Eutectic growth in two-phase multicomponent alloys

Abstract

A theory of two-phase eutectic growth for a multicomponent alloy is presented.This theory employs the thermodynamic equilibrium at the solid/liquid interface and thus makes it possible to use standard CALPHAD databases to determine the effects of multicomponent phase equilibrium on eutectic growth. Using the same hypotheses as the Jackson Hunt theory, we find that the growth law determined for binary alloys in the Jackson Hunt theory can be generalized to systems with N elements. In particular, a new model is derived from this theory for ternary two-phase eutectics. The use of this model to predict the eutectic microstructure of systems is discussed.

Revisiting Jackson-Hunt calculations: Unified theoretical analysis for generic multi-phase growth in a multi-component system

“…This along with Eqs.11 implies that p c p i η p = c ∞ i , which is the mass conservation equation used by Senninger and Voorhees [37]. However, given that the thermodynamical relations…”

“…For this, we need to describe the functional dependence between the solid compositions c p i and the liquid compositions c pl i . We do this by calling upon the relations of the phase compositions c p,pl A point to note here is that, Senninger and Voorhees [37], replace the Eqs.11 with a mass conservation con-…”

“…Magnin and Trivedi [34] Here, the solid phase fractions are determined from the criterion of equal undercoolings at the two solid-liquid interfaces. A more rigorous extension is provided recently by Senninger and Voorhees [37], where they take into account the composition variations of both the solid phases.…”

Pearlite in Multicomponent Steels: Phenomenological Steady-State Modeling

“…Cahn has constructed an approximate solution which connects low-and high-velocity limits (Eqs. [16][17][18]Reference 24). Using the k 1 and k 2 coefficients defined in the previous two equations, the expression is:…”

“…The theory of pearlite formation has its stage set by Zener [7] and has been further developed by Hillert, [8][9][10] Cahn, [11,12] and others. [13][14][15][16][17][18] Industrially relevant calculation tools for pearlite include DICTRA as part of Thermo-Calc [19] based on the work of Jo¨nsson, [20] and JMatPro based on the formulation by Kirkaldy et al, [21] with various levels of predictability and user-friendliness.…”