The c/a Ratio in Quenched Fe-C and Fe-N Steels - A Heuristic Story


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The body-centered tetragonal (BCT) structure in quenched Fe-C steels is usually illustrated to show a linear change in the c and a axes with an increase in carbon content from 0 to 1.4%C. The work of Campbell and Fink, however, shows that this continuous linear relationship is not correct. Rather, it was shown that the body-centered-cubic (BCC) structure is the stable structure from 0 to 0.6 wt%C with the c/a ratio equal to unity. An abrupt change in the c/a ratio to 1.02 occurs at 0.6 wt%C. The BCT structure forms, and the c/a ratio increases with further increase in carbon content. An identical observation is noted in quenched Fe-N steels. This discontinuity is explained by a change in the transformation process. It is proposed that a two-step transformation process occurs in the low carbon region, with the FCC first transforming to HCP and then from HCP to BCC. In the high carbon region, the FCC structure transforms to the BCT structure. The results are explained with the Engel-Brewer theory of valence and crystal structure of the elements. An understanding of the strength of quenched iron-carbon steels plays a key role in the proposed explanation of the c/a anomaly based on interstitial solutes and precipitates.



Materials Science Forum (Volumes 539-543)

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Edited by:

T. Chandra, K. Tsuzaki, M. Militzer , C. Ravindran




O. D. Sherby et al., "The c/a Ratio in Quenched Fe-C and Fe-N Steels - A Heuristic Story", Materials Science Forum, Vols. 539-543, pp. 215-222, 2007

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March 2007




[1] E.C. Bain and H.W. Paxton: Alloying Elements in Steel (ASM, Metals Park, Ohio, 1966).

[2] W.L. Fink and E.D. Campbell: Trans. Am. Soc. Steel Treat, Vol. 9 (1926), pp.717-752.

[3] K. Honda and Z. Nishiyama: Science Reports, Tohoku Imperial Univ. Vol. 21 (1932), p.299; Trans. Am. Soc. Metals Vol. 20 (1932), p.464.

[4] M. Cohen: Phase Transformations in Solids (John Wiley & Sons, New York 1951), p.588.

[5] W.S. Owen, E.A. Wilson and T. Bell: High Strength Materials (V.F. Zackay Ed., John Wiley & Sons, New York 1965), pp.167-212.

[6] L. Brewer: ibid, p.12.

[7] W. Hume-Rothery: Prog. Mater. Sci. Vol. 13 (1968), p.229.

[8] O.D. Sherby and J. Wadsworth: LLNL reports, May 25, 1999 and Nov. 4, (1999).

[9] J.R. Cahoon and O.D. Sherby: Metall. Mater. Trans. Vol. 23A (1992), p.2491.

[10] O.D. Sherby and C.M. Young: Plastic Deformation of Materials (J.C.M. Li and A.K. Mukherjee, Eds. Am. Soc. Metals, Metals Park, Ohio 1975), Vol. 6, pp.487-541.

[11] M. Cohen: Trans. Metall. Society of AIME Vol. 224 (1962). p.638.

[12] B.A. Bilby and J.W. Christian: Jnl. Iron and Steel Inst. Vol. 197 (1961), p.122.

[13] P.G. Winchell: The Structure and Mechanical Properties of Iron-Nickel-Carbon Martensites (Sc.D. Thesis, MIT 1958).

[14] V. Seetharamen and R. Krishman: J. Mater. Sci. Vol. 16 (1981), p.523.

[15] A.R. Marder and G. Krauss: Trans. ASM Vol. 60 (1967), p.651.

[16] C. Zener: Trans. AIME Vol. 167 (1946), p.550.

[17] A.H. Cottrell: An Introduction to Metallurgy (Edward Arnold Publishers, Ltd, London 1967).

[18] E.C. Bain: Trans. AIME Vol. 70 (1924), p.25.

[19] G.R. Speich: Trans. Met. Soc. AIME Vol. 245 (1969), p.2553.

[20] H. Carpenter and J.M. Robertson: Metals (Oxford University Press, 1939).

[21] A.B. Greninger and A.R. Troiano: Trans. ASM Vol. 28 (1940), p.537.

[22] M.C. Zhao, Y. Hanamura, H. Qui, and K. Yang: Mater. Trans. JIM Vol. 46 (2005), p.784.

[23] C.K. Syn, D.R. Lesuer and O.D. Sherby: Mater. Sci. Tech. Vol. 21 (2005), p.317.

[24] D.R. Lesuer, C.K. Syn and O.D. Sherby: submitted to Mater. Trans. JIM (2006).

[25] G.V. Kurdjumov: J. Iron and Steel Inst. Vol. 195 (1960), p.26.