Young’s modulus of silicon nitride used in scanning force microscope cantilevers

The Young’s modulus and Poisson’s ratio of high-quality silicon nitride films with 800 nm thickness, grown on silicon substrates by low-pressure chemical vapor deposition, were determined by measuring the dispersion of laser-induced surface acoustic waves. The Young’s modulus was also measured by mechanical tuning of commercially available silicon nitride cantilevers, manufactured from the same material, using the tapping mode of a scanning force microscope. For this experiment, an expression for the oscillation frequencies of two-media beam systems is derived. Both methods yield a Young’s modulus of 280–290 GPa for amorphous silicon nitride, which is substantially higher than previously reported (E5146 GPa). For Poisson’s ratio, a value of n 50.20 was obtained. These values are relevant for the determination of the spring constant of the cantilever and the effective tip–sample stiffness

Variation in dynamic elastic shear modulus of sandstone upon fluid saturation and substitution

Experimental acoustic measurements on sandstone rocks at both sonic and ultrasonic frequencies show that fluid saturation can cause a noticeable change in both the dynamic bulk and shear elastic moduli of sandstones. We observed that the change in dynamic shear modulus upon fluid saturation is highly dependent on the type of saturant, its viscosity, rock microstructure, and applied pressures. Frequency dispersion has some influence on dynamic elastic moduli too, but its effect is limited to the ultrasonic frequency ranges and above. We propose that viscous coupling, reduction in free surface energy, and, to a limited extent, frequency dispersion due to both local and global flow are the main mechanisms responsible for the change in dynamic shear elastic modulus upon fluid saturation and substitution, and we quantify influences.

The vibrational spectrum and ultimate modulus of polyethylene

We have performed the first completely ab initio lattice dynamics calculation of the full orthorhombic cell of polyethylene using periodic density functional theory in the local density approximation (LDA) and the generalized gradient approximation (GGA). Contrary to current perceptions, we show that LDA accurately describes the structure whereas GGA fails. We emphasize that there is no parametrization of the results. We then rigorously tested our calculation by computing the phonon dispersion curves across the entire Brillouin zone and comparing them to the vibrational spectra, in particular the inelastic neutron scattering (INS) spectra, of polyethylene (both polycrystalline and aligned) and perdeuteriopolyethylene. The F-point frequencies (where the infrared and Raman active modes occur) are in good agreement with the latest low temperature data. The near-perfect reproduction of the INS spectra, gives confidence in the results and allows Lis to deduce a number of physical properties including the elastic moduli, parallel and perpendicular to the chain. We find that the Young's modulus for an infinitely long, perfectly crystalline polyethylene is 360.2 GPa at 0 K. The highest experimental value is 324 GPa, indicating that current high modulus fibers are similar to 90% of their maximum possible strength.

Dynamic shear modulus of isotropic elastomers

We have investigated the dynamic mechanical behavior of two cross-linked polymer networks with very different topologies: one made of backbones randomly linked along their length; the other with fixed-length strands uniformly cross-linked at their ends. The samples were analyzed using oscillatory shear, at very small strains corresponding to the linear regime. This was carried out at a range of frequencies, and at temperatures ranging from the glass plateau, through the glass transition, and well into the rubbery region. Through the glass transition, the data obeyed the time-temperature superposition principle, and could be analyzed using WLF treatment. At higher temperatures, in the rubbery region, the storage modulus was found to deviate from this, taking a value that is independent of frequency. This value increased linearly with temperature, as expected for the entropic rubber elasticity, but with a substantial negative offset inconsistent with straightforward enthalpic effects. Conversely, the loss modulus continued to follow time-temperature superposition, decreasing with increasing temperature, and showing a power-law dependence on frequency.

The univalent polynomial of Suffridge as a summability kernel

A positive summability trigonometric kernel {K(n)(theta)}(infinity)(n=1) is generated through a sequence of univalent polynomials constructed by Suffridge. We prove that the convolution {K(n) * f} approximates every continuous 2 pi-periodic function f with the rate omega(f, 1/n), where omega(f, delta) denotes the modulus of continuity, and this provides a new proof of the classical Jackson`s theorem. Despite that it turns out that K(n)(theta) coincide with positive cosine polynomials generated by Fejer, our proof differs from others known in the literature.

The position effect of structural Eucalyptus round timber on the flexural modulus of elasticity

A madeira roliça possui grande emprego nas construções civis, desempenhando a função de vigas, colunas, fundações, postes para distribuição de energia elétrica, entre outras, apresentando a vantagem de não ser processada, como é o caso da madeira serrada. O projeto envolvendo elementos roliços requer, além de outras variáveis estruturais, o conhecimento do módulo de elasticidade. No Brasil, os documentos normativos que tratam da determinação das propriedades de rigidez e resistência para peças roliças de madeira estão em vigência há mais de vinte anos sem revisão técnica. A madeira roliça, por geralmente possuir eixo com curvatura não nula, pode apresentar, segundo a posição da peça no ensaio de flexão, valores diferentes do módulo de elasticidade. Este trabalho tem como objetivo analisara influência da posição de peças roliças de madeira de Eucalyptus grandis na determinação do módulo de elasticidade na flexão. O ensaio de flexão utilizado é o de três pontos, sendo cada peça avaliada em duas posições distintas, definidas mediante o giro da seção transversal em torno do eixo. Os resultados encontrados indicam a necessidade do ensaio de flexão em, pelo menos, duas posições distintas da peça.

Hardness and elastic modulus of carbon-germanium alloys

This work reports on the mechanical properties of germanium-rich amorphous carbon-germanium alloys prepared by RF sputtering of a germanium/graphite target under an argon/hydrogen atmosphere. Nano-hardness, elastic modulus and stress were investigated as a function of the carbon content. The stress, which is reduced by the incorporation of carbon, was related to the film structure and to the difference in the Ge-Ge and Ge-C bond length. Contrary to what was expected, the hardness and elastic modulus of the alloys are lower than the corresponding values for pure amorphous hydrogenated germanium film, which in turn has both properties also smaller than those of crystalline germanium. These properties are analyzed in terms of the structural properties of the films. (C) 2001 Elsevier B.V. B.V All rights reserved.

Influence of Wood Moisture Content on the Modulus of Elasticity in Compression Parallel to the Grain

Brazilian Standard ABNT NBR7190:1997 for timber structures design, adopts a first degree equation to describe the influence of wood moisture content. Periodically, when necessary, the referred standard is revised in order to analyze inconsistencies and to adopt considerations according new realities verified. So, the present paper aims to examine the adequacy of its equation which corrects to 12% of moisture the values of rigidity properties obtained on experimental tests. To quantify the moisture influence on modulus of elasticity, it was applied tests of compression parallel to the grain for six specimens of different strength classes, considering nominal moisture of 12; 20; 25; 30%. As results, modulus of elasticity in the moisture range 25-30% showed statistically equivalents, and was obtained a first degree equation to correlate the studied variables which leads to statically equivalent estimations when compared with results by ABNT NBR7190:1997 equation. However, it was indicated to maintain the current expression for the next text of the referred document review, without prejudice to statistical significance of the estimates.

Heating time required for an MgO-graphite refractory during a hot modulus of rupture test

In the work described in the present paper, an analytical solution of the general heat conduction equation was employed to assay the temperature profile inside a solid slab which is initially at room temperature and is suddenly plunged into a fluid maintained at a high temperature. The results were then extrapolated to a simulation of a hot modulus of rupture test of typical MgO-graphite refractory samples containing different amounts of graphite in order to evaluate how fast the temperature equilibrates inside the test specimens. Calculations indicated that, depending on the graphite content, the time to full temperature homogenization was in the range of 80 to 200 s. These findings are relevant to the high temperature testing of such refractories in oxidizing conditions in view of the graphite oxidation risks in the proper evaluation of the hot mechanical properties.

Peirce's mathematical-logical approach to discrete collections and the premonition of continuity

According to Peirce one of the most important philosophical problems is continuity. Consequently, he set forth an innovative and peculiar approach in order to elucidate at once its mathematical and metaphysical challenges through proper non-classical logical reasoning. I will restrain my argument to the definition of the different types of discrete collections according to Peirce, with a special regard to the phenomenon called premonition of continuity (Peirce, 1976, Vol. 3, p. 87, c. 1897). © 2012 Copyright Taylor and Francis Group, LLC.

ECLAC: forty years of continuity with change

Discurso inaugural del 22 periodo de sesiones de la CEPAL efectuado por el senor Gert Rosenthal, en el cual se refiere en especial al papel pasado, presente y futuro de la Comision en el desarrollo economico y social de la region.

Effect of peroxide bleaching on the biaxial flexural strength and modulus of bovine dentin

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)