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For decades, much effort has been devoted to developing proton conductors applicable to electrochemical devices at intermediate temperatures. However, promising materials that possess sufficient conductivity have not been realized yet. This study demonstrates the development of novel proton conductors that are operative at intermediate temperatures, especially 300–400 °C, through the simple ion-exchange method. The Li+/H+ ion-exchange process was conducted for Li14Zn(GeO4)4, one of the members of lithium super ionic conductors (LISICONs), in non-aqueous solutions. The chemical formula of the resultant sample was determined as Li3.13H0.37Zn0.25GeO4 from instrumental analyses. The electrical conductivity of this material was evaluated to be 87.0 mS cm−1, 39.0 mS cm−1, and 5.5 mS cm−1 at 400 °C, 300 °C, and 200 °C, respectively, in 10% H2O–90% N2. Furthermore, the main charge carrier in this electrolyte was identified as a proton from the H/D isotopic exchange study. These findings open up the possibility of realizing new electrochemical devices that are operative at 200–400 °C. [ABSTRACT FROM AUTHOR]

This paper discusses the eigenvalue problem for the real symmetric matrix, especially the determination of the largest eigenvalue. The largest eigenvalue is the maximum extremum of the objective function called the Rayleigh quotient and can be determined by the steepest descent method. It is known, however, that the steepest descent method suffers from slow convergence because it converges linearly. Especially, when the largest and the nest largest eigenvalues have very close values, the convergence is particularly slow. This paper analyzes this situation and shows that the convergence can be accelerated by combining the steepest descent method with a technique called shaking. Finally, it is demonstrated by a numerical example that the convergence is accelerated drastically by the proposed technique. [ABSTRACT FROM AUTHOR]