1. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 Magnetic grain boundaries in Ni and Fe Jan Kuriplach Department of Low Temperature Physics Faculty of Mathematics and Physics Charles University

2. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 2Cooperation O. Melikhova O. Melikhova Charles University, Prague, Czech Republic M. Hou M. Hou Université Libre de Bruxelles, Belgium E. Zhurkin E. Zhurkin St. Petersburg State Technical University, Russia T. Ossowski, A. Kiejna T. Ossowski, A. Kiejna Wroclaw University, Poland M. Šob M. Šob Masaryk University & Institute of Physics of Materials, Brno, Czech Republic P. Lejček, V. Paidar P. Lejček, V. Paidar Institute of Physics, Prague, Czech Republic

3. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 3 Outline GBs  Motivation  GB construction, typology  Methods  Results   5 (210) [001] tilt GB in Ni & segregation of S and Sb   5 (210) [001] and  3 (111) [-111] tilt GBs in Fe & segregation of Cr  Conclusion & outlook

4. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 4Motivation  Magnetic properties of GBs are rarely studied and far from being sufficiently understood. M.R. Fitzsimmons et al., Nanostructured Materials 6, 539 (1995).  37 (001) twist GB in Ni (bicrystal)

5. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 5Motivation  The structure of nc-Ni is influenced by magnetic field. K. Harada et al., Scripta Mater. 49, 367 (2003). Fig. 2. Grain size distributions of nanocrystalline nickel annealed at 573 K for 120 s, 300 s and 1.8 ks without and with an applied magnetic field of 1.2 MA/m. Note that the mean grain size d and the standard deviation r are shown in each histogram.

6. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 6Motivation  It seems that there is an enhancement of magnetic moment at GBs K. Hampel et al., Phys. Rev. B 47, 4810 (1993)  5 (310) [001] tilt GB in Fe

7. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 7Motivation  Noncollinear magnetism predicted for a  3 (111) [-110] tilt GB in Fe  K. Nakamura et al., Appl. Phys. Lett. 84, 4974 (2004)  Magnetocrystalline anisotropy energy in (111) plane enhanced by one order of magnitude compared to bulk

8. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 8Motivation  Impurities may segregate to GBs and enhance or embrittle the GB strength.  S and Sb are known to embrittle GBs in Ni.  Ni GB decohesion due to S segregation studied by M. Yamaguchi et al., Science 307, 393 (2005)   5 (210) in Ni is well known and studied, at least theoretically

9. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 9Motivation  Fe-Cr system:  prospective application material  considered for new generation of nuclear power plants  Cr segregation in low Cr steels may affect materials properties

10. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 10 GB typology  In general, GBs are quite difficult to characterize.  Here, we restrict to coherent GBs.  Then, 5 parameters related to the GB plane and orientation of grains are enough.  In order to perform structure simulations and other calculations, we mostly need periodic boxes containing GBs.  The two basic ways how to construct such GBs are to make twist or tilt of the lattice with respect to the given crystallographic plane.

11. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 11 GB typology  Demonstration for twin GBs (Si, (111) plane): twist Reference: http://www.tf.uni-kiel.de/matwis/amat/def_en/index.html

12. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 12 GB typology  Demonstration for twin GBs (Si, (111) plane): tilt Reference: http://www.tf.uni-kiel.de/matwis/amat/def_en/index.html

13. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 13 GB typology  To characterize a GB we need:  Miller indices of the GB plane,  twist or tilt (+axis) type,  and rotation angle  or  value.  The CSL is the lattice created by lattice sites of the rotated lattice that coincide with lattice sites of the original lattice.   is the ratio between the volume of the coincidence site lattice (CSL) cell and the original lattice cell.   is always an odd number.

14. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 14Methods  VASP code  US or PAW pseudopotentials  LDA & GGA spin-polarized (SP) calculations  Ni, Fe are transition metals  slow convergence  Boxes relaxed with Fermi level smearing and small number of k -points  Tetrahedron integration, larger energy cutoff and more k - points are employed to get precise energy and magnetic moments  Damped molecular dynamics at 0 K is used in some cases to get starting GB configurations  Metropolis Monte Carlo Algorithm employed to study segregation in the Fe-Cr system

15. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 15  5 (210) in Ni  Bulk lattice constant of Ni: LSDA: 3.436 Å(~ -2.5%) GGA:3.533 Å(~ +0.3%) experiment :3.524 Å

16. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 16  5 (210) in Ni  GB construction CSL principle, GB plane (210), tilt axis [001], rotation angle 36.87° (one of two known configurations considered)  The GB box contains 40 atoms (20 planes) – O(40,1) cell  Box size in c-direction optimized (~4% extension)

17. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 17  5 (210) in Ni  Grain boundary energy (VASP US potentials): (a GGA value of 1.43 J/m 2 obtained by M. Yamaguchi et al., J. Phys.: Condens. Matter 16, 3933 (2004) with WIEN2k code) supercell  /  (%) V fv ( Å 3 / Å 2 )  (J/m 2 ) LSDA O(40,1)4.200.3231.54 M(20,1)4.130.3181.52 M(40,2)1.960.3011.50 GGA O(40,1)4.450.3511.24 M(20,1)4.390.3471.22 M(40,2)2.040.3221.20

18. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 18  5 (210) in Ni  Magnetic moments:

19. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 19  5 (210) in Ni  Vacancies and impurities in bulk:  32 atom 2x2x2 fcc supercell, both spin-polarized (SP) and non-SP calculations done, all values in eV LDAGGA NSPSPNSPSP E f (V)1.671.751.391.43 E b (V+S Ni )0.470.500.430.49 E b (V+Sb Ni )0.490.540.410.46 E p (S)1.581.761.091.39 E p (Sb)-(4.96)-- E f (V) – vacancy formation energy E f (V) = E bulk (V) - E bulk + E bulk /32 E b (V+X Ni ) – binding energy of vacancy and 1nn X atom E b (V+X Ni ) = [E bulk (V) + E bulk (X Ni )] - [E bulk + E bulk (V+X Ni )] E st (X) – atom X’s preference to be substitutional or interstitial E p (X) = [E bulk (X i ) - E bulk /32] - E bulk (X Ni ) => Both S and Sb should be substitutional and bind vacancies.

20. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 20  5 (210) in Ni  Vacancies at GB:  two configurations studied ¤ GB+V1 – vacancy keeps its open volume ¤ GB+V2 – vacancy becomes ‘delocalized’’ ¤ GB+V2 obtained from GB+V1 by a small change of the cell dimension perpendicular to the GB plane ¤ a larger cell O(80,1) also tested to confirm the effect

21. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 21  5 (210) in Ni  Vacancies at GB: energies and V-GB binding E f – vacancy formation energy E f (V-GB) = E GB (V) – E GB + E bulk /40 E b – binding energy of vacancy to GB E b (V-GB) = [E GB + E bulk (V)] – [E bulk + E GB (V)]  – GB energy of the GB with vacancy (considering the second GB unaffected) configurati on E f (eV)E b (eV)  (J/m 2 ) LSDA GB+V11.89-0.131.60 GB+V20.60+1.160.82 GGA GB+V11.54-0.091.27 GB+V20.52+0.930.69 => Some vacancy configurations may have a lower formation energy at the GB than in bulk. => Such vacancy configurations lower the GB energy. => Vacancies must naturally exist on GBs !

22. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 22  5 (210) in Ni  Vacancies at GB: magnetic moments Too small effect to explain experimental data !

23. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 23  5 (210) in Ni  Antimony at GB: E b (Sb-GB) = [E bulk (Sb) + E GB ] - [E bulk + E GB (Sb)] substitutional E b = +0.81 eV interstitial E b = -2.81 eV 2 x substitutional E b = +0.87 eV

24. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 24  5 (210) in Ni  Sulphur at GB: substitutional E b = +0.29 eV interstitial? Eb = +0.22 eV 2 x substitutional -> interstitial E b = +1.88 eV

25. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 25  5 (210) in Ni  Antimony and vacancy at GB: E b (Sb-GB+V2) = [E bulk (Sb) + E GB (V2)] - [E bulk + E GB (Sb+V)] case I E b = -0.55 eV case II E b = +0.33 eV case III E b = +1.14 eV case IV E b = +1.97 eV ?

26. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 26  5 (210) in Ni  Sulphur and vacancy at GB: case I E b = +1.15 eV case II E b = +1.90 eV case III E b = +1.17 eV case IV E b = +1.64 eV

27. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 27  5 (210) in Ni  Segregation at  5 (210) in Ni:  Vacancies affects the GB structure.  Vacancies at the GB significantly influence the binding energy of segregants to the GB.  It would be desirable to perform a more systematic study using a Monte Carlo method (potential?) to have an idea about the GB structure in real materials.  Comparison with experiment?

28. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 28  5 (210) in Ni  Magnetic anisotropy:  Spin-orbit coupling perturbation approach  Many k -points needed, M(20,1) cell used  Ni bulk magnetic anisotropy: 1  eV/atom  001-100 +0.8 meV  001-010 -0.4 meV  010-100 +1.2 meV  MAE estimate: ~0.3 meV  Similar to surfaces

29. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 29  5 (210) in Fe  Damped molecular dynamics (MD) first used at 0 K to find possible structural modifications of  5 (210) [001].  Two Fe-Cr potentials employed:  two band TB (Olsson et al, PRB 72, 214119 (2005))  EAM type (Bonny et al., to be published)  Totally 50 random configurations examined  => 5 different configurations found

30. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 30  5 (210) in Fe  5 configurations (atoms colored by pressure): cI cII cIIIcIVcV

31. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 31  5 (210) in Fe  GB energies: MD VASP  cI1.42 J/m 2 1.98 J/m 2  cII1.26 J/m 2 1.71 J/m 2  cIII1.54 J/m 2 2.03 J/m 2  cIV1.12 J/m 2 1.64 J/m 2  cV1.64 J/m 2  cI VASP calculations done using PAW GGA potentials considering MD configurations cI- cV.

32. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 32  5 (210) in Fe  Vacancy and Cr binding energies to the GB (cIV) E b (V) E b (Cr) p1  0.05 +0.27 p2 +0.49  0.11 p3 +0.41  0.05 p4 +0.29  0.07 no vacancy delocalization found so far GB positions that attract vacancies repel Cr atoms

33. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 33  5 (210) in Fe  Cr binding energies to vacancies in bulk Olsson Bonny E f 1.721 1.712 E b (1nn)  0.038  0.013 E b (2nn)  0.083  0.038 E b (3nn) +0.003 +0.012 E b (4nn) +0.005 +0.001 binding energies small in magnitude Cr and V repelled in 1nn and 2nn configurations

34. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 34  5 (210) in Fe  Cr segregation at the GB:  Metropolis Monte Carlo, 8400 atom cells effect decreases with increasing temperature effect increases with increasing Cr concentration

35. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 35  3 (111) in Fe  3 different configurations found using both potentials cIcII cIII

36. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 36  3 (111) in Fe  E GB (cI) < E GB (cII) ~ E GB (cIII)  Work in progress to check stability of cII and cIII with VASP

37. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 37  3 (111) in Fe  Cr segregation at the GB: effect decreases with increasing temperature effect increases with increasing Cr concentration

38. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 38 Fe-Cr system  Our work has started just recently  Literature not consistent whether Cr segregates at GBs or not in calculations/simulations  Vacancies introduced into MMC to check their effect on segregation of Cr

39. Seminar, Department of Condensed Matter Theory, Institute of Physics, CSAS, March 23, 2010 39 T h a n k y o u !