Surface studies on polycrystalline YBa2Cu3O7−δ with Auger electron and low-energy electron energy-loss spectroscopy

Chemical and electronic properties of scrapecleaned YBa₂Cu₃O_7–(YBCO) ceramics, which were also annealed in vacuum or exposed to H atoms or O₂ molecules, were studied at room temperature by applying Auger electron (AES) and low-energy electron energy-loss spectroscopy (LEELS). Scanning electron micrographs showed such scraped surfaces to consist mainly of small, fractured YBCO crystallites, i.e. of clean YBCO surfaces. With only one exception, all low-energy AES lines were found to be shifted in energy compared to data recorded with surfaces of metallic Cu and Y. The analysis of the high-energy AES lines indicated the existence of non-stoichiometric material in grain boundaries. At least 25 different LEELS features were recorded. The 24.9-eV energy loss, which is due to the excitation of bulk valence-electron plasmons, indicates an enhanced oxygen deficit _s 0.8 at scrape-cleaned YBCO surfaces. Annealing of scraped YBCO samples at approximately 700 K in vacuum and also their exposure to hydrogen atoms resulted in an additional oxygen depletion within a few atomic layers near to the surfaces. These oxygen deficiencies were found to increase the intensity ratios of low-and high-energy AES lines of Cu, Ba, and Y and to intensify the energy-loss peak at 4.4 eV which has been attributed to O–Cu–O dumbbells.     

Instability of the paramagnetic state towards incommensurate magnetic order in the 2-d Hubbard model

We determine the instability line separating the paramagnetic phase in the phase diagram of the 2-d Hubbard Model from a phase with incommensurate magnetic order. A mean-field approximation of the Kotliar-Ruckenstein slave boson representation is used to calculate the wave-vector dependent magnetic susceptibility. For largeU/t the instability occurs at a densityn0.37, and a wave-vector close toq=(0,). The dependence ofq onU andn is also given.     

Perturbation analysis of the orthogonal procrustes problem

Given two arbitrary real matricesA andB of the same size, the orthogonal Procrustes problem is to find an orthogonal matrixM such that the Frobenius norm MA – B is minimized. This paper treats the common case when the orthogonal matrixM is required to have a positive determinant. The stability of the problem is studied and supremum results for the perturbation bounds are derived.     

Zur krümmungsverwandtschaft von zwangläufen in affinen ck — Ebenen II

In part I we have studied a map of osculating elements of an affine Cayley-Klein (CK-) plane into the Lie algebra A₄(²) of the aequiform transformations A₄(²) of the given plane A₂(, ²). If we use the real projective space P₃() over A₄(²) each osculating element defines a straight line in P₃(). We now give a one parameter motion in A₄(²) and study second order properties and their analogon in the Lie algebra and P₃(), respectively. We show that the wellknown relationship between the points of the moving frame and the osculating circles of the point paths in the fixed frame may be interpreted as part of a quadratic map of certain straight Lines of P₃(). An analogous result holds for the curvature of pairs of envelopes; the mapV induced in P₃() than is contained in a cubic relationship of straight lines.

---

---

Herrn Professor Oswal Giering zum 60. Geburtstag gewidmet