In recent years, Lattice Boltzmann Methods (LBM’s) have emerged as a popular class of paradigms for the simulation of multiphase flows. These methods rely on discretized Boltzmann equations to represent the individual multiphase species. Among LBM’s advantages is its ability to explicitly account for interfacial physics and its local streaming/collision operations which make it ideally suited for parallelization. However, one drawback of LBM is in the simulation of incompressible multiphase flow, whereby the density should remain constant along material characteristics. Because LBM uses a state equation to relate pressure and density, incompressibility cannot be enforced directly. This is true even for incompressible single-phase LBM calculations, in which a finite density drop is needed to drive through the flow. This is also the case for compressible Navier-Stokes algorithms when applied to low Mach number flow. To mitigate compressibility effects, LBM can be used in low Mach regimes which should keep material density variation small. In this work, we demonstrate that the assumption of low Mach number is not sufficient in multiphase internal flows. In such flows, in the absence of a Pressure Poisson constraint to enforce incompressibility, LBM predicts a compressible solution whereby a density gradient must develop to conserve mass. Imposition of inflow/outflow boundary conditions or a mean body force can ensure that mass is conserved globally, thereby quelling density variation. The primary numerical problem we study is the deformation of a liquid droplet immersed in another fluid. Though LBM is not typically conducted with a pressure Poisson equation, we incorporate one in this work and demonstrate that its inclusion can significantly lower the density variation in view of maintaining an incompressible flow.

During service and/or storage, Sn-Ag-Cu (SAC) solder alloys are subjected to temperatures ranging from 0.4 to 0.8 Tm (where Tm is the melting temperature of SAC alloys), making them highly prone to significant microstructural coarsening. The microstructures of these low melting point alloys continuously evolve during service. This results in evolution of creep properties of the joint over time, thereby influencing the long-term reliability of microelectronic packages. Here, we study microstructure evolution and creep behavior of two Sn-Ag-Cu (SAC) alloys, namely Sn-3.0Ag-0.5Cu and Sn-1.0Cu-0.5Cu, isothermally aged at 150°C for various lengths of time. Creep behavior of the two SAC solders after different aging durations was systematically studied using impression creep technique. The key microstructural features that evolve during aging are Ag 3 Sn particle size and inter-particle spacing. Creep results indicate that the creep rate increases considerably with increasing inter-particle spacing although the creep stress exponent and creep activation energy are independent of the aging history.

During service, micro-cracks form inside solder joints, making a microelectronic package prone to failure particularly during a drop. Hence, the understanding of the fracture behavior of solder joints under drop conditions, synonymously at high strain rates and in mixed mode, is critically important. This study reports: (i) the effects of processing conditions (reflow parameters and aging) on the microstructure and fracture behavior of Sn-3.8%Ag-0.7%Cu (SAC387) solder joints attached to Cu substrates, and (ii) the effects of the loading conditions (strain rate and loading angle) on the fracture toughness of these joints, especially at high strain rates. A methodology for calculating critical energy release rate, G C , was employed to quantify the fracture toughness of the joints. Two parameters, (i) effective thickness of the interfacial intermetallic compounds (IMC) layer, which is proportional to the product of the thickness and the roughness of the IMC layer, and (ii) yield strength of the solder, which depends on the solder microstructure and the loading rate, were identified as the dominant quantities affecting the fracture behavior of the solder joints. The fracture toughness of the solder joint decreased with an increase in the effective thickness of the IMC layer and the yield strength of the solder. A 2-dimensional fracture mechanism map with the effective thickness of the IMC layer and the yield strength of the solder as two axes and the fracture toughness as well as the fraction of different fracture paths as contour-lines was prepared. Trends in the fracture toughness of the solder joints and their correlation with the fracture modes are explained using the fracture mechanism map.

In this study, a novel architecture composed of uniformly distributed high melting phase (HMP, e.g. Cu) in a low melting phase (LMP, e.g. In) matrix, which can be produced via liquid phase sintering (LPS), is proposed to produce next generation thermal interface materials (TIMs) and interconnect (IC) materials. The LMP determines the shear compliance of these composites whereas the HMP determines its thermal and electrical conductivities. The volume fraction of In was optimized to produce a Cu-In solder with suitable mechanical, electrical and thermal properties for TIM and IC applications. Since, Cu and In react to form several Cu-In intermetallic compounds (IMCs), which may deteriorate the long-term performance of these solders, interfacial-layers of Au and Al 2 O 3 were applied on Cu to further improve the performance of the Cu-In solders. The effect of interfacial-layers on the reaction between Cu and In, during sintering at 160°C and during aging at 125°C, was studied and its impact on the mechanical, thermal and electrical properties was evaluated. Au interfacial layer (50∼200nm) quickly reacted with In to form AuIn 2 IMC, which acted as a tenacious diffusion-barrier and slowed down the reactions between Cu and In. 8-monolayer thick Al 2 O 3 did not react with either Cu or In and inhibited reactions between Cu and In. During short-time sintering, the effect of interfacial layer on the thicknesses of IMCs was insignificant to affect the yield strength of the as-sintered composites. However, IMC layer thickened rapidly in the Cu-In composites without an interfacial-layer, which led to a drastic decrease in the volume fraction of unreacted In leading to an increase in the yield strength of the solder. On the other hand, the interfacial-layers effectively suppressed the growth of IMCs during aging and hence the yield strength of such composites increased at slower rates. Since, the IMCs formed at the interface radically affect the contact resistance, significant differences in the thermal and electrical conductivities were recorded for the solders with different interfacial-layers.

This paper reports on a new paradigm for highly flexible solder design, proffering high electrical and thermal conductivity, in conjunction with good mechanical compliance, via a novel Liquid Phase Sintering (LPS) approach. The new LPS solders comprise a high melting point phase HMP (e.g., Cu or Sn) with a small amount of a low melting-point phase LMP (e.g., In) at grain boundaries, such that different properties can be controlled by different constituents. In general, conductivity is dominated by the majority HMP constituent, while deformation is controlled by the minority, LMP grain boundary constituent. The LPS solders are suitable for both thermal interface material (TIM) and interconnect applications. As the application space for solders shifts in the future, and requirements for new property-sets emerge, the flexibility of the LPS solder approach will allow integration of different materials into new LPS solder-systems.

Electronic packages in mobile devices are often subjected to drops, leading to impact loading. Since solder joints, which serve as mechanical and electrical interconnects in a package, are particularly prone to failure during a drop, the fracture behavior of solders at high strain rates is a critical design parameter for building robust packages. Here we report on a methodology for measuring mixed-mode fracture toughness of Sn3.5Ag0.7Ag (SAC387) solder joints under dynamic loading conditions (at strain rates up to 100s −1 ), and use this method to investigate the role of solder microstructure and interfacial intermetallic compound (IMC) layer thickness on the joint fracture toughness at different mode-mixities and strain rates. Modified compact mixed mode (CMM) samples with adhesive solder joints between Cu plates and a thin film interfacial starter crack were used for the measurements. The interfacial IMC layer thickness was adjusted by controlling the dwell time during reflow, while the solder microstructure was controlled via the post-reflow cooling rate and subsequent thermal aging. The critical strain energy release rate (G c ) was measured as a function of these microstructural and loading variables, and these data were correlated with the associated crack path, details of which were elicited through fractography as well as crack-profile observations. The crack profile studies were based on samples with double interfacial starter cracks, one of which propagated only partially. Associated with the alteration of the joint microstructure, transitions in the fracture behavior were noted. In all cases, the cracks remained confined to the interfacial region, although the details of the crack propagation path and its interaction with interfacial IMCs, the adjacent solder and the pad surface finish varied significantly. Fracture toughness decreased with an increase in the strain rate and decreased with increasing mode-mixity. A thicker/coarser interfacial IMC layer (due to high dwell times) decreased toughness, while coarser solder microstructures (due to slow cooling during reflow or post-reflow aging) increased toughness. Correlations between joint microstructure and the observed deformation and fracture mechanisms will be highlighted, and a qualitative model based explanation for the inter-play between solder and IMC, and the associated interfaces will be presented.

PFBR, India’s first commercial fast breeder reactor employing fast fission is a challenging project from technological point of view to meet the energy security of the country. It is currently under advanced stage of construction at Kalpakkam, India. PFBR is equipped with two independent, fast acting and diverse shutdown systems. A shutdown system comprises of sensors, logic circuits, drive mechanisms and neutron absorbing rods. The absorber rods of the second shutdown system of PFBR are called as Diverse Safety rods (DSR) and their drive mechanisms are called as Diverse Safety Rod Drive Mechanisms (DSRDM). DSR are normally parked above active core by DSRDM. On receiving scram signal, Electromagnet of DSRDM is de-energised and it facilitates fast shutdown of the reactor by dropping the DSR in to the active core. For the prototype development of DSR and DSRDM, three phases of testing namely individual component testing, integrated functional testing in room temperature and endurance testing at high temperature sodium were planned and are being done. The electromagnet of DSRDM operates at high temperature sodium environment continuously. It has been separately tested at room temperature, in furnace and in sodium. Specimens simulating the contact conditions between Electromagnet and armature of DSR have been tested to rule out self welding possibility. The Dashpot provided to decelerate the DSR at the end of its free fall has been initially tested in water and then in sodium. The prototype of DSR has been tested in flowing water to determine the pressure drop and drop time. The functional testing of the integrated prototype DSRDM and DSR in aligned and misaligned conditions in air/water has been completed. The performance testing of the integrated system in sodium has been done in three campaigns. Based on the performance testing in the first two campaigns of sodium testing, design modifications and manufacturing quality improvement were done. Methods of drop time measurement based on ultrasonics and acoustics were also developed along with the first two campaigns. During the third campaign of sodium testing, the performance of the system has been verified with 30 mm misalignment at various temperatures. The third campaign has qualified the system for 10 years of operation in reactor. This paper describes the test setup for all the above mentioned testing and also gives typical test results.

The prediction of elastohydrodynamic lubrication (EHL) film thickness requires knowledge of the lubricant properties. Today, in many instances, the properties have been obtained from a measurement of the central film thickness in an optical EHL point contact simulator and the assumption of a classical Newtonian film thickness formula. This technique has the practical advantage of using an effective pressure-viscosity coefficient which compensates for shear-thinning. We have shown by a perturbation analysis and by a full EHL numerical solution that the practice of extrapolating from a laboratory scale measurement of film thickness to the film thickness of an operating contact within a real machine may substantially overestimate the film thickness in the real machine if the machine scale is smaller and the lubricant is shear-thinning in the inlet zone.

In this paper, we investigate the effects of laminar double-diffusive natural convection on directional solidification of binary fluids when cooled and solidified from the top. The study is performed using aqueous ammonium chloride solution as the model fluid. The experiments are performed with an initial concentration of ammonium chloride is less than the eutectic composition, leading to an aiding double-diffusive convection. In this case, solidification leads to the formation of a diffused matrix of dendritic crystals (mushy region) separating the pure solid and liquid regions. Below the two-phase mushy region, Rayleigh-Benard type of cellular convective motions are observed. The cellular motions, which are caused by thermal buoyancy, die once the thickness of the liquid layer falls below a critical value. The features of convective transport are visualised using a sheet of laser light scattered through neutrally buoyant glass particles seeded in the solution. Numerical simulations are also performed, and the agreement with experimental results is found to be good.