Layer-by-layer growth of thin amorphous solid water films on Pt(111) and Pd(111)

The growth of amorphous solid water (ASW) films on Pt(111) is investigated using rare gas (e.g., Kr) physisorption. Temperature programmed desorption of Kr is sensitive to the structure of thin water films and can be used to assess the growth modes of these films. At all temperatures that are experimentally accessible (20-155 K), the first layer of water wets Pt(111). Over a wide temperature range (20-120 K), ASW films wet the substrate and grow approximately layer by layer for at least the first three layers. In contrast to the ASW films, crystalline ice films do not wet the water monolayer on Pt(111). Virtually identical results were obtained for ASW films on epitaxial Pd(111) films grown on Pt(111). The desorption rates of thin ASW and crystalline ice films suggest that the relative free energies of the films are responsible for the different growth modes. However, at low temperatures, surface relaxation or "transient mobility" is primarily responsible for the relative smoothness of the films. A simple model of the surface relaxation semiquantitatively accounts for the observations.     

Complexation of trivalent lanthanoid ions with 4-benzoyl-3-phenyl-5-isoxazolone and p-tert-butylcalix[4]arene fitted with phosphinoyl pendant arms in solution during synergistic solvent extraction and structural study of solid complexes by IR and NMR

The liquid extraction of 14 lanthanoids with a 4-benzoyl-3-phenyl-5-isoxazolone (HPBI) alone in CHCl₃ as a diluent from perchlorate medium at constant ionic strength μ = 0.1 is investigated. The synergistic solvent extraction of five selected lanthanoid ions (La³⁺, Nd³⁺, Eu³⁺, Ho³⁺ and Lu³⁺) with 4-benzoyl-3-phenyl-5-isoxazolone (HPBI) and 5,11,17,23-tetra-tert-butyl-25,26,27,28-tetrakis-(dimethylphosphinoylmethoxy)calix[4]arene, (S) in CHCl₃ has been studied too. The stoichiometry of the extracted species was characterised by a classical log–log plot analysis. It was found that the composition of the extracted species with HPBI are Ln(PBI)₃ and in the presence of the phosphorus-containing calix[4]arene the lanthanoid ions have been extracted as [Ln(PBI)₃S₂]. The values of the equilibrium constants and the separation factors have been calculated. The influence of the synergistic agent on the extraction process has been discussed.     

The Moduli Space of Points in the Boundary of Complex Hyperbolic Space

We consider the space M(n,m)\mathcal{M}(n,m) of ordered m-tuples of distinct points in the boundary of complex hyperbolic n-space, H_\mathbbCⁿ\mathbf{H}_{\mathbb{C}}^{n}, up to its holomorphic isometry group PU(n,1). An important problem in complex hyperbolic geometry is to construct and describe the moduli space for M(n,m)\mathcal{M}(n,m). In particular, this is motivated by the study of the deformation space of complex hyperbolic groups generated by loxodromic elements. In the present paper, we give the complete solution to this problem.     

Stability and Instability of the KDV Solitary Wave Under the KP-I Flow

We consider the KP-I and gKP-I equations in \mathbbR × (\mathbbR/2p\mathbbZ){{\mathbb{R}}\,\times\,({\mathbb{R}}/2\pi{\mathbb{Z}})}. We prove that the KdV soliton with subcritical speed 0 < c < c* is orbitally stable under the global KP-I flow constructed by Ionescu and Kenig (Ann Math Stud 163:181–211, 2007). For supercritical speeds c > c*, in the spirit of the work by Duyckaerts and Merle (GAFA 18:1787–1840, 2009), we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity. This last result also holds for the gKP-I equation.     

Rationality of Conformally Invariant Local Correlation Functions on Compactified Minkowski Space

Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification of Minkowski space M and yields a strong form of locality valid for all non-isotropic intervals if assumed true for space-like separations. Received: 20 October 2000 / Accepted: 5 December 2000     

Simple Equations Method and Non-Linear Differential Equations with Non-Polynomial Non-Linearity

We discuss the application of the Simple Equations Method (SEsM) for obtaining exact solutions of non-linear differential equations to several cases of equations containing non-polynomial non-linearity. The main idea of the study is to use an appropriate transformation at Step (1.) of SEsM. This transformation has to convert the non-polynomial non- linearity to polynomial non-linearity. Then, an appropriate solution is constructed. This solution is a composite function of solutions of more simple equations. The application of the solution reduces the differential equation to a system of non-linear algebraic equations. We list 10 possible appropriate transformations. Two examples for the application of the methodology are presented. In the first example, we obtain kink and anti- kink solutions of the solved equation. The second example illustrates another point of the study. The point is as follows. In some cases, the simple equations used in SEsM do not have solutions expressed by elementary functions or by the frequently used special functions. In such cases, we can use a special function, which is the solution of an appropriate ordinary differential equation, containing polynomial non-linearity. Specific cases of the use of this function are presented in the second example.     

Mononuclear Transition Metal Cymantrenecarboxylates as Precursors for Spinel-Type Manganites

Novel mononuclear cymantrenecarboxylate complexes of transition metals, [Co(H₂O)₆](CymCO₂)₂·4H₂O (Cym = (η⁵-C₅H₄)Mn(CO)₃) (1), [Ni(H₂O)₆](CymCO₂)₂·4H₂O (2), [Zn(H₂O)₆](CymCO₂)₂·4H₂O (3), [Co(CymCO₂)₂(imz)₂] (imz = imidazole, 4), [Co(CymCO₂)₂(bpy)₂]·2PhMe (bpy = 2,2′-bipyridyl, 5), [Ni(CymCO₂)(bpy)₂(H₂O)][CymCO₂]·0.5MePh·2H₂O (6), [Cu(CymCO₂)₂(imz)₂] (7), and [Cu(CymCO₂)₂(bpy)(H₂O)] (8), were obtained and characterized by single-crystal X-ray analysis. Complexes 1–3 are isostructural. Magnetism of the Co complexes 1, 4, and 5 was studied; it was shown that they exhibit the properties of field-induced single-molecule magnets with magnetization reversal barriers (ΔE/k_B) of 44, 13, and 10 K, respectively. Thermal decomposition of complexes 1–8 was studied by means of DSC and TGA methods. The final products of thermolysis of 1–6 in air, according to powder XRD data, are the pure spinel phases MMn₂O₄; for the cases of copper complexes, the mixtures of CuMn₂O₄ and CuO were found in the products.     

Zn Doping Effect on the Performance of Fe-Based Catalysts for the Hydrogenation of CO2 to Light Hydrocarbons

In this work, we studied the role of zinc in the composition of supported iron-containing catalysts for the hydrogenation of CO₂. Various variants of incipient wetness impregnation of the support were tested to obtain catalyst samples. The best results are shown for samples synthesized by co-impregnation of the support with a common solution of iron and zinc precursors at the same molar ratio of iron and zinc. Catalyst samples were analyzed by various methods: Raman, DRIFT-CO, TPR-H₂, XPS, and UV/Vis. The introduction of zinc leads to the formation of a mixed ZnFe₂O₄ phase. In this case, the activation of the catalyst proceeds through the stage of formation of the metastable wustite phase FeO. The formation of this wustite phase promotes the formation of metallic iron in the composition of the catalyst under the reaction conditions. It is believed that the presence of metallic iron is a necessary step in the formation of iron carbides—that is, active centers for the formation and growth of chain in the hydrocarbons. This leads to an increase in the activity and selectivity of the formation of hydrocarbons in the process of CO₂ hydrogenation.