Towards elucidating microscopic structural changes in Li-ion conductors Li1+yTi2–yAly[PO4 ]3 and Li1+yTi2–yAly[PO4 ]3–x [MO4 ]x(M=V and Nb) : X-ray and27Al and31P NMR studies

A combination of X-ray powder diffraction (XRD) and nuclear magnetic resonance (NMR) studies has demonstrated that attempted substitutions of Al, V and Nb into the framework of LiTi₂(PO₄)₃ yield several impurity phases in addition to direct substitutions of Al into Ti and V, Nb into P sites. Direct substitutions were confirmed by changes in the unit cell dimensions as indicated by the peak shifts observed in the X-ray diffractographs and by analyses of the ²⁷Al and ³¹P magic angle spinning (MAS) spectra. A major impurity phase was identified as AlPO₄ (found in at least two polymorphs) and the amount present increases with increasing Al additions. The formation of AlPO₄ appeared to be enhanced by further V but suppressed by Nb substitution. These results suggest that the presence of AlPO₄ , together with the non-stoichiometric modified LTP, may be the cause for the observed densification of this material upon sintering and the increased ionic conductivity.

An amoeboid algorithm for solving linear transportation problem

Transportation Problem (TP) is one of the basic operational research problems, which plays an important role in many practical applications. In this paper, a bio-inspired mathematical model is proposed to handle the Linear Transportation Problem (LTP) in directed networks by modifying the original amoeba model Physarum Solver. Several examples are used to prove that the provided model can effectively solve Balanced Transportation Problem (BTP), Unbalanced Transportation Problem (UTP), especially the Generalized Transportation Problem (GTP), in a nondiscrete way. © 2013 Elsevier B.V. All rights reserved.