Kinetic Monte Carlo simulation of strained heteroepitaxial growth with intermixing

An efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic Monte Carlo is presented. The model used is based on a solid-on-solid bond counting formulation in which elastic effects are incorporated using a ball and spring model. While idealized, this model nevertheless captures many aspects of heteroepitaxial growth, including nucleation, surface diffusion, and long-range effects due to elastic interaction. The algorithm combines a fast evaluation of the elastic displacement field with an efficient implementation of a rejection-reduced kinetic Monte Carlo based on using upper bounds for the rates. The former is achieved by using a multigrid method for global updates of the displacement field and an expanding box method for local updates. The simulations show the importance of intermixing on the growth of a strained film. Further, the method is used to simulate the growth of self-assembled stacked quantum dots.     

弯曲衬底上应变异质外延薄膜形态失稳的相场模拟

本文旨在研究弯曲衬底上应变异质外延薄膜的表面非线性演化行为,研究采用了基于Eshelby等效方法的相场微弹性模型来模拟二维应变 薄膜/衬底系统的形态失稳。建立了关于等效特征应变和长程序参量的自由能泛函,数值求解了时间相关的Ginzburg-Landau动力学方程。系统自由能包括化学能,弹性应变能以及薄膜、衬底与真空相两两之界面能。跟踪了全时的形态演化过程,给出了指定时刻的量子点形态轮廓图。结果表明,量子点倾向于沉积在弯曲衬底的波谷处,波谷处是能量有利位置,量子点在此处比在波峰处更加稳定。本文所做的相场模拟可以用来预测量子点形成的轮廓、尺寸和位置,可以为控制和生成周期性自组装表面纳米结构提供理论指导。     

Atomic resolution in noncontact AFM by probing cantilever frequency shifts

Rutile TiO2 （001） quantum dots （or nano-marks） in different shapes were used to imitate uncleaved material surfaces or materials with rough surfaces. By numerical integration of the equation of motion of cantilever for silicon tip scanning along the [110] direction over the rutile TiO2 （001） quantum dots in ultra high vacuum （UHV）, scanning routes were explored to achieve atomic resolution from frequency shift image. The tip-surface interaction forces were calculated from Lennard-Jones （12-6） potential by the Hamaker summation method. The calculated results showed that atomic resolution could be achieved by frequency shift image for TiO2 （001） surfaces of rhombohedral quantum dot scanning in a vertical route, and spherical cap quantum dot scanning in a superposition route.2007 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V.     

Atomic-scale finite element analysis of vibration mode transformation in carbon nanorings and single-walled carbon nanotubes

Atomic-scale finite element analyses show that 2:1 internal resonance mechanism exists in a range of single-walled carbon nanorings (10–60). When an initial radial breathing mode (RBM) vibration with sufficiently high velocity is imposed to a nanoring, circumferential flexural modes (CFMs) can be excited after a period of RBM-dominated vibration. Then, mode transformations between RBM and the excited CFMs can be observed in the subsequent vibration process. When single-walled carbon nanorings are assembled to make double- or triple-walled carbon nanorings, the 2:1 internal resonance may change to 1:1 internal resonance in a specific ring due to the strong interactions between these nanorings. Furthermore, mode transformations between RBM and the excited CFMs can become unstable in a specific ring if the excited CFMs in neighbouring layer rings are not symmetrically matching between each other. 2:1 internal resonance is also shown in selected armchair single-walled carbon nanotubes except in a special case (armchair (9, 9)), in which 1:1 internal resonance occurs.     

多功能室温液态金属在不同摩擦副条件下的润滑性能研究

室温液态金属是一类物理化学行为非常独特的新型功能物质,其诸多性能和用途尚未可知.本论文中初步探索了Ga_(75.5)In_(24.5)和Ga_(65)In_(22)Sn_(13)两种液态金属润滑特性与摩擦配副选材间的关系.结果表明:镓基液态金属在钢及陶瓷表面的润湿性能不佳,接触角大于120°.采用AISI 52100钢和陶瓷配副时,镓基液态金属表现出良好的润滑特性和极佳的承压能力;采用AISI 52100钢自配副时,镓基液态金属的减摩效应不明显,但能较大幅度降低材料的磨损率;采用陶瓷-陶瓷配副时,镓基液态金属几乎没有润滑作用.镓基液态金属润滑特性差异与其在材料表面的摩擦化学反应有关.     

Further consideration of the shape-factor relationship for turbulent boundary layers

The lag-entrainment predictive scheme developed by Green et al. has been modified to include the pressure-gradient parameter Π₁. In the original model suggested by Green et al. the mass-flow shape factor H₁ is related to the common shape factor H, H₁ = f(H). In the present model H₁ is related to H, Reynolds number based on the local momentum thickness θ, and Π₁; thus H₁ = f(H, R_eθ, Π₁). The modified formula for H₁, is introduced into the original lag-entrainment integral model. Calculations are made to examine the present model for the predictions of the development of boundary layers approaching separation studied experimentally by the authors. Slightly improved predictions are obtained using the model developed by El Telbany et al. However, the present model proved to give an improved representation of the development of wall shear stress in cases the two-equation turbulence model proved to be unsuccessful.     

单模大扰动的Richtmyer-Meshkov不稳定性

采用高精度的多介质Ghost-Fluid方法,对马赫数为1.15的激波分别作用于单模大扰动Air-CO2、Air-SF6、Air-N2和Air-He界面后的Richtmyer-Meshkov不稳定现象进行了数值研究,得到了不同时刻扰动界面的演化图像,给出了流场的密度等值线和密度纹影图,同实验结果吻合较好。给出了界面的扰动增长随时间变化的情况,并同理论模型进行了对比。对激波从轻气体进入重气体的情况,扰动增长可采用Sadot模型描述线性阶段和早期非线性阶段;对于弱激波同密度接近的气体界面的相互作用,线性阶段时间较长,可用线性模型描述。     

Energetics of misfit dislocation dipoles in anisotropic epitaxial films with nanoscale compositional modulation

The elastic strain and stress fields associated with nanoscale compositional modulation in an anisotropic epitaxial film on an anisotropic substrate are obtained by using Stroh formalism and the Eshelby-type inclusion method. The composition of the epitaxial film is considered to periodically fluctuate in a surface soft mode, with the amplitude of the composition modulation maximal near the growing surface and decreasing exponentially into the film. It has been experimentally observed that the composition modulation affects the formation of a new type of crystal defects, i.e., misfit dislocation dipoles, in III–V compound semiconductor materials. The formation energy of a misfit dislocation dipole under the elastic fields due to the composition modulation is calculated in this study. It is composed of the core and self energies of two dislocations, the interaction energy between two dislocations, and the interaction energies between the composition modulation and two dislocations. Numerical calculations are performed for a dislocation dipole in a lattice-matched Ga_0.5In_0.5P film on a GaAs substrate.     

Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part II. Application to InxGa1−xAs/InP system

Cracking phenomena in tensile-strained In_xGa_1?xAs epitaxial film on an InP substrate are analyzed via the formulation given in Part I [Lee, S., Choi, S.T., Earmme, Y.Y., 2006. Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part I. Mathematical formulation. International Journal of Solids and Structures 43, 3401–3413], where the solution for a dislocation in an anisotropic trimaterial is used as a fundamental solution and the crack is modeled by the continuous distribution of dislocations. Misfit strains and stresses are evaluated as a function of indium content x in an In_xGa_1?xAs/InP system. A single crack and periodic cracks, respectively, induced by the misfit stresses are considered. The crack opening profile, the crack mouth displacement, and the energy release rate as a function of the crack length are obtained. The critical conditions for a single crack and periodic cracks, respectively, are thus obtained, and are found to depend on the film thickness, the crack length, and the period of the cracks. The results of these analyses are also compared with published data obtained from experiments.     

Theoretical confirmation of the crystallization of a compound alloy using the AHP crystal growth method

The crystallization of In_xGa_1−xSb for $x=0.06$ by the AHP-method (Axial Heat flux, close to the Phase interface) is considered. Heavy indium is rejected during crystal growth close to the interface. Indium significantly decreases the crystallization temperature, and has an influence on the melt convection. The AHP-heater serves as a partition; due to this partition a small well-mixed liquid zone with high In concentration exists and causes a stable crystal growth with high composition after the crucible is moved down. The grown crystal is very homogeneous. Numerical modelling has also been performed, using finite difference schemes. To cite this article: M. Marchenko, C. R. Mecanique 335 (2007).     

A new ALS model for dilute polymer solutions in flows with strong shear components

Ghosh et al. (J Rheol 46:1057–1089, 2002) developed a new model for dilute polymer solutions in flows with strong extensional components. The model based on introducing an adaptive length scale (ALS) as an internal variable was developed to reproduce the fine-scale physics of the Kramers chain. The ALS model describes the polymer molecule as a set of identical segments in which each segment represents a fragment of the polymer that is short enough so that it can sample its entire configuration space on the time scale of an imposed deformation and therefore stretch reversibly. As the molecule unravels, the number of the segments decreases, but the maximum length of each segment increases, so that the constant maximum contour length of the molecule is preserved. Though the single-segment-based ALS model accounts for the orientability of the polymer molecules, it cannot describe the internal motions of the molecules due to the lack of internal nodes. Hence, in this work we consider the more realistic chain (multi-segments) model composed of N _seg springs connected linearly. The model presented in this work is an extension of the ALS model developed by Ghosh et al. (J Rheol 46:1057–1089, 2002). We demonstrate that the ALS varies with the flow strength. Specifically, it is found that as the flow strength increases, the ALS decreases. This implies that as the flow strength increases, the polymer molecule is required to divide into finer and finer segments such that each segment can locally equilibrate with the imposed flow. However, there is a critical number of such subdivisions beyond which further subdivision of the polymer molecule is not required to capture the polymer dynamics for a given flow strength. Both shear viscosity and first normal stress coefficient predictions from ALS model show shear thinning behavior with Weissenberg number. In weak flows, the ALS model and the finitely extensible non-linear elastic model exhibit the same behavior.     

A Comparison of Nonlinear Water Wave Models

We compare the numerical evolution of one-dimensional gravity waves in response to a traveling surface pressure pulse using a highly accurate boundary integral method and two relatively efficient approximate models (West et al. and Benney–Luke). In both water of finite-depth and in the deep-water limit, the steady state effect of the decaying pressure ramp is to create a profile which approximates a Stokes wave. Moreover, the transient surface profile appears to evolve through a series of Stokes waves of time-varying amplitude. Results show all three models yield similar predictions for lower amplitude waves, while the West et al. and boundary integral predictions differ from the Benney–Luke model at higher amplitudes.     

An explicit algebraic Reynolds stress and heat flux model for incompressible turbulence: Part II Buoyant flow

This paper presents a derivation of an explicit algebraic model for two-dimensional (2-D) buoyant flows. It is an extension of the work reported in Part I (So et al. [27]). The tensor representation method of Jongen and Gatski [14] is extended to derive an explicit algebraic Reynolds stress model (EASM) for 2-D buoyant flow invoking the Boussinesq approximation. The projection methodology is further extended to treat the heat flux transport equation in the derivation of an explicit algebraic heat flux model (EAHFM) for buoyant flow. Again, the weak equilibrium assumption is invoked for the scaled Reynolds stress and scaled heat flux equation. An explicit algebraic model for buoyant flows is then formed with the EASM and EAHFM. From the derived EAHFM, an expression for the thermal diffusivity tensor in buoyant shear flows is deduced. Furthermore, a turbulent Prandtl number (Pr_T) for each of the three heat flux directions is determined. These directional Pr_T are found to be a function of the gradient Richardson number. Alternatively, a scalar Pr_T can be derived; its value is compared with the directional Pr_T. The EASM and EAHFM are used to calculate 2-D homogeneous buoyant shear flows and the results are compared with direct numerical simulation data and other model predictions, where good agreement is obtained. Dedicated to the memory of the late Professor Charles G. Speziale of Boston University     

Remarks on orthogonal superposition of small amplitude oscillations on steady shear flow

The paper demonstrates that experimental data (Simmons, 1968) for orthogonal superposition of small amplitude oscillations on steady shear flow, coincide well enough with the theoretical predictions (Leonov et al., 1976) of simple multi-modal version of Leonov model (Leonov, 1976, 1987; Leonov et al., 1976). It was also shown that the recent theoretical calculations (Wong and Isayev, 1989) of the problem, which used the same Leonov model, are wrong.     

Vortex rings interacting with a wall

Accurate numerical simulations of vortex rings impinging on flat boundaries have revealed the same features observed in the experiment of Walkeret al. (1987). They observed atRe _v >1250 the formation of azimuthal instabilities in the secondary ring during its compression within the primary ring. In the present numerical simulation the number of waves agrees very well with those observed in the experiment. The distributions of the vorticities together with the distribution of each term in the vorticity equations give insights on the formation of azimuthal instabilities.     

Numerical confirmation of the hysteresis phenomenon in the regular to the Mach reflection transition in steady flows

Numerical calculations based on the Navier-Stokes equations are carried out to investigate the reflection of shock waves over straight reflecting surfaces in steady flows. The results for a flow Mach number of M₀=4.96 confirm the recent experimental findings of Chpoun et al. (1995) concerning the transition from regular to Mach reflection. Numerical calculations as well as experimental results show a hysteresis phenomenon during this transition and the regular reflection is found to be stable in the dual-solution domain in which theoretically both regular and Mach reflection wave configurations are possible.     

The structure of multidimensional strained flames under transcritical conditions

Strained flames are commonly used to study the structure of reactive layers and describe the local properties of turbulent combustion. This model is attractive because constant strain rate flames only depend on a transverse coordinate and can be treated as a one-dimensional problem. This configuration is considered in a multidimensional context in which the strained flow is obtained by two counterflowing streams of reactants. It is used to examine the structure of transcritical strained flames in which one or two reactants are injected at a high pressure exceeding the critical value while their temperature is below the critical value. Calculations are carried out in a two-dimensional domain to test numerical models developed for multidimensional simulations and test thermodynamic and transport models devised to deal with high pressure real gas effects. Multidimensional strained flame calculations carried out in this study serve to check the validity of a new version of a Navier–Stokes flow solver (AVBP) conceived to deal with transcritical combustion of interest to liquid propellant rocket applications. This article describes the basic elements of such simulations and discusses results of calculations. It is shown that the calculated multidimensional strained flames have the expected features in terms of structure and response to the imposed strain rate. To cite this article: L. Pons et al., C. R. Mecanique 337 (2009).     

Modelling the Effect of Surface Tension on the Onset of Natural Convection in a Saturated Porous Medium

Abstract. Comments are made about limitations of the model proposed by Hennenberg et al. for convection in a porous medium layer driven by the Marangoni effect, and an alternative model for this problem is presented. The predictions of the two models are significantly different.     

A new low-Reynolds-number k--fμ model for predictions involving multiple surfaces

A new k--f_μ turbulence model is proposed, in which the near-wall effect without reference to distance and the non-equilibrium effect are incorporated. In this model, the non-local near-wall effect in a general coordinate system is taken into account by the f_μ equation, and the local anisotropy in strongly strained turbulent flows in introduced in the equation. The near-wall characteristics of the present model are ascertained from the DNS data. Also, the validation is explored to separate and reattaching flows. The backward-facing step flow is selected for benchmark test of the present model and the response of the model to flows involving complex surfaces is assessed. The predictions of the present model are checked with the existing measurements. The model performance is shown to be generally satisfactory.