One-dimensional dynamics of nano-scale oxidation

A continuum model is proposed to describe the process of scanned probe oxidation in the presence of a thin water layer on the surface of a substrate. The model describes the electric field and ion transport in both the liquid and the oxide layers and incorporates the reaction mechanism at the substrate/oxide interface. Further, the influence of the space charge due to ions trapped near the substrate/oxide interface is taken into account.Separation of time scales for the chemical reactions and ion transport as well as the asymptotic limit in terms of a small aspect ratio of the oxide layer are used to reduce the complex system of partial differential equations to a one-dimensional system of ordinary differential equations. The analytical solution of the reduced system results in the evolution equation for the oxide thickness. Numerical simulations of the evolution equation predict features of oxide growth that qualitatively agree with the experimental observations. A parametric study is conducted to determine the influence of the key operating and material parameters on the thickness of the oxide, the electric field, and ion concentration in the system.     

固体表面液滴铺展与润湿接触线的移动分析

液滴在固体表面上的铺展行为与润湿特性对许多工业生产过程的研究具有重要意义.根据液滴在光滑表面上的受力情况,建立了液滴平壁铺展的动力学模型.应用润滑近似方法和二维Navier-Stokes方程,建立了液滴沿理想表面铺展的动量和连续性方程.根据建立的方程,应用数值解法求解并详细分析了液滴在铺展过程中膜厚、接触线铺展半径以及铺展速度随时间的变化关系.研究结果表明:液滴的铺展过程可分为扩展和收缩两个阶段,铺展过程伴随着表面能、动能以及各种势能的相互转化,液滴最终的铺展半径大小由固体基面固有的润湿特性所决定;液滴在铺展过程中出现的"坍塌效应"与弯曲液面处的Laplace压力差有关;铺展半径随时间变化的标定律近似满足"1/7"次方标度律.     

Effect of longitudinal electric field on capillary instability of a thin axisymmetric layer of liquid dielectric coating a dielectric fiber

The flow of a viscous dielectric liquid surrounded with a gas is investigated in the process of capillary disintegration of a thin axisymmetric liquid layer on an undeformable cylindrical dielectric fiber in a uniform electric field is investigated. An asymptotic analysis of the system of equations and hydrodynamic boundary conditions written with allowance for surface ponderomotive forces is carried out for the case when the average thickness of the layer is much smaller than the radius of the fiber cross section. The problem of the transition of the liquid configuration from the state of a stationary cylindrical layer to the hydrodynamic state in the form of a regular sequence of drops is formulated. In this formulation, a nonlinear parabolic equation that describes the evolution of the local thickness of the layer on the time interval to the instant of drop formation is derived. The effect of the key parameters on the capillary instability is analyzed based on the linearized version of the resultant equation and the linearized electrostatic problem of calculating the field perturbations.     

SH surface acoustic wave propagation in a cylindrically layered piezomagnetic/piezoelectric structure

SH surface acoustic wave (SH-SAW) propagation in a cylindrically layered magneto-electro-elastic structure is investigated analytically, where a piezomagnetic (or piezoelectric) material layer is bonded to a piezoelectric (or piezomagnetic) substrate. By means of transformation, the governing equations of the coupled waves are reduced to Bessel equation and Laplace equation. The boundary conditions imply that the displacements, shear stresses, electric potential, and electric displacements are continuous across the interface between the layer and the substrate together with the traction free at the surface of the layer. The magneto-electrically open and shorted conditions at cylindrical surface are taken to solve the problem. The phase velocity is numerically calculated for different thickness of the layer and wavenumber for piezomagnetic ceramics CoFe₂O₄ and piezoelectric ceramics BaTiO₃. The effects of magnetic permeability on propagation properties of SH-SAW are discussed in detail. The distributions of displacement, magnetic potential and magneto-electromechanical coupling factor are also figured and discussed.     

Size and morphological effect of Au–Fe3O4 heterostructures on magnetic resonance imaging

In this paper, we analyse the melting of a spherically symmetric nanoparticle, using a continuum model which is valid down to a few nanometres. Melting point depression is accounted for by a generalised Gibbs–Thomson relation. The system of governing equations involves heat equations in the liquid and solid, a Stefan condition to determine the position of the melt boundary and the Gibbs-Thomson equation. This system is simplified systematically to a pair of first-order ordinary differential equations. Comparison with the solution of the full system shows excellent agreement. The reduced system highlights the effects that dominate the melting process and specifically that rapid melting is expected in the final stages, as the radius tends to zero. The results agree qualitatively with limited available experimental data.     

Peculiarities of evaporation of a thin water layer in the presence of a solvable surfactant

Evaporation of a thin layer of a polar liquid (water) having a free surface and located on a solid substrate is investigated. A solvable surfactant is placed on the free liquid-vapor interface. The surface tension is a linear function of the surface concentration of the surfactant. The surface energy of the solid-liquid contact line is a nonmonotonic function of the layer thickness and is the sum of the Van der Waals interaction and the specific interaction of the double electric layer on the interface. The effect of the solvable surfactant on the dynamics and stability of the propagation of the evaporation front in the thin liquid film is analyzed in the long-wave approximation in the system of Navier-Stokes equations.     

任意半径圆形电流在径向成层介质中产生的电磁场

采用递推矩阵方法计算径向成层介质中的二维Green函数.根据层界面处电场和磁场的连续性条件得到确定待定系数的矩阵方程组并通过递推方法快速求解.只需改变方程组中源项元素的位置,就可以方便地得到当源点和场点在任意层时的二维Green函数,并进而得到具有任意半径的圆形电流在介质中产生的电磁场.本文给出的Green函数具有表达方式简洁的优点.     

A Thin Liquid Film and Its Effects in an Atomic Force Microscopy Measurement

Recently, it has been observed that a liquid film spreading on a sample surface will significantly distort atomic force microscopy （AFM） measurements. In order to elaborate on the effect, we establish an equation governing the deformation of liquid film under its interaction with the AFM tip and substrate. A key issue is the critical liquid bump height yoc, at which the liquid film jumps to contact the AFM tip. It is found that there are three distinct regimes in the variation of yoc with film thickness H, depending on Hamaker constants of tip, sample and liquid. Noticeably, there is a characteristic thickness H^＊ physically defining what a thin film is; namely, once the film thickness H is the same order as H^＊, the effect of film thickness should be taken into account. The value of H^＊ is dependent on Hamaker constants and liquid surface tension as well as tip radius.     

Field extraction of ions from liquid solutions with the use of polymer track membranes

The general principles of the electric field assisted ion evaporation in the membrane ion source are considered. In the ion source, the liquid sample under investigation is placed in narrow channels of a polymer track membrane, which separates the liquid sample at atmospheric pressure from the vacuum chamber. Stability of the liquid at strong electric fields is provided by a choice of the diameters of channels and the liquid–polymer contact angle. The electric charge on the vacuum–polymer interface is of great importance for creation of the strong electric field near the liquid–vacuum interface. Such a conclusion is made from the computations of the electric field in the framework of the model developed. The mechanism of the electric field assisted evaporation of ions is discussed to explain the observed mass spectra for the ions extracted from liquid.     

The effect of subsurface doping on gate oxide charging damage

The effect of wells and substrate type on gate oxide charging damage during plasma processing, and more specifically plasma immersion ion implantation, is modeled. The simulation combines the equations governing the plasma currents and integrated circuit device models to determine the gate oxide stressing voltage during implantation. Depending on the substrate type and the surface potential (V_s), a depletion region may exist, reducing the gate oxide voltage, and hence the gate oxide damage. In addition, well structures, by the nature of their capacitance, modulate V_s, altering the oxide stressing voltage. For most PIII implant conditions, gate oxides with p-type channel doping will be damaged more than those oxides with n-type channel doping. Experimental results confirm the substrate and well effects on plasma charging damage     

Unified model equations for microstructure evolution

Unified model equations hidden in microstructure evolution are discovered in this paper. The governing equations in Lifshitz-Slyozov-Wagner theory, and diffusion screening theory are derived with some approximations from the unified model equations. The governing equations in multiparticle diffusion simulation and phase-field simulation in microstructure evolution are also derived from the unified model equations. The advantages and limitations for different theories and simulations in microstructure evolution are compared in detail. This comparison can guide scientists to select computational tools for their needs in microstructure evolution. The unified model equations can be applied in many new technological fields, such as self-assembly in nanoscience.     

高功率离子束辐照膜基双层靶温度场的数值研究

采用TRIM程序模拟高功率离子束与铝基钛膜双层靶的相互作用.计算了束流在靶材内的能量沉积及分布情况,并以此沉积能量为热源项,采用有限差分方法求解非线性热传导方程,得到了温度场的分布规律,分析了不同离子流密度对界面物质状态的影响.结果表明,离子束电流密度在100—200 A/cm²之间取值时,脉冲结束后界面处两种物质均达到熔融状态.     

The Electrodeless Arc with Radial Inflow

An energy balance analysis has been performed for a confined cylindrical arc column heated inductively by high-frequency fields. The analysis includes the convective energy transport due to a radial inflow in addition to the radiative and conductive transport considered in the Ellenbaas-Heller equation. The resulting non-linear, two-point boundary value equations were solved numerically. Calculations were performed for an argon arc operating at atmospheric pressure using experimentally determined transport properties. Temperature profiles were found to be in better agreement with measured values, when radial inflow was included. There was no indication that the arc attained some natural diameter based on a specific plasma radius to skin depth ratio.     

New Concepts from the Evans Unified Field Theory. Part One: The Evolution of Curvature,Oscillatory Universe Without Singularity,Causal Quantum Mechanics,and General Force and Field Equations

No Heading The Evans field equation is solved to give the equations governing the evolution of scalar curvature R and contracted energy-momentum T. These equations show that R and T are always analytical, oscillatory, functions without singularity and apply to all radiated and matter fields from the sub-atomic to the cosmological level. One of the implications is that all radiated and matter fields are both causal and quantized, contrary to the Heisenberg uncertainty principle. The wave equations governing this quantization are deduced from the Evans field equation. Another is that the universe is oscillatory without singularity, contrary to contemporary opinion based on singularity theorems. The Evans field equation is more fundamental than, and leads to, the Einstein field equation as a particular example, and so modifies and generalizes the contemporary Big Bang model. The general force and conservation equations of radiated and matter fields are deduced systematically from the Evans field equation. These include the field equations of electrodynamics, dark matter, and the unified or hybrid field.     

液滴撞击液膜过程的格子Boltzmann方法模拟

本文采用格子Boltzmann方法对液滴撞击液膜过程进行了研究, 主要考察了雷诺数(Re)、韦伯数(We)、相对液膜厚度 (h) 以及表面张力 (σ) 等物理参数对界面运动过程的影响. 首先, 随着Re数和We数的增加, 可以明显观察到液滴撞击液膜过程中形成的皇冠状水花以及卷吸现象; 当Re数较大时, 液体会发生飞溅, 由液体飞溅形成的小液滴则会继续下落, 并与液膜再次发生碰撞. 其次, 当相对液膜厚度较小时, 液滴撞击液膜并最终导致液膜断裂; 然而随着相对液膜厚度的增大, 尽管撞击过程溅起的液体会越来越多, 但是液膜并不会发生断裂. 再次, 随着表面张力的增大, 界面变形阻力增大, 撞击过程中产生的界面形变也逐渐减弱. 最后还发现皇冠(由液滴溅起形成)半径r 随时间满足r/(2R) ≈ α√Ut/(2R), 这一结果与已有结论是一致的.     

Scaling effects of single-event gate rupture in thin oxides

The dynamics of the excess carriers generated by incident heavy ions are considered in both SiO2 and Si substrate. Influences of the initial radius of the charge track, surface potential decrease, external electric field, and the LET value of the incident ion on internal electric field buildup are analyzed separately. Considering the mechanisms of recombination, impact ionization, and bandgap tunneling, models are verified by using published experimental data. Moreover, the scaling effects of single-event gate rupture in thin gate oxides are studied, with the feature size of the MOS device down to 90 nm. The walue of the total electric field decreases rapidly along with the decrease of oxide thickness in the first period （1 2 nm to 3.3 nm）, and then increases a little when the gate oxide becomes thinner and thinner （3.3 nm to 1.8 nm）.     

A phase field method for simulating morphological evolution of vesicles in electric fields

A phase field method is developed to investigate the morphological evolution of a vesicle in an electric field, taking into account coupled mechanical and electric effects such as bending, osmotic pressure, surface tension, flexoelectricity, and dielectricity of the membrane. The energy of the system is formulated in terms of a continuous phase field variable and the electric potential. The governing equations of the phase field and the electric field are solved using the Galerkin weighted residual approach. The validation and robustness of the algorithm are verified by direct comparisons of the obtained numerical solutions with relevant experimental results. The morphological evolution of an axisymmetric vesicle under an electric field is studied in detail. The results demonstrate that the present method can simulate complex morphological evolutions of vesicles under coupled mechanical–electrical fields.     

An interface capturing method for the simulation of multi-phase compressible flows

A novel finite-volume interface (contact) capturing method is presented for simulation of multi-component compressible flows with high density ratios and strong shocks. In addition, the materials on the two sides of interfaces can have significantly different equations of state. Material boundaries are identified through an interface function, which is solved in concert with the governing equations on the same mesh. For long simulations, the method relies on an interface compression technique that constrains the thickness of the diffused interface to a few grid cells throughout the simulation. This is done in the spirit of shock-capturing schemes, for which numerical dissipation effectively preserves a sharp but mesh-representable shock profile. For contact capturing, the formulation is modified so that interface representations remain sharp like captured shocks, countering their tendency to diffuse via the same numerical diffusion needed for shock-capturing. Special techniques for accurate and robust computation of interface normals and derivatives of the interface function are developed. The interface compression method is coupled to a shock-capturing compressible flow solver in a way that avoids the spurious oscillations that typically develop at material boundaries. Convergence to weak solutions of the governing equations is proved for the new contact capturing approach. Comparisons with exact Riemann problems for model one-dimensional multi-material flows show that the interface compression technique is accurate. The method employs Cartesian product stencils and, therefore, there is no inherent obstacles in multiple dimensions. Examples of two- and three-dimensional flows are also presented, including a demonstration with significantly disparate equations of state: a shock induced collapse of three-dimensional van der Waal’s bubbles (air) in a stiffened equation of state liquid (water) adjacent to a Mie-Grüneisen equation of state wall (copper).     

Nanoparticle transport effect on magnetohydrodynamic mixed convection of electrically conductive nanofluids in micro-annuli with temperature-dependent thermophysical properties

This is a numerical investigation of nanoparticle transport effect on magnetohydrodynamic mixed convective heat transfer of electrically conductive nanofluids in micro-annuli with temperature-dependent thermophysical properties. The modified Buongiorno's non-homogeneous model is applied for the nanoparticle-fluid suspension to simulate the migration of nanoparticles into the base fluid, originating from the thermophoresis (nanoparticle migration because of temperature gradient) and Brownian motion (nanoparticle slip velocity because of concentration gradient). Due to surface roughness at the solid–fluid interface in micro-annuli, the wall surfaces are subjected to a linear slip condition to assess the non-equilibrium region near the interface. The fluid flow has been assumed to be fully developed, and the governing equations including continuity, momentum, energy, and nanoparticle transport equation are reduced to a system of ordinary differential equations, before they have been solved numerically. The results are presented with and without considering the dependency of thermophysical properties upon the temperature. It is indicated that ignoring the temperature dependency of thermophysical properties does not significantly affect the flow fields and heat transfer behavior of nanofluids, but it changes the relative magnitudes. Furthermore, in the presence of magnetic field, smaller nanoparticles are more appropriate than larger ones.     

Evolution of two-dimensional lump nanosolitons for the Zakharov-Kuznetsov and electromigration equations

The evolution of lump solutions for the Zakharov-Kuznetsov equation and the surface electromigration equation, which describes mass transport along the surface of nanoconductors, is studied. Approximate equations are developed for these equations, these approximate equations including the important effect of the dispersive radiation shed by the lumps as they evolve. The approximate equations show that lump-like initial conditions evolve into lump soliton solutions for both the Zakharov-Kuznetsov equation and the surface electromigration equations. Solutions of the approximate equations, within their range of applicability, are found to be in good agreement with full numerical solutions of the governing equations. The asymptotic and numerical results predict that localized disturbances will always evolve into nanosolitons. Finally, it is found that dispersive radiation plays a more dominant role in the evolution of lumps for the electromigration equations than for the Zakharov-Kuznetsov equation.