### First-principles study of the metallic fcc/bcc interfaces

```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.