移运动,再次出现晶界发射位错;滑移位错与其它位错在晶内相遇发生湮没。【结论】位错在晶界处湮没,自由能曲线的谷较浅,而在晶粒内部湮没,能量曲线的谷较深;晶界攀移的位错越多,能量曲线的峰越高。

材料裂纹扩展分叉机理的晶体相场法研究

[目的]进一步探索材料裂纹扩展分叉的机理。[方法]采用晶体相场模型研究平面应力作用下材料裂纹扩展的动态演化过程,分析裂纹扩展过程体系自由能G、裂纹面积分数S、裂口周长L的变化特征;分别从G、S、L的变化阐述裂纹扩展以及三者与裂纹扩展临界应变εc的对应关系;探讨裂口扩展和主裂纹分叉与体系能量G的内在关联。[结果]无应力施加时期,裂纹面积分数S和裂口周长L没有变化;施加拉伸应力后,当系统应变达到一定程度时,S和L开始同时增加,此时的应变大小对应于裂纹启裂临界应变εc值。[结论]应力施加导致材料中心裂口处应力集中,体系能量上升,系统能量曲线一阶导数的拐点对应于中心裂纹启裂时刻或临界应变。自由能曲线一阶导数拐点处能量上升速率变缓,表明此时弹性应变能得到释放。

相场法模拟冷冻浓缩过程冰晶生长的可行性探讨

为解决在冷冻浓缩过程中可溶性固体被冰晶夹带损失的问题,从冷冻浓缩的原理出发,利用冰晶是一种凝固组织的性质,探讨了国内外金属微观结构研究领域非常热门的相场模型,阐述了其从微观上模拟冷冻浓缩过程冰晶生长的可行性及其理论意义。

晶体相场模型的研究进展

晶体相场方法是一种能在原子尺度和扩散时间尺度模拟材料微观结构演化的新方法,它能够自洽地耦合弹塑性形变和多重晶粒位向,并能用于模拟与此相关的很多物理现象。从晶体相场模型与经典密度泛函理论之间的关系出发,详细论述了晶体相场模型的一些新进展,包括八阶拟合晶体相场模型、双模数晶体相场模型和幅值方程模型等。还描述了晶体相场方法在异质外延、多晶凝固和位错迁移等方面的应用,并展望了其未来的应用前景。

相场模型模拟强界面能各向异性作用下晶体生长

用Eggleston等提出的方案对界面能各向异性函数进行重整化处理,并使用相场模型对强各向异性情形下的晶体生长进行了模拟。在晶体平衡形态模拟中再现了晶向缺失现象,并与理论预测结果相一致。在自由枝晶生长过程中,当各向异性低于临界值时,枝晶生长速度随着各向异性系数增大而增大;在临界值附近生长速度突然降低5%;当高于临界值时生长速度又开始增加直到在0.20处达到最大值,其后基本不变。

平均空位径向扩散通量对直拉硅单晶空洞演化影响的相场模拟

直拉硅单晶中空洞的大小和数目对其性能有着至关重要的影响.采用已有的与晶体生长温度场有限元模型相耦合的空洞演化相场模型及其应用程序,模拟研究了不同的平均径向扩散通量对直拉单晶硅生长过程中空洞形貌及其分布状态演化的影响规律.结果表明:平均空位径向扩散通量的变化对于空洞演变阶段性及其形貌特征影响不大;随着平均空位径向扩散通量的增加,空洞的孕育阶段缩短,形核长大阶段延长,空洞平均尺寸及分数增加.

高温应变作用下小角度晶界湮没过程的晶体相场模拟

【目的】采用晶体相场模型模拟应变作用下晶界的变形过程。【方法】分别模拟了对称倾侧双晶体系在远离熔点温度和接近熔点温度时,在外加应力作用下小角度晶界的湮没过程。【结果】研究表明,小角度晶界同一侧晶界处相邻位错组的柏氏矢量夹角为60°,并且当体系接近熔点温度时,晶界处位错组周围出现预熔区域。【结论】晶界处的位错组在应力作用下进行滑移运动,两种情况中晶界位错的湮没规律基本相同,但由于预熔情况的出现,使得位错运动的阻力降低,位错运动的速度较快,湮没时体系能量减小得更多。

马氏体相变的相场模型研究进展

马氏体相变是一种无扩散位移型一阶相变,会形成针状、表面浮凸等复杂的特征微结构。马氏体相变的特征微结构会显著影响材料的宏观物理力学特性,相关研究具有重要的科学和工程价值。相场模型具有可处理复杂界面演化问题的独特优势,已成为模拟马氏体相变的有力的理论与计算工具。概述了马氏体相变相场模型的研究进展,并分析了相场模型应用于弱马氏体相变和重构型马氏体相变的特点。