First-principles study of fcc-Ag/bcc-Fe interfaces

Ab initio calculations are employed to determine the lower and upper bounds of the interfacial energy and work of separation of a fcc-Ag/bcc-Fe interface. The strain-free interfacial energy of the coherent interface is taken as the lower bound and the interfacial energy of the commensurate incoherent interface as the upper bound of the interfacial energy of a realistic semicoherent interface. The latter is estimated by applying an averaging scheme based on the interfacial energies obtained for the coherent interfaces. Similar calculations are performed for determining the bounds of the work of separation. We justify the use of the averaging scheme by carrying out large supercell calculations for a semicoherent interface. For a Fe(110)/Ag(111) semicoherent interface, we show that taking either Fe or Ag as the underlying lattice, our averaging scheme can yield a reasonable estimation of the work of separation of the semicoherent interface. However, when taking Ag as the underlying lattice, the averaged interfacial energy of the semicoherent interface is significantly underestimated due to the magnetism. The structure and magnetism at the coherent and semicoherent interfaces are discussed.

Figure 1

Schematic of the (a) Fe(001)/Ag(001) interface and the (b) Fe(110)/Ag(111) interface. The cross symbols mark the high-symmetry sites with respect to the Ag plane for the successive Fe atom at interface. The layers around the interface are indexed by numbers.

Figure 2

The calculated work of separation ($W$) and interfacial energy ($\gamma$) with respect to the number of Fe(001) layers for the Fe(001)/Ag(001) interface. The lateral lattice constants of the supercell are fixed to those of Ag(001).

Figure 3

The calculated work of separation with respect to the number of Ag(001) layers for the Fe(001)/Ag(001) interface. Full relaxation is performed.

Figure 4

The calculated work of separation for the $N$-Fe(110)/9-Ag(111) interface for different stacking sequences with respect to $N$.

Figure 5

The calculated interfacial energy for the $N$-Fe(110)/9-Ag(111) interface for different stacking sequences with respect to $N$.

Figure 6

The map of the work of separation obtained by shifting the bcc Fe part above the fcc Ag(111) plane for the 7-Fe(110)/9-Ag(111) interface. The Ag atoms and the high-symmetry positions are marked on the map.

Figure 7

Schematic of the semicoherent interface. Only the Fe and Ag layers at the interface are shown. The upper panel is the side view and the lower panel the top view of the interface. The positions of Fe atoms at the interface after relaxation are indexed by numbers.

Figure 8

The interlayer distance for the coherent interfaces with different translation states at the interface taking Ag as the underlying lattice (a) and Fe as underlying lattice (b). The interlayer distance for the semicoherent interface is also shown in (a). Notice that the averaged atomic position in one layer was used as the position of the layer in the semicoherent interface.

Figure 9

The magnetic moment of the Fe atom with respect to its position relative to the interface for coherent interface and semicoherent interface. The magnetic moment for one layer of the semicoherent interface is averaged over magnetic moments of all the atoms in that layer. Magnetic moments taking Ag and Fe as the underlying lattice are represented by solid and open symbols, respectively.

Figure 10

The distance between Fe atoms in the Fe layer at interface relative to the averaged position of the Ag layer at interface. The interface separation for the coherent interfaces with different translation states are marked by dashed lines. See Fig. 7 for the explicit positions of Fe atoms at interface.

Figure 11

The magnetic moment (right axis) and Wigner-Seitz volume (left axis) for the Fe atoms at the semicoherent interface. See Fig. 7 for the explicit positions of Fe atoms at interface.