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Yuri Gornostyrev Institute of quantum materials science Institute of metal physics UB RAS Ekaterinburg, IQMS MISiS, In collaboration with O.I.Gorbatov, I.K. Razumov, S.V. Okatov, A.R. Kuznetsov (IQMS), P.V. Korzhavyi, A.V. Ruban (KTH), A.I. Lichtenstein (Hamburg Uni), M.I. Katsnelson (Radboud Uni) V.N. Urtsev, A.V. Shmakov (RTC Ausferr)

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Problem of Fe. Effect of magnetism on fundamental properties IQMS C. Zener (1952): the start temperature of martensitic transformation M s ~ T C Experiment: M s = 1020K (C. Liu et al, J Mater. Proc. Tech., 2001) Fragment of phase diagram Fe-C H. Hasegava, D.G. Pettifor, PRL, 50, 130 (1983) L. Kaufman, E.V. Clougherty, R.J. Weiss, Acta Metall., 11, 323 (1963) Free energy of Fe with taking into account magnetic fluctuations Magnetism play crucial role in phase equilibrium and transformation kinetic C. Zener, 1952 T C ~ T - 2 MISiS, L. Kaufman, et. al., 1963 M. Hillert, et. al., 1967 G. Inden, 1976 M. Hillert, et. al., 1978 T. Nishizawa, et. al., 1979 G. Inden, 1981 B. Jonsson, 1992, 1994, 1995 Y. Liu, et. al., 2009 Wei Xiong, et. al., 201 2

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IQMS Selected problems initiated by the metallurgical needs 3 Mechanism polymorphous – transformation in steel Transformation kinetic and microstructure formation Effect of alloying elements on phase equilibrium and transformation Precipitation of alloying elements and carbonitride in steels Clustering of foreign atoms in maraging steels Grain boundaries segregations and more … Scheme of controlled rolling low alloying pipe steel MISiS, Thus, there is close relation between quantum mechanics and technology

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The purpose and methods of calculations Motivation: elucidate the effect of magnetism on thermodynamic of iron-based alloy We employed the following methods and approximations 1. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965) 2. P. Soven, Phys. Rev. 156, 809 (1967) 3. J. Korringa. Physica 13, 392 (1947); W. Kohn and N. Rostoker. Phys. Rev. 94, 1111 (1954) 4. J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) 5. I.A. Abrikosov, A.M.N. Niklasson, S.I. Simak, B. Johansson, A.V. Ruban, H.L. Skriver. Phys. Rev. Lett. 76, 22, 4203 (1996); I.A. Abrikosov, S.I. Simak, B. Johansson, A.V. Ruban, H.L. Skriver. Phys. Rev. B 56, 15, 9319 (1997) 6. B.L. Gyorffy, A.J. Pindor, J.B. Stauton, G.M. Stocks, H. Winter, J Phys. F 15, 1337 (1985); J.B. Stauton, B.L. Gyorffy, Phys. Rev. Lett. 69, 371 (1992) 7. G. Kresse and J. Furthmuller, Phys. Rev. B 54, P (1996); G. Kresse and J. Hafner, Journal Phys. Condensed Matter, 6, 8245 (1994); G. Kresse and J. Joubert, Phys. Rev. B 59, 1758 (1999). 4 MISiS,

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Play important role in pipe steels and maraging steels and use to control phase stability, transformation and strengthening MISiS, IQMS

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Precipitation in steel. Important cases Distribution of copper atoms in steel with 1.2 at.% Cu after annealing [1]. Strength, plasticity and toughness. This steel proposed in prof. M. Fine group at NWU [1] D. Isheim, M. S. Gagliano, M. E. Fine, D. N. Seidman, Acta Materialia V. 54 p. 841 (2006). IQMS 1. Nb carbonitride precipitation Nb(CN) at T < 1100 C to prevent austenite grain growth 2. Cu-reach nano-size precipitate at T < 700 C 3. Complex precipitation Ti-Al-Mn in maraging steels T < 500 C High strength and plasticity 6KTH,

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IQMS 7 Thermodynamics and structure of alloys from first principles Experiment (HREM, 3D AP) properties V (2) Electronic structure and chemical bonding CVS alloy energy Microstructure formation Interaction with dislocation, hardening Effective cluster interactions energy MISiS,

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8 Ab-initio interaction energies between alloying elements Interatomic interactions follow to the number of element in the periodic table The strongest effect of magnetism is for Cr, Mn, Ni, Cu, V The tendency to decomposition for Cu and Zn O.I. Gorbatov, S.V. Okatov, Yu.N. Gornostyrev, P.A. Korzhavyi, A.V. Ruban, PMM, 2013 « + » is repulsion « - » is attraction local ordering decomposition MISiS,

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9 Total effective pair interaction in bcc-Fe with 1 at.% Cu for different global magnetization Dependence of the effective pair interactions in the nn positions on square of global magnetization O.I. Gorbatov, I.K. Razumov, Yu.N. Gornostyrev, V.I. Razumovskiy, P.A. Korzhavyi, A.V. Ruban, PRB in press Effective pair Cu-Cu interactions Interactions depend on the temperature and the concentration of the alloy Dependence on the concentration is more pronounced in the ferromagnetic state chemical contribution relaxation contribution IQMS MISiS,

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10 Increase of copper concentration results in smoothing magnetic effect Concentration dependent Cu-Cu interactions with strained-induce interactions give agreement with the experiment 1% Cu – isolated Cu atoms in pair 12.5% Cu – the nearest neighbor in first coordination shell. Solubility Cu in bcc Fe: results of Monte Carlo modeling ● - G. Salje and M. Feller-Knipmeier, J. Appl.Phys. 48, 1833 (1977) ■ - M. Perez et. al, Philos. Mag. 85, 2197 (2005) IQMS MISiS,

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11 O.I. Gorbatov, I.K. Razumov, Yu.N. Gornostyrev, V.I. Razumovskiy, P.A. Korzhavyi, A.V. Ruban, PRB, in press TTT diagram of decomposition of dilute Fe-Cu alloy showed the time needed to attain the precipitation fraction equal 0.2 from maximal value at given temperature. Accounting of changes in magnetic state is necessary for correct description of the transformation Time-Temperature-Transformation (TTT) diagram of decomposition of dilute Fe-Cu alloy It is in a good agreement with experimental kinetics MISiS, PDLM FM IQMS

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SRO is responsible for induced magnetic anisotropy in Fe-Si, Fe-Al and for large magnetostriction in Fe-Ga MISiS, IQMS

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Profiles of superstructure peak (300) and (003) of single crystal Fe (1-x) Si x (x = 0.08) diffuse scattering [N.V. Ershov et al. 2008, 2009] After cooling from 850°C SRO B2 type is dominate Relative volume of D0 3 regions increases after annealing at 450°C. B2 D0 3 B2 D0 3 Effect of temperature on SRO in Fe-Si 850°C 450°C Different SRO appear in T > T C and T < T C regions What is mechanism of SRO formation in Fe-Si alloys? Why SRO change nearby Curie temperature? MISiS,

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Effective Si-Si interaction energies for Fe – 8% Si alloy Energy of effective pair interactions 1.The interactions are mostly repulsion and short-ranged 2.Sensitive to magnetic state of iron 3.Interaction energy of 2-th neighbors significant decrease in PM state Chemical interactions Total interactions MISiS, IQMS

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- Metropolis Monte Carlo predicts B2 type SRO for T > T C and C Si 8%. - D0 3 type SRO corresponds to T < T C. B2 D0 3 Monte Carlo simulation of short-range order in Fe-Si Τ = 900 o C Τ = 300 o C – the probability of finding an atom Β in the n-th coordination sphere of another atom Β MISiS, IQMS

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1.Short-ranged order formation in Fe-Si and Fe-Al has been investigated by Monte Carlo with ab-initio calculated of interatomic interaction energies. 2.We found essential effect of magnetism on SRO formation - B2 type SRO form at T > T C, and It inherits during cooling down; - D0 3 type SRO is preferable for temperatures T < T C and appears after annealing of quenches samples; 3. The results support the model of the induced magnetic anisotropy based on ordering Si-Si pairs. However, these pairs do not appear during annealing below T C and rather quenched from paramagnetic state MISiS,

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Give main contribution to microstructure formation The microscopic mechanism is still not clear MISiS, IQMS

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18 What mechanism of martensitic transformation? Martensitic transformation appear at T < Ms as results of lattice instability What reasons for lattice instability in fcc Fe ? MISiS, But there is not soft modes in phonon spectra of fcc Fe Leonov, I., Poteryaev, A.I., Anisimov, V.I. & Vollhardt, D., PRB, 2012

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Bain path energetics. Importance of magnetic short range order (MSRO). The energy of Fe in dependence on tetragonal distortions for different magnetic states Ferromagnetic FCC Fe is unstable. Paramagnetic (DLM) FCC Fe is stable, however transition do not lead to energy gain. Paramagnetic BCC Fe stabilize by MSRO Energy barrier connected with magnetic structure SS – FM transition. There is magnetic instability in FM FCC Fe. Cooling down to T T C – nucleation and grows. S.V. Okatov et al, PRB IQMS MISiS,

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IQMS 20 Bain path in dependence on temperature For description of BP at intermediate temperature the exchange interactions in dependence on deformation are nesessary From Fe FM 0K calculation (PM) (FM) Fe From Fe DLM calculation Intermidiate T?Martensitic transformation Nucleation and grows MISiS,

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Spin lattice coupling in - Fe. Exchange energy appear big and comparable with T in distorted FCC Fe Follow expect strong spin lattice coupling Exchange parameters from spin-spiral calculations (VASP) IQMS S.V. Okatov et al, PRB MISiS,

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IQMS 22 Simple model of Bain path in dependence on temperature Energy Free energy magnetic contribution (Hellmann-Feynman) Bain path energetics from ab-initio for FM and PM(DLM) states MISiS,

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Kinetic equations of model For displacements The solution this equation is determined thee new phase nucleation (with taking into account thermal fluctuations and microstructure formation and composition evolution where 23 IQMS MISiS,

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IQMS 24 Results of modeling Martensitic transformation after fast (a)/slow(b) cooling at T < M S MISiS,

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ИКМ Towards of consistent model of polymorphic transformation in steel Effective Hamiltonian (free energy) parameterization from ab-inito 2. Taking into account effect of carbon on BP energetics and phase equilibrium 3. Taking into account mechanism of plastic relaxation of internal stress associated with transformation What we need to be happy ? MISiS,

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IQMS 26 Effect carbon on Bain path and critical points Description of plastic relaxation is still open MISiS, C=0% C=1%

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27 Thank you for attention MISiS,

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28 Backup MISiS,

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IQMS 29 Transformation in Fe-c. Results of modeling Ferrite transformation in Fe-2%C at T=1100K with taking into account carbon distribution (2-nd row) and plastic relaxation (black and white – ferrite two orientations, gray – austenite) MISiS, E E+04 1E+05 6E+05 2E E+05 Bainite transformation in Fe-2%C at T=900K with taking into account carbon distribution (2-nd row) and plastic relaxation (black and white – ferrite two orientations, gray – austenite) Proposed model catch main observed features of polymorphic transformation

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Effect of magnetism on solubility Magnetic state of the host (iron) exerts an influence Solubility anomaly in Fe-Cu and Fe-Zn at the Curie temperature is the most pronounced effect A.P. Miodownik, Bulletin of Alloy Phase Diagrams, Volume 2, Issue 4, March 1982, Pages KTH,

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31 Solubility of 3d elements in bcc iron The strongest effect of magnetism is for Cr, Ni, Cu, V, Ti Sc has the largest relaxation contribution O.I. Gorbatov, S.V. Okatov, Yu.N. Gornostyrev, P.A. Korzhavyi, A.V. Ruban, 2008 mRy

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Multiscale approach: Application to decomposition and hardening in Fe-Cu alloy IQMS ( I ) Ab-initio calculation of the interaction energy between Cu atoms in bcc Fe ( II ) Monte-Carlo simulations of the alloys decomposition with ab- initio parameters Prediction solubility Cu in Fe and phase diagram Precipitate size and morphology vs. time and temperature annealing ( III ) Molecular dynamic modeling of the interaction between dislocation and Cu particles ( IV ) Determination of the shear resistance in dependence on composition and size Cu particles Assessment strengthening Fe due to embedded Cu nano particles Prediction of treatment regimes to obtain high strength and plasticity d=4.5nm Dislocation energy Dislocation locking cr MISiS,

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IQMS 33 Effective cluster interactions from SGPM calculations Precipitation kinetics in Fe-Cu-Nb Monte-Carlo modeling with first-principle parameterization KTH,

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IQMS 34 Effect carbon on Bain path and critical points Description of plastic relaxation is still open a 1 /a a 1 /a a 1 /a 2 C=1% C=0% C=3% T,KT,K FSFS BSBS MSMS c, at.% 1000 bcc+fcc fcc+Cem fcc MISiS,

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ИКМ Towards of consistent model of polymorphic transformation in steel deformation magnetism carbon (FM) (PM) 1300К 1200К 1100К 1000К (FM) Fe Bain path energetics for FM and PM states Finite T from effective Hamiltonian 35MPIE, The construction of effective Hamiltonian for finite T is nesessary

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