A new interpretation of the diffusion mechanism for polaron-Li vacancy complexes in Li 2FeSiO 4 is presented based on first principles calculations within the GGA+U framework. A polaron-Li vacancy complex model is proposed for the first time for the lithium silicate systems. The formation of the bound polaron was found to be favorable at the third nearest iron neighbor to the Li vacancy. Four elementary processes occurring during Li ion diffusion are discussed along with possible diffusion pathways. The diffusion of the Li ions proceeds along the [100] and [001] directions with activation energy barriers of 0.84 and 0.88 eV, respectively.

The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants, {lambda(k)}(k=1)(infinity), that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. We present a series of results for associated sets of constants c(n) and d(n), n = 0, 1, ..., and give the precise relation of these to the Li/Keiper constants. In the course of our investigation, we obtain new representations of classical special functions under a Mobius transformation. Among the conclusions is that the leading behavior (1/2) ln n of lambda(n)/n is absent in c(n), suggesting that the Riemann hypothesis for c(n) based upon quantities derivable from elementary functions. The quantitative estimation of this recursion could provide a result stronger than the Riemann hypothesis itself.

The ZnO nanorods have been prepared on lime-glass substrate by doping Li + and/or Mg 2+ using a sol-gel method. The results show that the degree of C-orientation of Li/Mg doped ZnO nanorods is much high compared with that of Li doped and undoped ones. The individual nanorod exhibits an asymmetric hexagonal morphology with uniform diameter (50-80nm) along its length (300nm), and few abnormal ZnO rods (with about 3mum length) can be observed on the surface in the SEM images. The growth mechanism of ZnO nanorods has also been discussed. [All rights reserved Elsevier]

Lithium transport across the cell membrane is interesting in the light of general cell physiology and because of its alteration during numerous human diseases. The mechanism of Li+ transfer has been studied mainly in erythrocytes with a slow kinetics of ion exchange and therefore under the unbalanced ion distribution. Proliferating cultured cells with a rapid ion exchange have not been used practically in study of Li+ transport. In the present paper, the kinetics of Li+ uptake and exit, as well as its balanced distribution across the plasma membrane of U937 cells, were studied at minimal external Li+ concentrations and after the whole replacement of external Na+ for Li+. It is found that a balanced Li+ distribution attained at a high rate similar to that for Na+ and Cl− and that Li+/Na+ discrimination under balanced ion distribution at 1–10 mM external Li+ stays on 3 and drops to 1 following Na, K-ATPase pump blocking by ouabain. About 80% of the total Li+ flux across the plasma membrane under the balanced Li+ distribution at 5 mM external Li+ accounts for the equivalent Li+/Li+ exchange. The majority of the Li+ flux into the cell down the electrochemical gradient is a flux through channels and its small part may account for the NC and NKCC cotransport influxes. The downhill Li+ influxes are balanced by the uphill Li+ efflux involved in Li+/Na+ exchange. The Na+ flux involved in the countertransport with the Li+ accounts for about 0.5% of the total Na+ flux across the plasma membrane. The study of Li+ transport is an important approach to understanding the mechanism of the equivalent Li+/Li+/Na+/Na+ exchange, because no blockers of this mode of ion transfer are known and it cannot be revealed by electrophysiological methods. Cells cultured in the medium where Na+ is replaced for Li+ are recommended as an object for studying cells without the Na,K-ATPase pump and with very low intracellular Na+ and K+ concentration.

The influence of 90 degrees domain boundaries in (La,Li)TiO3 (LLTO) on the Li conduction mechanism has been examined by a combination of state-of-the-art electron microscopy techniques and first-principles calculations. The atomistic structure of 90 degrees domain boundaries in LLTO was determined from aberration-corrected scanning transmission electron microscopy images. At 90 degrees domain boundaries, each perovskite unit of one domain is connected by an La-rich layer to units of the neighboring domain. First-principles calculations of a model domain boundary show that Li migration through the La layer has a very high activation energy, E-a, of 3.58 eV, indicating that La layers serve to block Li migration. However, if La vacancies are present within La layers, the migration energy decreases significantly to 0.58 eV, a value more in line with experimental observation. The results show that Li conduction in LLTO is strongly influenced by 90 degrees domain boundaries. The activation energy in a single crystal (E-a = 0.19 eV) is much lower, suggesting that if 90 degrees domain boundaries could be eliminated, an increase in conductivity of approximately three orders of magnitude compared with conventional LLTO could be achieved. (C) 2014 Elsevier B.V. All rights reserved.

(7)Li MAS NMR spectra of 2.5 MeV electron-irradiated LiF crystals have been measured in a field of 9.4 T. Besides the resonance line of the ionic compound, a second well-separated spectrum is observed in the region of the Knight shift value for metallic lithium. At room temperature, the latter can be decomposed into two components with different Knight shift and linewidth values. When the temperature is increased, line narrowing takes place at first, indicating shortening of correlation times for self-diffusion, independently in both components. Above 370 K, both lines broaden and approach each other before collapsing into a single line. The high ppm component disappears after crossing the melting temperature of metallic lithium (454 K). The two lines are attributed to different types of metallic Li: one to bulk-like metal, the other to Li present initially under pressure and relaxing to the former under thermal treatment.