Terms Of Interfacial Energy Research Articles

Heterogeneous wires made of martensitic materials

In this paper we present a direct derivation of a theory of heterogeneous wires starting from three-dimensional nonlinear hyperelasticity augmented by an interfacial energy term. The derivation involves no a priori choice of asymptotic expansion or ansatz. It yields a wire theory with two Cosserat vector fields. The theory is applied to multiwell energy functions appropriate for martensitic materials. A formal derivation of higher theories of homogeneous wires is given, which yields three additional Cosserat vector fields and an explicit form for the bending and torsion energy. To cite this article: H. Le Dret, N. Meunier, C. R. Acad. Sci. Paris, Ser. I 337 (2003).

Microstructure, adhesion strength and failure path at a polymer/roughened metal interface

Metals and polymers are extensively used in microelectronics packaging where they are joined together. Since both the yield and reliability of packages are strongly affected by the interfacial adhesion between polymers and metals, extensive studies have been performed in order to improve the resistance to debonding of many resulting interfaces. In the present work, the interfacial fracture energy of representative polymer/metal interfaces commonly encountered in micoroelectronics packaging was characterized. A copper-based alloy leadframe was used as the metal and an epoxy molding compound (EMC) was used as the polymer. The leadframe surfaces were roughened by chemical oxidation in a hot alkaline solution and molded with the EMC. In general, roughening of metal surfaces enhances their adhesion to polymers by mechanical interlocking, yet often produces a cohesive failure in the polymer. Sandwiched double-cantilever beam (SDCB) specimens were employed to measure the adhesion strength in terms of interfacial fracture energy. After the adhesion test, the microstructures of metal surfaces before molding with the EMC were correlated to the adhesion strength, and the fracture surfaces were analyzed using various techniques to determine the failure path.

A New Molecular Modeling Approach To Predict Concomitant Nucleation of Polymorphs

This paper describes the onset of a new approach for the prediction of the nucleation rates of polymorphs crystallized from solution. The first step in the development of the new method is to come to an accurate prediction of the interfacial energy between the nucleus and solution, one of the key factors in the nucleation process. This prediction method is described in the paper and is tested for a simple binary Lennard−Jones mixture. The interfacial energy term shows a decreasing trend with increasing cluster size at cluster sizes between 300 and 750 atoms.

Interfacial Energies for Incoherent Inclusions

We study a variational problem describing an incoherent interface between a rigid inclusion and a linearly elastic matrix. The elastic material is allowed to slip relative to the inclusion along the interface, and the resulting mismatch is penalized by an interfacial energy term that depends on the surface gradient of the relative displacement. The competition between the elastic and interfacial energies induces a threshold effect when the interfacial energy density is non-smooth: small inclusions are coherent (no mismatch); sufficiently large inclusions are incoherent. We also show that the relaxation of the energy functional can be written as the sum of the bulk elastic energy functional and the tangential quasiconvex envelope of the interfacial energy functional.

Computational thermodynamics and the kinetics of martensitic transformation

To assist the science-based design of alloys with martensitic microstructure, a multicomponent database kMART (kinetics of MARtensitic Transformation) encompassing the components Al, C, Co, Cr, Cu, Fe, Mn, Mo, N, Nb, Ni, Pd, Re, Si, Ti, V, and W has been developed to calculate the driving force for martensitic transformation. Built upon the SSOL database of the Thermo-Calc software system, a large number of interaction parameters of the SSOL database have been modified, and many new interaction parameters, both binary and ternary, have been introduced to account for the heat of transformation, T0 temperatures, and the composition dependence of magnetic properties. The critical driving force for face-centered cubic (fcc) → body-centered cubic (bcc) heterogeneous martensitic nucleation in multicomponent alloys is modeled as the sum of a strain energy term, a defect-size-dependent interfacial energy term, and a composition-dependent interfacial work term. Using our multicomponent thermodynamic database, a model for barrierless heterogeneous martensitic nucleation, a model for the composition and temperature dependence of the shear modulus, and a set of unique interfacial kinetic parameters, we have demonstrated the efficacy of predicting the fcc → bcc martensitic start temperature (Ms) in multicomponent alloys with an accuracy of ± 40 K over a very wide composition range.

Tem Investigation Of Precipitate Shapes And New Interface Phenomena In Al-Pb Alloys

Abstract Transmission electron microscopy plays a key role in the investigation of precipitates and inclusions because it provides direct information at high spatial resolution, on their shape, orientation relationship, interface structure and composition. This work has utilized high resolution and in-situ electron microscopy to study the equilibrium shapes and thermal behavior of Pb precipitates in Al. It was found that PB precipitates within Al grains form in parallel-cube orientation relationship, are cuboctahedral in shape, adopt a sequence of magic sizes, and display an increase in aspect ratio with decreasing size. These observations have been explained in terms of interfacial energy and residual strain energy. When the same Pb precipitates form on grain boundaries, their shapes are significantly different. This is apparent from figure 1 which shows a 90° <110> tilt grain boundary in Al with a small cuboctahedral Pb precipitate in the upper grain and a large complex-shaped Pb particle on the grain boundary.

Regularity and convergence results for a phase-field model with memory

A phase–field model based on the Coleman–Gurtin heat flux law is considered. The resulting system of non-linear parabolic equations, associated with a set of initial and Neumann boundary conditions, is studied. Existence, uniqueness, and regularity results are proved. An asymptotic analysis is also carried out, in the case where the coefficient of the interfacial energy term tends to 0. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.

Interfacial and Bulk Contributions to Peeling Energy

Abstract Thin polyurethane films, having low adhesion to dried protein, were developed as candidate materials for non-adhesive surgical dressings. In order to model wound-adhesion, gelatine was cast from solution on to the film and allowed to dry. The film was peeled from the gelatine at 180° peel angle, and the peel force measured as a function of the temperature of test. The dynamic mechanical properties of the films were measured over the range −90°C to 110°C and values of tan δ were determined at the temperatures employed for peeling. Thus, a correlation was obtained between peeling energy and tan δ for each of eight films. The generalised theory of fracture mechanics states that the adhesive failure energy is given by the product of an interfacial energy term and a “loss function” involving the hysteresis ratio of the material. If the strains are small the hysteresis ratio is proportional to tan δ. The experimental results show excellent agreement with the theory, but the interfacial term turns out t...

Interfacial dislocation based criterion for the prediction of rafting behavior in superalloys

The effect that the morphological changes in {gamma}/{gamma}{prime} superalloys have on the mechanical properties of these materials is still an unresolved issue of the greatest interest. Experimental studies on [001] oriented single crystals have shown, for instance, that when a microstructure consisting of evenly spaced cuboids of {gamma}{prime} embedded in {gamma} was subjected to externally applied stresses at high temperature, then the coalescence occurred in an orientation-dependent way, and also that these rafting phenomenon can have a significant influence on the creep or fatigue life in load-bearing applications. In some alloys, the coalescence produced long rods or needles of {gamma}{prime} oriented parallel to the axis of stress, and others produced flat plates or rafts in an orientation perpendicular to the stress axis. In most alloys this orientation dependence was found to invert when a stress of opposite sign was applied. Recent attempts to predict the rafting behavior of these materials have suggested using a combined Monte Carlo/finite element approach which relies on the elastic strain energy and an isotropic interfacial energy term. While this approach succeeded in reproducing the map developed by Pineau and based on the elastic energy of inclusions, a large amount of computation was needed even formore » small lattices in simulations of the microstructural evolution. The present study, which is part of a wider research program on the mechanical performance of superalloys, is aimed at presenting a novel criterion providing an improved rafting prediction map and also a simpler way to model the energy anisotropy, so as to allow simulations of larger systems or for longer microstructural evolutions.« less

Elaboration and TEM structural study of interfaces in composites produced by precipitation

Model ceramic matrix composites have been manufactured in a wide range of materials using the precipitation of a metal (Cu, Ni, Cr) in a ceramic matrix (nitride AlN or oxides MgO, Al 2 O 3 ) providing, in each case, low energy configurations at the heterophase interfaces. In connection to microelectronic applications, copper metallic particles precipitate in AlN after implantation by copper ions and anneal of the ceramic matrix. Faceted particles are imaged by HRTEM an are associated to a low energy structural and chemical configuration. Internal reduction experiments have been carried out on (Mg,Ni)O, (Mg,Cu)O and (Al,Cr)203 mixed oxides; the morphology, chemical composition and orientation relationship of the different precipitates are obtained through TEM observations and discussed in terms of interfacial energy and precipitate growth mechanism and kinetics. Conventional and high resolution TEM in conjonction to structural models have allowed a comprehensive description of the interface

Lamellar microstructure of discontinuous precipitation reaction front in Cu-7.5%In

There is an increasing body of evidence for discontinuous precipitation (DP) as a general solid state phase transformation in materials. The understanding of the DP phenomenon, however, requires to establish its energy balance. The lamellar microstructure at the grain boundary reaction front (RF) is of particular interest since it results from the optimization of, at least, chemical, capillary and interfacial energy terms coupled with the boundary mobility at a given undercooling. Our investigation into this field has lead us to the conclusion that an additional term reflecting the residual stresses in the transformed product should be incorporated. In the present paper, microstructural features focused at the lamellar growth front are illustrated and discussed supporting the idea that DP is a non-equilibrium reaction.The alloy used for this study, Cu-7.5at.%In, was prepared at the Max-Planck-Institut, Stuttgart, from high purity components by induction melting under argon atmosphere and chill cast. After homogenization at 600°C/300h samples were directly aged isothermally at different temperatures and quenched. The parent FCC matrix α decomposes into depleted α lamellae and tetragonal Cu3In β lamellar precipitates.

In-situ observation of high temperature silicate solutions

An in-situ observation method of growth or dissolution of crystals at high temperatures is briefly explained. As examples of the application of the method, metastable nucleation phenomena observed in silicate systems, and the effect of Cr upon nucleation behavior are analyzed. It was demonstrated that the interfacial energy term has the definitive effect upon nucleation behavior.

Overview no. 86: The effect of surface stress on crystal-melt and crystal-crystal equilibrium

The effect of surface stress on the equilibrium conditions at crystal-melt, coherent crystal-crystal and greased crystal-crystal interfaces is investigated by using a variational method to test for equilibrium. In all three cases, the interface between the phases is modelled as a Gibbsian dividing surface, and the excess internal energy associated with the interface is allowed to depend on both the deformation of the interface and the crystallographic normal to the interface. The position of an interface can vary due to both deformation at the interface and transformation between the two phases at the interface (accretion), and so we define a special variation that accounts for both. Thus, surface stress appears explicitly in both the force and energy balances at crystal-melt and coherent crystal-crystal interfaces. In particular, an interfacial strain energy term appears in the energy balance at these interfaces; this term gives the energy of deforming the interface against the force associated with the surface stress, and is a new result from this analysis. Anisotropy also appears in this energy balance through a term that can be expressed by using Cahn and Hoffman's ξ-vector. Finally, it is shown that a greased crystal-crystal system differs from crystal-melt and coherent crystal-crystal systems in that two independent deformations and crystallographic normals can be defined at a greased interface. However, by partitioning the excess energy associated with a greased interface between these deformations and normals, one can reduce the equilibrium conditions at a greased interface to those that obtain if the two crystals would interact only through a thin fluid layer at the interface.

Experimental Study of the Relative Energy of Symmetrical <110> Tilt Boundaries in a Semi-Conducting F.C.C. Oxide (NiO).

ABSTRACTLarge size bicrystalline samples of NiO corresponding to tilt configurations around a < 110 > axis have been grown by the flame fusion technique, the misorientation angles varying from 0 to 180°. The variation of the relative energy of the grain boundary with misorientation has been studied and has indicated a very different behaviour from that previously observed by the authors on <100> tilt boundaries. High relative energy values and deep cusps on the energy curve at high coincidence angles are observed. The results are discussed in terms of interface energy.

A Comprehensive Presentation of the Thermodynamics of Adsorption Excess Quantities

Abstract A common general framework of thermodynamic relations between interfacial excess quantities in multicomponent systems is derived, based essentially on the fundamental Gibbsian treatment of adsorption phenomena. Both adjoining bulk phases are regarded as equivalent constituents of the system concerned—not only in the case of fluid interfaces, which are approached in this way in any current exact treatment, but also in the case of S/G and S/L interfaces, respectively. The algebraic mode of definition of the surface excesses of the components and of the coupled thermodynamic quantities is adopted, but without reference to imaginary Gibbs dividing surfaces positioned within the actual system, in order to avoid the necessity of admitting the concept of an adsorption excess of the solid, when considering the most common mode of evaluation of adsorption from liquid solutions by immersion experiments. Applications of the general relations to L/G, S/G and S/L interfaces respectively are demonstrated. In connection with the latter two, no use is made of the controversial concept of surface tension of the solid. Instead an extra interfacial free energy term is introduced, as a mean specific quantity for adsorbents with a fixed colloidal texture, but whose surfaces are inhomogeneous, both geometrically as well as energetically. The aim of the proposed representation is not the derivation of fundamentally new thermodynamic relations, but to obtain a unified picture of adsorption at different kinds of interfaces, and to rely as far as possible only on operational definitions.

Interfacial Energy Terms from Dissolution Rate Data

Interfacial Energy Terms from Dissolution Rate Data

Interaction of dislocations with interfaces

The effect on mechanical behavior of a differential elastic modulus across an interface was investigated using single crystal composite specimens prepared in configurations which minimized the influence of other factors. Tensile specimens were prepared from thin copper single crystals and epitaxial metal films were grown on the surfaces by vapor deposition to provide desired interfaces. The principal material combinations studied were copper-nickel and copper-cobalt. In addition, copper films grown onto copper tensile specimens substrate were used to evaluate the influence of certain imperfections. The elastic modulus difference was found to provide the primary strengthening mechanism for Cu-Xi and Cu-Co interfaces. Surface and interfacial energy terms were also evaluated and found not significant compared to contributions from other interface factors. Crystal structure changes induced in cobalt coatings with deformation resulted in high work-hardening compared to that of the Cu-Ni systems.

The solubility of disperse dyes in an aqueous sodium dodecyl sulfate solution

The solubilities of the following compounds in an aqueous sodium dodecyl sulfate solution were determined at 25°, 30°, 35° and 40°C: biphenyl, azobenzene, p-chloroazobenzene, p-aminoazobenzene, p-N,N-dimethylaminoazobenzene and p-nitroazobenzene. From the results the thermodynamic parameters for the transfer of the model compounds from water to SDS micellar environment were calculated. The resulting thermodynamic parameters were not so certain, but suggested that with biphenyl, azobenzene and p-chloroazobenzene which seem to be solubilized in the SDS micellar interior the solubilizing process is a result of a favourable increase in entropy, and that with p-aminoazobenzene, p-N, N-dimethylaminoazobenzene and p-nitroazobenzene which seem to be solubilized in the SDS micellar surface the solubilizing process is a result of a favourable decrease in enthalpy. The favourable increase in entropy was explained in terms of iceberg and the favourable decrease in enthalpy in terms of interfacial energy.

Grain Growth in Polycrystalline Ice

AbstractLiterature is not available on the grain growth in polycrystalline ice. The present paper deals with such grain growth in pure ice and ice doped with sodium chloride. The technique consists in measuring grain size distributions as a function of time and deriving the numberaverage equivalent “diameter”, considering the grains as spheres. The functional relationship between the average diameter and time of growth is, for pure and doped ice, of the same form as that found for metals. Arrhenius plots show that the energy of activation is higher for doped ice than for pure ice. The results are discussed in terms of interfacial free energy as being ultimately responsible for grain growth. On a molecular scale, processes take place, which lead to diffusion of units consisting of a number of water molecules across the boundaries.

Study of the Properties of an Excess Electron in Liquid Helium. II. A Refined Description of Configuration Changes in the Liquid

In this paper we present a study of the structural changes in liquid helium in the vicinity of an excess electron. We have used the formal similarity between the pair distribution function of an N-boson system, with the wavefunction expressed as the product of pair wavefunctions, and the pair distribution function of a classical fluid. The present model leads to an interfacial surface energy term which is in good agreement with the observed surface tension of liquid helium at 0°K. An important contribution to the bubble energy arises from the volume kinetic energy arising from the excess kinetic energy of the fluid atoms removed from the boundary layer. The bubble radius of 12.4 Å calculated herein is found to be in excellent agreement with the available experimental data.