Significant differences exist among literature for thermal conductivity of various systems computed using molecular dynamics simulation. In some cases, unphysical results, for example, negative thermal conductivity, have been found. Using GaN as an example case and the direct non-* X. W. Zhou: xzhou@sandia.gov Both the direct and Green-Kubo approaches require long simulations (e.g. at least 1 ns) to reduce the uncertainty due to thermal fluctuations. For the direct method, another difficulty encountered is that the computed thermal conductivity depends strongly on the system length L along the propagation direction, which is typically limited to at most a few hundred nanometers. This means that for perfect bulk crystals the phonon mean free path is comparable to the system size and transport occurs in a partially ballistic regime [17,18,[21][22][23]. It follows from kinetic theory that the computed values of κ are smaller than that of a true bulk system. To obtain values that can be meaningfully compared with experiments, it is therefore necessary to perform several simulations for different cell lengths, and then

We present a set of efficient numerical algorithms to accurately compute the forces on dislocations in free-standing thin films. We first present a spectral method for computing the image stress field of dislocations in an isotropic elastic half space and a free-standing thin film. The traction force on the free surface is decomposed into Fourier modes by a discrete Fourier transform and the resulting image stress field is obtained by superimposing analytic solutions in the Fourier space. Dislocations intersecting free surfaces are discussed, including the use of virtual segments and the associated uniqueness of their solutions. The efficiency of the algorithm is enhanced by incorporating the analytical solutions for straight dislocations intersecting free surfaces. A comprehensive algorithm, including a flow diagram, is formulated and the numerical convergence of these algorithms discussed. As a benchmark, we compute the equilibrium orientation of a threading dislocation in a free-standing thin film. Good agreement is observed between the predictions from the dislocation dynamics model and those from molecular static simulations and the line tension model.

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The thermal conductivity of a nanostructure is sensitive to its dimensions. A simple analytical scaling law that predicts how conductivity changes with the dimensions of the structure, however, has not been developed. The lack of such a law is a hurdle in "phonon engineering" of many important applications. Here, we report an analytical scaling law for thermal conductivity of nanostructures as a function of their dimensions. We have verified the law using very large molecular dynamics simulations.1 arXiv:1206.5357v1 [cond-mat.mtrl-sci]

The deformation of micro-twinned polycrystalline magnesium (Mg) was studied using three-dimensional discrete dislocation dynamics (DDD). A systematic interaction model between dislocations and f1 0 1 2g tension twin boundaries (TBs) was proposed and introduced into the DDD framework. In addition, a nominal grain boundary (GB) model based on experimental results was also introduced to mimic the GB's barrier effect. The current simulations show that tension TBs act as strong obstacles to gliding dislocations, and contribute significantly to the overall hardening response, while twin growth results in a softening effect. Therefore, the Mg concave stress-strain curve can be explained in terms of the competition between TB induced hardening and twin growth induced softening. At low strain levels, twin growth induced softening dominates and a decreasing hardening rate is observed in Stage-I. In Stage-II, the TB induced hardening dominates, which leads to an increasing hardening rate.

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We present a practical algorithm for partially relaxing multiwell energy densities such as pertain to materials undergoing martensitic phase transitions. The algorithm is based on sequential lamination, but the evolution of the microstructure during a deformation process is required to satisfy a continuity constraint, in the sense that the new microstructure should be reachable from the preceding one by a combination of branching and pruning operations. All microstructures generated by the algorithm are in static and configurational equilibrium. Owing to the continuity constrained imposed upon the microstructural evolution, the predicted material behavior may be path-dependent and exhibit hysteresis. In cases in which there is a strict separation of micro and macrostructural lengthscales, the proposed relaxation algorithm may effectively be integrated into macroscopic finite-element calculations at the subgrid level. We demonstrate this aspect of the algorithm by means of a numerical example concerned with the indentation of an Cu-Al-Ni shape memory alloy by a spherical indenter.