first-principles study of the fcc/bcc interfaces song lu material science and engineering, kth-royal...

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

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)

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

2.55

2.24

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.

70.0

86.1

W

57.088.145.2 FeFeW J m-2.

99.0

97.1

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.

Thanks for your attention!