Metallurgical and Materials Transactions A

, Volume 47, Issue 1, pp 19–25 | Cite as

Modeling C-Curves for the Growth Rate of Widmanstätten and Bainitic Ferrite in Fe-C Alloys

  • Lindsay Leach
  • Mats Hillert
  • Annika Borgenstam


When Zener formulated his maximum growth rate criterion for predicting the coarseness of various metallographic objects, he simplified the growth rate equations and predicted that the optimum coarseness should be twice the critical value for which all the driving force would be absorbed by interfacial energy. It is now emphasized that a composition dependence of the diffusion coefficient has a considerable influence and can result in a ratio much larger than two. Various approximations have now been removed from the growth rate equation. When applied to acicular ferrite in the Fe-C system, a C-curve for the growth rate is obtained that resembles the unusually wide C-curve obtained experimentally when information on Widmanstätten ferrite and bainite is combined. It is not necessary to explain that shape as a combination of separate curves for Widmanstätten ferrite and bainite. The main reason for the wide C-curve is the direct effect of the composition dependence of the diffusivity of carbon in austenite.


Ferrite Austenite Bainite Interfacial Energy Effective Diffusion Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


The authors wish to acknowledge the financial support rendered by VINNOVA, the Swedish Governmental Agency for Innovation Systems, Swedish industry and KTH Royal Institute of technology. The work has been performed within the VINN Excellence Centre Hero-m.


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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2015

Authors and Affiliations

  • Lindsay Leach
    • 1
  • Mats Hillert
    • 1
  • Annika Borgenstam
    • 1
  1. 1.Department of Materials Science and EngineeringKTH Royal Institute of TechnologyStockholmSweden

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