Growth conditions for molecular beam epitaxy of SrF2 directly on Si(111) have been optimized for excellent crystal quality. A χmin of 2.6% was demonstrated. Lattice distortion measurements were carried out by ion channeling along off-normal channeling directions in the strained SrF2 layers. The measured residual tensile strain versus the film thickness demonstrated a special thickness: When films were thinner than this thickness, their strain dropped dramatically as thickness decreased, and when films were grown thicker than it, the strain gradually decreased with increasing film thickness. This unique behavior was successfully modeled as the result of competition between the large lattice mismatch between SrF2 and Si and the large difference in thermal coefficients of expansion. Residual strain remained even in SrF2 films thicker than 600 nm, unlike CaF2 on Si(111) for which CaF2 films thicker than 300 nm were observed to have no strain.