RESUMO
Manipulating the shape and distribution of strengthening units, e.g. particles, fibers, and precipitates, in a bulk metal, has been a widely applied strategy of tailoring their mechanical properties. Here, we report self-assembled patterns of Gd nano-fibers in Mg-Gd alloys for the purpose of improving their strength and deformability. 1-nm Gd nano-fibers, with a ãcã-rod shape, are formed and hexagonally patterned in association with Gd segregations along dislocations that nucleated during hot extrusion. Such Gd-fiber patterns are able to regulate the relative activities of slips and twinning, as a result, overcome the inherent limitations in strength and ductility of Mg alloys. This nano-fiber patterning approach could be an effective method to engineer hexagonal metals.
RESUMO
We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires half of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.
