Short-Range Structure and Phonon Assignment of the Brownmillerite-Type Oxide Ba$_{2}$In$_{2}$O$_{5}$ and its Hydrated Proton-Conducting Form BaInO$_{3}$H

The vibrational spectra and short-range structure of the brownmillerite-type oxide Ba$_{2}$In$_{2}$O$_{5}$ and its hydrated form BaInO$_{3}$H, are investigated by means of Raman, infrared, and inelastic neutron scattering spectroscopies together withdensity functional theory calculations. For Ba$_{2}$In$_{2}$O$_{5}$, which may be described as an oxygen deficient perovskite structure with alternating layers of InO$_{6}$ octahedra and InO$_{4}$ tetrahedra, the results affirm a short-range structure of $Icmm$ symmetry, which is characterized by random orientation of successive layers of InO$_{4}$ tetrahedra. For the hydrated, proton conducting, form, BaInO$_{3}$H, the results suggest that the short-range structure is more complicated than the $P4/mbm$ symmetry that has been proposed previously on the basis of neutron diffraction, but rather suggest a proton configuration close to the lowest energy structure predicted by Martinez et al. [J.-R. Martinez, C. E. Moen, S. Stoelen, N. L. Allan, J. of Solid State Chem. 180, 3388, (2007)]. An intense Raman active vibration at 150 cm$^{-1}$ is identified as a unique fingerprint of this proton configuration.

U-Duality and the Compactified Gauss-Bonnet Term

We present the complete toroidal compactification of the Gauss-Bonnet Lagrangian from D dimensions to (D-n) dimensions. Our goal is to investigate the resulting action from the point of view of the U-duality symmetry SL(n+1,R) which is present in thetree-level Lagrangian when D-n=3. The analysis builds upon and extends the investigation of the paper [arXiv:0706.1183], by computing in detail the full structure of the compactified Gauss-Bonnet term, including the contribution from the dilaton exponents. We analyze these exponents using the representation theory of the Lie algebra sl(n+1,R) and determine which representation seems to be the relevant one for quadratic curvature corrections. By interpreting the result of the compactification as a leading term in a large volume expansion of an SL(n+1,Z)-invariant action, we conclude that the overall exponential dilaton factor should not be included in the representation structure. As a consequence, all dilaton exponents correspond to weights of sl(n+1,R), which, nevertheless, remain on the positive side of the root lattice.