First-principles study of the fcc/bcc interfaces
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Transcript of First-principles study of the fcc/bcc interfaces
First-principles study of the fcc/bcc interfaces
Song LuMaterial Science and Engineering, KTH-Royal institute of Technology, Sweden.
Co-work with:Levente Vitos, Qing-miao Hu, Marko P. J. Punkkinen, Börje Johansson.
• Coherent interface(Cu/Si)
• Semi-coherent interface(Fe/Cu, Cr/Ni, Cr/Cu, duplex steels, etc.)
• Incoherent interface (Cu-Nb)
Introduction
Aims
Calculate the lower and upper bounds of the interfacial energy.
Calculate the lower and upper bounds of the work of separation.
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)
The relationship between and W :
Interfacial energy (): the energy needed to form the interface referred to the bulk states
AEEEW AgvFevAgFe /)( /
AEEE bulkAg
bulkFeAgFe /)( /
WAgFe
’Fe is the surface energy of Fe(110) calculated at strained state. (Ag
underlylattice)
’Ag is the surface energy of Ag(111) calculated at strained state. (Fe
underlying lattice)
WAgFe OR
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.
Result: Coherent work of separation
Underlying lattice
Wtop Wfcc Wbridge Wbcc top fcc bridge bcc Ag Fe
Fe(110) 1.64 2.18 2.02 2.24 1.32 0.79 0.94 0.72 0.51 2.45Ag(111) 1.43 2.21 2.04 1.13 0.36 0.53 0.68 1.88
Results for high-symmetric points
Nonmagnetic: Fe
2.552.24
Averaging scheme for semicoherent/incoherent interface
Work of separation (W) Interfacial energy ()
n
iiWn
W
WWW
1
1
n
iin 1
1
57.0 FeFeW Taking Ag as underlying lattice:
Taking Fe as underlying lattice: 17.0 AgAgW
For incoherent interface:
Semicoherent interface
Underlying lattice: AgAveraging scheme: W=1.91 Jm-2 = 0.65 Jm-2
Direct calculation: W=2.05 Jm-2 = 1.18 Jm-2 7% 70%
Underlying lattice: FeAveraging scheme: W=2.00 Jm-2 = 0.96 Jm-2
Direct calculation: W=2.08 Jm-2 = 1.10 Jm-2
W
W
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:.
Fe underlying lattice:
J m-2.
70.086.1
W
57.088.145.2 FeFeW J m-2.
99.097.1
W 17.051.068.0 AgAgW J m-2.
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.