The kinetics of ferrite nucleation at austenite grain boundaries in Fe-C alloys
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I.
INTRODUCTION
MEASUREMENTS of nucleation kinetics of precipitates at grain boundaries and comparison of these data with the predictions of classical nucleation theory have yet to be accomplished with sufficient accuracy.l This investigation was undertaken in an attempt to improve upon both situations. Three high-purity hypoeutectoid Fe-C alloys were used to measure the nucleation kinetics of allotriomorphs of proeutectoid ferrite at austenite grain boundaries as a function of isothermal reaction time and temperature. Choice of the Fe-C system prevented study of the structure of the grain boundaries at which nucleation took place because the austenite not transformed to proeutectoid ferrite is converted to martensite during quenching to room temperature. However, the paucity of necessary ancillary data in other alloy systems (especially of interfacial energies) and the detailed knowledge now available of the proeutectoid ferrite reaction- made this transformation seem the most appropriate one for an initial investigation of this type.
II.
Classical nucleation theory expresses the time-dependent nucleation rate, J*, as: 2'3"4 exp~--~)
exp -
[1]
where J* is the nucleation rate; N is the density of atomic sites available for nucleation; Z, the Zeldovich nonequiW. E LANGE, III, formerly Graduate Student, Department of Metallurgical Engineering, Michigan Technological University, Houghton, Mt 49931, is Senior Engineer and Manager of Electronic Packaging Technology Group, IBM Corporation, V42/025-1, Boulder, CO 80302. M. ENOMOTO is Senior Researcher, Tsukuba Laboratories, National Research Institute for Metals, 1-2-1 Sengen, Sakura-Mura, NiihariGun, Ibaraki 305, Japan. H.I. AARONSON, formerly Professor at Michigan Technological University, is R. E Mehl Professor, Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213. Manuscript submitted August 25, 1986. METALLURGICALTRANSACTIONS A
j, =
ND 1/2v [ o -3 ] o-o7 ~X~K K exp a4(kT)l/2 t~* z q~2kT Kao.
[2]
where o-or is the interracial energy of a disordered ferrite: austenite boundary; D is the diffusivity of carbon in austenite at xv, the atom fraction of carbon in austenite prior to transformation; a is the average lattice parameter of both phases; 4~ is the algebraic sum of AGv, the volume free energy change associated with nucleation and W, the volume strain energy attending formation of the critical nucleus;* * L e e et al. 9 have shown that the strain energy is not likely to influence the critical nucleus shape unless W--> 0 . 7 5 1 A G v l . Consequently, under conditions usually encountered it is sufficient simply to sum AGv and W.
SUMMARY OF RELATIONSHIP FOR NUCLEATION KINETICS
J* = Zr
librium factor, corrects the equilibrium nucleation rate for nuclei that grow beyond the critical size; fl*, the frequency factor, is the rate at which single atoms are added to the critical nucleus; AG* is the free energy of activation for formation of the critical nucleus; r is the incubation time; t is the isoth
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