Amorphous and highly nonstoichiometric titania (TiOx) thin films close to metal-like conductivity

Oxygen-deficient titanium oxide films (TiOx) have been prepared by pulsed laser deposition at room temperature. Samples in their as-deposited state have an average composition of TiO1.6, are optically absorbing and show electronic conductivities in the range of 10 S cm−1. The films are metastable and consist of grains of cubic titanium monoxide (γ-TiO) embedded in an amorphous TiO1.77 matrix. Upon annealing in an argon atmosphere the electrical conductivity of the films increases and comes close to metal-like conductivity (1000 S cm−1) at about 450 °C whereas the local structure is changed: nanocrystalline grains of metallic Ti are formed in the amorphous matrix due to an internal solid state disproportionation. The highly conductive state can be frozen by quenching. During heat treatment in an argon atmosphere a stoichiometric rutile TiO2 surface layer forms due to oxidation by residual oxygen. The combination of a highly conductive TiOx film with such an approximately 20 nm thick rutile cover layer leads to a surprisingly high efficiency for the water-splitting reaction without the application of an external potential

Compactness of immersions with local Lipschitz representation

We consider immersions admitting uniform representations as an L-Lipschitz graph. In codimension 1, we show compactness for such immersions for arbitrary fixed finite L and uniformly bounded volume. The same result is shown in arbitrary codimension for L less than or equal to 1/4

New LpL_p Affine Isoperimetric Inequalities

We prove new $L_p$ affine isoperimetric inequalities for all $p \in [-\infty,1)$. We establish, for all $p\neq -n$, a duality formula which shows that $L_p$ affine surface area of a convex body $K$ equals $L_\frac{n^2}{p}$ affine surface area of the polar body $K^\circ$

Controlling the Electrical Properties of Undoped and Ta-doped TiO2 Polycrystalline Films via Ultra-Fast Annealing Treatments

We present a study on the crystallization process of undoped and Ta doped TiO2 amorphous thin films. In particular, the effect of ultra-fast annealing treatments in environments characterized by different oxygen concentrations is investigated via in-situ resistance measurements. The accurate examination of the key parameters involved in this process allows us to reduce the time needed to obtain highly conducting and transparent polycrystalline thin films (resistivity about $6 \times 10^{-4}$ {\Omega}cm, mean transmittance in the visible range about $81\%$) to just 5 minutes (with respect to the 180 minutes required for a standard vacuum annealing treatment) in nitrogen atmosphere (20 ppm oxygen concentration) at ambient pressure. Experimental evidence of superficial oxygen incorporation in the thin films and its detrimental role for the conductivity are obtained by employing different concentrations of traceable 18O isotopes during ultra-fast annealing treatments. The results are discussed in view of the possible implementation of the ultra-fast annealing process for TiO2-based transparent conducting oxides as well as electron selective layers in solar cell devices; taking advantage of the high control of the ultra-fast crystallization processes which has been achieved, these two functional layers are shown to be obtainable from the crystallization of a single homogeneous thin film.Comment: 30 pages (including Supporting Information and graphical TOC), 4 figure

On the Bergman representative coordinates

We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the Bergman metric, contained in this set. By concrete examples we show that these estimates are the best possible.Comment: 20 page

On the uniqueness of LpL_p-Minkowski problems: the constant pp-curvature case in R3\mathbb{R}^3

We study the $C^4$ smooth convex bodies $\mathbb{K}\subset\mathbb{R}^{n+1}$ satisfying $K(x)=u(x)^{1-p}$, where $x\in\mathbb{S}^n$, $K$ is the Gauss curvature of $\partial\mathbb{K}$, $u$ is the support function of $\mathbb{K}$, and $p$ is a constant. In the case of $n=2$, either when $p\in[-1,0]$ or when $p\in(0,1)$ in addition to a pinching condition, we show that $\mathbb{K}$ must be the unit ball. This partially answers a conjecture of Lutwak, Yang, and Zhang about the uniqueness of the $L_p$-Minkowski problem in $\mathbb{R}^3$. Moreover, we give an explicit pinching constant depending only on $p$ when $p\in(0,1)$.Comment: references update

The Szemeredi-Trotter Theorem in the Complex Plane

It is shown that $n$ points and $e$ lines in the complex Euclidean plane ${\mathbb C}^2$ determine $O(n^{2/3}e^{2/3}+n+e)$ point-line incidences. This bound is the best possible, and it generalizes the celebrated theorem by Szemer\'edi and Trotter about point-line incidences in the real Euclidean plane ${\mathbb R}^2$.Comment: 24 pages, 5 figures, to appear in Combinatoric