D. Temkin

MORPHOLOGY DIAGRAM OF POSSIBLE STRUCTURES IN DIFFUSIONAL GROWTH

A theory for the morphology diagram of possible structures in two-dimensional diffusional growth is presented. The main control parameters are undercooling Δ, anisotropy of surface tension e and the strength of noise. Basic patterns are dendrites and seaweed. The building block of the dendritic structure is a dendrite with parabolic tip, and the basic element of the seaweed structure is a doublon. The transition between these structures shows a jump in the growth velocity. The possible extension of these results to three-dimensional growth is shortly discussed.

Theory of discontinuous precipitation: importance of the elastic strain

Abstract In the framework of the approach developed in our previous paper, E.A. Brener and D.E. Temkin, Acta Materialia, 1999; 47, 3759, we consider discontinuous precipitation taking into account elastic effects. Elastic stresses arise because of the sharp concentration change ahead of the transformation front. The interface kinetics is assumed to be very fast and the process is controlled by interfacial diffusion along all interfaces. We show that the inclusion of elastic effects removes unphysical restrictions on material parameters required for steady-state solutions to exist. As usual in theories of the steady-state growth of periodic structures, the continuous spectrum of solutions with one free parameter exists. We calculate the growth velocity and the lamellar spacing as functions of the supersaturation, assuming that the dimensionless parameter, related to Cahn’s parameter, is approximately a constant close to 1 in a wide range of supersaturations. This nontrivial assumption, which does not follow directly from theory, is supported by experimental observations and allows to obtain α unique solution. The calculated dependencies agree with the experiments.

Velocity-selection problem for combined motion of melting and solidification fronts.

We discuss a free boundary problem for two moving solid-liquid interfaces that strongly interact via the diffusion field in the liquid layer between them. This problem arises in the context of liquid film migration (LFM) during the partial melting of solid alloys. In the LFM mechanism the system chooses a more efficient kinetic path which is controlled by diffusion in the liquid film, whereas the process with only one melting front would be controlled by the very slow diffusion in the mother solid phase. The relatively weak coherency strain energy is the effective driving force for LFM. As in the classical dendritic growth problems, also in this case an exact family of steady-state solutions with two parabolic fronts and an arbitrary velocity exists if capillary effects are neglected [D. E. Temkin, Acta Mater. 53, 2733 (2005)]. We develop a velocity-selection theory for this problem, including anisotropic surface tension effects.

Structure formation in diffusional growth and dewetting

Abstract The morphology diagram of possible structures in two-dimensional diffusional growth is given in the parameter space of undercooling Δ versus anisotropy of surface tension ϵ . The building block of the dendritic structure is a dendrite with a parabolic tip, and the basic element of the seaweed structure is a doublon. The transition between these structures shows a jump in the growth velocity. We show the analogy of diffusional growth with dewetting patterns of a fluid film on a substrate. We also describe the structures and velocities of fractal dendrites and doublons destroyed by noise. The extension of these results to three-dimensional growth is briefly discussed.

Pattern formation during diffusional transformations in the presence of triple junctions and elastic effects

We compare different scenarios for dendritic melting of alloys with respect to the front propagation velocity. In contrast to conventional dendritic growth, selection can here be also due to the presence of a grain boundary or coherence strains, and the propagation speed is higher. The most favorable situation is partial melting, where two parabolic fronts, one melting and one solidifying interface, are moving together, since the process is then determined by diffusion in the thin liquid layer. There, and also in phase field simulations of melting in peritectic and eutectic systems, we observe a rotation of the triple junction relative to the growth direction. Finally, we discuss the role of elastic effects due to density and structural differences on solid-state phase transformations, and we find that they significantly alter the selection principles. In particular, we obtain free dendritic growth even with isotropic surface tension. This is investigated by Greens function methods and a phase field approach for growth in a channel and illustrated for the formation of a twin phase.

Onsager approach to the one-dimensional solidification problem and its relation to the phase-field description.

We give a general phenomenological description of the steady-state 1D front propagation problem in two cases: the solidification of a pure material and the isothermal solidification of two-component dilute alloys. The solidification of a pure material is controlled by the heat transport in the bulk and the interface kinetics. The isothermal solidification of two-component alloys is controlled by the diffusion in the bulk and the interface kinetics. We find that the condition of positive-definiteness of the symmetric Onsager matrix of interface kinetic coefficients still allows an arbitrary sign of the slope of the velocity-concentration line near the solidus in the alloy problem or of the velocity-temperature line in the case of solidification of a pure material. This result offers a very simple and elegant way to describe the interesting phenomenon of a possible non-single-value behavior of velocity versus concentration that has previously been discussed by different approaches. We also discuss the relation of this Onsager approach to the thin-interface limit of the phase-field description.

Kinetics of Isothermal Phase Transformations by Phase-Field Simulations: An Analogy between the Peritectic and Monotectic Systems

We present phase-field simulations of isothermal phase transformations in the peritectic system below and above the peritectic temperature TP , and in the monotectic system below the monotectic temperature TM. We focus particularly on the Liquid-Film-Migration (LFM) mechanism, which appears to be the generic process for phase transformations above TP . Below TP , we obtain an assymetric LFM, suggesting the existence of a doublon structure in free space. In the monotectic system, the transformation from a liquid L1 to a solid+liquid L2 mixture proceeds via the migration of a L2 film, which is the analogous of the LFM process. When the metastable state consists of a liquid-liquid mixture, a dendritic-like solidification is obtained.

CREEP MOTION OF A SOLIDIFICATION FRONT IN A TWO-DIMENSIONAL BINARY ALLOY

The propagation of a solidification front in a two-dimensional binary alloy is studied by Monte Carlo simulations. A random atomic configuration is quenched and the atoms that prefer to be in the liquid phase act as quenched pinning centers to the advancing solidification front. For a system with large kink formation energye and finite system widthN, we show that the liquidus and solidus lines in the equilibrium phase diagram correspond to pinning-depinning transition lines, like in a one-dimensional system. In the one-phase region the front is depinned and propagates steadily, whereas in the two-phase region it is pinned and the velocity v decays as timet passes with a power-law behavior v(t);t, with n,1. For a moderate or for a large widthN, the pinning transition is smeared out and the front propagates steadily even in the two-phase region by thermal creep. When the driving force H is small, the velocityv decays exponentially withe and H. The size dependence is interpreted in terms of the height correlation. @S1063-651X~99!06601-5#