Motivated by the burgeoning interest in the epitaxial growth of hexago
nal and tetragonal semiconductors, we report expressions for the strai
n energy density for the high symmetry directions in these crystal sys
tems. In addition, we have calculated tile behaviour of the strain ene
rgy density as a function of epilayer surface normal orientation for t
he following systems: GaN on 6H-SiC, GaN on AlN, AlN on 6H-SiC and CuI
nSe2 on GaAs. For the first three cases, we suggest that substrate ori
entations not yet investigated may improve film quality as they will s
erve to reduce the strain energy density by approximately 30%, 17% and
65%, respectively, relative to the commonly employed (001) substrate
orientation.