Dislocation Instability in Nanoscale Particles
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Dislocation Instability in Nanoscale Particles C. Carlton and P.J. Ferreira Materials Science and Engineering Program University of Texas at Austin, Austin, TX, 78712, USA Understanding the mechanical behavior of nanoparticles has become a key factor for the success of many engineering applications. Classically, for polycrystalline materials one would expect an increase in the yield strength for smaller grain sizes according to the empirical Hall-Petch equation. However, at the nanoscale, this mechanism seems to break down. Despite the number of interesting papers published on this topic, controversy persists and consensus is still lacking. While this discussion is of great interest for polycrystalline nanoparticles, contemporary models for strengthening are inappropriate for single-crystal nanoparticles, which, altogether, pose a very different problem: the absence of grain boundaries to inhibit dislocations. In this context, we present a new model wherein the change in Gibbs Free Energy of an edge dislocation in a single-crystal particle provides a driving force for dislocation motion. These results show that dislocations become unstable and are spontaneously ejected from the particles below a certain critical size. 1. Introduction The study of the mechanical properties of nanocrystalline materials is a rapidly expanding field, specifically regarding the mechanisms related with plastic deformation. Classically, one would expect an increase in the yield strength for smaller grain sizes according to the empirical Hall-Petch equation [1, 2]. However, in the case of nanomaterials there is little agreement about the validity of the Hall-Petch relationship below a critical grain size. In fact, several investigators have found a critical grain size value below which the Hall-Petch relationship reverses [3, 4, 5]. Despite the significant amount of excellent research performed so far, a unified understanding of the mechanisms involved in the deformation of nanocrystalline materials does not yet exist. While this discussion is of great interest for polycrystalline nanoparticles, contemporary models for strengthening are inappropriate for single-crystal nanoparticles, which pose an altogether very different problem: the absence of grain boundaries to inhibit dislocations. Irradiation experiments conducted on single-crystal nanoparticles revealed fewer crystalline defects observed when compared with microcrystalline particles. In particular, the investigators reported an absence of dislocations, despite the fact that dislocation loops are common in radiation damaged conventional materials [6, 7, 8]. It seems that there may be a critical size under which dislocations are not stable. The purpose of this work is to consider a novel explanation for dislocation stability in nanoparticles that may lead to a better fundamental understanding of the behavior of dislocations in bulk materials with nanoscale grains. In this paper, the model will consider free standing particles of different sizes containing dislocations a
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