Origin of an unusual systematic variation in the heteroepitaxy of Ag on Ni – The roles of twinning and step alignment

A systematic variation in the orientation relationship (OR) of Ag films grown on Ni substrates previously discovered by a combinatorial approach is analyzed using concepts of grain boundaries, surface science and phase transformations. On roughly half of all Ni substrate orientations, Ag adopts a "special" OR that varies systematically from a twin OR, which develops on substrates lying along the (111)–(210) line of the standard stereographic triangle (SST), to the so-called oct-cube OR, which arises exclusively on (100) substrates. On the other half of Ni substrate orientations, Ag adopts the standard cube-on-cube OR. The special ORs are modeled by a) linear interpolation, b) 1D edge-to-edge matching and c) 2D transformation strains, using the twin relationship as a reference. The 1D model shows that the systematic variation in the special ORs can be understood in terms of a growth mechanism by attachment at steps and a lattice rotation due to the difference between the step heights in the substrate and the film. The 2D model explains why this mechanism does not apply to substrates on which Ag displays the cube-on-cube OR.