First-principles study of the fcc/bcc interfaces Song Lu Material Science and Engineering, KTH-Royal institute of Technology, Sweden. Co-work with: Levente Vitos, Qing-miao Hu, Marko P. J. Punkkinen, Börje Johansson. Introduction • Coherent interface(Cu/Si) • Semi-coherent interface(Fe/Cu, Cr/Ni, Cr/Cu, duplex steels, etc.) • Incoherent interface (Cu-Nb) An example in duplex stainless steel H. Jiao et al. Philo. Mag. 83, (2003)1867 Aims Calculate the lower and upper bounds of the interfacial energy. Calculate the lower and upper bounds of the work of separation. Model system: Fe(110)/Ag(111) coherent interface Mismatch:~ 3.4% Mismatch: ~25% Work of separation (W): the energy needed to separate the interface into two surfaces. (Here both the interface and the surfaces are constrained by the same lateral strain set by the underlying Ag lattice) W ( E Fe / Ag E Fev E Agv ) / A Interfacial energy (): the energy needed to form the interface referred to the bulk states ( E Fe / Ag E Fe E Ag ) / A bulk bulk The relationship between and W : Ag W Fe ’Fe is the surface energy of Fe(110) calculated at strained state. (Ag underlylattice) OR Fe Ag W ’Ag is the surface energy of Ag(111) calculated at strained state. (Fe underlying lattice) Result: Coherent work of separation Taking Ag as underlying lattice: Taking Fe as underlying lattice: Fig. Map of the work of separation obtained by shifting the upper part against the lower part of the coherent interface when taking (a) Ag, (b) Fe as the underlying lattice, respectively. Results for high-symmetric points Wbcc top fcc bridge bcc Ag Fe 2.18 2.02 2.24 1.32 0.79 0.94 0.72 0.51 2.45 2.21 2.04 1.13 0.36 0.53 0.68 1.88 Underlying lattice Wtop Wfcc Fe(110) 1.64 Ag(111) 1.43 Wbridge Nonmagnetic: Fe 2.55 2.24 Averaging scheme for semicoherent/incoherent interface Work of separation (W) W W W W 1 n W n i i 1 Interfacial energy () 1 n n i i 1 For incoherent interface: Taking Ag as underlying lattice: 0 . 57 W Fe Fe Taking Fe as underlying lattice: W Ag Ag 0 . 17 Semicoherent interface Underlying lattice: Ag Averaging scheme:W W=1.91 Jm-2 = 0.65 Jm-2 Direct calculation: W=2.05 Jm-2 = 1.18 Jm-2 70% 7% Underlying lattice: Fe Averaging scheme:W W=2.00 Jm-2 = 0.96 Jm-2 Direct calculation: W=2.08 Jm-2 = 1.10 Jm-2 Commensurate incoherent interface Putting the ideal (110)Fe on the ideal (111) Ag plane in the N-W orientation relationship without straining both lattices. Ag underlying lattice: . W 1 . 86 J m-2. W 0 . 70 2 . 45 1 . 88 0 . 57 Fe Fe J m-2. Fe underlying lattice: W 1 . 97 0 . 99 J m-2. W Ag Ag 0 . 68 0 . 51 0 . 17 J m-2. Summary Using first-principles method, we can define the lower bound of the interfacial energy of the fcc/bcc interface, and the upper bound maybe properly estimated by an averaging scheme. Thanks for your attention!