Ideal, Defective, and Gold--Promoted Rutile TiO2(110) Surfaces: Structures, Energies, Dynamics, and Thermodynamics from PBE+U

Extensive first principles calculations are carried out to investigate gold-promoted TiO2(110) surfaces in terms of structure optimizations, electronic structure analyses, ab initio thermodynamics calculations of surface phase diagrams, and ab initio molecular dynamics simulations. All computations rely on density functional theory in the generalized gradient approximation (PBE) and account for on-site Coulomb interactions via inclusion of a Hubbard correction, PBE+U, where U is computed from linear response theory. This approach is validated by investigating the interaction between TiO2(110) surfaces and typical probe species (H, H2O, CO). Relaxed structures and binding energies are compared to both data from the literature and plain PBE results. The main focus of the study is on the properties of gold-promoted titania surfaces and their interactions with CO. Both PBE+U and PBE optimized structures of Au adatoms adsorbed on stoichiometric and reduced TiO2 surfaces are computed, along with their electronic structure. The charge rearrangement induced by the adsorbates at the metal/oxide contact are also analyzed and discussed. By performing PBE+U ab initio molecular dynamics simulations, it is demonstrated that the diffusion of Au adatoms on the stoichiometric surface is highly anisotropic. The metal atoms migrate either along the top of the bridging oxygen rows, or around the area between these rows, from one bridging position to the next along the [001] direction. Approximate ab initio thermodynamics predicts that under O-rich conditions, structures obtained by substituting a Ti5c atom with an Au atom are thermodynamically stable over a wide range of temperatures and pressures.Comment: 20 pages, 12 figures, accepted for publication in Phys. Rev.

Quantum Fluctuations Driven Orientational Disordering: A Finite-Size Scaling Study

The orientational ordering transition is investigated in the quantum generalization of the anisotropic-planar-rotor model in the low temperature regime. The phase diagram of the model is first analyzed within the mean-field approximation. This predicts at $T=0$ a phase transition from the ordered to the disordered state when the strength of quantum fluctuations, characterized by the rotational constant $\Theta$, exceeds a critical value $\Theta_{\rm c}^{MF}$. As a function of temperature, mean-field theory predicts a range of values of $\Theta$ where the system develops long-range order upon cooling, but enters again into a disordered state at sufficiently low temperatures (reentrance). The model is further studied by means of path integral Monte Carlo simulations in combination with finite-size scaling techniques, concentrating on the region of parameter space where reentrance is predicted to occur. The phase diagram determined from the simulations does not seem to exhibit reentrant behavior; at intermediate temperatures a pronounced increase of short-range order is observed rather than a genuine long-range order.Comment: 27 pages, 8 figures, RevTe

Mathematical Models for Natural Gas Forecasting

It is vital for natural gas Local Distribution Companies (LDCs) to forecast their customers\u27 natural gas demand accurately. A significant error on a single very cold day can cost the customers of the LDC millions of dollars. This paper looks at the financial implication of forecasting natural gas, the nature of natural gas forecasting, the factors that impact natural gas consumption, and describes a survey of mathematical techniques and practices used to model natural gas demand. Many of the techniques used in this paper currently are implemented in a software GasDayTM, which is currently used by 24 LDCs throughout the United States, forecasting about 20% of the total U.S. residential, commercial, and industrial consumption. Results of GasDay\u27sTM forecasting performance also is presented

Pattern formation without heating in an evaporative convection experiment

We present an evaporation experiment in a single fluid layer. When latent heat associated to the evaporation is large enough, the heat flow through the free surface of the layer generates temperature gradients that can destabilize the conductive motionless state giving rise to convective cellular structures without any external heating. The sequence of convective patterns obtained here without heating, is similar to that obtained in B\'enard-Marangoni convection. This work present the sequence of spatial bifurcations as a function of the layer depth. The transition between square to hexagonal pattern, known from non-evaporative experiments, is obtained here with a similar change in wavelength.Comment: Submitted to Europhysics Letter

Superconducting NdCeCuO Bicrystal Grain Boundary Josephson Junctions

We have studied the electric transport properties of symmetrical [001] tilt NdCeCuO bicrystal grain boundary Josephson junctions (GBJs) fabricated on SrTiO bicrystal substrates with misorientation angles of 24 and 36.8 degree. The superconducting properties of the NdCeCuO-GBJs are similar to those of GBJs fabricated from the hole doped high temperature superconductors (HTS). The critical current density Jc decreases strongly with increasing misorientation angle. The products of the critical current Ic and the normal resistance Rn (about 0.1 mV at 4.2 K) are small compared to the gap voltage and fit well to the universal scaling law (IcRn is proportional to the square root of Jc) found for GBJs fabricated from the hole doped HTS. This suggests that the symmetry of the order parameter, which most likely is different for the electron and the hole doped HTS has little influence on the characteristic properties of symmetrical [001] tilt GBJs.Comment: 3 pages, 4 figures, to be published in Applied Physics Letter

Composition, structure, and stability of the rutile TiO_2(110) surface: oxygen depletion, hydroxylation, hydrogen migration and water adsorption

A comprehensive phase diagram of lowest-energy structures and compositions of the rutile TiO_2(110) surface in equilibrium with a surrounding gas phase at finite temperatures and pressures has been determined using density functional theory in combination with a thermodynamic formalism. The exchange of oxygen, hydrogen, and water molecules with the gas phase is considered. Particular attention is given to the convergence of all calculations with respect to lateral system size and slab thickness. In addition, the reliability of semilocal density functionals to describing the energetics of the reduced surfaces is critically evaluated. For ambient conditions the surface is found to be fully covered by molecularly adsorbed water. At low coverages, in the limit of single, isolated water molecules, molecular and dissociative adsorption become energetically degenerate. Oxygen vacancies form in strongly reducing, oxygen-poor environments. However, already at slightly more moderate conditions it is shown that removing full TiO_2 units from the surface is thermodynamically preferred. In agreement with recent experimental observations it is furthermore confirmed that even under extremely hydrogen-rich environments the surface cannot be fully hydroxylated, but only a maximum coverage with hydrogen of about 0.6-0.7 monolayer can be reached. Finally, calculations of migration paths strongly suggest that hydrogen prefers to diffuse into the bulk over desorbing from the surface into the gas phase.Comment: 17 pages, 11 figures, to appear in PR

Interaction of short cracks with the local microstructure

AbstractIncreasing the resistance of a material against fatigue crack growth by optimizing the microstructure is one of the major tasks of modern materials science. Thereby grain and phase boundaries are microstructural elements which can decelerate the propagation rate especially of short cracks. However, in different materials cracks and grain boundaries interact differently. For instance in some steels the blocking effect was only found for large angle grain boundaries while small angle boundaries showed nearly no effect. On the other hand in nickel based superalloys a retardation of cracks was found even for small angle boundaries when the crack was propagating in stage I. Even in front of the same grain boundary, the blocking effect varies for different cracks. To investigate this behaviour systematically focused ion beam (FIB) initiated cracks were used. By this method of artificial crack initiation the crack parameters like crack length and distance to the obstacle can be varied separately. Additionally special grain boundaries can be selected after a microstructural characterisation by electron backscatter diffraction (EBSD). Finally FIB tomography helps to understand the process how a crack overcomes a grain boundary