Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1

Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional $F_4$-homogeneous manifold associated to a short simple root.Comment: 22 page

Synergistic multi-doping effects on the Li7La3Zr2O12 solid electrolyte for fast lithium ion conduction.

Here, we investigate the doping effects on the lithium ion transport behavior in garnet Li7La3Zr2O12 (LLZO) from the combined experimental and theoretical approach. The concentration of Li ion vacancy generated by the inclusion of aliovalent dopants such as Al(3+) plays a key role in stabilizing the cubic LLZO. However, it is found that the site preference of Al in 24d position hinders the three dimensionally connected Li ion movement when heavily doped according to the structural refinement and the DFT calculations. In this report, we demonstrate that the multi-doping using additional Ta dopants into the Al-doped LLZO shifts the most energetically favorable sites of Al in the crystal structure from 24d to 96 h Li site, thereby providing more open space for Li ion transport. As a result of these synergistic effects, the multi-doped LLZO shows about three times higher ionic conductivity of 6.14 × 10(-4) S cm(-1) than that of the singly-doped LLZO with a much less efforts in stabilizing cubic phases in the synthetic condition