Continuum strain-gradient elasticity from discrete valence force field model for diamond-like crystals

In this paper using polynomial approximation of the dispersion relations near the center of the first Brillouin zone, we construct a continuum model with internal length scale starting from the discrete valence force field model. As a consequence, and in agreement with a recent result by Maranganti and Sharma, we obtain an explicit estimate of the internal lengths which is ≃0.1Å.