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In this work, we study vacancy energetics in the equiatomic Nb-Mo-Ta-W alloy, especially vacancy formation and migration energies, using molecular statics calculations based on a spectral neighbor analysis potential specifically developed for Nb-Mo-Ta-W. We consider vacancy properties in bulk environments as well as near edge dislocation cores, including the effect of short-range order (SRO) by preparing supercells through Metropolis Monte-Carlo relaxations and temperature on the calculation. The nudged elastic band (NEB) method is applied to study vacancy migration energies. Our results show that both vacancy formation energies and vacancy migration energies are statistically distributed with a wide spread, on the order of 1.0 eV in some cases, and display a noticeable dependence on SRO. We find that, in some cases, vacancies can form with very low energies at edge dislocation cores, from which we hypothesize the formation of stable ‘superjogs’ on edge dislocation lines. Moreover, the large spread in vacancy formation energies results in an asymmetric thermal sampling of the formation energy distribution towards lower values. This gives rise to effective vacancy formation energies that are noticeably lower than the distribution averages. We study the effect that this phenomenon has on the vacancy diffusivity in the alloy and discuss the implications of our findings on the structural features of Nb-Mo-Ta-W.
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An Eigenanalysis of Angle-Based Deformation Energies
Angle-based energies appear in numerous physics-based simulation models, including thin-shell bending and isotropic elastic strands. We present a generic analysis of these energies that allows us to analytically filter the negative eigenvalues of the second derivative (Hessian), which is critical for stable, implicit time integration. While these energies are usually formulated in terms of angles and positions, we propose an abstract edge stencil that succinctly parameterizes the edge deformation, and allows us to derive generic, closed-form analytical expressions for the energy eigensystems. The resultant eigenvectors have straightforward geometric interpretations. We demonstrate that our method is readily applicable to a variety of 2D and 3D angle-based elastic energies, including both cloth and strands, and is up to 7x faster than numerical eigendecomposition.
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- Award ID(s):
- 2132280
- PAR ID:
- 10431371
- Editor(s):
- Ye, Yuting; Wang Huamin
- Date Published:
- Journal Name:
- Proceedings of the ACM on computer graphics and interactive techniques
- ISSN:
- 2577-6193
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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