B. Caroli

Interface kinetics and solidification of alloys: A discussion of some phenomenological models

Abstract We discuss various phenomenological descriptions of uniform interface kinetics in binary mixtures. We show that the linearized description provided by out-of-equilibrium thermodynamics is unambiguous and internally coherent. We discuss how various simple microscopic pictures of atomic attachment are reflected in the values of the corresponding Onsager coefficients. We discuss the far-from-equilibrium models of Aziz and Jackson-Gilmer-Leamy and the relationship between solute trapping and interspecies atomic drag. We propose another type of model in which the interaction between the kinetics of the two species is of the catalytic type. We show that such an interaction may give rise to oscillatory modes of growth, i.e. to kinetically-induced striations of the solid alloy.

Lamellar eutectic growth of CBr4-C2Cl6: effect of crystal anisotropy on lamellar orientations and wavelength dispersion

Abstract Directional solidification samples of eutectic alloys generally appear divided into numerous “eutectic grains”, i.e. regions of uniform orientation of the two solid phases. Differences of behavior from grain should provide information about the effect of crystal anisotropy on solidification dynamics of eutectics. In thin samples of CBr 4 -C 2 Cl 6 , we observed two types of grains: “locked”, or epitaxial, grains and “floating” grains, with no epitaxy between the two solid phases. We present a systematic experimental study of the stationary basic state in floating grains. The parity of this state appears generally broken: within a grain, the lamellae are tilted to a small (⪅ 5°), but definite angle Φ S with respect to the pulling direction. Φ S and the wavelength λ S are grain dependent. The interpretation of this tilting as an effect of the weak anisotropy of the interface energies is supported by a perturbative analytical calculation, completely developed in the limit of small triple-point pinning angles. The phase diffusion coefficient ¢D(λ) is also calculated in this limit to account for the observed slowness of phase diffusion. Eutectic grain boundaries are permanent sources of instabilities and of λ-gradients which do not spread out by phase diffusion for the duration of experiments, and the principal source of λ dispersion.

Effect of elastic stresses on the morphological stability of a solid sphere growing from a supersaturated melt

Abstract We examine the effect of the stresses induced by the composition dependence of the lattice parameter on the quasi-stationary growth dynamics of a spherical solid particle in a supersaturated melt. The problem is formulated using the Larche-Cahn thermodynamic formalism. The elastic field generated by the “self-stress” depends on the entire concentration profile in the grown solid. As a result, the “self-stress” induces a “memory” of the interfacial concentration in the solid at a given time on the values of the interfacial concentration at all earlier times. We find that, in the spherical growth regime, this effect modifies the shape of the concentration profile from its stress free profile, but affects only very weakly the growth velocity. We then perform a linear stability analysis and find that elastic effects destabilize the interface via a reduction in the critical radius for shape instability. Moreover, the elasticity induced memory gives rise to a new qualitative effect: l = 1 modes (describing the diffusional migration of the undeformed sphere) are no longer neutral and become weakly unstable.

Viscosity-induced stabilization of the spherical mode of growth from an undercooled liquid

Abstract The growth of a solid sphere from a very viscous undercooled melt (glass-forming liquid) is studied in the presence of the flow induced by the density difference between the two phases. It is shown that, when the growth dynamics are controlled by diffusion of either heat or chemically heterogeneous impurities, melt viscosity slows down the growth and strongly stabilizes the spherical morphology. This mechanism could be of importance in understanding some features of spherulitic crystallization.

Addendum to “non-equilibrium thermodynamics of the solidification problem”

Abstract We point out and correct a misleading ambiguity in the expression of energy conservation at the surface of a growing solid that we established in a recent paper [J. Crystal Growth 66 (1984) 575].