Abstract
Carbon ordering in supersaturated body-centered iron was investigated by means of atomic-scale simulations. Beyond the well-known Zener ordering of carbon atoms, our results reveal a first-order transition occurring upon temperature change when a single crystal is subjected to axial compression. This ordering produces orthorhombic martensite due to unequal carbon redistribution over the three octahedral interstitial sites. The resulting phase diagram is of the rare homotectoid type. Connection is made with the thermoelastic behavior of martensitic alloys, which proves to be similar to that of shape-memory alloys.
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W.L. Fink and E.D. Campbell, Influence of Heat Treatment and Carbon Content on the Structure of Pure Iron Carbon Alloys, Trans. Am. Soc. Steel Treat., 1926, 9, p 717
L. Morsdorf, C.C. Tasan, D. Ponge, and D. Raabe, 3D Structural and Atomic-Scale Analysis of Lath Martensite: Effect of the Transformation Sequence, Acta Mater., 2015, 95, p 366-377. https://doi.org/10.1016/j.actamat.2015.05.023
P. Zhang, Y. Chen, W. Xiao, D. Ping, and X. Zhao, Twin Structure of the Lath Martensite in Low Carbon Steel, Prog. Nat. Sci. Mater. Int., 2016, 26, p 169-172. https://doi.org/10.1016/j.pnsc.2016.03.004
W. Zhang, Y.M. Jin, and A.G. Khachaturyan, Phase Field Microelasticity Modeling of Heterogeneous Nucleation and Growth in Martensitic Alloys, Acta Mater., 2007, 55, p 565-574. https://doi.org/10.1016/j.actamat.2006.08.050
A. Stormvinter, G. Miyamoto, T. Furuhara, P. Hedström, and A. Borgenstam, Effect of Carbon Content on Variant Pairing of Martensite in Fe-C Alloys, Acta Mater., 2012, 60, p 7265-7274. https://doi.org/10.1016/j.actamat.2012.09.046
H.K.D.H. Bhadeshia, Bainite in Steels: Theory and Practice, 3rd ed., Maney Publishing, Leeds, 2015
J.H. Jang, H.K.D.H. Bhadeshia, and D.-W. Suh, Solubility of Carbon in Tetragonal Ferrite in Equilibrium with Austenite, Scr. Mater., 2013, 68, p 195-198. https://doi.org/10.1016/J.SCRIPTAMAT.2012.10.017
C. Garcia-Mateo, J.A. Jimenez, H.W. Yen, M.K. Miller, L. Morales-Rivas, M. Kuntz et al., Low Temperature Bainitic Ferrite: Evidence of Carbon Super-Saturation and Tetragonality, Acta Mater., 2015, 91, p 162-173. https://doi.org/10.1016/j.actamat.2015.03.018
C. Zener, Theory of Strain Interaction of Solute Atoms, Phys. Rev., 1948, 74, p 639-647. https://doi.org/10.1103/PhysRev.74.639
A.G. Khachaturyan and G.A. Shatalov, On the Theory of the Ordering of Carbon Atoms in a Martensite Crytal, Fiz. Met. Met., 1971, 32, p 1-9
P.V. Chirkov, A.A. Mirzoev, and D.A. Mirzaev, Tetragonality and the Distribution of Carbon Atoms in the Fe-C Martensite: Molecular-Dynamics Simulation, Phys. Met. Metallogr., 2016, 117, p 34-41. https://doi.org/10.1134/S0031918X1601004X
K.A. Taylor and M. Cohen, Ageing of Ferrous Martensites, Prog. Mater Sci., 1992, 36, p 225-272
G.V. Kurdjumov and A.G. Khachaturyan, Nature of Axial Ratio Anomalies of the Martensite Lattice and Mechanism of Diffusionless Gamma to Alpha Transformation, Acta Metall., 1975, 23, p 1077-1088. https://doi.org/10.1016/0036-9748(75)90354-3
Z. Fan, L. Xiao, Z. Jinxiu, K. Mokuang, and G. Zhenqi, Lattice-Parameter Variation with Carbon Content of Martensite. II. Long-Wavelength Theory of the Cubic-to-Tetragonal Transition, Phys. Rev. B., 1995, 52, p 9979-9987
A. Udyansky, J. von Pezold, A. Dick, and J. Neugebauer, Orientational Ordering of Interstitial Atoms and Martensite Formation in Dilute Fe-Based Solid Solutions, Phys. Rev. B., 2011, 83, p 184112. https://doi.org/10.1103/PhysRevB.83.184112
A. Udyansky, J. Von Pezold, V.N. Bugaev, M. Friák, and J. Neugebauer, Interplay Between Long-Range Elastic and Short-Range Chemical Interactions in Fe-C Martensite Formation, Phys. Rev. Condens. Matter Mater. Phys., 2009, 79, p 224112. https://doi.org/10.1103/physrevb.79.224112
R. Naraghi, M. Selleby, Stability of Fe-C Martensite-Effect of Zener-Ordering, in: P.C. and G.S. John Allison (Ed.), 1st World Congrress on Integrated Computational Materials and Engineering, TMS, pp. 235–240.
R. Naraghi, M. Selleby, and J. Ågren, Thermodynamics of Stable and Metastable Structures in Fe-C System, CALPHAD: Comput. Coupling Phase Diag. Thermochem., 2014, 46, p 148-158. https://doi.org/10.1016/j.calphad.2014.03.004
C.W. Sinclair, M. Perez, R.G.A. Veiga, and A. Weck, Molecular Dynamics Study of the Ordering of Carbon in Highly Supersaturated Alpha-Fe, Phys. Rev. B., 2010, 81, p 224204. https://doi.org/10.1103/PhysRevB.81.224204
O. Waseda, J. Morthomas, F. Ribeiro, P. Chantrenne, C.W. Sinclair, and M. Perez, Ordering of Carbon in Highly Supersaturated α-Fe, Model. Simul. Mater. Sci. Eng., 2019, 27, p 015005. https://doi.org/10.1088/1361-651X/aaef22
S. Djaziri, Y. Li, G.A. Nematollahi, B. Grabowski, S. Goto, C. Kirchlechner et al., Deformation-Induced Martensite: A New Paradigm for Exceptional Steels, Adv. Mater., 2016, 28, p 7753-7757. https://doi.org/10.1002/adma.201601526
D.V. Wilson, B. Russell, and J.D. Eshelby, Stress Induced Ordering and Strain-Ageing in Low Carbon Steels, Acta Metall., 1959, 7, p 628-631. https://doi.org/10.1016/0001-6160(59)90132-4
J.Y. Yan and A.V. Ruban, Configurational Thermodynamics of C in Body-Centered Cubic/Tetragonal Fe: A Combined Computational Study, Comput. Mater. Sci., 2018, 147, p 293-303. https://doi.org/10.1016/j.commatsci.2018.02.024
A.V. Ruban, Self-Trapping of Carbon Atoms in Alpha′-Fe During the Martensitic Transformation: A Qualitative Picture from ab Initio Calculations, Phys. Rev. B Condens. Matter Mater. Phys., 2014, 90, p 144106. https://doi.org/10.1103/physrevb.90.144106
P. Maugis, Nonlinear Elastic Behavior of Iron-Carbon Alloys at the Nanoscale, Comput. Mater. Sci., 2019, 159, p 460-469. https://doi.org/10.1016/J.COMMATSCI.2018.12.024
M.A. Shtremel and F.F. Satdarova, Influence of Stresses on Order in Interstitial Solutions, Fiz. Met. Met., 1972, 34, p 699-708
P. Chirkov, A. Mirzoev, and D. Mirzaev, Carbon Ordering in Martensite Lattice Under External Stress: Thermodynamic Theory and Molecular Dynamics Simulation, Phys. Status Solidi., 2018, 1700665, p 1700665. https://doi.org/10.1002/pssb.201700665
P.V. Chirkov, A.A. Mirzoev, and D.A. Mirzaev, Role of Stresses and Temperature in the Z Ordering of Carbon Atoms in the Martensite Lattice, Phys. Met. Metallogr., 2016, 117, p 1138-1143. https://doi.org/10.1134/S0031918X16110041
P. Maugis, Ferrite, Martensite and Supercritical Iron: A Coherent Elastochemical Theory of Stress-Induced Carbon Ordering in Steel, Acta Mater., 2018, 158, p 454-465. https://doi.org/10.1016/J.ACTAMAT.2018.08.001
P. Maugis, F. Danoix, H. Zapolsky, S. Cazottes, and M. Gouné, Temperature Hysteresis of the Order-Disorder Transition in Carbon-Supersaturated α-Fe, Phys. Rev. B., 2017, 96, p 214104. https://doi.org/10.1103/PhysRevB.96.214104
R.W. Balluffi, Introduction to Elasticity Theory for Crystal Defects, Cambridge University Press, Cambridge, 2012, https://doi.org/10.1017/CBO9780511998379
P. Maugis, S. Chentouf, and D. Connétable, Stress-Controlled Carbon Diffusion Channeling in bct-Iron: A Mean-Field Theory, J. Alloys Compd., 2018, 769, p 1121-1131. https://doi.org/10.1016/J.JALLCOM.2018.08.060
S. Chentouf, S. Cazottes, F. Danoix, M. Goune, H. Zapolsky, and P. Maugis, Effect of Interstitial Carbon Distribution and Nickel Substitution on the Tetragonality of Martensite: A First-Principles Study, Intermetallics, 2017, 89, p 92-99. https://doi.org/10.1016/j.intermet.2017.05.022
L.D. Landau and E.M. Lifshitz, Statistical Physics, 2nd ed., Pergamon Press, New York, 1969, https://doi.org/10.1016/0368-3265(59)90121-5
H. Okamoto, A Two-Peak Miscibility Gap, J. Phase Equilibria, 1993, 14, p 336-339. https://doi.org/10.1007/BF02668230
J.L. Meijering, Thermodynamic Analysis and Synthesis of Phase Diagrams, Physica, 1981, 103B, p 123-130
T. Nishizawa, Progress of CALPHAD, Mater. Trans., JIM, 1992, 33, p 713-722
S. Djaziri, Y.J. Li, A. Nematollahi, C. Kirchlechner, B. Grabowski, S. Goto et al., Deformation-Induced Martensite in Severely Cold-Drawn Pearlitic Steel: A New Mechanism at Play, Dusseldorf, 2016, https://doi.org/10.13140/RG.2.2.28444.28806
R. Rementeria, J.A. Jimenez, S.Y.P. Allain, G. Geandier, J.D. Poplawsky, W. Guo et al., Quantitative Assessment of Carbon Allocation Anomalies in Low Temperature Bainite, Acta Mater., 2017, 133, p 333-345. https://doi.org/10.1016/j.actamat.2017.05.048
M.J. Genderen, M. Isac, A. Böttger, and E.J. Mittemeijer, Aging and Tempering Behavior of Iron-Nickel-Carbon and Iron-Carbon Martensite, Metall. Mater. Trans. A, 1997, 28, p 545-561. https://doi.org/10.1007/s11661-997-0042-5
L. Cheng, N. Van Der Pers, A. Böttger, T.H. de Keijser, and E.J. Mittemeijer, Lattice Changes of Iron-Nitrogen Marteniste on Aging at Room Temperature, Metall. Trans. A, 1991, 22A, p 1957-1967
V.G. Veeraraghavan and P.G. Winchell, 200, 020, and 002 X-Ray Peaks in Tempered Fe-18 Ni-C Martensites, Metall. Trans. A, 1975, 6, p 701-705. https://doi.org/10.1007/BF02672289
P.C. Chen and P.G. Winchell, Martensite Lattice Changes During Tempering, Metall. Trans. A, 1980, 11, p 1333-1339. https://doi.org/10.1007/BF02653487
A.G. Khachaturyan, Theory of Structural Transformations in Solids, Dover Publications, New York, 2008
J.D. Eshelby, The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems, Proc. R. Soc. A., 1957, 241, p 376-396. https://doi.org/10.1007/1-4020-4499-2_18
M. Hillert, Phase Equilibria, Phase Diagrams and Phase Transformations, Cambridge University Press, Cambridge, 2007
H.K.D.H. Bhadeshia and R.W.K. Honeycombe, Steels: Microstructure and Properties, 3rd ed., E. Arnold, London New York, 2006
K. Bhattacharya, Microstructure of Martensite, Oxford University Press, Oxford, 2003
Acknowledgments
This work was supported by the French Agence Nationale de la Recherche (Contract C-TRAM ANR-18-CE92-0021). The author thanks J. M. Joubert and P. Benigni for fruitful discussions on the topology of phase diagrams.
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Maugis, P. A Temperature–Stress Phase Diagram of Carbon-Supersaturated bcc-Iron, Exhibiting “Beyond-Zener” Ordering. J. Phase Equilib. Diffus. 41, 269–275 (2020). https://doi.org/10.1007/s11669-020-00816-2
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DOI: https://doi.org/10.1007/s11669-020-00816-2