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Role of magnetism in phase stability and kinetic of transformation in iron and steel

IQMS. Yuri Gornostyrev Institute of quantum materials science Institute of metal physics UB RAS Ekaterinburg , http:// www.iqms.ru. Role of magnetism in phase stability and kinetic of transformation in iron and steel. In collaboration with

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Role of magnetism in phase stability and kinetic of transformation in iron and steel

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  1. IQMS Yuri Gornostyrev Institute of quantum materials science Institute of metal physics UB RAS Ekaterinburg, http://www.iqms.ru Role of magnetism in phase stability and kinetic of transformation in iron and steel 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 (RadboudUni) V.N. Urtsev, A.V. Shmakov (RTC Ausferr) MISiS, 20-10-2013

  2. IQMS Problemof Fe. Effect of magnetism on fundamental properties • C. Zener (1952): the start temperature of martensitictransformationMs ~ TC • Experiment: Ms = 1020K (C. Liu et al, J Mater. Proc. Tech., 2001) Fragment of phase diagramFe-C 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., 2012 TC ~ Tg-a Free energy of Fe with taking into account magnetic fluctuations C. Zener, 1952 L. Kaufman, E.V. Clougherty, R.J. Weiss, Acta Metall., 11, 323 (1963) H. Hasegava, D.G. Pettifor, PRL, 50, 130 (1983) • Magnetism play crucial role in phase equilibrium and transformation kinetic MISiS, 20-10-2013

  3. IQMS Selected problems initiated by the metallurgical needs Mechanism polymorphous g – a 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 Clusteringof foreign atoms in maraging steels Grain boundaries segregations and more … Scheme of controlled rolling low alloying pipe steel Thus, there is close relation between quantum mechanics and technology MISiS, 20-10-2013

  4. MISiS, 20-10-2013 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.11169 (1996); G. Kresse and J. Hafner, Journal Phys. Condensed Matter, 6, 8245 (1994); G. Kresse and J. Joubert, Phys. Rev. B 59, 1758 (1999).

  5. IQMS Play important role in pipe steels and maraging steels and use to control phase stability, transformation and strengthening Effects of magnetism on precipitation MISiS, 20-10-2013

  6. IQMS Precipitation in steel. Important cases 1. Nbcarbonitride precipitation Nb(CN) at T < 1100 C to prevent austenite grain growth 2. Cu-reach nano-size precipitate at T < 700 C Strength, plasticity and toughness. This steel proposed in prof. M. Fine group at NWU Distribution of copper atoms in steel with 1.2 at.% Cu after annealing [1]. 3. Complex precipitation Ti-Al-Mn in maraging steels T < 500 C High strength and plasticity KTH, 15-05-2013 [1] D. Isheim, M. S. Gagliano, M. E. Fine, D. N. Seidman, ActaMaterialia V. 54 p. 841 (2006).

  7. IQMS Thermodynamics and structure of alloys from first principles CVS alloy energy V(2) Electronic structure and chemical bonding Effective cluster interactions energy Interaction with dislocation, hardening Microstructure formation properties Experiment (HREM, 3D AP) MISiS, 20-10-2013

  8. Ab-initio interaction energies between alloying elements « + » is repulsion « - » is attraction local ordering decomposition • 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 MISiS, 20-10-2013

  9. IQMS Effective pair Cu-Cu interactions Dependence of the effective pair interactions in the nnpositions on square of global magnetization Total effective pair interaction in bcc-Fe with 1 at.%Cu for different global magnetization chemical contribution relaxation contribution • Interactions depend on the temperature and the concentration of the alloy • Dependence on the concentration is more pronounced in the ferromagnetic state O.I. Gorbatov, I.K. Razumov, Yu.N. Gornostyrev, V.I. Razumovskiy, P.A. Korzhavyi, A.V. Ruban, PRB in press MISiS, 20-10-2013

  10. IQMS Solubility Cu in bcc Fe: results of Monte Carlo modeling 1% Cu – isolated Cu atoms in pair 12.5% Cu – the nearest neighbor in first coordination shell. ● - G. Salje and M. Feller-Knipmeier, J. Appl.Phys. 48, 1833 (1977) ■ - M. Perez et. al, Philos. Mag. 85, 2197 (2005) • Increase of copper concentration results in smoothing magnetic effect • Concentration dependent Cu-Cu interactions with strained-induce interactions give agreement with the experiment MISiS, 20-10-2013

  11. Time-Temperature-Transformation (TTT) diagram of decomposition of dilute Fe-Cu alloy IQMS 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 PDLM FM • It is in a good agreement with experimental kinetics O.I. Gorbatov, I.K. Razumov, Yu.N. Gornostyrev, V.I. Razumovskiy, P.A. Korzhavyi, A.V. Ruban, PRB, in press MISiS, 20-10-2013

  12. IQMS SRO is responsible for induced magnetic anisotropy in Fe-Si, Fe-Al and for large magnetostriction in Fe-Ga Effects of magnetism on short range order in soft magnetic alloy Fe-X (X=Si,Al,Ga,Ge) MISiS, 20-10-2013

  13. Effect of temperature on SRO in Fe-Si Profiles of superstructure peak (300) and (003) of single crystal Fe(1-x)Six(x = 0.08) diffuse scattering [N.V. Ershov et al. 2008, 2009] 850°C 450°C D03 B2 B2 D03 Different SRO appear in T > TC and T < TC regions Relative volume ofD03regions increases after annealing at 450°C. After cooling from 850°C SRO B2 type is dominate What is mechanism of SRO formation in Fe-Si alloys? Why SRO change nearby Curie temperature? MISiS, 20-10-2013

  14. IQMS Energy of effective pair interactions Effective Si-Si interaction energies for Fe–8% Si alloy Total interactions Chemical interactions • The interactions are mostly repulsion and short-ranged • Sensitive to magnetic state of iron • Interaction energy of 2-th neighbors significant decrease in PM state MISiS, 20-10-2013

  15. IQMS Monte Carlo simulation of short-range order in Fe-Si • theprobabilityoffindinganatom Β inthe n-thcoordinationsphereofanotheratom Β Τ = 900 oC Τ = 300 oC B2 D03 - Metropolis Monte Carlo predicts B2 type SRO for T > TC and CSi 8%. - D03 type SRO corresponds to T < TC. MISiS, 20-10-2013

  16. Short-ranged order formation in Fe-Si and Fe-Al has been investigated by Monte Carlo with ab-initio calculated of interatomic interaction energies. • We found essential effect of magnetism on SRO formation • - B2 type SRO form at T > TC, and It inherits during cooling down; • - D03 type SRO is preferable for temperatures T < TC 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 TC and rather quenched from paramagnetic state MISiS, 20-10-2013

  17. IQMS Give main contribution to microstructure formation The microscopic mechanism is still not clear Polymorphic transformation in iron and steel MISiS, 20-10-2013

  18. IQMS What mechanism of martensitic transformation? Martensitic transformation appear at T < Msas results of lattice instability But there is not soft modes in phonon spectra of fcc Fe Leonov, I., Poteryaev, A.I., Anisimov, V.I. & Vollhardt, D., PRB, 2012 What reasons for lattice instability in fcc Fe ? MISiS, 20-10-2013

  19. IQMS Bain path energetics. Importance of magnetic short range order (MSRO). The energy of Fe in dependence on tetragonal distortionsfor different magnetic states • Ferromagnetic FCC Fe is unstable. • Paramagnetic (DLM) FCC Fe is stable, however g - a transition do not lead to energy gain. • Paramagnetic BCC Fe stabilize byMSRO • Energy barrier connected with magnetic structure SS – FM transition. • There is magnetic instability in FM FCC Fe. • Cooling down toT < TC(FM curve) lead to high driving force and small energy barrierDE << kT – martensitic mechanism; for T > TC– nucleation and grows. MISiS, 20-10-2013 S.V. Okatov et al, PRB 2009

  20. IQMS Bain path in dependence on temperature From Fe DLM calculation Nucleation and grows Fe (PM) Intermidiate T? Martensitic transformation (FM) From Fe FM 0K calculation For description of BP at intermediate temperature the exchange interactions in dependence on deformation are nesessary MISiS, 20-10-2013

  21. IQMS Spin lattice couplinging-Fe. Exchange parameters from spin-spiral calculations (VASP) Exchange energy appear big and comparable with T in distorted FCC Fe Follow expect strong spin lattice coupling MISiS, 20-10-2013 S.V. Okatov et al, PRB 2012

  22. IQMS 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, 20-10-2013

  23. IQMS Kinetic equations of model For displacements and composition evolution where The solution this equation is determined thee new phase nucleation (with taking into account thermal fluctuations and microstructure formation MISiS, 20-10-2013

  24. IQMS Results of modeling Martensitic transformation after fast (a)/slow(b) cooling at T < MS MISiS, 20-10-2013

  25. Towards of consistent model of polymorphic transformation in steel What we need to be happy ? 1. 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 MISiS, 20-10-2013

  26. IQMS Effect carbon on Bain path and critical points C=0% C=1% Description of plastic relaxation is still open MISiS, 20-10-2013

  27. Thank you for attention MISiS, 20-10-2013

  28. Backup MISiS, 20-10-2013

  29. IQMS 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) 5E+047.5E+041E+05 6E+052E+06 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) 1 1.37 1.5 15 7.5E+05 Proposed model catch main observed features of polymorphic transformation MISiS, 20-10-2013

  30. Effect of magnetism on solubility A.P. Miodownik, Bulletin of Alloy Phase Diagrams, Volume 2, Issue 4, March 1982, Pages 406-412 • 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 KTH, 15-05-2013 30

  31. Solubility of 3d elements in bcc iron mRy • 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

  32. IQMS d=4.5nm Multiscale approach: Application to decomposition and hardening in Fe-Cu alloy Prediction solubility Cu in Fe and phase diagram Precipitate size and morphology vs. time and temperature annealing ( 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 Assessment strengthening Fe due to embedded Cu nano particles Predictionof treatment regimes to obtainhigh strength and plasticity ( 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 Dislocation locking scr Dislocation energy MISiS, 20-10-2013

  33. IQMS Monte-Carlo modeling with first-principle parameterization • Precipitation kinetics in Fe-Cu-Nb • Effective cluster interactions from SGPM calculations KTH, 15-05-2013

  34. 0.2 0.2 0.2 IQMS 0.15 0.15 0.15 0.1 0.1 0.1 0.05 0.05 0.05 a1/a2 a1/a2 a1/a2 0 0 0 0.65 0.65 0.65 0.7 0.7 0.7 0.75 0.75 0.75 0.8 0.8 0.8 0.85 0.85 0.85 0.9 0.9 0.9 0.95 0.95 0.95 1 1 1 T,K fcc 1184 FS fcc+Cem bcc+fcc 1000 840 BS MS 373 0 3.4 c, at.% Effect carbon on Bain path and critical points C=3% C=1% C=0% Description of plastic relaxation is still open MISiS, 20-10-2013

  35. Towards of consistent model of polymorphic transformation in steel Bain path energetics for FM and PM states Finite T from effective Hamiltonian Fe (PM) 1300К 1200К 1100К 1000К (FM) deformation magnetism (FM) carbon The construction of effective Hamiltonian for finite T is nesessary MPIE, 2-10-2012

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