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\begin{document}%
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\PaperTitle{PARTITIONING AND SUPERSATURATION OF CARBON IN LOW-TEMPERATURE BAINITE}%
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%Author(s) Name(s), Author(s) Affiliation(s), and Keywords%
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\AuthorList{M. J. Peet$^1$, C. N. Hulme-Smith$^1$, H. J. Stone$^1$}%
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\AuthorAffiliations{$^1$University of Cambridge, Department of Materials Science and Metallurgy\\
27 Charles Babbage Road, Cambridge, CB3 0FS, UK}%
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\Keywords{bainite, synchrotron, in situ diffraction, tetragonality.}%
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In silicon alloyed high carbon steels, transformation in the temperature range 200-350$^\circ$C can result in extremely fine or nanostructured bainitic-ferrite and austenite. This transformation to low-temperature bainite leads to carbon-supersaturated bainitic ferrite, when considering the level expected from paraequilibrium between ferrite and austenite. The large supersaturation results in a greater fraction of ferrite forming than is otherwise expected. 

Atom probe observations have shown that carbon inhomogeneity in ferrite has been found to be associated with carbon clustering at dislocations, but also that carbon remains in solid solution above the saturation limit within defect-free regions of bainitic ferrite~\cite{Caballero:2012,Pereloma:2012,Caballero:2013}. The carbon content of ferrite only slowly decreases during tempering despite being conspicuously above the equilibrium solubility limit for body-centred cubic iron. In other work it has been proposed that this can be explained by tetragonality of the ferrite, \textit{in situ} synchrotron experiments are analysed to investigate this possibility.


 The results of first principle calculations suggests that the supersaturation remaining after transformation may be stabilised by forming ferrite with a symmetry other than cubic~\cite{Jang:2012}. Recently, analysis of diffraction data showed that the peak shape is more consistent with non-cubic ferrite after transformation to bainitic ferrite~\cite{Hulme-Smith:2013, Hulme-Smith:2014}.


\section{Low-temperature Bainite} 
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\subsection{Finite difference model for partitioning of carbon}
Using a semi-infinite 1-D continuum model~\cite{Mujahid:1992}, the calculated time for carbon partitioning from the a freshly transformed ferrite plate to the surrounding austenite is substantial; 1900\,s at 200$^\circ$C, 70\,s at 250$^\circ$C, and 4.2\,s at 300$^\circ$C. Although, since these times are always much lower than the holding time required for bainite transformation, the inhomogenities of carbon observed cannot be simply a result their being insufficient time for carbon partitioning to complete.

\subsection{Diffraction patterns of transformed material}

High quality data were acquired using a counter diffractometer on ID31 at the ESRF. For diffraction patterns measured at room temperature for steels previously transformed at 200$^\circ$C the best fit using the Rietveld technique was achieved using a body-centred-cubic bainite, allowing for a small fraction of martensite to be present.


\subsection{In situ transformation}
Analysis of data acquired \textit{in situ} during transformation completely excludes the possibility of artefacts introduced by any changes that could occur on cooling post transformation. An alloy Fe-0.79C-1.56Si-1.98Mn-0.24Mo-1.01Cr-1.51Co-1.01Al\,wt\% transformed at 300$^\circ$C showed no significant evidence of deviation from the body-centred-cubic unit cell during the \textit{in situ} experiments, when analysed using single peak fitting to the ferrite \{110\}. The ferrite \{200\} peak is of lower intensity, however the shape is not as expected for BCC or BCT unit cell -- slanted to higher angles (the opposite expected from tetragonality). The shape is consistent with a body-centred orthorombic lattice as previously observed~\cite{Hulme-Smith:2013}.

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\section{Conclusions}

Diffraction data for bainitic alloys in transformed condition and \textit{in situ} have been analysed considering the possibility of reduced symmetry of the ferrite unit cell. 

Finite difference calculations have been made to investigate the time needed for carbon partitioning, this time is much shorter than the time required for bainite transformation.



%\bibliography{refs}
%\bibliographystyle{unsrt}
\begin{thebibliography}{1}

\bibitem{Caballero:2012}
F.~G. Caballero et al.,
\newblock ``Temperature dependence of carbon supersaturation of ferrite in
  bainitic steels,''
\newblock {\em Scripta Materialia}, 67 (10) (2012), 846--849.

\bibitem{Pereloma:2012}
E.~Perelomo et al.,
\newblock ``Understanding the behaviour of advanced high-strength steels using
  atom probe tomography,''
\newblock {\em Metallurgical and Materials Transactions A}, 43 (11) (2012), 3958--3971.

\bibitem{Caballero:2013}
F.~G. Caballero et al.,
\newblock ``New experimental evidence of the diffusionless transformation nature of bainite,''
\newblock {\em Journal of Alloys and Compounds}, 577 (S1) (2013), S626--S630.

\bibitem{Jang:2012}
J.~H. Jang, H.~K.~D.~H. Bhadeshia, and D.~W. Suh.
\newblock ``Solubility of carbon in tetgragonal ferrite in equilibrium with
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\newblock {\em Scripta Materialia}, 68 (2012), 195--198.

\bibitem{Hulme-Smith:2013}
C.~N. Hulme-Smith et al.,
\newblock ``Experimental evidence for non-cubic bainitic ferrite,''
\newblock {\em Scripta Materialia}, 69 (5) (2013), 409--412.

\bibitem{Hulme-Smith:2014}
C.~N. Hulme-Smith et al.,
\newblock ``Further evidence of tetragonality in bainitic ferrite,''
\newblock {\em Materials Science and Technology}, 31 (2) (2015), 254--256.

\bibitem{Mujahid:1992}
S.~A. Mujahid and H.~K.~D.~H. Bhadeshia.
\newblock ``Partitioning of carbon from supersaturated ferrite plates,''
\newblock {\em Acta Metallurgica et Materialia}, 40 (2) (1992), 389--396.

\end{thebibliography}

\end{document}%
