Curvature-driven Coarsening Research Articles

Phase decomposition in nanoporous Au-Pt

This study explores microstructure and phase decomposition in nanoporous Au-Pt made by dealloying. The starting alloy, Ag75Au12.5Pt12.5, forms a uniform solid solution. Removing the Ag by dealloying at room temperature forms nanoporous equimolar Au-Pt with a ligament size as small as 4 nm. That alloy’s composition is in the Au-Pt phase diagram’s regime of spinodal instability. Surprisingly, in view of the instability and of the substantial atomic rearrangements accompanying dealloying, X-ray diffraction and transmission electron microscopy reveal a homogeneous single-phase state in the bulk of the nanoporous material. This can be traced back to enrichment of Pt at the surface, which depletes the bulk in Pt. The Pt-depleted bulk is in the metastable region of the alloy phase diagram, between the binodal and the spinodal. Annealing prompts curvature-driven coarsening by diffusion, diminishing the number of sites for Pt surface segregation. The ensuing enrichment of the bulk in Pt is accompanied by the formation first of crystallographically coherent, Pt-rich regions and later of semi-coherent regions of the Pt-rich phase. The morphology of the coherent regions is compatible with spinodal decomposition. Yet, the microstructure evolution pathway is nonstandard, since decomposition here concurs with rapid coarsening of the porous microstructure. Among the prospect of the nanoporous alloy are its high kinetic stability and the opportunity to tune the surface composition through the annealing temperature.

Topological aspects responsible for recrystallization evolution in an IF-steel sheet – Investigation with cellular-automaton simulations

A cellular automaton algorithm for curvature-driven coarsening is applied to a cold-rolled interstitial-free steel’s microstructure - obtained through electron backscatter diffraction (EBSD). Recrystallization nucleation occurs naturally during the simulation, due to the highly heterogeneous and hence competitive growth among pre-existing (sub) grains. The spatial inhomogeneity of the subgrain growth that takes place derives from the large local variations of subgrain sizes and misorientations that comprise the prior deformed state. The results show that capillary-driven selective growth takes place to the extent that the prior elongated and deformed grains are replaced by equiaxed grains with no interior small-angle boundaries. Additionally, during the simulation certain texture components intensify and others vanish, which indicates that preferential growth occurs in a fashion that relates to the crystal orientations’ topology. The study of the early stages of recrystallization (i.e. nucleation) shows that the pre-existing subgrains that eventually recrystallize, exhibit certain topological characteristics at the prior deformed state. Successful nucleation occurs mostly for pre-existing matrix subgrains abutting shear bands or narrow deformation bands and particularly at regions where the latter intersect.

General evolution equation for the specific interface area of dendrites during alloy solidification

The specific area of the solid-liquid interface of an assembly of dendrites is an important integral measure of the morphology of the microstructure forming during alloy solidification. It represents the inverse of a characteristic length scale and is needed for the prediction of solidification defects and material properties. In the present study, the evolution of the interfacial area of dendrites is analysed using 3D phase-field simulations. A general evolution equation is developed for the specific interface area as a function of time and solid volume fraction that accounts for the effects of growth, curvature-driven coarsening and interface coalescence. The relation is validated using data from previously performed synchrotron X-ray tomography and isothermal coarsening experiments. It is found to be valid for arbitrary and even varying cooling rates and for a wide range of binary alloys. The rate constant in the evolution equation is successfully related to alloy properties.

Particles with selective wetting affect spinodal decomposition microstructures.

We have used mesoscale simulations to study the effect of immobile particles on microstructure formation during spinodal decomposition in ternary mixtures such as polymer blends. Specifically, we have explored a regime of interparticle spacings (which are a few times the characteristic spinodal length scale) in which we might expect interesting new effects arising from interactions among wetting, spinodal decomposition and coarsening. In this paper, we report three new effects for systems in which the particle phase has a strong preference for being wetted by one of the components (say, A). In the presence of particles, microstructures are not bicontinuous in a symmetric mixture. An asymmetric mixture, on the other hand, first forms a non-bicontinuous microstructure which then evolves into a bicontinuous one at intermediate times. Moreover, while wetting of the particle phase by the preferred component (A) creates alternating A-rich and B-rich layers around the particles, curvature-driven coarsening leads to shrinking and disappearance of the first A-rich layer, leaving a layer of the non-preferred component in contact with the particle. At late simulation times, domains of the matrix components coarsen following the Lifshitz-Slyozov-Wagner law, R1(t) ∼ t1/3.

Evolution of mixed cementite morphologies during non-cooperative eutectoid transformation in Fe–C steels

We numerically investigate the characteristics of concurrent carbon redistribution pathways, as the ferrite–austenite front evolves during an isothermal eutectoid transformation starting from a random distribution of preexisting cementite particle. By analyzing the influence of initial interparticle spacing, arrangement and undercooling (below A1 temperature) on the curvature-driven coarsening, we generalize the present criteria of non-cooperative eutectoid transformation. We also propose plausible mechanisms that result in mixed cementite morphologies (spherical and non-spherical) in the transformed microstructure. For the chosen set of parameters, the present phase-field simulations suggest a strong competition between the cooperative, non-cooperative and coarsening regimes, as the transformation proceeds. The predominance of one or more of the three regimes during the intermittent stages, which depend on the local conditions, determine the cementite size distribution in the transformed microstructure.

Curvature-driven coarsening in the two-dimensional Potts model

We study the geometric properties of polymixtures after a sudden quench in temperature. We mimic these systems with the q -states Potts model on a square lattice with and without weak quenched disorder, and their evolution with Monte Carlo simulations with nonconserved order parameter. We analyze the distribution of hull-enclosed areas for different initial conditions and compare our results with recent exact and numerical findings for q=2 (Ising) case. Our results demonstrate the memory of the presence or absence of long-range correlations in the initial state during the coarsening regime and exhibit superuniversality properties.

Exact results for two-dimensional coarsening

We consider the statistics of the areas enclosed by domain boundaries (‘hulls’) during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area, n h (A, t)dA, with enclosed area in the range (A,A + dA), is described, for large time t, by the scaling form n h (A, t) = 2c h /(A + λ h t)2, demonstrating the validity of dynamical scaling in this system. Here $$ c_h = {1 \mathord{\left/ {\vphantom {1 8}} \right. \kern-\nulldelimiterspace} 8}\pi \sqrt 3 $$ is a universal constant associated with the enclosed area distribution of percolation hulls at the percolation threshold, and λ h is a material parameter. The distribution of domain areas, n d (A, t), is apparently very similar to that of hull areas up to very large values of A/λ h t. Identical forms are obtained for coarsening from a critical initial state, but with c h replaced by c h /2. The similarity of the two distributions (of areas enclosed by hulls, and of domain areas) is accounted for by the smallness of c h . By applying a ‘mean-field’ type of approximation we obtain the form n d (A, t) ≃ 2c d [λ d (t+t 0)] τ−2/[A+λ d (t+t 0)] τ , where t 0 is a microscopic timescale and τ = 187/91 ≃ 2.055, for a disordered initial state, and a similar result for a critical initial state but with c d → c d /2 and τ → τ c = 379/187 ≃ 2.027. We also find that c d = c h + O(c 2 ) and λ d = λ h (1 + O(c h )). These predictions are checked by extensive numerical simulations and found to be in good agreement with the data.

Exact Results for Curvature-Driven Coarsening in Two Dimensions

We consider the statistics of the areas enclosed by domain boundaries ("hulls") during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than A has, for large time t, the scaling form Nh(A,t)=2c/(A+lambdat), demonstrating the validity of dynamical scaling in this system, where c=1/8pisquare root 3 is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of A/lambdat. Identical forms are obtained for coarsening from a critical initial state, but with c replaced by c/2.

Front dynamics in an oscillatory bistable Belousov-Zhabotinsky chemical reaction

We observe breathing front dynamics which select three distinct types of bistable patterns in the 2:1 resonance regime of the periodically forced oscillatory Belousov-Zhabotinsky reaction. We measure the curvature-driven shrinking of a circular domain R approximately t(1/2) at forcing frequencies below a specific value, and show that the fast time scale front oscillations (breathing) drive this slow time scale shrinking. Above a specific frequency, we observe fronts of higher curvature grow instead of shrink and labyrinth patterns form. Just below the transition frequency is a relatively narrow range of frequencies where the curvature-driven coarsening is balanced by a competing front interaction, which leads to a pattern of localized structures. The length scale of the localized structure and labyrinth patterns is set by the front interactions.

Formation and evolution of grain structures in thin films

We describe an approach to studying grain structure formation and evolution in polycrystalline thin films using a “grain continuum” representation of the solid. Formation and evolution of grain structure are tracked using level-set-based geometry software we call PLENTE. We demonstrate the approach using two processes; (1) vapor deposition and (2) grain boundary migration during curvature-driven coarsening. We employ several codes in concert to track the development of grains during deposition while accounting for reaction kinetics, ballistic transport, and re-emission of reactive species.