Shallow water flow with cylindrical symmetry

A numerical scheme is presented tor the solution of the shallow water equations in a single radial coordinate. This can prove useful when testing codes for the two-dimensional shallow water equations. The scheme is applied with success to problems involving converging and diverging bores.

The Structure of the chiral Pt{531} surface: a combined LEED and DFT study

The structure of the chiral kinked Pt{531} surface has been determined by low-energy electron diffraction intensity-versus-energy (LEED-IV) analysis and density functional theory (DFT). Large contractions and expansions of the vertical interlayer distances with respect to the bulk-terminated surface geometry were found for the first six layers (LEED: d(12) = 0.44 angstrom, d(23) = 0.69 angstrom, d(34) = 0.49 angstrom, d(45) = 0.95 angstrom, d(56) = 0.56 angstrom; DFT: d(12) = 0.51 angstrom, d(23) = 0.55 angstrom, d(34) = 0.74 angstrom, d(45) = 0.78 angstrom, d(56) = 0.63 angstrom; d(bulk) = 0.66 angstrom). Energy-dependent cancellations of LEED spots over unusually large energy ranges, up to 100 eV, can be explained by surface roughness and reproduced by applying a model involving 0.25 ML of vacancies and adatoms in the scattering calculations. The agreement between the results from LEED and DFT is not as good as in other cases, which could be due to this roughness of the real surface.

The structure of the mixed OH+H2O overlayer on Pt{111}

The structure of the mixed p(3x3)-(3OH+3H(2)O) phase on Pt{111} has been investigated by low-energy electron diffraction-IV structure analysis. The OH+H2O overlayer consists of hexagonal rings of coplanar oxygen atoms interlinked by hydrogen bonds. Lateral shifts of the O atoms away from atop sites result in different O-O separations and hexagons with only large separations (2.81 and 3.02 angstrom) linked by hexagons with alternating separations of 2.49 and 2.81/3.02 A. This unusual pattern is consistent with a hydrogen-bonded network in which water is adsorbed in cyclic rings separated by OH in a p(3x3) structure. The topmost two layers of the Pt atoms relax inwards with respect to the clean surface and both show vertical buckling of up to 0.06 angstrom. In addition, significant shifts away from the lateral bulk positions have been found for the second layer of Pt atoms. (C) 2005 American Institute of Physics.

Effect of oxygen adsorption on the chiral pt{531} surface

The adsorption of oxygen on the chiral Pt{531} surface was studied by high-resolution X-ray photoelectron spectroscopy (HRXPS) and low energy electron diffraction (LEED). After the surface is annealed in oxygen (3 x 10(-7) mbar), three O 1s peaks are observed in XPS. One peak, at 529.5 eV, is assigned to chemisorbed oxygen; it disappears after annealing in vacuo to temperatures above 900 K. The other two peaks at 530.8 and 532.3 eV are stable up to at least 1250 K. They are associated with oxide clusters on the surface. These clusters readily react with coadsorbed carbon monoxide at temperatures between 315 and 620 K.

Structures of Pd(CN)2and Pt(CN)2: intrinsically nanocrystalline materials?

Analysis and modeling of X-ray and neutron Bragg and total diffraction data show that the compounds referred to in the literature as “Pd(CN)2”and“Pt(CN)2” are nanocrystalline materials containing of small sheets of vertex-sharing square-planar M(CN)4 units, layered in a disordered manner with an intersheet separation of 3.44 A at 300 K. The small size of the crystallites means that the sheets’ edges form a significant fraction of each material. The Pd(CN)2 nanocrystallites studied using total neutron diffraction are terminated by water and the Pt(CN)2 nanocrystallites by ammonia, in place of half of the terminal cyanide groups, thus maintaining charge neutrality. The neutron samples contain sheets of approximate dimensions 30 A x 30 A. For sheets of the size we describe, our structural models predict compositions of Pd(CN)2-xH2O and Pt(CN)2-yNH3 (x = y = 0.29). These values are in good agreement with those obtained from total neutron diffraction and thermal analysis, and are also supported by infrared and Raman spectroscopy measurements. It is also possible to prepare related compounds Pd(CN)2-pNH3 and Pt(CN)2-qH2O, in which the terminating groups are exchanged. Additional samples showing sheet sizes in the range 10 A x 10 A (y = 0.67) to 80 A x 80 A (p = q = 0.12), as determined by X-ray diffraction, have been prepared. The related mixed-metal phase, Pd1/2Pt1/2(CN)2-qH2O(q = 0.50), is also nanocrystalline (sheet size 15 A x 15 A). In all cases, the interiors of the sheets are isostructural with those found in Ni(CN)2. Removal of the final traces of water or ammonia by heating results in decomposition of the compounds to Pd and Pt metal, or in the case of the mixed-metal cyanide, the alloy, Pd1/2Pt1/2, making it impossible to prepare the simple cyanides, Pd(CN)2, Pt(CN)2 or Pd1/2Pt1/2(CN)2, by this method.

Rotational symmetry of a methane molecule and the bond angle

The rotational symmetry of a methane molecule can be used to great advantage to calculate the bond angle. The problem is worked out in this article.

Mononuclear Pt(II) and Pd(II) 1,4-dithiolato complexes. Crystal structures of [Pt((−) DIOS) (PPh3)2] and [Pd(S(CH2) 4S)(Ph2P(CH2) 3PPh2)]. Application in styrene hydroformylation

Addition of 1,4-dithiols to dichloromethane solutions of [PtCl2(P-P)] (P-P = (PPh3)2, Ph2P(CH2)3PPh2, Phd2P(CH2)4PPh2; 1,4-dithiols = HS(CH2)4SH, (−)DIOSH2 (2,3-O-isopropylidene-1,4-dithiol-l-threitol), BINASH2 (1,1′-dinaphthalene-2,2′-dithiol)) in the presence of NEt3 yielded the mononuclear complexes [Pt(1,4-dithiolato)(P-P)]. Related palladium(II) complexes [Pd(dithiolato)(P-P)] (P-P=Ph2P(CH2)3PPh2, Ph2P(CH2)4PPh2; dithiolato = −S(CH2)4S−, (−)-DIOS) were prepared by the same method. The structure of [Pt((−)DIOS)(PPh3)2] and [Pd(S(CH2)4S)(Ph2P(CH2)3PPh2)] complexes was determined by X-ray diffraction methods. Pt—dithiolato—SnC12 systems are active in the hydroformylation of styrene. At 100 atm and 125°C [Pt(dithiolate)(P-P)]/SnCl2 (Pt:Sn = 20) systems provided aldehyde conversion up to 80%.

Structures, reactivity, and catalytic activity of dithiolato-bridged heterobimetallic MRh (M = Pt, Pd) complexes

Heterobimetallic complexes [(P−P)Pt(μ-S−S)Rh(cod)]ClO4 (P−P = (PPh3)2, Ph2P(CH2)3PPh2 (dppp), and Ph2P(CH2)4PPh2 (dppb); S−S = -S(CH2)2S- (EDT), -S(CH2)3S- (PDT), -S(CH2)4S- (BDT), cod = 1,5-cyclooctadiene) reacted with CO to form the carbonyl complexes [(P−P)Pt(μ-S−S)Rh(CO)2]ClO4 and then with PR3 ligands to give [(P−P)Pt(μ-S−S)Rh(CO)(PR3)]ClO4. The binuclear framework of these cod complexes was maintained in the reactions reported. The cod complexes were tested as catalyst precursors in the hydroformylation of styrene. HPNMR in situ studies showed that mononuclear species formed under catalytic conditions.

From symmetry breaking to Poisson Point Process in 2D Voronoi Tessellations: the generic nature of hexagons

We bridge the properties of the regular triangular, square, and hexagonal honeycomb Voronoi tessellations of the plane to the Poisson-Voronoi case, thus analyzing in a common framework symmetry breaking processes and the approach to uniform random distributions of tessellation-generating points. We resort to ensemble simulations of tessellations generated by points whose regular positions are perturbed through a Gaussian noise, whose variance is given by the parameter α2 times the square of the inverse of the average density of points. We analyze the number of sides, the area, and the perimeter of the Voronoi cells. For all valuesα >0, hexagons constitute the most common class of cells, and 2-parameter gamma distributions provide an efficient description of the statistical properties of the analyzed geometrical characteristics. The introduction of noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α = 0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise withα <0.12. For all tessellations and for small values of α, we observe a linear dependence on α of the ensemble mean of the standard deviation of the area and perimeter of the cells. Already for a moderate amount of Gaussian noise (α >0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α >2, results converge to those of Poisson-Voronoi tessellations. The geometrical properties of n-sided cells change with α until the Poisson- Voronoi limit is reached for α > 2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established. This law allows for an easy link to the Lewis law for areas and agrees with exact asymptotic results. Finally, for α >1, the ensemble mean of the cells area and perimeter restricted to the hexagonal cells agree remarkably well with the full ensemble mean; this reinforces the idea that hexagons, beyond their ubiquitous numerical prominence, can be interpreted as typical polygons in 2D Voronoi tessellations.

Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec−1) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f3/2 power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

Symmetry-break in Voronoi tessellations

We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α<0.12. Basically, the same happens in the 3D case, where only the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. In both 2D and 3D cases, already for a moderate amount of Gaussian noise (α>0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomaly in the scaling indicates that large cells preferentially feature large isoperimetric quotients. As the number of faces is strongly correlated with the sphericity (cells with more faces are bulkier), in 3D it is shown that the anomalous scaling is heavily reduced when we perform power law fits separately on cells with a specific number of faces.

Surface chemistry of glycine on Pt{111} in different aqueous environments

Adsorption of glycine on Ptf111g under UHV conditions and in different aqueous environments was studied by XPS (UHV and ambient pressure) and NEXAFS. Under UHV conditions, glycine adsorbs in its neutral molecular state up to about 0.15 ML. Further deposition leads to the formation of an additional zwitterionic species, which is in direct contact with the substrate surface, followed by the growth of multilayers, which also consist of zwitterions. The neutral surface species is most stable and decomposes at 360 K through a multi-step process which includes the formation of methylamine and carbon monoxide. When glycine and water are co-adsorbed in UHV at low temperatures (< 170 K) inter-layer diffusion is inhibited and the surface composition depends on the adsorption sequence. Water adsorbed on top of a glycine layer does not lead to significant changes in its chemical state. When glycine is adsorbed on top of a pre-adsorbed chemisorbed water layer or thick ice layer, however, it is found in its zwitterionic state, even at low coverage. No difference is seen in the chemical state of glycine when the layers are exposed to ambient water vapor pressure up to 0.2 Torr at temperatures above 300 K. Also the decomposition temperature stays the same, 360 K, irrespective of the water vapor pressure. Only the reaction path of the decomposition products is affected by ambient water vapor.

Redox behavior of the model catalyst Pd/CeO2-x/Pt(111)

Photoelectron spectroscopy and scanning tunneling microscopy have been used to investigate how the oxidation state of Ce in CeO2-x(111) ultrathin films is influenced by the presence of Pd nanoparticles. Pd induces an increase in the concentration of Ce3+ cations, which is interpreted as charge transfer from Pd to CeO2-x(111) on the basis of DFT+U calculations. Charge transfer from Pd to Ce4+ is found to be energetically favorable even for individual Pd adatoms. These results have implications for our understanding of the redox behavior of ceria-based model catalyst systems.

Substitutional and orientational disorder in organic crystals: a symmetry-adapted ensemble model

Modelling of disorder in organic crystals is highly desirable since it would allow thermodynamic stabilities and other disorder-sensitive properties to be estimated for such systems. Two disordered organic molecular systems are modeled using a symmetry-adapted ensemble approach, in which the disordered system is treated as an ensemble of the configurations of a supercell with respect to substitution of one disorder component for another. Computation time is kept manageable by performing calculations only on the symmetrically inequivalent configurations. Calculations are presented on a substitutionally disordered system, the dichloro/dibromobenzene solid solution, and on an orientationally disordered system, eniluracil, and the resultant free energies, disorder patterns, and system properties are discussed. The results are found to be in agreement with experiment following manual removal of physically implausible configurations from ensemble averages, highlighting the dangers of a completely automated approach to organic crystal thermodynamics which ignores the barriers to equilibration once the crystal has been formed.

Mode-specific reactivity of CH4 on Pt(110)-(1Ã2): The concerted role of stretch and bend excitation

The state-resolved reaction probability of CH4 on Pt�110-�1�2 was measured as a function of CH4 translational energy for four vibrational eigenstates comprising different amounts of C-H stretch and bend excitation. Mode-specific reactivity is observed both between states from different polyads and between isoenergetic states belonging to the same polyad of CH4. For the stretch/bend combination states, the vibrational efficacy of reaction activation is observed to be higher than for either pure C-H stretching or pure bending states, demonstrating a concerted role of stretch and bend excitation in C-H bond scission. This concerted role, reflected by the nonadditivity of the vibrational efficacies, is consistent with transition state structures found by ab initio calculations and indicates that current dynamical models of CH4 chemisorption neglect an important degree of freedom by including only C-H stretching motion.