Compliant substrate epitaxy: Au on MoS$_2$

The epitaxial growth of {111} oriented Au on MoS$_2$ is well documented despite the large lattice mismatch (~8% biaxial strain), and the fact that a Au {001} orientation results in much less elastic strain. An analysis based on density functional and linear elasticity theories reveals that the {111} orientation is stabilized by a combination of favorable surface and interfacial contributions to the energy, and the compliance of the first layer of the MoS$_2$.