Phase-Field Modeling and Numerical Simulation for Ice Melting

In this paper, we propose a mathematical model and present numerical simulations for ice melting phenomena. The model is based on the phase-field modeling for the crystal growth. To model ice melting, we ignore anisotropy in the crystal growth model and introduce a new melting term. The numerical solution algorithm is a hybrid method which uses both the analytic and numerical solutions. We perform various computational experiments. The computational results confirm the accuracy and efficiency of the proposed method for ice melting.     

Semiconductor quantum dots and related systems: Electronic,optical, luminescence and related properties of low dimensional systems

This review seeks to extend the scope of both the experimental and theoreticalwork carried out since I completed my 1993 review on the electronic, optical, andto a lesser extent, the transport properties of a variety of semiconductor quantumdots (QDs). In addition to the many advances that have been made on topics suchas quantum confinement effects (QCE), optical and luminescence properties,energy levels, and theoretical models that were dealt with in outline then, anumber of new themes have emerged. These include detailed studies on singleQDs such as InAs, InP, CuCl, etc, and this became possible due to thedevelopment of several microtechniques such as scanning near field opticalmicroscopy, SNOM or NSOM, as well as the use of improved growth proceduressuch as those involving MBE and the Stranski-Krastanow (SK) growth method, orby better chemical processing. By concentrating on single dots, it has provedpossible to limit the extent of the line broadening for the optical absorption andluminescence peaks due to the variation in dot sizes in the more usual types of films used. Line half widths (FWHM) in the microvolt region have now been recorded, and this has helped in the identification and resolution of excitons, biexcitons, higher excited states, and both positive and negative charged excitons, when these lie close together in energy. Quantum dots such as CdSe and CuCl which can be considered as the model systems have been the most extensively investigated, and in the case of CdSe dots, reasonable theoretical models have been developed to predict energy levels and optical properties as a function of dot size even for the difficult case of strong confinement, when R ≤ α_B, the bulk exciton Bohr radius. Although problems still exist in relating predictions to all the experimental data, they have helped to identify exciton features near to and above the first main absorption peak and other optoelectronic features. A good deal of effort has now gone into the study of the III-V systems such as InP, InAs, GaAs, and GaN QDs, as well as on porous Si (PS) and Si and Ge dots. This has been largely driven by the possibility that devices such as lasers, LEDs and devices depending on single electron transport and tunnelling might be developed, an area where there is significant technological potential. For dots such as InAs etc prepared by the SK method, where there is a mismatch in lattice parameters between the InAs and the substrate such as GaAs, the dots tend to have a roughly pyramidal shaped profile, and the dot also sits on a thin InAs wetting layer. Both 2d and 3d ordered arrays of QDs can be formed using this procedure. The photoluminescence (PL) efficiency for such systems can be unexpectedly high, and there have been attempts to explain this effect as being due to the avoidance of the so-called 'phonon bottleneck' by Auger type transitions, but this is still a controversial matter. Other phenomena that are discussed include: (1) exciton- phonon coupling interactions, particularly as applied to QDs such as those formed from CuCl, CuBr, PbS, etc.; (2) coupled QDs for which dot- dot interactions need to be considered; (3) porous Si (PS), a system of considerable interest since the observation of strong PL emission features in the PL spectra by Canham in 1990, even though Si has an indirect gap, and on the practical side there has been much effort in the development of devices such as lasers, LEDs and other electroluminescence (EL) devices, and more recently for biological and medical applications, where PS, because of its porous structure, can be a host lattice for biochemical compounds in a manner similar to some zeolites. However the structure of PS is rather complex, and filaments, embryonic Si dots, as well as well formed dots, oxide interfaces of uncertain composition, and compounds containing hydrogen may all be present, and this makes it difficult to make reasonable assignments to some of the optical features present in the spectra. (4) Type II QDs that concern spatially indirect systems, and this can refer to both space and wave vector k. Instead of the electron e and hole h for an e- h pair (exciton) both residing in dot, for most of the Type II systems the h resides in the dot while the e is in the matrix in which the dots are distributed or at the interfaces. The systems considered depend on the band of sets, and include combinations such as GaAs- AlAs and CdTe- HgTe etc. (5) Hydrogenic-type donors in semiconductor QDs. (6) Excitons, biexcitons, charged excitons (both positive and negative), or trions. (7) Quantum dot- quantum well (QD-QW) combinations, also described as thin film-QD or core- shell composites, for example CdS QDs coated with a thin layer of the smaller band gap semiconductor HgS acting as a QW followed by a further CdS coating or 'clad' or 'shell'. (8) QD- conjugated organic polymer composites, a topic developed by Alivisatos, Greenham and Bawendi and their colleagues in the mid nineties, where the polymer acts as a hole conductor in an EL or LED type of device, where the wavelength of the emitted light due to e- h recombination that occurs preferably near the interface, can be varied by altering the QD radius. The possible formation of hybrid Mott-Wannier and Frenkel excitons is also briefly considered. (9) The variation of the QD dielectric constant with QD size E ₂(R), has been considered by several investigators, their calculations suggest that the dielectric constant decreases substantially as R is reduced. This effect has been ignored in many contributions even though E ₂ enters into the equations dealing with QSE or quantum size effects, a _B, E _b, and oscillator strengths (OS), and its omission will influence the calculated estimates for these quantities. (10) Finally, single electron transport and tunnelling in single and coupled QDs, and the Coulomb blockade (CB) are considered, but only in outline since this is a large problem, but it is clearly an important topic particularly in connection with the development of computing and information processing systems.     

SPLITTING SCHEMES FOR A NAVIER-STOKES-CAHN-HILLIARD MODEL FOR TWO FLUIDS WITH DIFFERENT DENSITIES

In this work, we focus on designing efficient numerical schemes to approximate a ther- modynamically consistent Navier-Stokes/Cahn-Hilliard problem given in [3] modeling the mixture of two incompressible fluids with different densities. The model is based on a diffuse-interface phase-field approach that is able to describe topological transitions like droplet coalescense or droplet break-up in a natural way. We present a splitting scheme, decoupling computations of the Navier-Stokes part from the Cahn-Hilliard one, which is unconditionally energy-stable up to the choice of the potential approximation. Some nu- merical experiments are carried out to validate the correctness and the accuracy of the scheme, and to study the sensitivity of the scheme with respect to different physical pa- rameters.     

Phase-field modeling of faceted growth in solidification of alloys

A regularization of the surface tension anisotropic function used in vapor-liquid-solid nanowire growth was introduced into the quantitative phase-field model to simulate the faceted growth in solidification of alloys. Predicted results show that the value of δ can only affect the region near the tip, and the convergence with respect to δ can be achieved with the decrease of δ near the tip. It can be found that the steady growth velocity is not a monotonic function of the cusp amplitude, and the maximum value is approximately at ε=0.8 when the supersaturation is fixed. Moreover, the growth velocity is an increasing function of supersaturation with the morphological transition from facet to dendrite.     

Fe-Cr合金辐照空洞微结构演化的相场法模拟

Fe-Cr合金作为包壳材料在高温高辐照强度等极端环境下服役,产生空位和间隙原子等辐照缺陷,辐照缺陷簇聚诱发空洞、位错环等缺陷团簇,引起辐照肿胀、晶格畸变,导致辐照硬化或软化致使材料失效.理解辐照缺陷簇聚和长大过程的组织演化,能更有效调控组织获得稳定服役性能.本文采用相场法研究Fe-Cr合金中空洞的演化,模型考虑了温度效应对点缺陷的影响以及空位和间隙的产生和复合.选择400—800 K温度区间、0—16 dpa辐照剂量范围的Fe-Cr体系为对象,研究在不同服役温度和辐照剂量下的空位扩散、复合和簇聚形成空洞的过程.在400—800 K温度区间,随着温度的升高,Fe-Cr合金空洞团簇形核率呈现出先升高后下降的趋势.考虑空位与间隙的重新组合受温度的影响可以很好地解释空洞率随温度变化时出现先升高后降低的现象.由于温度的变化将影响Fe-Cr合金中原子离位阀能,从而影响产生空位和间隙原子.同一温度下,空洞半径和空洞的体积分数随辐照剂量的增大而增大.辐照剂量的增大,级联碰撞反应加强,空位与间隙原子大量产生,高温下空位迅速的扩散聚集在Fe-Cr合金中将形成更多数量以及更大尺寸的空洞.     

等温凝固多晶粒生长相场法模拟

采用Kim模型，利用耦合溶质场的相场模型对Al-2-mole-Cu合金等温凝固过程中多晶粒相互影响下枝晶的生长过程进行数值模拟，为了提高计算效率，采用差分去实现宏微观场之间的耦合.研究了不同过冷度对多晶粒枝晶形貌和溶质分布的影响，结果表明：成分过冷对枝晶生长速度和溶质分配有着重大的影响，溶质元素Cu在固液界面前沿重新分布，结果导致实际热过冷减小，进而影响枝晶的生长和溶质向外层的扩散，致使相互接触的枝晶产生萎缩而其余没有受到抑制的枝晶生长方向产生择优现象. 关键词： 相场法 模拟 择优生长 等温凝固 二元合金     

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.     

二元合金多晶粒的枝晶生长的等温相场模型

基于Ginzburg-Landau理论和单晶粒的枝晶生长模型,发展了一个单相场控制的多个晶粒的枝晶生长模型. 采用相场和溶质场耦合的方法,以Al-2%Cu合金为例模拟了二元合金等温凝固过程中多个晶粒的生长过程. 结果表明,这个模型的计算结果展现了多个晶粒枝晶的竞争生长,能较真实的再现凝固过程中的枝晶的生长过程. 关键词： 相场法 多晶粒 等温凝固 二元合金     

多晶材料晶粒生长粗化过程的相场方法模拟

基于采用晶体有序化程度参量ψ和晶体学取向θ来表示多晶粒结构的相场模型,利用自适应有限元方法模拟了多晶材料等温过程中的晶粒粗化现象.模拟结果显示,在曲率作用下,通过晶界迁移弯曲晶界逐渐平直化,小晶粒逐渐被大晶粒吞并,当晶界之间的取向差较小时,满足一定能量和几何条件的两晶粒在界面能作用下会发生转动,合并为单个晶粒.模拟结果与实验结果符合较好.因此,该相场模型可以很好地用来模拟固态相变中多晶材料的生长粗化等现象. 关键词： 相场 晶界迁移 晶粒转动 粗化     

Phase-field simulation of the coupled evolutions of grain and twin boundaries in nanotwinned polycrystals

Nanotwinned polycrystals exhibit an excellent strength-ductility combination due to nanoscale twins and grains. However, nanotwin-assisted grain coarsening under mechanical loading reported in recent experiments may result in strength drop based on the Hall-Petch law. In this paper, a phase-field model is developed to investigate the effect of coupled evolutions of twin and grain boundaries on nanotwin-assisted grain growth. The simulation result demonstrates that there are three pathways for coupled motions of twin and grain boundaries in a bicrystal under the applied loading, dependent on the amplitude of applied loading and misorientation of the bicrystal. It reveals that a large misorientation angle and a large applied stress promote the twinning-driven grain boundary migration. The resultant twin-assisted grain coarsening is confirmed in the simulations for the microstructural evolutions in twinned and un-twinned polycrystals under a high applied stress.