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Magnetic grain boundaries in Ni and Fe

This research paper explores the construction, segregation, and properties of magnetic grain boundaries in Ni and Fe, focusing on the tilt and twist grain boundaries. The study investigates the segregation of impurities and its impact on the magnetic properties of the grain boundaries. The findings enhance the understanding of magnetic grain boundaries and their potential applications in various materials.

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Magnetic grain boundaries in Ni and Fe

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  1. Magnetic grain boundaries in Ni and Fe Jan Kuriplach Department of Low Temperature Physics Faculty of Mathematics and Physics Charles University

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

  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. Motivation • 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. Motivation • The structure of nc-Ni is influenced by magnetic field. 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. K. Harada et al., Scripta Mater. 49, 367 (2003).

  6. Motivation • 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. Motivation • 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. Motivation • 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. Motivation • 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. 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. GB typology • Demonstration for twin GBs (Si, (111) plane): twist Reference: http://www.tf.uni-kiel.de/matwis/amat/def_en/index.html

  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. 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. Methods • 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. 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. 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. 5 (210) in Ni • Grain boundary energy (VASP US potentials): (a GGA value of 1.43 J/m2 obtained by M. Yamaguchi et al., J. Phys.: Condens. Matter 16, 3933 (2004) with WIEN2k code)

  18. 5 (210) in Ni • Magnetic moments:

  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 Ef(V) – vacancy formation energy Ef(V) = Ebulk(V) - Ebulk + Ebulk/32 Eb(V+XNi) – binding energy of vacancy and 1nn X atom Eb(V+XNi) = [Ebulk(V) + Ebulk(XNi)] - [Ebulk + Ebulk(V+XNi)] Est(X) – atom X’s preference to be substitutional or interstitial Ep(X) = [Ebulk(Xi) - Ebulk/32] - Ebulk(XNi) => Both S and Sb should be substitutional and bind vacancies.

  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. 5 (210) in Ni • Vacancies at GB: energies and V-GB binding Ef – vacancy formation energy Ef(V-GB) = EGB(V) – EGB + Ebulk/40 Eb– binding energy of vacancy to GB Eb(V-GB) = [EGB + Ebulk(V)] – [Ebulk + EGB(V)]  – GB energy of the GB with vacancy (considering the second GB unaffected) => 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. 5 (210) in Ni • Vacancies at GB: magnetic moments Too small effect to explain experimental data !

  23. 5 (210) in Ni • Antimony at GB: Eb(Sb-GB) = [Ebulk(Sb) + EGB] - [Ebulk + EGB(Sb)] substitutional Eb = +0.81 eV interstitial Eb = -2.81 eV 2 x substitutional Eb = +0.87 eV

  24. 5 (210) in Ni • Sulphur at GB: substitutional Eb = +0.29 eV interstitial? Eb = +0.22 eV 2 x substitutional -> interstitial Eb = +1.88 eV

  25. 5 (210) in Ni • Antimony and vacancy at GB: Eb(Sb-GB+V2) = [Ebulk(Sb) + EGB(V2)] - [Ebulk + EGB(Sb+V)] case I Eb = -0.55 eV case III Eb = +1.14 eV case II Eb = +0.33 eV case IV Eb = +1.97 eV ?

  26. 5 (210) in Ni • Sulphur and vacancy at GB: case I Eb = +1.15 eV case III Eb = +1.17 eV case II Eb = +1.90 eV case IV Eb = +1.64 eV

  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. 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. 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. 5 (210) in Fe • 5 configurations (atoms colored by pressure): cI cII cIII cIV cV

  31. 5 (210) in Fe • GB energies: MD VASP • cI 1.42 J/m2 1.98 J/m2 • cII 1.26 J/m2 1.71 J/m2 • cIII 1.54 J/m2 2.03 J/m2 • cIV 1.12 J/m2 1.64 J/m2 • cV 1.64 J/m2  cI VASP calculations done using PAW GGA potentials considering MD configurations cI-cV.

  32. 5 (210) in Fe • Vacancy and Cr binding energies to the GB (cIV)         Eb(V)      Eb(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. 5 (210) in Fe • Cr binding energies to vacancies in bulk      Olsson       Bonny Ef         1.721      1.712 Eb(1nn)   0.038     0.013 Eb(2nn)   0.083     0.038 Eb(3nn)   +0.003     +0.012 Eb(4nn)   +0.005     +0.001 binding energies small in magnitude Cr and V repelled in 1nn and 2nn configurations

  34. 5 (210) in Fe • Cr segregation at the GB: • Metropolis Monte Carlo, 8400 atom cells • effect decreaseswith increasing temperature • effect increaseswithincreasingCr concentration

  35. 3 (111) in Fe • 3 different configurations found using both potentials cI cII cIII

  36. 3 (111) in Fe • EGB(cI) < EGB(cII) ~ EGB(cIII) • Work in progress to check stability of cII and cIII with VASP

  37. 3 (111) in Fe • Cr segregation at the GB: • effect decreaseswith increasing temperature • effect increaseswithincreasingCr concentration

  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. Thank you !

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