Microstructure Formation in Rapidly Solidified Alloys

Abstract

ABSTRAcr 81In order to apply solidification theory to the interpretation of microstructures produced by rapid solidification, several modifications are required. Different degrees of non-equilibrium occur during solidification and constitute a hierarchy which is followed with increasing solidification rate.Analytical expressions are given for a model of non-equilibrium interface conditions which describe the temperatures and compositions at the liquid solid interface as a function of solidification velocity. For solidification at intermediate veloici ties ('" 1 0 cm/ s) the assumption of local interfacial equilibrium remains valid but microstructures are often produced under conditions where the solute Peclet number Pc = Vl/2D, is greater than one. '!he parameters V, 1 and D are the solidification velocity, relevant microstructural length scale and liquid diffusion coefficient respectively. '!his fact requires that several topics in solidification theory be modified. SUch a modification is presented for alloy dendritic growth theory. For alloys solidifying dendri tically into undercooled melts, solute redistribution dominates the relatinship between growth rate and initial undercooling when the initial undercooling is smaller than the alloy freezing range (difference between liquidus and solidus temperatures). '!his fact has several important consequences for the eutectic coupled zone boundaries and for arrayed dendritic growth.

Solidification of Highly Undercooled Liquid Droplets

“…In both cases the thermal signal exhibits a sharp onset followed by an isothermal arrest (neglecting a slight instrumental effect of <0.5° C) which is characteristic of an invariant reaction. In addition, the measured temperatures of this reaction exhibit little, if any, heating rate dependence over the range investigated and agree to within 1.5° C with the T 0 temperatures calculated from thermodynamic analysis and those estimated using a dilute solution approximation (75). Based on this evidence, it is proposed that the melting event detected at T[ during continuous heating corresponds to the partitionless melting of C 0 solid retained metastably within the droplets and therefore can provide an experimental measurement of the alloy T 0 25 temperature.…”

Phase-field investigation on the non-equilibrium interface dynamics of rapid alloy solidification

“…[54] (Merchant-Davis [78]) may trigger the dynamics for the banded structure formation, a numerical analysis was carried out and confirms that the growth condition predicted by Merchant-Davis's stability analysis actually leads to the oscillatory interface dynamics of planar front [80,81] as suggested in a phenomenological model [54]. Their sharp-interface numerical model of directional solidification [87] employed the solute trapping model of Aziz [2], attachment kinetic effect, and velocity-dependent liquidus from thermodynamically consistent model by BoettingerCoriell [26] for the boundary conditions at the solid-liquid interface. When the calculation started from a point on the up-sloping part of T S curve (between V 1 and V 3 in Figure 2.31)…”

“…2.12) needs to be formulated. Boettinger-CoriellSekerka [25,26] derived a thermodynamically consistent model for T * as a function of V * and the interface concentration. In order to relate T * to V * , Turnbull's collision-limited growth model [27] was employed.…”

“…Thus, Boettinger-Coriell [26] obtained more rigorous expression for minimum wavelength which can be employed even for large P c (but small P t ) using Mullins-Sekerka's stability criterion (MS) [10], and later Lipton-Kurz-Trivedi (LKT) [50] extended it for large P c and large P t . The wavelength obtained by LKT model is…”

Phase transformations in an AISI 410S stainless steel observed in directional and laser-induced cooling regimes

“…where C o is the alloy composition, m v is the velocity dependent non-equilibrium liquidus slope and k v is the nonequilibrium partition coefficient 25 . Equation 2 reduces to ∆T 0 when k v approaches the equilibrium value k e .…”