Irregular Characteristics of Bond Interface Formation in Ultrasonic Wire Wedge Bonding

The mechanism of ultrasonic wire wedge bonding, one of the die/chip interconnection methods, was investigated based on the characteristics of the ultrasonic wire bonding joints. The Al-1%Si wire of 25 μm in diameter was bonded on Au/Ni/Cu pad and the joint cross-section was analyzed by scanning electron microscopy （SEM） and energy-dispersive X-ray spectroscopy （EDX）. The results indicated that it is irregular for the ultrasonic bond formation, non-welded at the centre but joining well at the periphery, especially at the heel and toe of the joint. Furthermore, the diffusion and/or reaction at the cross-section interface are not clear at C-zone, while there exists a strip layer microstructure at P-zone, and the composition is 78.96 at. pct Al and 14.88 at. pct Ni, close to the Al3Ni intermetallic compound. All these observations are tentatively ascribed to the plastic flow enhanced by ultrasonic vibration and repeated cold deformation driving interdiffusion between AI and Ni at bond interface.

Interface diffusion of sputtered CoZrNb films on silicon substrate

The amorphous CoZrNb films were deposited by DC magnetron sputtering.The depth distributions of the elements were analyzed by Rutherford backscattering spectrometry(RBS).The results indicate that when the deposition time is longer than 37 min,the film composition keeps constant along the depth.When the deposition time is longer than 45 min,the Co concentration at the interface of the silicon substrate is higher than the average value in the whole film.When the deposition time is longer than 52 min,the Co atoms diffuse into the substrate during the deposition.According to the Co composition profile in the substrate,which were determined from the RBS spectra,the Co diffusion coefficients in the substrate were calculated using the solution of Fick′s second law corresponding to an infinite source with a constant diffusion coefficient.The calculated diffusion coefficients indicate an interstitial assisted diffusion mechanism.

Multilayer laminated Cu coil/CaO-Li_(2)O-B_(2)O_(3)-SiO_(2)glass-ceramic preparation via a novel insulation packaging strategy for flat wire motor applications

A new insulation packaging strategy for the stator windings of flat wire motors based on LTCC technology was studied for the first time.The study aimed to replace traditional plastic packaging methods and avoid aging issues by fabricating a novel multilayer laminated Cu coil/CaO–Li_(2)O–B_(2)O_(3)–SiO_(2)glass-ceramic structure.The analysis of the interface microstructure of the laminated structure revealed that the CaO–Li_(2)O–B_(2)O_(3)–SiO_(2)glass-ceramic matrix consisted of a crystalline phase of CaSiO_(3)and an amorphous phase of SiO_(2).The interface between the Cu coil and CaO–Li_(2)O–B_(2)O_(3)–SiO_(2)glass-ceramic exhibited good bonding with no formation of secondary phases.Additionally,the strong bonding between the Cu coil and CaO–Li_(2)O–B_(2)O_(3)–SiO_(2)glass-ceramic was attributed to the diffusion of Cu atoms at the interface.The novel multilayer laminated structure based on LTCC technology proposed in this study can help achieve high-reliability insulation packaging for the stator windings of future high-power density and miniaturized flat wire motors.

Process optimization,microstructures and mechanical/thermal properties of Cu/Invar bi-metal matrix composites fabricated by spark plasma sintering

An orthogonal experiment scheme was designed to investigate the effects of the Cu content,compaction pressure,and sintering temperature on the microstructures and mechanical and thermal properties of(30−50)wt.%Cu/Invar bi-metal matrix composites fabricated via spark plasma sintering(SPS).The results indicated that as the Cu content increased from 30 to 50 wt.%,a continuous Cu network gradually appeared,and the density,thermal conductivity(TC)and coefficient of thermal expansion of the composites noticeably increased,but the tensile strength decreased.The increase in the sintering temperature promoted the Cu/Invar interface diffusion,leading to a reduction in the TC but an enhancement in the tensile strength of the composites.The compaction pressure comprehensively affected the thermal properties of the composites.The 50wt.%Cu/Invar composite sintered at 700℃ and 60 MPa had the highest TC(90.7 W/(m·K)),which was significantly higher than the TCs obtained for most of the previously reported Cu/Invar composites.

Diffusion welding of SiCp/2014Al composites using Ni as interlayer

SiCp/2014Al composites were bonded with the vacuum diffusion welding technique using Ni as the interlayer metal. Ni and Al were interdiffused and there were intermetallic compounds formed in the inter transition layer, which was composed of Ni3Al//NiAl//NiAl3. The relation between the diffusion distance and the element concentration was calculated according to Fick＇s second law. The relations of the diffusion concentration and the diffusion welding technique parameters were calculated.

STABILITY AND CONVERGENCE ANALYSIS OF SECOND-ORDER SCHEMES FOR A DIFFUSE INTERFACE MODEL WITH PENG-ROBINSON EQUATION OF STATE

In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mass conservation, energy decay property, unique solvability and L~ convergence of these two schemes are proved. Numerical results demon- strate the good approximation of the fourth order equation and confirm reliability of these two schemes.

Simulation of Seawater Intrusion in Coastal Confined Aquifer Using a Point Collocation Method Based Meshfree Model

Seawater intrusion caused by groundwater over-exploitation from coastal aquifers poses a severe problem in many regions. Formulation of proper pumping strategy using a simulation model can assure sustainable supply of fresh water from the coastal aquifers. The focus of the present study is on the development of a numerical model based on Meshfree (MFree) method to study the seawater intrusion problem. For the simulation of seawater intrusion problem, widely used models are based on Finite Difference (FDM) and Finite Element (FEM) Methods, which demand well defined grids/meshes and considerable pre-processing efforts. Here, MFree Point Collocation Method (PCM) based on the Radial Basis Function (RBF) is proposed for the simulation. Diffusive interface approach with density-dependent dispersion and solution of flow and solute transport is adopted. These equations are solved using PCM with appropriate boundary conditions. The developed model has been verified with Henry’s problem, and found to be satisfactory. Further the model has been applied to another established problem and an attempt is made to examine the influence of important system parameters including pumping and recharge on the seawater intrusion. The PCM based MFree model is found computationally efficient as preprocessing is avoided when compared to other numerical methods.

Simulation of flows with moving contact lines on a dual-resolution Cartesian grid using a diffuse-interface immersed-boundary method

In this paper, we investigate flows with moving contact lines on curved solid walls on a dual-resolution grid using a diffuse-interface immersed-boundary（DIIB） method. The dual-resolution grid, on which the flows are solved on a coarse mesh while the interface is resolved on a fine mesh, was shown to significantly improve the computational efficiency when simulating multiphase flows. On the other hand, the DIIB method is able to resolve dynamic wetting on curved substrates on a Cartesian grid, but it usually requires a mesh of high resolution in the vicinity of a moving contact line to resolve the local flow. In the present study, we couple the DIIB method with the dual-resolution grid, to improve the interface resolution for flows with moving contact lines on curved solid walls at an affordable cost. The dynamic behavior of moving contact lines is validated by studying drop spreading, and the numerical results suggest that the effective slip length λ_n can be approximated by 1.9Cn, where Cn is a dimensionless measure of the thickness of the diffuse interface. We also apply the method to drop impact onto a convex substrate, and the results on the dual-resolution grid are in good agreement with those on a single-resolution grid. It shows that the axisymmetric simulations using the DIIB method on the dual-resolution grid saves nearly 60% of the computational time compared with that on a single-resolution grid.

Solute trapping model based on solute drag treatment

A solute trapping model is developed based on a so-called solute drag treatment.By adopting a basic approach of phase-field models,and defining the free energy density in the interfacial region,a suitable interface shape function is introduced to derive the current model,in which the equilibrium and non-equilibrium interface behaviours can be described using a dimensionless parameter L (i.e.an important parameter in the present interface shape function).When applying the current model to Si-9%As (molar fraction) alloy with L=0.5,a good prediction of the steeper profile for high interface velocity,which is analogous to that using a phase-field model of DANILOV and NESLTER,has been obtained.

Discussions on the non-equilibrium effects in the quantitative phase field model of binary alloys

All the quantitative phase field models try to get rid of the artificial factors of solutal drag, interface diffusion and interface stretch in the diffuse interface. These artificial non-equilibrium effects due to the introducing of diffuse interface are analysed based on the thermodynamic status across the diffuse interface in the quantitative phase field model of binary alloys. Results indicate that the non-equilibrium effects are related to the negative driving force in the local region of solid side across the diffuse interface. The negative driving force results from the fact that the phase field model is derived from equilibrium condition but used to simulate the non-equilibrium solidification process. The interface thickness dependence of the non-equilibrium effects and its restriction on the large scale simulation are also discussed.

A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows

We propose a hybrid scheme combing the level set method and the multicomponent diffuse interface method to simulate complex multi-phase flows.The overall numerical scheme is based on a sharp interface framework where the level set method is adopted to capture the material interface,the Euler equation is used to describe a single-phase flow on one side of the interface and the six-equation diffuse interface model is applied to model the multi-phase mixture or gas-liquid cavitation on the other side.An exact Riemann solver,between the Euler equation and the six-equation model with highly nonlinear Mie-Gr¨uneisen equations of state,is developed to predict the interfacial states and compute the phase interface flux.Several numerical examples,including shock tube problems,cavitation problems,air blast and underwater explosion applications are presented to validate the numerical scheme and the Riemann solver.

MICROSCOPIC KINETICS OF NON-EQUILIBRIUM SOLIDIFICATION

Theoretical model for non -equilibrium solidification is constructed with consideration of diffuse interface and multiphase fluctuation. It can he degenerated to Aziz continuous growth model in the case of mono-atomic approximation. for large undercooling, the change of heat capacity should not he neglected and it usually gives an increase in the interface partition coefficient. Solute trapping may happen at a rather slow growth rate compared with that predicted by other models, because the undercooling and structural relaxation ahead of the S/ L interface lowers the interfacial diffusivity to a great extent. Plase fluctuation has two contending effects, decrease in energy barrier and increase in atomic dragging, therefore exerts dual influences on the partition coefficient.

A Hybrid Fluid-Solid Interaction Scheme Combining the Multi-Component Diffuse Interface Method and the Material Point Method

We propose a hybrid scheme combing the diffuse interface method and the material point method to simulate the complex interactions between the multiphase compressible flow and elastoplastic solid.The multiphase flow is modelled by the multi-component model and solved using a generalized Godunov method in the Eulerian grids,while the elastoplastic solid is solved by the classical material point method in a combination of Lagrangian particles and Eulerian background grids.In order to facilitate the simulation of fluid-solid interactions,the solid variables are further interpolated to the cell center and coexist with the fluid in the same cell.An instantaneous relaxation procedure of velocity and pressure is adopted to simulate the momentum and energy transfers between various materials,and to keep the system within a tightly coupled interaction.Several numerical examples,including shock tube problem,gasbubble problem,air blast,underwater explosion and high speed impact applications are presented to validate the numerical scheme.

A Diffuse-Interface Lattice Boltzmann Method for the Dendritic Growth with Thermosolutal Convection

In this work,we proposed a diffuse-interface model for the dendritic growth with thermosolutal convection.In this model,the sharp boundary between the fluid and solid dendrite is firstly replaced by a thin but nonzero thickness diffuse interface,which is described by the order parameter,and the diffuse-interface based governing equations for the dendritic growth are presented.To solve the model for the dendritic growth with thermosolutal convection,we also developed a diffuse-interface multirelaxation-time lattice Boltzmann(LB)method.In this method,the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction,and the treatment on the complex fluid-solid interface can be avoided.In addition,four LB models are designed for the phase-field equation,concentration equation,temperature equation and the Navier-Stokes equations in a unified framework.Finally,we performed some simulations of the dendritic growth to test the present diffuse-interface LB method,and found that the numerical results are in good agreements with some previous works.

Retrieving Topological Information of Implicitly Represented Diffuse Interfaces with Adaptive Finite Element Discretization

We consider the finite element based computation of topological quantities of implicitly represented surfaces within a diffuse interface framework.Utilizing an adaptive finite element implementation with effective gradient recovery techniques,we discuss how the Euler number can be accurately computed directly from the numerically solved phase field functions or order parameters.Numerical examples and applications to the topological analysis of point clouds are also presented.

Estimating the thickness of diffusive solid electrolyte interface

electrolyte. The properties of lithium-ion (Li-ion) battery, such as cycle life, irreversible capacity loss, self-discharge rate, electrode corrosion and safety are usually ascribed to the quality of the SEI, which are highly dependent on the thickness. Thus, understanding the formation mechanism and the SEI thickness is of prime interest. First, we apply dimensional analysis to obtain an explicit relation between the thickness and the number density in this study. Then the SEI thickness in the initial charge-discharge cycle is analyzed and estimated for the first time using the Cahn-Hilliard phase-field model. In addition, the SEI thickness by molecular dynamics simulation validates the theoretical results. It has been shown that the established model and the simulation in this paper estimate the SEI thickness concisely within order-of-magnitude of nanometers. Our results may help in evaluating the performance of SEI and assist the future design of Li-ion battery.

Multiphysic Two-Phase Flow Lattice Boltzmann:Droplets with Realistic Representation of the Interface

Free energy lattice Boltzmann methods are well suited for the simulation of two phase flow problems.The model for the interface is based on well understood physical grounds.In most cases a numerical interface is used instead of the physical one because of lattice resolution limitations.In this paper we present a framework where we can both follow the droplet behavior in a coarse scale and solve the interface in a fine scale simultaneously.We apply the method for the simulation of a droplet using an interface to diameter size ratio of 1 to 280.In a second simulation,a small droplet coalesces with a 42 times larger droplet producing on it only a small capillary wave that propagates and dissipates.

Motion of a small bubble in forced vibrating sessile drop

In this letter,the motion of small gas bubbles within sessile water drops on a vibrating substrate is investigatednumerically using a two-phase diffuse interface method.Depending on the amplitude of the plate vibration,themotion of the gas bubbles falls into three distinct regimes:oscillating within the drop,sticking to the substrate,orescaping from the drop.In particular,the motion of oscillating bubbles follows a harmonic function,and is foundto be closely related to a combined effect of the deformation of the sessile drop and the vibration of the plate.Tointerpret the underlying mechanism,we analyze the dominant forces acting on the bubbles in the non-inertialframework fixed to the plate,and take account of the periodic deformation of the drop,which effectively inducesflow acceleration inside the drop.As a result,we establish a theoretical model to predict the bubble motion,andcorrelate the amplitude and phase difference of the bubble with the Bond and Strouhal numbers.The theoreticalprediction agrees with our numerical results.These findings and theoretical analysis provide new insights intocontrolling bubble motion in sessile drops.

Motion of a small bubble in forced vibrating sessile drop

In this letter,the motion of small gas bubbles within sessile water drops on a vibrating substrate is investigatednumerically using a two-phase diffuse interface method.Depending on the amplitude of the plate vibration,themotion of the gas bubbles falls into three distinct regimes:oscillating within the drop,sticking to the substrate,orescaping from the drop.In particular,the motion of oscillating bubbles follows a harmonic function,and is foundto be closely related to a combined effect of the deformation of the sessile drop and the vibration of the plate.Tointerpret the underlying mechanism,we analyze the dominant forces acting on the bubbles in the non-inertialframework fixed to the plate,and take account of the periodic deformation of the drop,which effectively inducesflow acceleration inside the drop.As a result,we establish a theoretical model to predict the bubble motion,andcorrelate the amplitude and phase difference of the bubble with the Bond and Strouhal numbers.The theoreticalprediction agrees with our numerical results.These findings and theoretical analysis provide new insights intocontrolling bubble motion in sessile drops.

A Semi-implicit Finite Volume Scheme for Incompressible Two-Phase Flows

This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase,a solid phase,and the surrounding void.According to the so-called diffuse interface approach,the different phases and consequently the void are described by means of a scalar volume fraction function for each phase.In our numerical scheme,the dynamics of the liquid phase and the motion of the solid are decoupled.The solid is assumed to be a moving rigid body,whose motion is prescribed.Only after the advection of the solid volume fraction,the dynamics of the liquid phase is considered.As usual in semi-implicit schemes,we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly,while the pressure terms are treated implicitly.The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach.The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique.The time step size is only limited by the velocities of the two phases contained in the domain,and not by the gravity wave speed nor by the stiff algebraic relaxation source term,which requires an implicit discretization.The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.