Evolution Of Microstructures In Nano-multilayers At High Temperatures

Investigation into the evolution of microstructures in nano-multilayers at hightemperatures could provid a guildline for the structure design, performance improvementand lifetime prediction in practice. Two mulitilayer systems have been studied in thispaper:(1) the constituents in multilayers are completely miscible (e.g. Mo/V) and (2) theconstituents in multilayers are immiscible (e.g. Cu/Nb). For the first type of multilayers,a model for interdiffusion across coherent multilayer interfaces is developed to explorethe effects of coherency stress and vacancy sources/sinks on the interface sharpening andintermixing rate; for the other type of multilayers, a model addressing the migration ofinterphase and grian boundaries and triple junctions is developed to investigate theformation mechanism of Zig-zag microstructure and the stability against pinch-off. Themain contents and important results are summaries as follows.1. A model corresponding to vacancy-mediated interdiffusion across interfaces incoherent multilayers with completely miscible constituents is developed using thephase-field approach. The effects of several factors on interdiffusion across coherentmultilayer interfaces are incorporated, such as:(1) the dependence of diffusion potentialsand mobilities on coherency stress,(2) the dependence of diffusion potentials andmobilities on composition, correspondingly,(3) the elastic constants inhomogeneityresulted from compositional distribution, and (4) the properties of vacancy sources/sinks.The Gibbs free energy of the system consists of chemical and elastic energies. Thegradient energy usually appearing in phase-field models is neglected as multilayersconsidered can be chemically well approximated by an ideal substitutional solutionmodel. Elastic energy is a functional of the stress-free strain and inhomogeneous elastic moduli distribution, while the stress is solved by anisotropic phase-field microelasticitytheory. The diffusion potentials are obtained quite straightforwardly as functionalderivatives of free energy with respect to compositions and are in keeping with previousderivations that involved many mathematical manipulations or quite advanced theories.The diffusion mobilities are affected by the stress through its modification to the vacancyformation and migration energies. Two limiting cases of vacancy sources/sinks aretaken into account: ideal vacancy sources/sinks are uniformly and densely distributed, ornot present at all, so the vacancy concentration is in equilibrium all the times asdetermined by local stress and compositions in the former case, but deviates from theequilibrium concentration in the latter. The model can be conveniently extended toconsider the non-ideal activity of vacancy sources/sinks by introducing a general kineticrelation for the vacancy creation rate.2. The phase-field model is applied to interdiffusion in coherent Mo/V and Cu/Nimultilayers, aiming to explore the effects of coherency stress and vacancy sources/sinkson the interface sharpening and intermixing rate. Interface sharpening is found to stemfrom the large asymmetry in diffusion coefficients across the interface and it is originatedfrom the great difference in vacancy migration and formation energies between the twolayers, which in turn can be affected by the coherency stress and vacancy sources/sinks.Introduction of vacancy sources/sinks can enhance interface sharpening, more effectivelyin multilayers with similar vacancy migration energies but greatly different vacancyformation energies. Coherency stress affects the intermixing rate through itsmodification to the diffusion potentials and diffusion mobilities, but the formermodification is dominant when the vacancy sources/sinks are parallel to the interfaces ornot present at all, and the latter is dominant when the vacancy sources/sinks areperpendicular to the interfaces or distributed in all orientations. Introduction of vacancysources/sinks affects the intermixing rate mainly from three aspects:(1) allowing thetotal number of vacancies, and thereby the average diffusion coefficient over the wholespecimen, to vary significantly with the progress of intermixing, while it is nearly stable at the absence of sources/sinks;(2) changing the rate-controlling component, from theslower component at the absence, to the faster component at the presence, of vacancysources/sinks that are parallel to interfaces;(3) developing additional stress by latticecreations/annihilations to suppress intermixing when the vacancy sources/sinks arenormal to the interfaces or uniformly in all orientations. Those simulations couldprovide a useful guideline for the improvement of interface sharpness or better predictionfor the lifetime of multilayers. If one wants to obtain interfaces with better sharpness byshortly annealing in Cu/Ni and Mo/V multilayers, it is recommended that Cu/Ni beproduced with dense vacancy sources/sinks and in initially non-coherent state, and Mo/Vbe produced, either with dense vacancy sources/sinks and in initially coherent state, orfewer sources/sinks and in non-coherent state to minimize the suppressing effect of thecoherency stress. If one wants to have the layered structures in Cu/Ni and Mo/Vmultilayers maintained as long as possible at high temperatures, it is recommended thatCu/Ni be produced with fewer vacancy sources/sinks and in non-coherent state, butMo/V be produced with dense vacancy sources/sinks and in non-coherent state.3. A predictive model for microsture evolution in multilayers with immiscibleconstituents is developed to study formation mechanism of experiemtally-observedZig-zag microstructure in Cu/Nb multilayers and the stability of layered structure. Themodel addresses the coordinated migration of triple junctions, interphase and grainboundaries. As an extension to the previous models for grooving analysis, the triplejunctions are assumed to have temperature-dependent mobility and to move in thedirection in the imbalance in tensions of interphase and grain boundaries, in coordinationwith motion of its neighboring points on the interphase boundary following the principleof mass conservation. Further, the current model unifies the two separated treatmentsfor the aligned and classical staggered grain geometries, which become two limiting onesof this unified model. Two conditions are found to be necessary for the formation ofZig-zag structure:(1) the grains in multilayers are initially staggered in a manner thatgrains in each upper layer shift in the same direction a distance less than the half in-plane grain size relative to the lower one, and (2) non-equilibrium triple junctions can movealong path deviating from the original grain boundaries, as driven by the imbalance intensions of interphase and grain boundaries. The motion of a finite mobility junctioncan effectively impede the development of grooves, suggesting the prediction of time topinch-off using the classical t1/4dependence of groove depth assuming infinite triplejunction mobility might be questionable at low temperatures. Further, a map for thestability of layered structure in Cu/Nb system is developed in terms of the aspect ratio ofgrain sizes and the ratio of the distance between two nearest triple junctions to thein-plane grain size. A criterion for such stability is also proposed for multilayers withsimilar grain boundary energies based on simplified geometrical consideration. Boththe map and the simple criterion are in good agreement with the experiments for Cu/Nbmultilayers. The multilayer stability also show a relation with the way in which thegrains are stacked in the layers. The aligned grain geometry has the highest stabilityagainst pinch-off, followed by the staggered one with grains shifting in the samedirection, then the staggered one with grains shifting to the left and right alternativelyand finally the classical staggered one.