Abstract
The growth of proeutectoid ferrite in Fe-C-X alloys containing ∼3 at. pct X, where X is Mn, Ni, Cr, and Si, is re-examined in terms of solute drag using the Hillert–Sundman theory. The differences of measured growth rates from those calculated under paraequilibrium (PE) reported previously were accounted for taking into account not only the binding energy of substitutional solute with the boundary, but also the transformation temperature of the alloy. The ferrite growth in quaternary Fe-C-Mn-Si alloys was modeled using the stationary-interface approximation for the matrix of finite grain size. The principal features of growth in these alloys, i.e., initial fast unpartitioned growth and subsequent slow partitioned growth with a high level of carbon supersaturation in austenite, were reproduced incorporating cosegregation of Mn and Si at the boundary. Thus, a strong Mn-Si interaction is likely to enhance accumulation of these elements at the boundary and yield the growth behavior that resembles the growth stasis in Fe-C-Mo alloys.
Similar content being viewed by others
Notes
It is noted that the growth rates calculated under local equilibrium become greater than those under PE at lower temperatures. This occurs due to a peculiar shape of the (α + γ) two-phase field in the isothermal section of the Fe-C-Cr phase diagram.[39] This is a direct consequence of the fact that Cr is an austenite stabilizer at lower concentrations and becomes a ferrite stabilizer at higher concentrations.[40]
The E i values taken from experiment (Table II) include the terms of self-interaction coefficients ε i(i).
References
M. Hillert: “Paraequilibrium,” Internal Report, Swedish Institute of Metals, Stockholm, 1947
J.S. Kirkaldy: Can. J. Phys., 1958, vol. 36, pp. 907–16
G.R. Purdy, D.H. Weichert, J.S. Kirkaldy: Trans. TMS-AIME, 1964, vol. 230, pp. 1025–34
H.I. Aaronson, H.A. Domian: Trans. TMS-AIME, 1966, vol. 236, pp. 781–96
J.B. Gilmour, G.R. Purdy, J.S. Kirkaldy: Metall. Trans., 1972, vol. 3, pp. 1455–64
D.E. Coates: Metall. Trans., 1973, vol. 4, pp. 1077–86
K.R. Kinsman, H.I. Aaronson: Metall. Trans., 1973, vol. 4, pp. 959–67
J.R. Bradley, H.I. Aaronson: Metall. Trans. A, 1981, vol. 12A, pp. 1729–41
M. Enomoto, H.I. Aaronson: Metall. Trans. A, 1987, vol. 18A, pp. 1547–57
M. Hillert: Scripta Mater., 2002, vol. 46, pp. 447–53
K. Oi, C. Lux, G.R. Purdy: Acta Mater., 2000, vol. 48, pp. 2147–55
C.R. Hutchinson, A. Fuchsmann, Y.J.M. Brechet: Metall. Mater. Trans. A, 2004, vol. 35A, pp. 1211–21
A. Phillion, H.S. Zurob, C.R. Hutchinson, H. Guo, D.V. Malakhov, J. Nakano, G.R. Purdy: Metall. Mater. Trans. A, 2004, vol. 35A, pp. 1237–42
M. Enomoto: Metall. Mater. Trans. A, 2006, vol. 37A, pp. 1703–10
P.G. Boswell, K.R. Kinsman, G.J. Shiflet, and H.I. Aaronson: in Mechanical Properties and Phase Transformations in Engineering Materials, S.D. Antolovich, R.O. Ritchie, and W.W. Gerberich, eds., TMS, Warrendale, PA, 1986, pp. 445–66
G.J. Shiflet, H.I. Aaronson: Metall. Trans. A, 1990, vol. 21A, pp. 1413–32
W.T. Reynolds Jr., F.Z. Li, C.K. Shui, H.I. Aaronson: Metall. Trans. A, 1990, vol. 21A, pp. 1433–63
K.M. Wu, M. Kagayama, M. Enomoto: Mater. Sci. Eng., 2003, vol. A343, pp. 143–50
R.E. Hackenberg, G.J. Shiflet: Acta Mater., 2003, vol. 51, pp. 2131–47
E.S. Humphreys, H.A. Fletcher, J.D. Hutchins, A.J. Garratt-Reed, W.T. Reynolds Jr., H.I. Aaronson, G.R. Purdy, G.D.W. Smith: Metall. Mater. Trans. A, 2004, vol. 35A, pp. 1223–35
H.I. Aaronson, W.T. Reynolds Jr., G.R. Purdy: Metall. Mater. Trans. A, 2004, vol. 35A, pp. 1187–1210.
H.I. Aaronson, W.T. Reynolds Jr., G.R. Purdy: Metall. Mater. Trans. A, 2006, vol. 37A, pp. 1731–45
T. Tanaka, H.I. Aaronson, M. Enomoto: Metall. Mater. Trans. A, 1995, vol. 26A, pp. 561–80
H. Guo, G.R. Purdy, M. Enomoto, H.I. Aaronson: Metall. Mater. Trans. A, 2006, vol. 37A, pp. 1721–29
M. Hillert, B. Sundman: Acta Metall., 1976, vol. 24, pp. 731–43
H.B. Aaron, D. Fainstein, G.R. Kotler: J. Appl. Phys., 1970, vol. 41, pp. 4404–10
R.A. Vandermeer: Acta Metall. Mater., 1990, vol. 38, pp. 2461–70
M. Enomoto: Acta Mater., 1999, vol. 47, pp. 3533–40
J. Odqvist, M. Hillert, J. Ågren: Acta Mater., 2002, vol. 50, pp. 3211–25.
G.R. Purdy, Y.J.M. Brechet: Acta Metall. Mater., 1995, vol. 43, pp. 3763–74
M. Enomoto, M. Kagayama, N. Maruyama, and T. Tarui: in Proc. Int. Conf. on Solid-Solid Phase Transformations’99, M. Koiwa, K. Otsuka, and T. Miyazaki, eds., The Japan Institute of Metals, Sendai, 1999, pp. 1453–50
M. Hillert: in H.I. Aaronson, ed., Phase Transformations, ASM, Metals Park, OH, 1970, pp. 181–218
M. Enomoto, H.I. Aaronson: Scripta Metall., 1985, vol. 19, pp. 1–3
E.D. Hondros: in Precipitation Processes in Solids, K.C. Russell, and H.I. Aaronson, eds., TMS, Warrendale, PA, 1978, pp. 1–30
M. Enomoto, C.L. White, H.I. Aaronson: Metall. Trans. A, 1988, vol. 19A, pp. 1807–18
M. Enomoto, N. Nojiri, Y. Sato: Mater. Trans. JIM, 1994, vol. 35, pp. 859–67
J.S. Kirkaldy, B.A. Thomson, and E.A. Baganis: in Hardenability Concepts with Applications to Steel, D.V. Doane, and J.S. Kirkaldy, eds., TMS-AIME, Warrendale, PA, 1978, pp. 82–125
G. Inden and C.R. Hutchinson: in Austenite Formation and Decomposition, B. Damm and M.J. Merwin, eds., TMS, Warrendale, PA, 2003, pp. 65–79
B. Uhrenius: in Hardenability Concepts with Applications to Steel, D.V. Doane and J.S. Kirkaldy, eds., TMS, Warrendale, PA, 1978, pp. 28–81
M. Enomoto: Trans. ISIJ, 1988, vol. 28, pp. 826–35
C.R. Hutchinson, H.S. Zurob, Y. Brechet: Metall. Mater. Trans. A, 2006, vol. 37A, pp. 1711–20
C.H.P. Lupis: Chemical Thermodynamics of Materials, North-Holland, New York, 1983, pp. 235–62
J. Crank: The Mathematics of Diffusion, 2nd ed., Clarendon Press, Oxford, United Kingdom, 1975, pp. 44–68
Acknowledgments
The authors are grateful to the members of the ALEMI (Alloying Effects on Migrating Phase Interfaces) group for valuable discussion.
Author information
Authors and Affiliations
Corresponding author
Additional information
Manuscript submitted September 26, 2006.
Appendix
Appendix
Stationary interface approximation for the growth of ferrite in a finite austenite matrix
For the diffusion fields in ferrite and austenite (Figure 1), the solution is given by an infinite series as[43]
and
respectively, where x i is the solute concentration (or mole fraction) in the matrix, and x α i and x γ i are the concentrations at the boundary in ferrite and austenite. The term x 0 i is the bulk concentration; \( D_{i} ^{\nu } \) (ν = α or γ) is the solute diffusivity; d is half the grain size; s is the distance; and S is the location of the boundary at the real time t, which is determined by the condition of mass balance in ferrite and austenite as
Performing integration with respect to s, Eq. [A3] becomes
where Ω i = (x γ i – x 0 i )/(x γ i – x α i ) is the supersaturation of solute i, and
and
Differentiating Eq. [A4] with respect to t,
where
and
As described in Section II–B, when diffusion in ferrite can be neglected, one can put
in Eqs. [A4] and [A7].
Rights and permissions
About this article
Cite this article
Guo, H., Enomoto, M. Effects of Substitutional Solute Accumulation at α/γ Boundaries on the Growth of Ferrite in Low Carbon Steels. Metall Mater Trans A 38, 1152–1161 (2007). https://doi.org/10.1007/s11661-007-9139-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11661-007-9139-0