Ultrasonic velocities and elastic constants in tin-indium alloys

Ultrasonic velocities, elastic constants and internal friction are studied in Sn-In alloys in the concentration range of 0 to 30 wt% of In using composite oscillator technique. Anomalies observed in the vicinity of the phase transitions of these alloys at fourteen concentrations are interpreted in the light of the phase changes in the phase diagram.     

Computation of collective modes and acoustic investigations at different temperatures of vitrous silica

This paper is mainly concerned with elastic and acoustic properties of vitrous silica besides the computation of phonon frequencies. Thus the phonon frequencies of vitrous silica have been calculated assuming the electronic bulk modulus,K _e, as equal to zero. New equations have been derived to relate the pressure derivatives of second order elastic constants to the acoustic Gruneisen’s parameters using both Bhatia-Singh’s parameters and Schofield’s equations. The calculated longitudinal and transverse Gruneisen’s parameters and the predicted absorption band spectra from Nagendranath’s equation and Bhatia Singh’s parameters are in good agreement with experiment. The calculated mean acoustic mode Gruneisen’s parameter evaluated from the pressure derivative of Nagendranath’s equation is also in good agreement with experiment. An erratum to this article is available at .     

Calculated elastic constants of dilute alloys based on bcc metals

The elastic constants of dilute alloys based on bcc metals have been calculated using the Green’s function method obtaining explicit expressions for change in elastic constants in terms oft-matrix. The crystal impurity problem is discussed within an impurity model containing central and non-central force constant changes extended up to second neighbours of the impurity. The effect of volume change on elastic constants and a contribution from electron pressure term are considered. Numerical results for changes in three elastic moduli have been presented for a number of dilute alloys based on Mo, Nb, W, Ta and V.     

A Monte Carlo and continuum study of mechanical properties of nanoparticle based films

A combination Monte Carlo and equivalent-continuum simulation approach was used to investigate the structure-mechanical property relationships of titania nanoparticle deposits. Films of titania composed of nanoparticle aggregates were simulated using a Monte Carlo approach with diffusion-limited aggregation. Each aggregate in the simulation is fractal-like and random in structure. In the film structure, it is assumed that bond strength is a function of distance with two limiting values for the bond strengths: one representing the strong chemical bond between the particles at closest proximity in the aggregate and the other representing the weak van der Waals bond between particles from different aggregates. The Young’s modulus of the film is estimated using an equivalent-continuum modeling approach, and the influences of particle diameter (5–100 nm) and aggregate size (3–400 particles per aggregate) on predicted Young’s modulus are investigated. The Young’s modulus is observed to increase with a decrease in primary particle size and is independent of the size of the aggregates deposited. Decreasing porosity resulted in an increase in Young’s modulus as expected from results reported previously in the literature.     

On the Material Invariant Formulation of Maxwell’s Displacement Current

Maxwell accounted for the apparent elastic behavior of the electromagnetic field by augmenting Ampere’s law with the so-called displacement current, in much the same way that he treated the viscoelasticity of gases. Maxwell’s original constitutive relations for both electrodynamics and fluid dynamics were not material invariant. In the theory of viscoelastic fluids, the situation was later corrected by Oldroyd, who introduced the upper-convective derivative. Assuming that the electromagnetic field should follow the general requirements for a material field, we show that if the upper convected derivative is used in place of the partial time derivative in the displacement current term, Maxwell’s electrodynamics becomes material invariant. Note, that the material invariance of Faraday’s law is automatically established if the Lorentz force is admitted as an integral part of the model. The new formulation ensures that the equation for conservation of charge is also material invariant in vacuo. The viscoelastic medium whose apparent manifestation are the known phenomena of electrodynamics is called here the metacontinuum.     

Adiabatic anholonomy and canonical transformations

Biswas and Soni [4] have surmised a semiclassical formula for Berry’s phase in terms of a generating function. We derive this formula apart from showing that it is not true in general and investigate its domain of validity. We also derive transformation formulae for Berry’s phase (Hannay’s angle) under general canonical transformations. A simpler proof for total angle invariance than hitherto available, is given.     

Comparison between Weber’s electrodynamics and classical electrodynamics

We present the main aspects of Weber’s electrodynamics and of Maxwell’s equations. We discuss Maxwell’s point of view related to Weber’s electrodynamics. We compare Weber’s force with Lorentz’s force. We analyse the relation between Weber’s law and Maxwell’s equations. Finally, we discuss some experiments performed and proposed with which we can distinguish Weber’s force from Lorentz’s one.     

Ultrasonic measurement of the elastic properties of benzoyl glycine single crystals

Certain organic crystals are found to possess high non-linear optical coefficients, often one to two orders of magnitude higher than those of the well-known inorganic non-linear optical materials. Benzoyl glycine is one such crystal whose optical second-harmonic generation efficiency is much higher than that of potassium dihydrogen phosphate. Single crystals of benzoyl glycine are grown by solvent evaporation technique usingN, N-dimethyl formamide as the solvent. All the nine second-order elastic stiffness constants of this orthorhombic crystal are determined from ultrasonic wave velocity measurements employing the pulse echo overlap technique. The anisotropy of elastic wave propagation in this crystal is demonstrated by plotting the phase velocity, slowness, Young’s modulus and linear compressibility surfaces along symmetry planes. The volume compressibility, bulk modulus and relevant Poisson’s ratios are also determined. Variation of the diagonal elastic stiffness constants with temperature over a limited range are measured and reported.     

Equation of state and temperature variation of the bulk modulus of the alkaline earth fluorides

The isotherms for the alkaline earth fluorides (CaF₂, SrF₂ and BaF₂) have been computed using the expression for the total free energy of a crystal in the quasiharmonic approximation. The theoretical points for SrF₂ and BaF₂ have been compared with the points derived from Bridgman’s experimental relation. The temperature variation of the isothermal bulk modulus of the alkaline earth fluorides has been worked out on the basis of Axe’s shell model. The theoretica points are compared with the points obtained from the temperature variation of the elastic constants data. It is found that the vibrational contribution to the temperature variation of the elastic constants in these crystals is significant.     

Concentration dependences of the elastic constants of the two-dimensional graphene-silicene system

The concentration dependences of the elastic constants of the two-dimensional Si _x C_{1 − x} system have been investigated with the use of the Harrison bonding-orbital method and the Keating model. The central and non-central force constants and the Grüneisen parameter have been considered by means of the bonding-orbital method. All quantities under consideration have been shown to exhibit a nonlinear behavior during the transition from graphene to silicene. A nontrivial role of the short-range repulsion has been discussed. The second-order and third-order elastic constants, the pressure dependences of the second-order elastic constants, as well as the Poisson’s ratio and Young’s modulus have been investigated in the Keating model. It has been found that the elastic constants and Young’s modulus change almost linearly upon the transition from graphene to silicene, whereas the other quantities under consideration exhibit nonlinearity.     

Elastic properties of graphene: The Keating model

The elastic properties of graphene have been described in terms of the Keating model. It has been shown that the two-dimensional structure of graphene is described by two independent elastic constants, like an isotropic solid. The Young’s modulus and the Poisson’s ratio have been determined. The results are compared with the experimental data obtained for graphite.     

Young’s modulus and internal friction in porous biocarbon white pine wood precursors

This paper reports on a study performed in the temperature range 100–293 K, in air and in vacuum, for the amplitude and time dependences of the Young’s modulus and the internal friction (ultrasound damping) of biocarbon precursors prepared from white pine wood at two pyrolysis (carbonization) temperatures of 1000 and 2400°C. The measurements have been conducted by the resonance technique with a composite vibrator on samples cut along and across the tree growth direction. The desorption of molecules of the external medium at low amplitudes of ultrasonic vibrations has been found to produce the pronounced influence on the effective elastic modulus and elastic vibration decrement. The data obtained from acoustic measurements of the amplitude dependences of the elastic modulus have been used to estimate the microplastic properties of the samples. It has been shown that increasing the carbonization temperature gives rise to noticeable changes in the Young’s modulus and internal friction, as well as to reduction of the microplastic stress σ _y of the biomaterial studied. The stress σ _y of the samples cut across the growth direction has been found to be substantially smaller than that of the “longitudinal” samples. The elastic and microplastic properties of precursors prepared from white pine wood have been compared with those of the white eucalyptus wood.     

Focusing of an electromagnetic plane wave into a uniaxial crystal by a Wood lens

High frequency fields, refracted by a geometry containing a Wood lens placed at a certain distance from a planar uniaxial interface, are derived by using Maslov’s method. The geometrical optics approximation generally valid for high frequency fields fails in the vicinity of a caustic. Maslov’s method is a systematic procedure for predicting the field in the caustic region, combining the simplicity of the ray and the generality of the transform method. Numerical computations are made for the field pattern around the caustic by using Maslov’s method. The results are found to be in good agreement with those obtained using Kirchhoff’s approximation.      

Ab initio calculation of the electronic structure,Fermi surface,and elastic properties of the new 7.5-K superconductor Nb<Subscript>2</Subscript>InC

Ab initio calculations were performed to investigate electronic and elastic properties of the newly discovered 7.5 K superconductor: layered Nb₂InC. As a result, electronic bands, total and site-projected l—decomposed density of states at the Fermi level, shape of the Fermi surface for Nb₂InC were obtained for the first time. Besides, independent elastic constants, bulk modulus, compressibility, shear modulus, Young’s modulus, Poisson’s ratio together with the elastic anisotropy parameters and indicator of brittle/ductile behavior of Nb₂InC were evaluated and analyzed in comparison with the available data.     

Micromechanical properties of carbon–silica aerogel composites

Materials’ endurance to mechanical stress is desirable from a technological point of view. In particular, in the case of silica aerogels, an improvement of the material elasticity is needed for some applications. Carbon–silica aerogel composites have been obtained and their mechanical properties, Young’s modulus, elastic parameter and hardness, have been evaluated with a dynamical, non-destructive microindentation technique. Large changes are found in Young’s modulus when only a small amount of carbon is added. This is clearly shown in the shape of the indentation curves as well as in the increase of the elastic parameter value, which evaluates the percentage of elasticity versus plasticity. Young’s modulus values obtained for carbon–silica aerogels show a similar variation with the carbon mass fraction to that predicted by a commonly used model for composite materials. The measured hardness values corresponding to the total elastoplastic deformation do not show such a prominent dependency on the carbon mass fraction as the elastic parameter and Young’s modulus do and they are similar to those measured for the pure-silica aerogel. Received: 18 May 2001 / Accepted: 30 July 2001 / Published online: 30 October 2001     

Nanometer-scale displacement sensing using self-mixing interferometry with a correlation-based signal processing technique

A self-mixing interferometer is proposed to measure nanometre-scale optical path length changes in the interferometer’s external cavity. As light source, the developed technique uses a blue emitting GaN laser diode. An external reflector, a silicon mirror, driven by a piezo nanopositioner is used to produce an interference signal which is detected with the monitor photodiode of the laser diode. Changing the optical path length of the external cavity introduces a phase difference to the interference signal. This phase difference is detected using a signal processing algorithm based on Pearson’s correlation coefficient and cubic spline interpolation techniques. The results show that the average deviation between the measured and actual displacements of the silicon mirror is 3.1 nm in the 0–110 nm displacement range. Moreover, the measured displacements follow linearly the actual displacement of the silicon mirror. Finally, the paper considers the effects produced by the temperature and current stability of the laser diode as well as dispersion effects in the external cavity of the interferometer. These reduce the sensor’s measurement accuracy especially in long-term measurements.     

Local Causality and Completeness: Bell <Emphasis Type="Italic">vs.</Emphasis> Jarrett

J.S. Bell believed that his famous theorem entailed a deep and troubling conflict between the empirically verified predictions of quantum theory and the notion of local causality that is motivated by relativity theory. Yet many physicists continue to accept, usually on the reports of textbook writers and other commentators, that Bell’s own view was wrong, and that, in fact, the theorem only brings out a conflict with determinism or the hidden-variables program or realism or some other such principle that (unlike local causality), allegedly, nobody should have believed anyway. Moreover, typically such beliefs arise without the person in question even being aware that the view they are accepting differs so radically from Bell’s own. Here we try to shed some light on the situation by focusing on the concept of local causality that is the heart of Bell’s theorem, and, in particular, by contrasting Bell’s own understanding with the analysis of Jon Jarrett which has been the most influential source, in recent decades, for the kinds of claims mentioned previously. We point out a crucial difference between Jarrett’s and Bell’s own understanding of Bell’s formulation of local causality, which turns out to be the basis for the erroneous claim, made by Jarrett and many others, that Bell misunderstood the implications of his own theorem.     

Mach’s principle and the notion of time

The role of time coordinate in the realization of March’s principle is highlighted. It is shown that Mach’s principle is linked to the definition of a ‘particle’. These results suggest a deep connection between quantum gravity and Mach’s principle.     

Bell’s Theorem without Inequalities and without Unspeakable Information

A proof of Bell’s theorem without inequalities is presented in which distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups.