An assessment of studies on homogeneous diffusional nucleation kinetics in binary metallic alloys

Abstract

A critical review is presented of all studies on homogeneous nucleation kinetics in crystalline binary metallic alloys located in the literature. Emphasis was first placed upon examining the data on the number of precipitates per unit volume of matrix phase,N _v , recorded as a function of isothermal reaction or aging time. With the exception of the results of a few studies on Cu-rich Cu-Co alloys, all of these data were extensively “contaminated” by significant overlapping of the diffusion fields of adjacent precipitates and especially by concurrent coarsening. The use of the “nucleation window” concept was advocated as a means of finding a range of alloy compositions and reaction temperatures in a particular alloy system within which sufficient data onN _v vs time can be collected to evaluate the steady-state nucleation rate,J _s ^* without significant intervention by either disturbing effect. Transmission electron microscopy (TEM) was identified as a particularly valuable experimental tool for measuringN _v . However, smallangle neutron scattering (SANS) is also proving useful for this purpose, and the combination of SANS with FIM-AP (field ion microscope-atom probe) has uncovered information of crucial importance to understanding the transformation sequence in Cu-Co alloys. Wagner and co-workers^{[52,62,63,64-78-79]} have demonstrated the presence of precursor Co segregations large in extent but small in amplitude, of which the most successful lead to the formation of identifiable precipitates (within which segregation is very much larger in amplitude but considerably smaller in extent). The Wagneret al. work suggests that the supersaturations at which they formed were insufficient to permit the fluctuations which did not eventually fulfill exactly the specifications for critical nuclei to evolve into precipitates. While classical, the Cahn-Hilliard continuum nonclassical [su2] and Cook-deFontaine discrete lattice point nonclassical nucleation theories^[25,26,27] yield nearly identical results in the temperature-Co concentration range experimentally studied, theJ* _s values thus calculated are a few orders of magnitude smaller than the experimentally measured rates when the concentration of vacancies present at the reaction temperature is (reasonably) assumed operative. On the basis of theoretical and computer simulation studies by Binderet al. ^{[84,87,89,90]} and Kleinet al.,^[91–94] the observed precursor concentration fluctuations are indicative of relatively long-range interactions among adjacent atoms in Cu-Co alloys, whereas the solution thermodynamics so far applied to this system is based upon the use of short interaction distances. This is suggested to be the principal source of the discrepancy between measured and calculated nucleation kinetics in Cu-Co alloys. Suggestions are offered for future research intended to clarify some of the complexities which have recently become apparent in studies of homogeneous nucleation kinetics in binary metallic alloys.