Charge Distribution Near Oxygen Vacancies in Reduced Ceria

Understanding the electronic charge distribution around oxygen vacancies in transition metal and rare earth oxides is a scientific challenge of considerable technological importance. We show how significant information about the charge distribution around vacancies in cerium oxide can be gained from a study of high resolution crystal structures of higher order oxides which exhibit ordering of oxygen vacancies. Specifically, we consider the implications of a bond valence sum analysis of Ce$_{7}$O$_{12}$ and Ce$_{11}$O$_{20}$. To illuminate our analysis we show alternative representations of the crystal structures in terms of orderly arrays of co-ordination defects and in terms of flourite-type modules. We found that in Ce$_{7}$O$_{12}$, the excess charge resulting from removal of an oxygen atom delocalizes among all three triclinic Ce sites closest to the O vacancy. In Ce$_{11}$O$_{20}$, the charge localizes on the next nearest neighbour Ce atoms. Our main result is that the charge prefers to distribute itself so that it is farthest away from the O vacancies. This contradicts \emph{the standard picture of charge localisation} which assumes that each of the two excess electrons localises on one of the cerium ions nearest to the vacancy. This standard picture is assumed in most calculations based on density functional theory (DFT). Based on the known crystal structure of Pr$_{6}$O$_{11}$, we also predict that the charge in Ce$_{6}$O$_{11}$ will be found in the second coordination shell of the O vacancy. Although this review focuses on bulk cerium oxides our approach to characterising electronic properties of oxygen vacancies and the physical insights gained should also be relevant to surface defects and to other rare earth and transition metal oxides.Comment: 20 pages, 23 figures. The replacement file has a new format for the figures are the document layout but no change in content. v3 has the following main changes: 1. The abstract and introduction were extensively revised. 2. Sec. IV was removed. 3. The Conclusion was rewritte

Full one-loop electroweak corrections to e+e- to 3 jets at linear colliders

We describe the impact of the full one-loop electroweak terms of O(alpha_s alpha_EM^3) entering the electron-positron into three-jet cross-section from sqrt(s)=M_Z to TeV scale energies. We include both factorisable and non-factorisable virtual corrections and photon bremsstrahlung. Their importance for the measurement of alpha_S from jet rates and shape variables is explained qualitatively and illustrated quantitatively, also in presence of b-tagging.Comment: 6 pages, to appear in the proceedings of the workshop "LC09 -- e+e- Physics at the TeV scale and the Dark Matter Connection", 21-24 September 2009, Perugia (Italy). Minor corrections, references added

Quasiharmonic elastic constants corrected for deviatoric thermal stresses

The quasiharmonic approximation (QHA), in its simplest form also called the statically constrained (SC) QHA, has been shown to be a straightforward method to compute thermoelastic properties of crystals. Recently we showed that for non-cubic solids SC-QHA calculations develop deviatoric thermal stresses at high temperatures. Relaxation of these stresses leads to a series of corrections to the free energy that may be taken to any desired order, up to self-consistency. Here we show how to correct the elastic constants obtained using the SC-QHA. We exemplify the procedure by correcting to first order the elastic constants of MgSiO$_3$-perovskite and MgSiO$_3$-post-perovskite, the major phases of the Earth's lower mantle. We show that this first order correction is quite satisfactory for obtaining the aggregated elastic averages of these minerals and their velocities in the lower mantle. This type of correction is also shown to be applicable to experimental measurements of elastic constants in situations where deviatoric stresses can develop, such as in diamond anvil cells.Comment: 4 figures, 1 table, submitted to Phys. Rev. B, July 200