A careful analysis of the available results on the basis of existing models suggests that there is a critical grain size below which the triple junction volume fraction ...
Grain size effects in nanocrystalline materials C. Suryanarayana, D. Mukhopadhyay, S. N. Patankar, and F. H. Froes Institute for Materials and Advanced Processes, University of Idaho, Moscow, Idaho 83843-4195 (Received 8 May 1991; accepted 21 April 1992)
Nanocrystalline materials have a grain size of only a few nanometers and are expected to possess very high hardness and strength values. Even though the hardness/strength is expected to increase with a decrease in grain size, recent observations have indicated that the hardness increases in some cases and decreases in other cases. A careful analysis of the available results on the basis of existing models suggests that there is a critical grain size below which the triple junction volume fraction increases considerably over the grain boundary volume fraction and this is suggested to be responsible for the observed softening at small grain sizes. I. INTRODUCTION Nanocrystalline materials are single-phase or multiphase equiaxed polycrystals with a grain size in the range of 1 to 10 n m . w Multilayer deposits of alternate metal layers with a thickness of at least one of the layers in the nanometer range are also nanostructures, in this case one-dimensional or lamellar nanostructures.3'5 Because of the small grain size, and consequent large volume fraction of atoms residing in the grain boundaries, nanocrystalline materials exhibit novel, and often improved, properties over those of conventional coarsegrained polycrystalline materials. 1 ^ One of the most significant changes resulting from a reduction in the grain size to the nanometer level is an increase in the strength and hardness. This has been interpreted in terms of the Hall-Petch relationship: ay = o-o +
