Importance of interfacial step alignment in hetero-epitaxy and orientation relationships: the case of Ag equilibrated on Ni substrates. Part 1 computer simulations

Abstract

Molecular dynamics simulations of Ag films equilibrated on Ni have been performed for 12 different Ni substrate orientations. The results show that well-equilibrated films display several different orientation relationships (ORs) depending on the Ni substrate orientation: cube-on-cube, twin, oct-cube, and a series of special ORs that are a consequence of the oct-cube OR that develops on Ni(100). It is found that an important feature displayed by the observed ORs is the alignment of the step edges of the Ag film with those of the Ni substrate at the interface. Such alignment is initiated during film formation, but also tends to produce minimum energy interfaces between film and substrate. This feature of hetero-epitaxy and of the resulting ORs has not previously been emphasized.

Appendix

On a Ni(100) substrate, the Ag crystal is oriented with a {111} plane (say the (111) plane) parallel to the substrate, in the oct-cube OR. At the other end of the (100)–(111) edge of the SST, i.e., on the Ni(111) substrate, the Ag crystal is oriented with another {111} plane (say the ($11\bar{1}$) plane) parallel to the substrate to produce either a cube-on-cube or a twin OR. For an intermediate case along this edge of the SST, let the angle between Ni(hkl) and Ni(100) be θ, as shown schematically in Fig. 10. Thus, θ will vary from 0 to 54.7° as Ni(hkl) changes from (100) to (111) by rotation about a common [$01\bar{1}$] direction that lies at the intersection of (100) and (111). Consider now the Ag side of the interface. Let the angle between Ag(hkl) and Ag(111) be ϕ. Thus, ϕ will vary from 0 to 70.5° as Ag(hkl) changes from (111) to ($11\bar{1}$) by rotation about a common [$1\bar{1}$ 0] direction that lies at the intersection of (111) and ($11\bar{1}$). This will result in Ag(hkl) that lies along the (111) to ($11\bar{1}$) arc of a stereogram that extends past (110) of the SST into the adjacent stereographic triangle. When referred back to the SST, all Ag orientations will therefore lie on the (111)–(110) edge. If we assume that the changes in both the Ni and Ag orientations are linear in rotation angles, then:

$$ \phi = \left( {70.5^\circ /54.7^\circ } \right) \uptheta = \, \left( {1 + 15.8^\circ /54.7^\circ } \right) \uptheta $$

(2)

where 15.7° (=70.5° − 54.7°) represents the relative angle of rotation between Ag and Ni. The results of applying this simple correlation are summarized in Table 2.

Fig. 10

Schematic of orientation relationship of Ag on Ni substrate lying along the (100)–(111) edge of the SST