 Because the volume fraction of grain boundaries in nanocrystalline materials can be as large as 30% , the mechanical properties of nanocrystalline materials are significantly influenced by this amorphous grain boundary phase.For example, the elastic modulus has been shown to decrease by 30% for nanocrystalline metals and more than 50% for nanocrystalline ionic materials .This is because the amorphous grain boundary regions are less dense than the crystalline grains, and thus have a larger volume per atom, formula_1.