Two-dimensional versus three-dimensional constraints in hetero-epitaxy/orientation relationships

Molecular dynamics simulations have been performed to compare the orientation relationships (ORs) that develop between Ag films/particles equilibrated with Ni, depending on whether the Ag is subjected to three-dimensional (3-D) confinement by being embedded in Ni, or to 2-D confinement by equilibration with a Ni substrate. Previous results of both simulations and experiments have shown that Ag films equilibrated with planar Ni substrates display a large number of different ORs; in particular, Ag equilibrated on Ni{100} displays an OR of Ag{111} <110> // Ni{100} <110>, often referred to as an oct-cube OR. Here it is shown that a Ag particle embedded in Ni displays an OR of Ag{111} <110> // Ni{111} <110>, i.e., a cube-on-cube OR. It has also been shown that as the confinement of a Ag particle is gradually increased from 2-D to 3-D, by equilibrating a Ag particle on Ni(100) substrates with progressively deeper dimples, a transition in OR occurs from oct-cube to cube-on-cube. This result contradicts the conventional notion which supposes that the ORs displayed in the presence of 3-D confinement (e.g., during phase transformations) will also tend to be displayed in epitaxy on a substrate.