 Assuming the interatomic potential, formula_2, is the same within the grain boundaries as in the bulk grains, the elastic modulus, formula_3, will be smaller in the grain boundary regions than in the bulk grains.Thus, via the rule of mixtures, a nanocrystalline material will have a lower elastic modulus than its bulk crystalline form.The exceptional yield strength of nanocrystalline metals is due to grain boundary strengthening, as grain boundaries are extremely effective at blocking the motion of dislocations.