Substrate-induced strain and orientational ordering in adsorbed monolayers

The influence of a rigid substrate on the static strain of an adsorbed incommensurate monolayer is discussed. It is shown that the strain energy is independent of relative translation of the two lattices but does depend on their relative orientation. A simple analytic form is given for the minimum energy orientation angle ${\theta }_{min}$ as a function of lattice parameters and monolayer sound velocities. Predicted values of ${\theta }_{min}$ for Ar on graphite are in good agreement with the recent measurements of Shaw et al.