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NN10.10 - Ab Initio Local-Energy and Local-Stress Calculations: Applications to Materials Interfaces 
December 4, 2014   4:45pm - 5:00pm

Ab initio plane-wave methods based on density-functional theory (DFT) such as ultrasoft pseudopotential and projector augmented wave methods coupled with efficient iterative ground-state computations enable us to deal with various defects, surfaces and interfaces in materials. In the plane-wave methods, total energies and stress tensors are given as integrated or averaged quantities in the supercell, and we cannot obtain local distributions of energies or stresses. If we could obtain such local distributions by the plane-wave methods, it should greatly contribute to the understanding of the nature of defects, surfaces and interfaces. We are engaged in the development of the computational technique for such local energies and stresses within the plane-wave DFT framework. In this talk, we present our recent development and applications [1-4] by using QMAS code [5]. The energy-density and stress-density schemes were proposed for the plane-wave methods, while there are inherent gauge-dependent problems. The kinetic terms in these densities depend on the selection of symmetric or asymmetric forms, leading to non-uniqueness. The differences between the symmetric and asymmetric forms in these densities, namely the gauge-dependent terms, are naturally integrated to be zero throughout the supercell. We consider local regions for which the gauge-dependent terms are also integrated to be zero. By integrating the energy and stress densities in such local regions, we can obtain unique local quantities. About the computational schemes to define such local regions, we use the layer-by-layer method [1] for layered structures, and the Bader method with the recent algorithm [6] for general systems. For grain boundaries (GBs) in Al, Cu and Fe, the local-energy and local-stress analyses showed general presence of tighter and looser sites at the interfaces. The tighter sites with smaller atomic volumes show lower local energies and compressive stresses, while the looser sites with larger atomic volumes show higher local energies and tensile stresses. These two kinds of sites show quite different magnetic moments in bcc Fe and quite different behaviors of impurity segregation in all the GBs. During ab initio tensile tests of such GBs, local-energy and local-stress analyses revealed contrasting behaviors of such tighter and looser sites. For coherent Fe/TiC (NbC) interface models, we observed that the distributions of energy and stress at the interface seriously depend on the local configurations.

[1] Y. Shiihara et al., Phys. Rev. B 81, 075441 (2010); ibid. 87, 125430 (2013)
[2] H. Wang et al., J. Phys.: Condens. Matter 25, 305006 (2013)
[3] S. Kr. Bhattacharya et al., J. Phys.: Condens. Matter 25, 135004 (2013); J. Mater. Sci. 49, 3980 (2014)
[4] V. Sharma et al., submitted (2014)
[5] S. Ishibashi et al., Phys. Rev. B 76 (2007) 153310
[6] M. Yu and D. R. Trinkle, J. Chem. Phys. 134, 064111 (2011); M. Yu et al., Phys. Rev. B 83, 115113 (2011)

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