Institute of Metals Division - Nonplanar Interfaces in Two-Phase Ternary Diffusion Couples

The extra degree of freedonz introduced by a second independetzt concentration in a tenzary system gives rise to the possibility of unstable planar phase interfaces in semi-infinite diffision layer couples. Diffusion paths which pass continuously in and out of too-phase regions of the phase diagram but which are not coincident with tie-lines give rise to super saturated zones which may be either adjacent to or isolated from planar phase interfaces, with corresponding nonisolated or isolated precipitates. Nonisolated precipitates are equivalent to morphological development of the interface. Selected couples in the ternary systems Fe-Ni-Cr and Cu-Zn-Sn have been examined nzetallographically and ifz the latter case both isolated and uo~zisolated precipitates have been observed. The diffusion path in one of the couples showing interface morphological developtnent has been examitled using electron probe microanalysis. IGNORING the spurious effects of preferential grain boundary diffusion and anisotropic crystal growth7 it can be unequivocally stated that it is impossible for a binary isothermal diffusion couple constructed of two unsaturated phases to sustain a nonplanar phase interface. Consider for demonstrative purposes the schematic phase diagram of Fig. l(a). Given an initial flat phase interface, semi-infinite boundary conditions and the internal boundary condition fixed by the constitution diagram, xB = xB(T), the unique solution of the diffusion equation requires a persistent flat interface. No other solution is possible. If, however, we anticipate the involvement of surface tension, then the internal boundary condition must be written xB = xB (T,Y) where r is the radius of curvature of a hypothetical nonplanar interface. The introduction of a new parameter such as r can be equivalent to the release of an internal constraint, so that a stable nonplanar interface may be possible after all. Consider a perturbation to the interface as indicated in Fig. 1(b). According to the Ostwald-Freundlich equation: which is applicable to a system of this constitution, the solubility of A in the matrix ß ,xB (Y), at a point of curvature r is given by where Va is the molar volume of the a-phase, R is the gas constant, and a is the interfacial tension. Since the right hand side is positive, xB(r) >xB cm, as indicated in Figs. 1(a) and 1(c). Accordingly, the perturbation will carry the interface concentration in a direction which is opposite to that which would sustain local equilibrium. Such a perturbation is necessarily moderated and the system is returned to its initial condition. This result is general for all binary couples since we can regard an interfacial perturbation as an attempt to precipitate within un-