An assessment of studies on homogeneous diffusional nucleation kinetics in binary metallic alloys
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I.
INTRODUCTION
W H I L E the thermodynamic basis for the theory of nucleation in condensed phases at small undercoolings was developed by Gibbs in 1878 [q and for nucleation at larger undercoolings by Cahn and Hilliard t2] in 1959, and the kinetic component of the theory largely evolved in the 1920s through 1940s, [3'4'5] serious experimental testing of the theory did not begin until the 1960s. In view of the formidable added obstacles to understanding and measurement posed by heterogeneous nucleation, these tests have been largely confined to homogeneous nucle-
H.I. AARONSON, R.F. Mehl Professor, is with the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213. F.K. LeGOUES, Manager, is with the Structure of Electronic Materials Department, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598. This paper is based on a presentation made in the "G. Marshall Pound Memorial Symposium on the Kinetics of Phase Transformations" presented as part of the 1990 fall meeting of TMS, October 8-12, 1990, in Detroit, MI, under the auspices of the ASM/MSD Phase Transformations Committee. METALLURGICAL TRANSACTIONS A
ation. The intrinsic difficulty of such experiments, even when conducted on homogeneous nucleation, and also the need to acquire large amounts of ancillary data of diverse types were probably responsible for this prolonged delay. Detailed tests of nucleation theory were first made on the homogeneous nucleation of one liquid phase within another [6-9J and on the nucleation of a vapor within a liquid phase. [1~ These tests were based upon determination of the "cloud point" supersaturation. In view of the violent supersaturation dependence of nucleation kinetics, [11 the particular supersaturation at which an initially transparent liquid becomes cloudy due to the formation of a high number density (=number of secondphase particles per unit volume = Nv) of precipitates was assumed equal to that required to achieve perceptible nucleation kinetics. However, the cloud point supersaturation was most surprisingly found invariably to be higher than that calculated from homogeneous nucleation theory, particularly since heterogeneous nucleation would yield the opposite outcome. This result strongly implied that the theory is fundamentally defective. Binder and Stauffer tH] were the first to recognize that the cloud VOLUME 23A, JULY 1992-- 1915
point is actually a complex resultant of nucleation, growth, and coarsening. Their analysis of the problem was succeeded by a more detailed study by Langer and Schwartz (LS), t12j combining the kinetics of nucleation and growth with the Wagner -t~31 Lifshitz-Slyozov (WLS) t14] analysis of coarsening kinetics. Applying this analysis to all available cloud point data, LS reached two important conclusions. The first is that with the exception of a single point, none of these data are seriously inconsistent with nucleation theory.* The second point is that when *For a sophisticated review of m o d e m theories of homogeneo
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