On the critical nucleus composition of ferrite in an Fe-C-Mn alloy
- PDF / 332,966 Bytes
- 4 Pages / 594 x 774 pts Page_size
- 74 Downloads / 152 Views
I.
INTRODUCTION
IN classical nucleation theory, the assumption is made that the critical nucleus size is large compared to the thickness of the interface, the region of compositional and structural change, and that the energy of the interface, o-, is independent of the nucleus size.l On common (but not accurate ~) practice, the volume free energy change, AG~, is then calculated at the bulk equilibrium composition (atom fraction of solute) of the precipitate phase, X E. This calculation is most nearly correct at the smallest supersaturations, i.e., as AG~ --~ 0, and when the free energy-composition curve of the precipitate phase is narrow. At finite undercoolings, however, the critical nucleus composition, X N, is not equal to X e, as a consequence of capillarity. The parallel tangent construction takes account of the influence of capillarity when the partial molar volumes of A and B in the nucleus phase are the same; a modification of this construction is required when these volumes are unequal. 2 In this paper, an apparently first attempt is made to access numerically the difference between X u and X E at constant interfacial energy. The calculation will be carried out for the nucleation of proeutectoid ferrite in an Fe-0.5 at. pct C-3 at. pct Mn alloy, chosen as representative (and particularly well furnished with ancillary data) from a set of five Fe-C-X alloys on which nucleation measurements are reported in a companion paper?
II.
CALCULATION
X N is determined by means of the following construction, illustrated in Figure 1.~ For simplicity, the figure is drawn here for a binary Fe-C system. A line is first drawn tangent to the free energy-composition curve of the matrix phase 3' at the bulk composition of the alloy Xcr and (automatically) to the capillarity-increased free energy-composition curve of the critical nucleus, c~'. A second line is then drawn tangent to the c~ curve so that the ratio of the distance M. ENOMOTO, formerly Graduate Student, Department of MetallurgicaI Engineering and Materials Science, Carnegie-Mellon University, is Senior Researcher, Tsukuba Laboratories, National Research Institute for Metals, 1-2-1 Sengen, Sakura-Mura, Niihari-Gun, Ibaraki 305, Japan. H. I. AARONSON is R. F. Mehl Professor, Department of Metallurgical Engineering and Materials Science, Carnegie-Mellon University, Pittsburgh, PA 15213. Manuscript submitted September 11, 1985. METALLURGICAL TRANSACTIONS A
P'Fs ,,a',/XF*,7 ~12"
t~sFe,a E E /ZF.,,,,/XF,,r . ~ -
)"
.
.
is
_
,,
,
P" ~.~
2.N Fe
I I I X~,a xN,a X~,a
Xr
r
C
,t~,a
Fig. l - A construction for the composition of the critical nucleus of a phase, X ~.~, formed from y phase matrix with composition Xc.~. P * is the pressure in the nucleus due to capillarity.
between the intercepts on both sides of the free energycomposition diagram is equal to VFr ~,/VC.~, the ratio of the partial molar volume of Fe to that of the solute C in the a phase. The point of tangency of the second line to the G-x curve for a identifies the nucleus composition XC, N o
Data Loading...
