过冷熔体中枝晶生长的相场法数值模拟

利用相场法模拟了过冷纯金属熔体中的枝晶生长过程,研究了各向导性、界面动力学、热扩散和界面能对枝晶生长的影响.结果表明,热噪声可以促发侧向分支的形成,但不影响枝晶尖端的稳态行为;随着各向异性的增加,枝晶尖端生长速度增加,尖端半径减小;当界面动力学系数减小及在界面动力学系数小于1的条件下热扩散系数减小时,枝晶尖端生长速度随之减小,而尖端半径相应增大;界面能趋于增大枝晶尺度并保持界面在扰动下的稳定,界面能越大,形成侧向分支的趋势越小 关键词： 过冷 枝晶生长 相场法 数值模拟     

基于MeshTV界面重构算法的二元合金自由枝晶生长元胞自动机模型

本文基于MeshTV界面重构算法, 发展了二元合金凝固自由枝晶生长的元胞自动机 (cellular automaton, CA) 模型. 通过采用MeshTV界面重构算法, 在细化的界面元胞内重构出了固液界面的位置. 在此基础上, 发展了一种同时适合描述纯物质与合金凝固界面生长的动力学模型. 与非界面重构的CA模型相比, 本文所发展的模型可以在较大的网格尺寸下实现模型的收敛, 同时网格各向异性不明显, 且能够反映界面能各向异性参数ε 对自由枝晶生长的影响. 在ε =0.02时, 通过与描述自由枝晶生长的LGK理论模型相比较, 发现计算的枝晶尖端速度与LGK理论模型的预测符合较好, 而计算的枝晶尖端半径比LGK理论预测值大于约20%.     

界面能各向异性对定向凝固枝晶生长的影响

采用元胞自动机 (cellular automaton, CA) 模型研究了界面能各向异性对二维定向凝固枝晶生长的影响. 模拟结果显示当晶体的择优生长方向与热流方向一致时, 随着界面能各向异性强度的增大, 凝固组织形态由弱界面能各向异性时的海藻晶转变为强界面能各向异性时的树枝晶. 同时, 界面能各向异性强度会影响稳态枝晶尖端状态的选择, 界面能各向异性越强, 定向凝固稳态枝晶尖端半径越小, 尖端界面前沿的液相浓度和过冷度越小. 稳态枝晶生长的尖端状态选择参数与界面能各向异性强度也存在标度律的指数关系, 而枝晶一次间距则受界面能各向异性强度影响较弱. 当晶体的择优生长方向与热流方向呈-40°夹角时随着界面能各向异性强度的增大, 凝固组织形态由海藻晶逐渐转变为退化枝晶, 后又逐渐转变为倾斜枝晶. 关键词： 元胞自动机 枝晶 界面能各向异性     

三维枝晶生长的相场法数值模拟研究

基于薄界面限制、耦合界面能各向异性的相场模型,采用动态计算区域的加速算法,对纯物质的三维枝晶生长进行了定量模拟,真实再现了枝晶的生长过程.对枝晶尖端进行了剖切分析,表明主枝截面上各向异性没有主枝方向各向异性明显;对枝晶尖端生长速度、尖端半径、Peclet数及临界稳定性参数σ^*进行模拟计算,并与同条件下报道值进行了对比分析,两者符合良好,并得到了与结晶理论相一致的枝晶生长规律,证实了相场方法模拟三维空间枝晶生长可行有效. 关键词： 相场方法 枝晶生长 微观组织 三维数值模拟     

BCC枝晶生长原子堆垛过程的晶体相场研究

通过在自由能泛函中引入各向异性参数得到了一个基于高斯内核的改进晶体相场模型, 并采用该模型研究了体心立方结构(BCC)枝晶生长的原子堆垛过程. 结果表明, 在BCC由正十二面体平衡形貌演化为枝晶组织过程中, 形核位置经历了由面心({110}面)到尖端(<100>取向)的转移, 进而发生界面失稳形成枝晶组织; 枝晶生长过程中, 新的固相原子首先在枝晶尖端附近形核, 并快速向尖端及根部生长, 枝晶尖端被新原子完全包覆后将再次诱发液相原子附着形核及生长; 随初始液相密度的增加, 固-液界面移动速率增加, 速率系数的各向异性也增强.     

六方小面相螺旋在各向异性、表面吸附、界面动力学作用下生长的相场

利用定量相场模型研究了强各向异性、表面吸附率以及界面动力学作用条件下六方Ga N螺旋结构的表面形貌与生长机理.通过引入小面相各向异性的相场修正方程,研究了不同各向异性的稳态螺旋形貌,发现各向异性通过改变台阶尖端的曲率作用影响螺旋生长.弱各向异性下稳态螺距及界面动力学特征相对稳定,各向异性较强时尖端的过饱和度随着各向异性的增强而增大,并使得界面平衡态向着有利于螺旋台阶推进的方向移动.研究了表面吸附率对小面相螺旋生长的作用机理,发现吸附率的增加导致了稳态螺旋间距的降低,通过分析螺旋间距随台阶宽度的变化趋势,发现增强的表面吸附和各向异性强度降低了螺旋间距的收敛性,并且具体分析了收敛性误差;通过探讨界面动力学作用条件下螺旋形貌特征以及螺旋间距变化趋势,发现界面动力学系数通过改变稳态螺旋间距与特征指数因子调控螺旋生长的动力学机理,与各向同性相比小面相螺旋生长表现出较低的界面动力学系数依赖性.     

相场法模拟NiCu合金非等温凝固枝晶生长

利用相场模型与溶质场、温度场进行耦合计算,以Ni-40.83%Cu合金为例模拟了二元合金枝晶生长过程.系统研究相场模型中相场和温度场耦合强度对枝晶形貌和浓度分布的影响.模拟结果表明:随着耦合强度的增加,相场受温度场的影响加大,界面前沿变得不稳,扰动被放大,主枝上出现了二次枝晶.同时,枝晶尖端的生长速率增大,而枝晶尖端的曲率半径减小,枝晶前沿的溶质富集现象也更严重;另外,计算结果与Ivantsov理论符合较好. 关键词： 相场法 NiCu合金 枝晶生长 Ivantsov理论     

二元合金等温凝固过程的相场模型

基于Ginzberg-Landau理论，发展了一个与WBM模型和KKS模型一致的新相场模型.并利用该相场模型与溶质场耦合计算，以Al-65%Cu合金为例模拟了不同过冷度条件下，二元合金凝固过程的等轴枝晶生长过程.研究过冷度对二元合金等温凝固过程的等轴枝晶生长以及溶质场分布的影响.结果表明：随着过冷度的增大，枝晶的二次枝晶更加发达，浓度Peclet数和枝晶尖端的生长速率增大，而枝晶尖端的曲率半径减小，枝晶前沿的溶质富集现象也更严重；另外，计算结果与Ivantsov理论符合较好. 关键词： 相场法 枝晶生长 溶质场 Ivantsov理论     

用CA方法模拟界面能各向异性对胞晶生长形态的影响

用元胞自动机（CellularAutomaton,CA）模型研究了界面能各向异性对二维定向凝固胞晶的生长形态的影响,建立了判定胞晶生长达到稳态的判据．结果显示,当界面能各向异性强度非常小时,胞晶尖端很容易分岔,胞晶形态不容易稳定．而当界面能各向异性强度足够大时,容易形成稳定的胞晶形态,同时界面能各向异性强度会显著影响稳定胞晶的形态,界面能各向异性越强,稳态胞晶间距越小,胞晶尖端半径越小,尖端半径与胞晶间距的比值越小,固液界面前沿的浓度与过冷度越小．     

各向异性系数对等温结晶冰晶生长相场法模拟的影响

采用国内外描述相变微观结构的相场模型,将果汁体系视为水和溶质组成的二元系统,探究各向异性系数取值对冰晶相貌及溶质分布模拟的的影响.结果表明:随着各向异性系数的增大,冰晶的二次分枝越来越发达,其尖端生长速度变快,且尖端速度波动的幅值增大;冰晶生长速度越快,则凝固时间越短,溶质扩散层越薄.各向异性系数在0.025左右取值,较能反映冰晶实际生长形貌.     

镁基合金自由枝晶生长的相场模拟研究

利用定量相场模型, 以Mg-0.5 wt.%Al合金为例模拟了基面((0001)面)内镁基合金的等温自由枝晶生长过程. 通过研究该合金体系数值模拟的收敛性, 获得了最优化值耦合参数λ = 5.5及网格宽度Δx/W₀ = 0.4, 并在该参数下系统研究了各向异性强度和过饱和度对枝晶尖端生长速度、尖端曲率半径、Péclet数及稳定性常数σ^* 的影响. 结果表明, 由微观可解性理论得到的稳定性系数σ^* 与ε₆ 拟合值σ^*≅ ε₆ ^1.81905, 更接近理想值σ ^* (ε₆) ≅ε₆ ^1.75. 此外, 当过饱和度Ω < 0.6时, 稳定性系数σ ^* 不随ε₆ 的变化而变化, 而当Ω > 0.6时, 稳定性系数σ ^* 随着ε₆ 的增加而减小. 这反映了枝晶的生长由扩散控制向动力学控制的转变. 随着过饱和度的增加, 枝晶形貌由雪花状枝晶向圆状枝晶转变.     

Linking Phase-Field and Atomistic Simulations to Model Dendritic Solidification in Highly Undercooled Melts

Even though our theoretical understanding of dendritic solidification is relatively well developed, our current ability to model this process quantitatively remains extremely limited. This is due to the fact that the morphological development of dendrites depends sensitively on the degree of anisotropy of capillary and/or kinetic properties of the solid-liquid interface, which is not precisely known for materials of metallurgical interest. Here we simulate the crystallization of highly undercooled nickel melts using a computationally efficient phase-field model together with anisotropic properties recently predicted by molecular dynamics simulations. The results are compared to experimental data and to the predictions of a linearized solvability theory that includes both capillary and kinetic effects at the interface.     

Steady needle growth with 3-D anisotropic surface tension

The effect of the anisotropic interfacial energy on dendritic growth has been an important subject, and has preoccupied many researchers in the field of materials science and condensed matter physics. The present paper is dedicated to the study of the effect of full 3-D anisotropic surface tension on the steady state solution of dendritic growth. We obtain the analytical form of the first order approximation solution in the regular asymptotic expansion around the Ivantsov’s needle growth solution, which extends the steady needle growth solution of the system with isotropic surface tension obtained by Xu and Yu (J. J. Xu and D. S. Yu, J. Cryst. Growth, 1998, 187: 314; J. J. Xu, Interfacial Wave Theory of Pattern Formation: Selection of Dendrite Growth and Viscous Fingering in a Hele-Shaw Flow, Berlin: Springer-Verlag, 1997). The solution is expanded in the general Laguerre series in any finite region around the needle-tip, and it is also expanded in a power series in the far field behind the tip. Both solutions are then numerically matched in the intermediate region. Based on this global valid solution, the dependence of Peclet number Pe and the interface’s morphology on the anisotropy parameter of surface tension as well as other physical parameters involved are determined. On the basis of this global valid solution, we explore the effect of the anisotropy parameter on the Peclet number of growth, as well as the morphology of the interface.      

Emergence of chaos during dendritic growth of ice

A transition from deterministic to chaotic growth behavior along the dendrite axis has been experimentally found and investigated. A “correlation structure” of a growing dendrite has been revealed in terms of relationship between oscillations of the dendrite tip velocity and the branching dynamics at different distances from the tip. It is shown that the dendritic growth of ice in supercooled water is an example of nonequilibrium morphogenesis of a dissipative system demonstrating deterministic chaos.     

The origin of noncollinear anisotropies and asymmetric magnetization reversal in FM/AFM bilayer system

The effects of the magnitude of the uniaxial anisotropy of a ferromagnet and the cooling field on the noncollinearity between uniaxial anisotropy and induced unidirectional anisotropy in a ferromagnet/antiferromagnet bilayer system are investigated. A diagram of noncollinear anisotropies and relative negative (positive) exchange bias field dependence upon cooling field and uniaxial anisotropy of the ferromagnet is obtained. The numerical result shows that the emergence of noncollinear anisotropies originates from the action of the cooling field and uniaxial anisotropy of the ferromagnet. The noncollinearity strongly depends on the magnitude of cooling field and uniaxial anisotropy of the ferromagnet. Moreover, the effect of noncollinear anisotropies and applied field on asymmetric magnetization reversal is also investigated. Amazingly, when the magnetic field is applied collinearly with unidirectional anisotropy, the hysteresis loop of ferromagnet/antiferromagnet bilayers is always symmetric even if there are noncollinear anisotropies. Our results indicate that the asymmetry of the hysteresis loop only originates from the noncollinearity between the induced unidirectional anisotropy and the applied field, rather than from the noncollinearity between the uniaxial and unidirectional anisotropies.     

Interfacial free energy anisotropy driven faceting of precipitates

Abstract

During solid–solid precipitation, interface free energy anisotropy is known to drive faceting of precipitates. In this paper, using a recently developed phase field formulation based on higher order tensor terms, we develop and implement a family of phase field models and indicate the parameter choices which lead to faceted precipitate morphologies. We also indicate how to choose the parameters given either the known precipitate morphology or the interfacial free energy anisotropy. Specifically, we study the faceting of precipitates in systems with cubic and hexagonal anisotropies; in 2 and 3D implementation of our phase field model, the precipitates do show facets in accordance with the Wulff plot – including cases where the Wulff plot predicts facets made up of more than one family of planes. We also indicate the possible extensions of our model to study other problems of interest.