Diffuse Interface Research Articles

The feasibility of an ultrathin dual-barrier scheme to inhibit interfacial diffusion and reactions in contact stacks of Co/NiSi/Si

Self-assembled monolayers (SAMs) and self-forming barriers (SFBs) are highly effective barriers of copper (Cu) interconnect systems. However, the barrier capability of SAMs and SFBs to contact metallization of cobalt (Co), a new important interconnect material, is yet to be explored. Here, contact layers of NiSi are grown by a two-step silicidation process on Si. Then, an all-wet SAM-seeding and electroless-plating process is used to coat (in sequence) an amine SAM and a MnO-added (only 0.1%) Co film onto NiSi/Si, using a specifically formulated N2H4-CoSO4-MnSO4 bath. The thermal stability of the Co(MnO)/SAM/NiSi/Si is evaluated, using (unalloyed) Co/SAM/NiSi/Si as a control. The 1.3 nm-thin SAM cannot protect the Co/SAM/NiSi/Si from catastrophic failure upon annealing, associated with serious Co/Si interfacial diffusion and the formation of faceted CoSi crystallites and a layered Co2Si/CoSi2 nanostructures at specific locations. By contrast, the Co(MnO)/SAM/NiSi/Si maintains an intact stack after annealing. Collaborative research results generated from (scanning) transmission electron microscopy, nanoscratch testing and surface-energy measurements suggest that the thermal stability enhancement of the whole Co(MnO)/SAM/NiSi/Si contact stack is related to the interfacial segregation of the added MnO as sub-5-nm dispersive crystalline particles, giving multiple functionalities as a SFB, Co-grain strengthening agent, and wetting/adhesion promoter.

Ultrastrong and ductile W–Cu composites via Al- mediated interfacial diffusion layers and matrix-nanoclusters networks

W–Cu composites are integrated materials with both structural and functional properties. However, the weak interfacial bonding capability leads to limited strain hardening, which makes it difficult to take full advantage of the coordination of the biphasic materials. In present work, a multistage strain-hardening (MSH) effect is created, which enables the W–Cu composites to possess a persistent and effective strain-hardening capability. The prepared W-30(CuAl5) (wt.%) alloy has significant tensile ductility (∼21 %) and ultra-high yield strength (∼840 MPa). Remarkably, compared to the original W–30Cu without Al alloying, the strength and ductility are over two and three times, respectively, accompanied by the preservation of an electrical conductivity of about 80 %. This excellent synergistic effect stems from the Al-mediated interpenetrating interfacial diffusion layers and matrix-nanoclusters interconnection networks. As a result, a high-density of dislocation segments, self-locking structures, and a variety of twinning mechanisms such as nanotwins and 9R configurations are sequentially activated, allowing the composites to accommodate ductility deformation while simultaneously facilitating interactions that produce three unusual rises in strain-hardening rate. The present work offers a critical perspective on the realization of a synergistic ultrahigh tensile ductility and strength combination in metal matrix composites.

Study on the wettability of Sn/Cu system under ultrasonic vibration

In this study, the wetting behavior of Sn solder on Cu substrate under ultrasonic vibration using the sessile drop method was investigated. The distribution of the vibration field on the substrate surface was analyzed via COMSOL Multiphysics finite element analysis, while the spreading behavior and interfacial reaction products of intermetallic compounds (IMCs) induced by varying ultrasonic amplitudes were explored. ultrasonic vibration demonstrates a significant influence on both wettability and interfacial reaction products. The wetting mechanism under ultrasonic vibration is primarily attributed to physical driving forces generated by ultrasound-induced interfacial viscous boundary layers, along with chemical driving forces facilitated by ultrasonic-accelerated interfacial atomic diffusion and reactions.

Nanorod Diffusion near the Solid-Liquid Interface with Varied Wall Nonuniformity.

The complex diffusion behaviors of rod-shaped nanoparticles near the solid-liquid interface are closely related to various biological processes and technological applications. Despite recent advancements in understanding the diffusion dynamics of nanoparticles near some specific solid-liquid interfaces, systematical studies to tune the interfacial interaction or fabricating nonuniform wall to see their effects on the nanorod (NR) diffusion are still lacking. This work utilized molecular dynamics simulations to investigate the rotational and translational diffusion dynamics of a single NR near the solid-liquid interface. We constructed a patterned wall featuring adjustable nonuniformity, which was accomplished by modifying the interaction between NR and the wall, noting that the resulting nonuniformity limits both the translational and rotational diffusion of NR, evident from decreases in diffusion coefficients and exponents. By trajectory analysis, we categorized the diffusion modes of NRs near the patterned wall with varied nonuniformities into three types: Fickian diffusion, desorption-mediated flight, and in-plane diffusion. Furthermore, energy analysis based on the adsorption-desorption mechanism has demonstrated that the three diffusion states are driven by interactions between the NR and the wall, which are primarily influenced by rotational diffusion. These results could significantly deepen the understanding of anisotropic nanoparticle interfacial diffusion and would provide new insights into the transport mechanisms of nanoparticles within confined environments.

Enhanced comprehension of the cross-scale forming mechanism in CF/PEEK resistance welding: Analysis of temperature gradients and meso–microscopic phase transitions

Resistance welding technology is an effective solution for connecting thermoplastic composites. However, limited research on non-uniform distribution of interfacial temperature and complex evolution mechanism of phase-change molding hinders its application. This reliance on traditional experimental and trial-and-error methods severely impedes its development. Therefore, this study employed a novel cross-scale numerical simulation method, being applied for the first time in the field of resistance welding for elucidating the underlying mechanism of joint formation through multi-component phase transformation. The constructed model accurately represented the transient heat transfer of a realistic wire mesh structure in three dimensions, while incorporating complex gradient effects arising from both spatial and temporal variations in heating element temperature due to air interference. Further, melting, flow, and consolidation behavior of the resin matrix in resistance welding of carbon fiber/polyetheretherketone (CF/PEEK) thermoplastic composite was investigated herein at a mesoscopic scale. To accomplish this objective, a three-phase flow spatial forming and evolution model for resistance welding was developed at the mesoscopic scale by integrating principles from fluid dynamics. Interestingly, introduction of an air phase reinstated the spatial voids formation and flow in resistance welding, providing robust evidence for the initiation mechanism of internal defects. Moreover, this study revealed variations in the melting mode of PEEK resin across different regions within the weld and highlighted distinct distributions of voids resulting from uneven heat transfer. The interfacial phenomenon and flow diffusion mechanism between components in resistance welding tests were further verified and discussed through analyzing scanning electron microscopy and energy dispersive spectroscopy results. Temporal and spatial correlation in void distribution within the welding zone was observed, which was found to be consistent with simulation results. Specifically, with the progress of the welding process, air near the wire mesh gradually dispersed into the laminate, with significantly more voids at weld seam edges than in central regions. This research methodology based on stepwise scale reduction offers a promising avenue for investigating resistance welding and other connection forming applications, in particular, within the context of engineering underlying logical behavior.

Effect of NiMo diffusion barrier plating preparation on microstructure and properties of Bi2Te3/Cu joints

Bismuth telluride (Bi2Te3) thermoelectric devices play a significant role in recovering low-grade waste heat. While for Bi2Te3/Cu joints, excessive interfacial reaction and diffusion usually happens, which greatly degrades their properties. In this work, the novel NiMo diffusion barrier plating was prepared on Bi2Te2.7Se0.3 (n-BST) surface prior to the soldering process. The joint interfacial microstructure, shear strength, contact resistance and thermal stability were systematically investigated. The maximum shear strength increased from 7 MPa to 12 MPa with the joint contact resistance decreasing from 11.86 μΩ⋅cm2 to 3.27 μΩ⋅cm2 after NiMo plating preparation. These n-BST/Cu joints were then annealed for different durations to investigate the joint thermal stability. After annealing at 110 °C for 250 h, a thin BiTe + NiTe2 reaction layer formed instead of the initial SnTe reaction layer. The joint shear strength maintained 9 MPa (less than 2 MPa without NiMo plating) and the joint contact resistance was only 12.39 μΩ⋅cm2 (249.89 μΩ⋅cm2 without NiMo plating). This work indicates that NiMo plating is an effective elemental diffusion barrier for n-BST/Cu joints.

Martingale solutions to stochastic nonlocal Cahn–Hilliard- Navier–Stokes systems with singular potentials driven by multiplicative noise of jump type

Abstract In the diffuse interface theory, the motion of two incompressible viscous fluids and the evolution of their interface are described by the well-known model H. The model consists of the Navier–Stokes equations, nonlinearly coupled with a convective Cahn–Hilliard type equation. Here we consider a stochastic version of the model driven by a noise of Lévy type, and where the standard Cahn–Hilliard equation is replaced by its nonlocal version with a singular (e.g., logarithmic) potential. The case of smooth potentials with arbitrary polynomial growth has been already analyzed in [G. Deugoué, A. Ndongmo Ngana and T. Tachim Medjo, Martingale solutions to stochastic nonlocal Cahn–Hilliard–Navier–Stokes equations with multiplicative noise of jump type, Phys. D 398 2019, 23–68]. Taking advantage of this previous result, we investigate this more challenging and physically relevant case. Global existence of a martingale solution is proved with no-slip and no-flux boundary conditions in both 2D and 3D bounded domains. In the two-dimensional case, we prove the uniqueness of weak solutions when the viscosity is constant.

Understanding interfacial polymerization in the formation of polyamide RO membranes by molecular simulations

Since the water permeation mechanisms of polyamide membranes are highly dependent on the micro-structure of polyamide membranes, a deeper understanding of the formation process of them is necessary for the optimization of the membrane performance. As most simulation works construct the polyamide membranes in an ideal way, the interfacial diffusion of monomers, which is crucial for the formation of polyamide membranes, is usually ignored. To address this issue, we mimic the experimental conditions to develop an atomic model of a highly crosslinked polyamide membrane by conducting molecular dynamics simulations. Via tuning the concentration and molar ratio of monomers, the diffusion of monomers and its influence on the subsequent reaction are altered, and the final membrane structure consequently changed. Simulation results reveal that increasing the trimesoyl chloride concentration results in thicker membranes with a reduced specific surface area and consequently decreased water permeance. On the other hand, increasing the m-phenylenediamine concentration will accelerate the reaction rate and reduce the final crosslinking degree. A deeper understanding of the mechanism of polyamide-membrane formation is unveiled in this work, which can aid in the design of high-performance polyamide membranes in the future.

Well-posedness of a bulk-surface convective Cahn–Hilliard system with dynamic boundary conditions

We consider a general class of bulk-surface convective Cahn–Hilliard systems with dynamic boundary conditions. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn–Hilliard type allow for dynamic changes of the contact angle between the diffuse interface and the boundary, a convection-induced motion of the contact line as well as absorption of material by the boundary. The coupling conditions for bulk and surface quantities involve parameters K,L∈[0,∞]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K,L\\in [0,\\infty ]$$\\end{document}, whose choice declares whether these conditions are of Dirichlet, Robin or Neumann type. We first prove the existence of a weak solution to our model in the case K,L∈(0,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K,L\\in (0,\\infty )$$\\end{document} by means of a Faedo–Galerkin approach. For all other cases, the existence of a weak solution is then shown by means of the asymptotic limits, where K and L are sent to zero or to infinity, respectively. Eventually, we establish higher regularity for the phase-fields, and we prove the uniqueness of weak solutions given that the mobility functions are constant.

Kinetics of voids evolution during diffusion bonding of dissimilar metals on consideration of the realistic surface morphology: Modeling and experiments

A comprehensive model for analyzing the kinetics of void evolution and shrinkage during dissimilar diffusion bonding is proposed based on the sinusoidal profile. The model incorporates atom accumulation at void tip to determine the curvature radius of void neck, and integrates the local effect of surface diffusion to quantify the contribution of surface diffusion, thus avoiding the unrealistic void evolution observed in previous models. Furthermore, the model utilizes a combined diffusion coefficient for multicomponent alloys under the effect of stress and concentration gradients, to determine the interfacial diffusion coefficient for dissimilar joints. In contrast to previous models, the current model demonstrates significant improvements in predicted accuracy, efficiently depicting the realistic void evolution and interpreting the formation of various interfacial voids, which can be applied in various bonding cases, including for the dissimilar base metals with different surface conditions. Simulation results from bonding between austenitic steel and ferritic steel with different surface roughness reveal that interfacial voids predominantly form on the side of the base metal with the rougher bonding surface. Additionally, as surface roughness decreases, the prevailing surface source diffusion and interface source diffusion mechanisms promote void evolution and shrinkage, resulting in a significant reduction of the final bonding time. To achieve a high-quality bonding joint, it's suggested to place the smoother bonding surface on the higher creep-resistant base metal, which can accelerate the void closure process.

Upscaling and Effective Behavior for Two-Phase Porous-Medium Flow Using a Diffuse Interface Model

We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore scale is modeled using a diffuse interface approach in the form of a coupled Allen–Cahn Navier–Stokes system with an additional momentum flux due to surface tension forces. Using periodic homogenization and formal asymptotic expansions, a two-scale model with cell problems for phase evolution and velocity contributions is derived. We investigate the computed effective parameters and their relation to the saturation for different fluid distributions, in comparison to commonly used relative permeability saturation curves. The two-scale model yields non-monotone relations for relative permeability and saturation. The strong dependence on local fluid distribution and effects captured by the cell problems highlights the importance of incorporating pore-scale information into the macro-scale equations.

Cu/Mo/NGs composites: Multilayer interconnected spatial net structure enhanced the mechanical properties

This study addresses the urgent problem of developing high-performance metal-based conductor materials capable of adapting to complex working environments. A novel method, called Accumulative Hot Pressing Roll Bonding (AHRB), is proposed for fabricating Cu/Mo/NGs multilayer composite materials. Through repetitive cold rolling and hot-pressing operations, nanoscale metal-based layered materials with thicknesses in the range of hundreds of nanometers are successfully obtained. This material features a multilayered interconnected net structure with Mo2C as the core and CuMo alloy as the framework. The layers are dislocated and connected to each other. The mechanical properties of the materials are significantly improved due to heterogeneous strengthening and grain refinement. The material achieves a tensile strength of 854 MPa, while the conductivity remains stable between 55% ∼ 60% IACS. The reaction between NGs and Mo leads to the formation of an Mo2C interface, while the hot-pressing operation promotes the formation of a CuMo diffusion interface. These two interfaces enhance the interlayer forces of the composites, thereby improving the material's integrity. The investigation of Cu/Mo/NGs multilayer composite materials presents a novel approach for alloying refractory metals Mo and Cu, offering promising prospects for future engineering applications.

A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening

A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. The method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.

Microstructure and Mechanical Properties of Mg-Li/Al Dissimilar Joints via Dynamic Support Friction Stir Lap Welding.

In this study, two-mm-thick dual-phase LA103Z Mg-Li and 6061 Al alloys, known for their application in lightweight structural designs, were joined using dynamic support friction stir lap welding (DSFSLW). The microstructural evolution and mechanical properties of dissimilar joints were investigated at different welding speeds. The analysis revealed two distinct interfaces: the diffusion interface and the mixed interface. The diffusion interface, characterized by a pronounced diffusion zone, is formed under slower welding speeds. The diffusion zone height, the effective lap width, and the interface layer thickness decrease with increasing welding speed due to low plastic deformation capacity and weak interfacial reactions. Conversely, the mixed interface, associated with higher welding speeds, contained large Al fragments. The extremely high microhardness values (130.5 HV) can be ascribed to the formation of intermetallic compounds (IMCs) and strain-hardened Al fragments. Notably, the maximum shear strength achieved was 175 N/mm at a welding speed of 20 mm/min. The fracture behavior varied significantly with the interface type; the diffusion interface showed enhanced mechanical strength due to better intermetallic reactions and interlocking structures, while the mixed interface displayed more linear crack propagation due to weaker IMCs and the absence of hook structures. Fracture surface analysis indicates that fractures are more likely to propagate through the Al matrix and interface layers.

Wetting Effect Induced Depletion and Adsorption Layers: Diffuse Interface Perspective.

When a multi-component fluid contacts arigid solid substrate, the van der Waals interaction between fluids and substrate induces a depletion/adsorption layer depending on the intrinsic wettability of the system. In this study, we investigate the depletion/adsorption behaviors of A-B fluid system. We derive analytical expressions for the equilibrium layer thickness and the equilibrium composition distribution near the solid wall, based on the theories of de Gennes and Cahn. Our derivation is verified through phase-field simulations, wherein the substrate wettability, A-B interfacial tension, and temperature are systematically varied. Our findings underscore two pivotal mechanisms governing the equilibrium layer thickness. With an increase in the wall free energy, the substrate wettability dominates the layer formation, aligning with de Gennes' theory. When the interfacial tension increases, or temperature rises, the layer formation is determined by the A-B interactions, obeying Cahn's theory. Additionally, we extend our study to non-equilibrium systems where the initial composition deviates from the binodal line. Notably, macroscopic depletion/adsorption layers form on the substrate, which are significantly thicker than the equilibrium microscopic layers. This macroscopic layer formation is attributed to the interplay of phase separation and Ostwald ripening. We anticipate that the present finding could deepen our knowledge on the depletion/adsorption behaviors of immiscible fluids.

Regulating interfacial exchange coupling in perpendicular magnetized Fe/DO22-Mn3Ga bilayer films

Manganese gallium alloy with DO22-type chemical ordering (DO22-Mn3Ga) thin film represents an intriguing candidate for fabricating the fundamental composition of magnetic devices. In this paper, we prepare the Fe/DO22-Mn3Ga composite films on thermal MgO (100) substrates with different annealing temperatures and report the interfacial exchange coupling between Fe and DO22-Mn3Ga bilayers. Fe layer thickness and annealing temperature are predominant in regulating the nature and strength of interfacial exchange coupling. It is found that there is a ferromagnetic coupling between Fe and DO22-Mn3Ga layers. Their exchange coupling strength can be regulated by changing the Fe soft magnetic layer thickness in a reasonable range. Additionally, the interface diffusion generated from heat treatment induces to change of the nature of exchange coupling. It is possible that Fe replaces Mn site in the DO22-Mn3Ga unit cell due to smaller atomic radius and higher electronegativity compared with Mn. Antiferromagnetic coupling from annealed Fe/DO22-Mn3Ga film with high perpendicular magnetic anisotropy is technologically important to research synthetic antiferromagnetic structure for spin-transfer-torque magnetoresistive random access memory. Our works is helpful for the exploration of interfacial science and development of magnetic devices.

Numerical modelling of large elasto-plastic multi-material deformations on Eulerian grids

Abstract The paper deals with an Eulerian model for heterogeneous multiphase (multi-material) elasto-plastic media based on the diffuse interface method in the one-dimensional uniaxial strain approximation. In this approximation, an equilibrium hypoelastic Wilkins bi-material model is derived. This is carried out on the basis of an analogy between the elasto-plastic Wilkins and hydrodynamic Euler models. For the obtained model, a Godunov-type numerical method is developed based on the approximate Riemann solver HLLC. The results of the proposed Eulerian diffuse interface model are compared with reference solutions on moving grids with explicit tracking interfaces. It is shown that the present diffuse interface numerical model describes with good accuracy strong shock-wave processes in heterogeneous multiphase elasto-plastic media.

Interfacial compatibility design of high-performance electrolytes for SiCO-based all-solid-state lithium battery

Abstract As a new type of Lithium-ion batteries technology, all-solid-state Lithium-ion battery is regarded as one of the cutting-edge directions for new-generation battery technology. The biggest challenge of solid-state Li battery technology is that interface compatibility and stability problems must be solved urgently. In this paper, we specialize in the overall design of solid electrolyte interfacial compatibility and study the interfacial compatibility and stability by calculating the interfacial region interactions, charge transfer, adhesion energy, adsorption energy, interface formation energy, diffusion barrier, and density of states changes through the first nature principle. We conclude that LLZO solid-state electrolytes exhibit excellent interfacial properties, and interfacial compatibility and stability are further improved after doping. This paper shows a theoretical framework for exploiting novel electrolyte materials in all-solid-state battery.

Design method of immiscible dissimilar welding (Mg/Fe) based on CALPHAD and thermodynamic modelling

Joining dissimilar metals is a major challenge in joining technology; the weldability of immiscible systems is especially challenging. In this study, a design methodology for dissimilar welding is suggested. The Miedema model and Toop model are developed to calculate the thermodynamics of quaternary alloy systems (Mg-Fe-Al-Cu). Finite element modelling (FEM) of temperature fields and the calculation of phase diagrams (CALPHAD) are combined to provide prerequisite information for modelling. As a test subject, laser welded lap configuration joints of AZ31B magnesium alloy and DP590 steel with a copper coating were put into the design scheme. The interfacial elemental diffusion and formation of intermetallics (IMCs) along the interface during the welding process are predicted. This simulation design scheme predicts the interfacial reaction kinetics and identifies whether the intermediate element works or not. The effects of the Cu coating thickness on the weld constitution, interfacial microstructures and mechanical properties were studied. Cu coating promotes the weld formation fostering the metallurgical reaction of the fusion zone (FZ) with the steel brazing interface. The mechanism of interfacial reactions during the welding-brazing process has been clarified. The Vickers hardness distribution across the interface shows that the Cu-IMCs are ductile.

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.