Effects of O ions beam irradiation on crystal structure of rare earth sesquioxides

We report the results of ion irradiation influence on rare earth sesquioxides structure, which are materials of practical importance as a radiation resistant ceramics in nuclear applications. Y₂O₃, Gd₂O₃ and Er₂O₃ sesquioxides in the pellet form were irradiated by oxygen ions (O²⁺) beam with the energy of 30 keV and implantation fluence of 5 × 10²⁰ m⁻². Samples are characterized by Grazing Incidence X-ray Diffraction (GIXRD), Raman spectroscopy and atomic force microscopy (AFM). By GIXRD it was found partial transformation from cubic (C) to monoclinic (B) phase only in Gd₂O₃, induced by O²⁺ irradiation. This was confirmed by Raman spectroscopy. Although full phase transition from C to B phase in Y₂O₃ was not observed, the splitting and broadening of the main intensity Raman band for C phase could be explained by the stress and the disorder induced by the quenching. Analysis done by AFM showed changes in surface topology, i.e. values of average roughness (Ra) and root mean squared roughness (RMS) were significantly changed after irradiation for all samples. RMSs in Y₂O₃ before and after irradiation were 35 nm and 26 nm, respectively.     

Generalized spherical functions on reductive -adic groups

Let be the group of rational points of a connected reductive -adic group and let be a maximal compact subgroup satisfying conditions of Theorem 5 from Harish-Chandra (1970). Generalized spherical functions on are eigenfunctions for the action of the Bernstein center, which satisfy a transformation property for the action of . In this paper we show that spaces of generalized spherical functions are finite dimensional. We compute dimensions of spaces of generalized spherical functions on a Zariski open dense set of infinitesimal characters. As a consequence, we get that on that Zariski open dense set of infinitesimal characters, the dimension of the space of generalized spherical functions is constant on each connected component of infinitesimal characters. We also obtain the formula for the generalized spherical functions by integrals of Eisenstein type. On the Zariski open dense set of infinitesimal characters that we have mentioned above, these integrals then give the formula for all the generalized spherical functions. At the end, let as mention that among others we prove that there exists a Zariski open dense subset of infinitesimal characters such that the category of smooth representations of with fixed infinitesimal character belonging to this subset is semi-simple.