CARBON ATOMS IN INTERSTITIAL SITES OF THE CEMENTITE CRYSTAL LATTICE: AB INITIO MODELLING
DOI:
https://doi.org/10.14529/met180404Keywords:
cementite, carbon positions, interstitial sites, vacancy formation energy, first-principles calculationAbstract
It was shown in previous works that iron sublattice in the structure of cementite Fe3C has four different types of interstitial sites that may potentially be occupied by carbon atoms, viz. ‘normal’ and ‘distorted’ prismatic (NP, DP) and ‘normal’ and ‘distorted’ octahedral (NO, DO) sites. Distances between their centres and the centres of z nearest-neighbour iron atoms are 1.99–2.04 Å (NP sites, z = 6); 1.80–1.87 Å (NO sites, z = 6); 1.62 Å (DP sites, z = 4) and 1.25 Å (DO sites, z = 2). It is usually believed that all carbon atoms are located in NP positions. In this work other possible variants are considered by ab initio calculations using FP-LAPW full-potential method as realized in WIEN2k program package and a cementite supercell containing 16 atoms (4 formula units).
It is found that the structure containing all carbon atoms in NP positions has the lowest energy and volume. The structure with all carbon atoms in NO positions has the energy 0.267 eV/f.u. higher and the volume 9.20 % greater. If only one of the four carbon atoms in the supercell is shifted from NP to NO site the energy and volume increase by 0.233 eV/f.u. and 3.59 % correspondingly. The structure with one carbon atoms located in DP site and the other three in DO sites has the energy 0.452 eV and the volume 3.75 % higher than those of cementite with all carbon atoms in NP sites. The structures with all carbon atoms in DP sites and one or all carbon atoms in DO sites are mecha-nically unstable and transform spontaneously to conventional NP structure. Thermodynamic estima-tion based on these data shows that even at temperatures below 1000 K the fraction of carbon atoms that may move from NP sites to other ones may be as great as 20 %.
Evaluation of the vacancy formation energy in cementite (supercell of 128 atoms containing 96 atoms of Fe and 32 atoms of C) resulted in the values of 0.50 eV for carbon vacancy and 1.34 (FeG) or 1.60 eV (FeS) for iron vacancy. In all these cases vacancy formation did not result in volume change of the system.
References
Andrews K.W. The Structure of Cementite and Its Relation to Ferrite. Acta Metallurgica, 1963, vol. 11, no. 8, pp. 939–946. DOI: 10.1016/0001-6160(63)90063-4
Andrews K.W., Dyson D.J., Keown S.R. Interpretation of Electron Diffraction Patterns. N.Y., Plenum Press, 1967. DOI: 10.1007/978-1-4899-6475-5
Fasiska E.J., Jeffrey G.A. On the Cementite Structure. Acta Crystallographica, 1965, vol. 19, pt. 3, pp. 463–471. DOI: 10.1107/S0365110X65003602
Lipson H., Petch N.J. The Crystal Structure of Cementite, Fe3C. Journal of the Iron and Steel In-stitute, 1940, vol. 142, no. 2, pp. 95–106.
Lyashchenko B.G., Sorokin L.M. [Determination of the Carbon Position on Cementite by Elec-tron Diffraction Method]. Kristallografiya, 1963, vol. 8, no. 3, pp. 382–387. (in Russ.)
Meinhardt D., Krisement O. Strukturuntersuchungen an Karbiden des Eisens, Wolframs und Chroms mit thermischen Neutronen. Archiv für das Eisenhüttenwesen, 1962, Jg. 33, H. 7, S. 493–499.
Wood I.G., Vočadlo L., Knight K.S., Dobson D.P., Marshall W.G., Price G.D., Brodholt J. Thermal Expansion and Crystal Structure of Cementite, Fe3C, between 4 and 600 K Determined by Time-of-Flight Neutron Powder Diffraction. Journal of Appplied Crystallography, 2004, vol. 37, no. 1, pp. 82–90. DOI: 10.1107/S0021889803024695
Gardin A.I. [Study of the Crystal Structure of Cementite by Electron Diffraction Analysis]. Doklady AN SSSR, 1962, vol. 146, no. 5, pp. 1068–1070. (in Russ.)
Gardin A.I. [Electron Diffraction Investigation of the Structure of Cementite]. Kristallografiya, 1962, vol. 67, no. 6, pp. 854–861. (in Russ.)
Zhukov A.A., Shalashov V.A., Tomas V.K. [On the Structure of Cementite]. Liteynoe proiz-vodstvo, 1965, no. 7, p. 46. (in Russ.)
Kagawa A., Okamoto T., Matsumoto H. Young’s Modulus and Thermal Expansion of Pure Iron-Cementite Alloy Castings. Acta Metallurgica, 1987, vol. 35, no. 4, pp. 797–803. DOI: 10.1016/0001-6160(87)90157-X
Stuart H., Ridley N. Thermal Expansion of Cementite and Other Phases. Journal of the Iron and Steel Institute, 1966, vol. 204, pt. 7, pp. 711–717.
Belikov A.M., Savinskaya A.A. [Anisotropy of Thermal Vibration of Atoms in Cementite Crys-tals]. Fizika metallov i metallovedenie, 1962, vol. 14, no. 2, pp. 299–301. (in Russ.)
Inoue A., Ogura T., Masumoto T. Deformation and Fracture Behaviours of Cementite. Transactions of the Japan Institute of Metals, 1976, vol. 17, no. 10, pp. 663–672. DOI: 10.2320/matertrans1960.17.663
Rokhmanov N.Ya., Sirenko A.F., Bakharev S.A. Thermal Expansion of Cementite in Hypereu-tectoid Iron-Carbon Alloy. Metal Science and Heat Treatment, 1997, vol. 39, no. 1, pp. 7–10. DOI: 10.1007/BF02467199]
Schastlivtsev, V.M., Yakovleva, I.L., Mirzaev, D.A., Okishev, K.Yu. On the Possible Positions of Carbon Atoms in the Cementite Lattice. Physics of Metals and Metallography, 2003, vol. 96, no. 3, pp. 313–320.)
Mirzaev D.A., Okishev K.Yu., Schastlivtsev V.M., Yakovleva I.L. [Pores in the Crystal Struc-ture of Cementite and Positions of Carbon Atoms]. Bulletin of the South Ural State University. Ser. Mathematics, Physics, Chemistry, 2003, no. 6 (22), issue 3, pp. 79–85. (in Russ.)
Okishev K.Yu. [Analysis of Possibility of Carbon Redistribution in Cementite Lattice. Bulletin of the South Ural State University. Ser. Metallurgy, 2011, no. 36 (253), issue 17, pp. 56–60. (in Russ.)
Mirzaev D.A., Okishev K.Yu. [Point and Planar Defects in Cementite]. Tsementit v uglero-distykh stalyakh [Cementite in Carbon Steels]. Schastlivtsev V.M (Ed.). Ekaterinburg, UMTs UPI Publ., 2017, pp. 326–347. (in Russ.)
Schastlivtsev V.M., Tabatchikova T.I., Yakovleva I.L., Kleinerman N.M., Serikov V.V., Mirzaev D.A. Crystal structure of cementite in the pearlite of a carbon steel: A Mössbauer study. Phy-sics of Metals and Metallography, 1996, vol. 82, no. 6, pp. 622–629.
Schastlivtsev V.M., Tabatchikova T.I., Yakovleva I.L., Kleinerman N.M., Serikov V.V., Mirzaev D.A. Evolution of the Cementite Structure in Carbon Steel: II. Mössbauer Studies. Physics of Metals and Metallography, 1997, vol. 84, no. 5, pp. 562–566.
Maratkanova A.N., Rats Yu.V., Surnin D.V., Deev A.N., Schastlivtsev V.M., Yakovleva I.L., Tabatchikova T.I., Gusev S.A., Salashchenko N.N. Effect of Heat Treatment on the Local Atomic Struc-ture of Cementite Fe3C in Steel. Physics of Metals and Metallography, 2000, vol. 89, no. 6, pp. 604–609.
Maratkanova A.N., Rats Yu.V., Yakovleva I.L. Studying Local Structure of Cementite. Physics of Metals and Metallography, 2004, vol. 98, no. 3, pp. 300–306.
Schastlivtsev V.M. Crystal Structure of Cementite. Bulletin of the Russian Academy of Sciences: Physics, 2005, vol. 69, no. 9, pp. 1447–1452.
Tabatchikova T.I., Kleinerman N.M., Schastlivtsev V.M., Maratkanova A.N., Serikov V.V. [Investigation of the Local Atomic Structure of Cementite]. Tsementit v uglerodistykh stalyakh [Cementite in Carbon Steels]. Schastlivtsev V.M (Ed.). Ekaterinburg, UMTs UPI Publ., 2017, pp. 193–217. (in Russ.)
Schastlivtsev V.M., Tabatchikova T.I., Yakovleva I.L., Mirzaev D.A., Kleinerman N.M., Serikov V.V. Evolution of the Cementite Structure in Carbon Steels: I. Diffraction Study. Physics of Metals and Metallography, 1997, vol. 84, no. 4, pp. 365–371.
Elsukov E.P., Fomin V.M., Vytovtov D.A., Dorofeev G.A., Zagainov A.V., Arsent'eva N.B., Lomaeva S.F. Structural and Phase Transformations during Isothermal Annealing of Mechanically Al-loyed Iron-Amorphous Fe-C Phase Nanocomposite: Formation of Cementite. Physics of Metals and Metallography, 2005, vol. 100, no. 3, pp. 251–269.
Elsukov E.P., Dorofeev G.A., Ul'yanov A.L., Vytovtov D.A. On the Problem of the Cementite Structure. Physics of Metals and Metallography, 2006, vol. 102, no. 1, pp. 76–82. DOI: 10.1134/S0031918X06070106
Ul'yanov A.I., Elsukov E.P., Chulkina A.A., Zagainov A.V., Arsent'eva N.B., Konygin G.N., Novikov V.F., Isakov V.V. The Role of Cementite in the Formation of Magnetic Hysteresis Properties of Plastically Deformed High-Carbon Steels: I. Magnetic Properties and Structural State of Cementite. Russian Journal of Nondestructive Testing, 2006, vol. 42, no. 7, pp. 452–459. DOI: 10.1134/S1061830906070047
Chulkina A.A., Ul'yanov A.I., Arsent'eva N.B., Zagainov A.V., Gorkunov E.S., Zadvorkin S.M., Somova V.M. The Role of Cementite in the Formation of Magnetic Hysteresis Properties of Plastically Deformed High-Carbon Steels: II. Magnetic Properties of Patented Wire Made of Steel 70. Russian Jour-nal of Nondestructive Testing, 2006, vol. 42, no. 7, pp. 460–467. DOI: 10.1134/S1061830906070059
Baikov A.A. [To the Question of the Diagram of Transformations of Alloys of Iron with Carbon]. Zhurnal Russkogo metallurgicheskogo obshchestva, 1910, no. 6, pt. I, pp. 344–355. (Baikov A.A. Sobranie trudov [Collection of Works]. Vol. 2. Moscow, Leningrad, AN SSSR Publ., 1948, pp. 70–81.) (in Russ.)
Petch N.J. The Interpretation of the Crystal Structure of Cementite. Journal of the Iron and Steel Institute, 1944, vol. 149, pp. 143–150.
Zhukov A.A., Shalashov V.A., Tomas V.K., Ul'yanova B.Ya. Variation of the Composition, Structure, and Hardness of Cementite with Quenching. Metal Science and Heat Treatment, 1970, vol. 12, no. 1, pp. 16–18. DOI: 10.1007/BF00651707
Okamoto T., Matsumoto H. Precipitation of Ferrite from Cementite. Metal Science, 1975, vol. 9, no. 1, pp. 8–12.
Battezzati L., Baricco M., Curiotto S. Non-Stoichiometric Cementite by Rapid Solidification of Cast Iron. Acta Materialia, 2005, vol. 53, no. 6, pp. 1849–1856. DOI: 10.1016/j.actamat.2004.12.035
Medvedeva N.I., Kar'kina L.E., Ivanovskii A.L. Effects of Atomic Disordering and Nonstoichiometry in the Carbon Sublattice on the Energy-Band Structure of Cementite. Physics of Me-tals and Metallography, 2003, vol. 96, no. 5, pp. 452–456.
Arzhnikov A.K., Dobysheva L.V., Demangeat C. Structural Peculiarities of Cementite and Their Influence of Magnetic Characteristics. Journal of Physics: Condensed Matter, 2007, vol. 19, no. 19, 196214. DOI: 10.1088/0953-8984/19/19/196214
Jiang C., Uberuaga B.P., Srinivasan S.G. Point Defect Thermodynamics and Diffusion in Fe3C: A First-Principles Study. Acta Materialia, 2008, vol. 56, no. 13, pp. 3236–3244. DOI: 10.1016/j.actamat.2008.03.012
Voronin V.I., Berger I.F., Gornostyrev Y.N., Kuznetsov A.R., Urtsev V.N., Shmakov A.V. Composition of Cementite in the Dependence on the Temperature. In Situ Neutron Diffraction Study and Ab Initio Calculations. Journal of Experimental and Theoretical Physics Letters (JETP Letters), 2010, vol. 91, no. 3, pp. 143–146. DOI: 10.1134/S0021364010030094
Levchenko E.V., Evteev A.V., Belova I.V., Murch G.E. Molecular Dynamics Simulation and Theoretical Analysis of Carbon Diffusion in Cementite. Acta Materialia, 2009, vol. 57, no. 3, pp. 846–583. DOI: 10.1016/j.actamat.2008.10.025
Schwarz K., Blaha P. Solid State Calculations Using WIEN2k. Computational Materials Sci-ence, 2003, vol. 28, no. 2, pp. 259–273. DOI: 10.1016/S0927-0256(03)00112-5
Kostenetskiy P.S., Safonov A.Y. SUSU Supercomputer Resources. Proceedings of the 10th Annual International Scientific Conference on Parallel Computing Technologies (PCT 2016), Arkhan-gelsk, Russia, March 29–31, 2016. CEUR Workshop Proceedings, 2016, vol. 1576, pp. 561–573.
Verkhovykh A.V., Mirzoev A.A., Mirzaev D.A. [Ab Initio Simulation of Silicon Influence on Fe3C Carbide Formation in Bcc-Iron]. Bulletin of the South Ural State University. Ser. Mathematics. Mechanics. Physics, 2018, vol. 10, no. 4, pp. 78–87. (in Russ.) DOI: 10.14529/mmph180409
Murnaghan F.D. The Compressibility of Media Under Extreme Pressures. Proceedings of the National Academy of Sciences, 1944, vol. 30, no. 9, pp. 244–247. DOI: 10.1073/pnas.30.9.244
Mirzaev D.A., Mirzoev A.A., Okishev K.Yu., Verkhovykh A.V. Hydrogen-Vacancy Interaction in BCC Iron: Ab Initio Calculations and Thermodynamics. Molecular Physics, 2014, vol. 112, no. 13, pp. 1745–1754. DOI: 10.1080/00268976.2013.861087
Meschel S.V., Kleppa O.J. Standard Enthalpies of Formation of Some 3d Transition Metal Car-bides by High Temperature Reaction Calorimetry. Journal of Alloys and Compounds, 1997, vol. 257, no. 1–2, pp. 227–233. DOI: 10.1016/S0925-8388(97)00023-6
Guillermet A.F., Grimvall G. Cohesive Properties and Vibrational Entropy of 3d-Transition Metal Carbides. Journal of Physics and Chemistry of Solids, 1992, vol. 53, no. 1, pp. 105–125. DOI: 10.1016/0022-3697(92)90019-A
Gutina O.Yu., Medvedeva N.I., Shein I.R., Ivanovskii A.L., Medvedeva J.E. Electronic Struc-ture and Magnetic Properties of Fe3C with 2p and 3p Impurities. Physica status solidi (b), 2009, vol. 246, no. 9, pp. 2167–2171. DOI: 10.1002/pssb.200945064
Ande C.K., Sluiter M.H.F. First-Principles Prediction of Partitioning of Alloying Elements Between Cementite and Ferrite. Acta Materialia, 2010, vol. 58, no. 19, pp. 6276–6281. DOI: 10.1016/j.actamat.2010.07.049
Shull C.G., Wilkinson M.K. Neutron Diffraction Studies of the Magnetic Structure of Alloys of Transition elements. Physical Review, 1955, vol. 97, no. 2, pp. 304–310. DOI: 10.1103/PhysRev.97.304
Schastlivtsev V.M., Yakovleva I.L., Mirzaev D.A. Structural Transformations in Pearlite on Heating. Communication 2. Source of Transformation Hardening and Ferrite Recrystallization. Fizika metallov i metallovedenie, 1994, vol. 78, no. 3, pp. 94–103. (in Russ.)
Hong M.H., Reynolds Jr. W.T., Tarui T., Hono K. Atom Probe and Transmission Electron Mi-croscopy Investigations on Heavily Drawn Pearlitic Steel Wire. // Metallurgical and Materials Transac-tions A, 1999, vol. 30, no. 3, pp. 717–727. DOI: 10.1007/s11661-999-0063-3
Schastlivtsev V.M., Mirzaev D.A., Yakovleva I.L., Okishev K.Yu., Tabatchikova I.L., Khlebnikova Yu.V. Perlit v uglerodistykh stalyakh [Pearlite in Carbon Steels]. Ekaterinburg, UrO RAN RAS Publ., 2006. 312 p.
