Plastic behavior of nanophase metals studied by molecular dynamics H. Van Swygenhoven Paul Scherrer Institut, 5232 Villigen PSI, Switzerland A. Caro Instituto Balseiro-Centro Ato´mico Bariloche, 8400 Bariloche, Argentina ~Received 1 April 1998! We report molecular-dynamics simulations of plastic deformation of Ni nanophase samples with different grain structures, temperature, and applied stress. We analyze the mechanical and thermal activation of the elementary process contributing to plastic deformation at the grain boundaries and provide a quantitative interpretation in terms of a general nonlinear viscous behavior whose temperature, stress, and grain-size dependence is determined. @S0163-1829~98!07941-7# INTRODUCTION Understanding the mechanical properties of nanophase materials is a challenging issue. These materials are charac- terized by a large amount of grain boundaries whose influ- ence on plasticity is crucial. While in coarse-grain samples interfaces represent obstacles for the deformation processes contributing to the strengthening, in nanophase materials they are probably responsible for most of the observed plasticity. 1 Qualitative arguments indicate that decreasing the grain size from the micrometer to the nanometer regime should reveal two distinct stages. First, it appears as the well-known behavior predicted by the Hall-Petch relation, 2,3 that is, an increase in hardness due to the increased difficulty in acti- vating dislocation sources in a small volume; it is quantita- tively described by a d 21/2 dependence of hardness on mean grain diameter d. For an even smaller grain size, intragrain plastic activity should become more and more difficult and a second stage would appear; dislocations can no longer be created and the Hall-Petch relation is expected to fail. Dif- ferent types of deviations have been reported, going from softening to an ever-increasing hardening, eventually with different slopes. 4–7 A review of the available data is reported in Ref. 8. This new regime, controlled by grain boundary plasticity, is still controversial. The difficulty of obtaining reproducible data that originated in the diversity of internal structure and density still precludes a precise characterization. 8–10 Grain boundaries are metastable structures characterized by five degrees of freedom. The energy surface in this 5- degree space has plateaus and valleys describing high- and low-energy boundaries, the latter resulting form particular misorientations that generate regular misfit dislocation nets or coincidence superlattices. For nanophase samples the mi- crostructure is strongly dependent on the synthesis tech- niques, all based on driving the material far from equilibrium using mechanical work or compaction. 11–13,19 Therefore the characterization is of great importance. Molecular-dynamics computer simulations can help in un- derstanding the relationship between grain-boundary struc- ture and overall properties. For some simple materials, like late transition metals and their compounds, the mean-field approximations such as the embedding atom or the Finnis- Sinclair models 14,15 provide a quite precise description of the atomic interactions, yet they are simple enough to deal with some hundred thousand atoms in present-day computers. It allows computer-generated samples to be in a one-to-one scale with real nanograins. Many physical properties ~like lattice parameter, cohesive energy, elastic constants, phonon-dispersion relations, point defect and thermodynamic properties, phase diagrams, stack- ing fault energies, surface structure and energy, etc.! are well reproduced within this model, which has been used for the last 10 years as a standard for large-scale simulations. It is then natural to apply this computational tool to study nanophase materials. It is important to realize that it is an empirical model, as opposed to ab initio, and its quantitative prediction capabilities, when extrapolated far from the region where it has been adjusted as is the case of very disordered interfaces, have to be considered with care. However, we believe the power of this technique is the highlighting of the physical processes involved and providing data for a quali- tative interpretation. Despite the fact that computer-generated samples have similar grain size to real samples, the total number of atoms that can be dealt with in the simulation limits the number of grains; in our samples we use around 15 grains, in cubic samples with approximately 22 nm in side. To reproduce bulk behavior, these samples are periodically repeated in an infinite array with no free surfaces. The small number of grains compared with real samples may induce anisotropy in the measured properties. We have measured elastic and plas- tic properties along the three cubic axes and concluded that fluctuations exist but are not significant. Careful analysis of grain boundaries in computer- generated pure metallic nanosamples has been reported; 16 the degree of disorder has been interpreted in terms of amor- phous structures. However, this computer representation is not fully accepted because some experiments have shown that the degree of disorder in the boundaries depends on the age of the sample and its thermal history. Only as-prepared samples show short-range uncorrelated atomic displace- ments, whereas in aged and annealed samples it has been PHYSICAL REVIEW B 1 NOVEMBER 1998-I VOLUME 58, NUMBER 17 PRB 58 0163-1829/98/58~17!/11246~6!/$15.00 11 246 ©1998 The American Physical Society