The geometrical and vibrational properties of the Rh(111) surface

Low-energy electron diffraction (LEED) data have been used to characterize the clean Rh(111) surface. The surface geometry, the degree of surface relaxation, and the Debye temperature have been determined. In the Debye temperature measurement, specular LEED beam intensities were monitored as a function of temperature over a range of electron energies from approximately 30 to 1000 eV. It was found that the bulk Debye temperature is 380 ± 23 K, and the normal component of the Debye temperature at the lowest electron energy used is 197 ± 12 K. The Rh(111) surface relaxation has been determined both by a convolution-transform analysis and by dynamical calculations. Within experimental error, neither expansion nor contraction of the topmost layer has been detected. The results of the convolution-transform analysis of specular beams at two angles of incidence and of a nonspecular beam at normal incidence suggest an expansion of the topmost layer of 3 ± 5% of the bulk layer spacing. In agreement with this, comparisons between the results of the dynamical calculation and experimental data for five nonspecular beams at normal incidence suggest that the surface layer relaxes by 0 ± 5%. In addition, the dynamical calculations indicate that the topmost layer maintains an fcc structure.     

A necessary and sufficient condition for the aggregation of linear diophantine equations

Summary The set of the integer values a linear form can take may be called its spectrum. Aggregating two equations means establishing a linear combination of the two left hand side spectra, the coefficients of which are the aggregation weights. If and only if this linear combination does not contain any spectral correlation point other than the right hand side vector, the equation found by aggregation is equivalent to the two given ones.Methods for calculating the spectrum and the spectral correlation set are given.

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Zusammenfassung Der Wertevorrat einer Diophantischen Linearform möge als deren Spektrum bezeichnet werden. Die Zusammenfassung zweier Diophantischer Gleichungen läuft auf die Bildung einer Linearkombination der Spektren hinaus, die zu den beiden auf der linken Seite stehenden Linearformen gehören. Die Koffizienten der Linearkombination sind gleich den für die Zusammenfassung verwendeten Gewichten. Wenn und nur wenn die erwähnte Linearkombination ausser dem Punkt, dessen Koordinaten die auf der rechten Seite des Gleichungssystems stehenden Zahlen sind, keine anderen Spektral-Korrelationspunkte enthält, ist die durch Zusammenfassung gebildete Gleichung äquivalent dem System der beiden Ausgangsgleichungen.Methoden für die Berechnung von einfachen und korrelierten Spektren werden gegeben.

     

Characterization of large molecular weight ester‐functionalized norbornene and hydroxylated norbornane carboxylic acid polymers prepared by ring‐opening metathesis polymerization

5‐Norbornene‐2‐ethyl ester (mixture of endo and exo) is polymerized via ring‐opening metathesis polymerization, yielding polymers with molecular weights ranging from 50,000 to 5,000,000 g/mol. The polymers are hydroxylated and saponified without alteration of the molecular weight. The polymers are analyzed by NMR, gel permeation chromatography, differential scanning calorimetry, and thermogravimetric analysis. Films are cast from the polymers at several molecular weights and their rheological properties are investigated. The results showed greater solid‐like character with increasing molecular weight for all polymers analyzed. Cell viability studies showed that the films possessed minimal cytotoxicity. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Void dynamics in lead-free Sn-Ag-Cu solder joints

As a result of thermal and mechanical loading of Sn-Ag-Cu solder joints pores, flaws and voids may nucleate and grow. Such void nucleation is studied here by means of a phase-field approach which accounts for the decomposition of the solder into phases described by its concentration c. In this investigation, the void growth results from boundary inward flux only, effects due to grain size and interstitials are not involved, cf. [1]. The free energy functional is approximated by a second order Taylor expansion and thus composed of a bulk free energy density and a Ginzburg-type gradient term. The bulk free energy density ϕ follows a classical Ginzburg-Landau double-well potential. The gradient-energy coefficient κ depends on ϕ and is calculated similar to [2]. Experimental data have been adapted for the modeling of the temporal evolution of the concentration of voids located on a square domain in 2D. The simulation is based on a B-spline finite element analysis. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimating Arterial Cyclic Strain from the Spacing of Endothelial Nuclei

Experimental Mechanics - The non-uniform distribution of atherosclerosis within the arterial system is widely attributed to variation in haemodynamic wall shear stress. It may also depend on...     

The fate of magnetically charged black holes

The magnetically charged Reissner-Nordström black hole solutions of Maxwell-Einstein theory cannot evaporate completely, because their Hawking temperature tends to zero as their mass to charge ratio approaches unity. This situation changes when these solutions are considered in the context of a non-Abelian gauge theory containing nonsingular magnetic monopoles. If the horizon is sufficiently small, the Reissner-Nordström solution develops a classical instability and evolves into a new type of magnetically charged black hole solution. The temperature of these new solutions increases monotonically as the horizon contracts, so that there is no obstacle to the complete evaporation of a magnetically charged black hole.     

The coadsorption of hydrogen and potassium on Ir(111)

The adsorption of gas-phase atomic hydrogen on potassium-precovered Ir(111) surfaces was investigated. Even very low coverages of potassium adatoms strongly inhibit the dissociative adsorption of molecular hydrogen. However, using gas-phase atomic hydrogen allows us to overcome the activation barrier for dissociative hydrogen adsorption. In addition, abstraction of hydrogen adatoms by impinging atomic hydrogen occurs. The probabilities and cross-sections for both reactions and the maximum number of hydrogen adsorption sites are derived and compared to data obtained on other surfaces. Furthermore, a kinetic isotope effect in the desorption of hydrogen and deuterium was observed. Implications of these results with respect to the potassium-hydrogen interaction are discussed.