First-principles calculation of grain boundary excess volume and free volume in nanocrystalline and ultrafine-grained aluminum

Abstract

We studied the relationship between the grain boundary energy and grain boundary excess free volume at the tilt grain boundaries in aluminum by applying the first-principles calculations. The grain boundary energy increased linearly as the grain boundary excess free volume increased. The value of the proportionality constant between the grain boundary energy and the grain boundary excess free volume, α, was 13.8 GPa for aluminum. The grain boundary elastic energy was calculated on the basis of first principles using a dummy boundary as well as the classical elasticity theory. The grain boundary elastic energies are close to the grain boundary energies. We discussed the free volume in nanocrystalline and ultrafine-grained materials and proposed a method for estimating the grain boundary energy using the density of nanocrystalline and ultrafine-grained materials with the proportionality constant, α. The grain boundary energy of nanocrystalline aluminum fabricated by mechanical milling and subsequent consolidation was estimated. The calculated grain boundary energy in the nanocrystalline aluminum is comparable to or lesser than that in coarse-grained aluminum. © 2012 The Japan Institute of Light Metals.