Relation between the Grüneisen ratio and the pressure dependence of Poisson's ratio for metals

The Grüneisen ratio of crystalline solids is shown to be dependent on a parameter n whose values are characteristic of each solid, and can be determined by two independent ways: from experimental shock data and from the pressure derivative of Poisson's ratio. The determinations are made for several metals, using data on the pressure derivatives of polycrystalline elastic moduli or of the second order elastic constants measured on single crystals, and giving the pressure derivatives of Poisson's ratio by means of the Voigt-Reuss-Hill averaging procedure. The values of the parameter n deduced from shock data are found to be in good agreement with those deduced from the pressure derivatives of Poisson's ratio. Positive and negative values of parameter n correspond respectively to increasing and decreasing Poisson's ratio with increasing pressure. Discussion of the results is made using the linear and the quadratic relationships between shock velocity and particle velocity. It is shown that shock wave data cannot yield directly an accurate estimation of the derivative of the initial slope of the Hugoniot.     

Ab initio calculation of the static structural properties of Be

An ab initio calculation of the static structural properties of Be is presented. The total structural energy is calculated using pseudopotentials and the local density-functional formalism with the atomic number as the only input. The lattice constant, Poisson's ratio, and the bulk modulus are predicted by calculating the total energy of the system. The deviations of the calculated results for lattice constants c, a, and c/a are approximately 1% when compared with experimental results. Poisson's ratio and the bulk modulus are also in reasonably good agreement with the measured values.     

Determination of modal coupling in vibrating rectangular plates

In square isotropic plates, some of the degenerate mode pairs are split in frequency due to coupling between longitudinal and transverse strain (which might be called Poisson coupling), and the same splitting of degenerate modes can occur in rectangular orthotropic plates having a certain length/width ratio. We have studied this coupling in free plates of aluminum and spruce (quarter cut and skew cut) and determined Poisson's ratios from the frequency ratios of the ($\text{2,0±0,2}$) modes (called the x and ring modes by luthiers). The critical length/width ratio was found to be considerably greater (3·17) in the skew-cut spruce than in quarter-cut spruce (2·08), due to a smaller cross-grain elastic modulus and Poisson's ratio.     

Justification of the local space charge neutrality hypothesis in metal oxidation

The important local charge neutrality hypothesis in metal oxidation theory is shown numerically to be self-consistent with Poisson's equation and the coupled transport equations for diffusion of oppositely-charged ionic and electronic defect species deep within very thick growing oxides.     

Thermodynamic,elastic, elastic anisotropy and minimum thermal conductivity of β-GaN under high temperature

The thermodynamic, elastic, elastic anisotropy and minimum thermal conductivity of β-GaN are investigated at ambient pressure and high temperature by using first-principles calculations method with the ultrasoft psedopotential scheme. The elastic constants calculations reveal β-GaN is mechanically stability at ambient pressure and high temperature. The elastic modulus (Poisson's ratio, shear modulus and Young's modulus) decreases with increasing temperature. The calculations of anisotropy show that β-GaN has a larger elastic anisotropy in Poisson's ratio, shear modulus, Young's modulus and Zener anisotropy index. In addition, when the temperature increases from 0 to 1500 K, the elastic anisotropy decreases for β-GaN. The quasi-harmonic Debye model is successfully applied to determine the thermodynamic properties at different pressures and temperatures. Using the quasi-harmonic Debye model, the thermodynamic properties including the Debye temperature, Grüneisen parameter, the heat capacity, adiabatic bulk modulus, and the thermal expansion coefficients of β-GaN are predicted under high temperature and high pressure.     

Poisson finite difference boundary equations for the magnetic potentials

Magnetostatic solutions may be obtained by using Laplace's equation in finite difference form. The boundary equations are of primary importance and even these have been put forward as special forms of Laplace's equation. They can be derived in what appears to be a simpler and more flexible manner by assuming that Poisson's equation applies at the interface for both scalar and vector potentials.     

Pressure-dependent mechanical and thermodynamic properties of newly discovered cubic Na2He

Recently for the first time, a stable compound of He and Na (Na₂He) is predicted at high pressure. We explore the pressure-dependent elastic, mechanical and thermodynamic properties of this newly discovered Na₂He by using ab initio technique. The calculation presents good accordance between the theoretical and experimental lattice parameters. Though the most stable structure of Na₂He is found at 300?GPa, present study ensures the mechanical stability of this compound up to 500?GPa. The study of Cauchy pressure, Pugh's ratio, and Poisson's ratio implies the ductile manner of Na₂He up to 500?GPa. According to the value of Poisson's ratio the bonding force exists in Na₂He is central. The study of Zener anisotropy factor indicates that Na₂He is an anisotropic material but near at 300?GPa approximately isotropic nature of Na₂He is revealed. The study of the bulk modulus, shear modulus, Young's modulus and Vickers hardness implies that the hardness of Na₂He can be improved by applying external pressure. However, the Debye temperature, melting temperature and minimum thermal conductivity of Na₂He are also calculated and discussed at different pressures.     

Two-dimensional analysis of natural frequencies and mode shapes of a wide beam: Application to the determination of mechanical characteristics of viscoelastic materials

The theory of plane elastodynamics is used to provide a simple method for calculating the natural frequencies and the normal mode shapes of a wide rectangular beam. The boundary conditions at both ends are prescribed in a mean-value sense. It is shown that the elementary (vibrating string) beam theory turns out to be an approximation of the theoretical model; the results obtained agree with those given by the Love theory. The method enables one to predict all frequency branches in terms of the width-to-length ratio, by comparatively simple calculations, in contrast to the situation when sufficiently elaborate one-dimensional theories are used. A second application is the determination of the complex Young's modulus and Poisson's ratio for viscoelastic materials.     

Natural frequencies of rectangular orthotropic plates with a pair of parallel edges simply supported

Solutions of the exact characteristic equations for the title problem derived earlier by an extension of Bolotin's asymptotic method are considered. These solutions, which correspond to flexural modes with frequency factor, R, greater than unity, are expressed in convenient forms for all combinations of clamped, simply supported and free conditions at the remaining pair of parallel edges. As in the case of uniform beams, the eigenvalues in the CC case are found to be equal to those of elastic modes in the FF case provided that the Kirchoff's shear condition at a free edge is replaced by the condition $\text{?M}{}_{\mathrm{n}}\text{?n = 0}$. The flexural modes with frequency factor less than unity are also investigated in detail by introducing a suitable modification in the procedure. When Poisson's ratios are not zero, it is shown that the frequency factor corresponding to the first symmetric mode in the free-free case is less than unity for all values of side ratio and rigidity ratios. In the case of one edge clamped and the other free it is found that modes with frequency factor less than unity exist for certain dimensions of the plate—a fact hitherto unrecognized in the literature.     

Analyses of cooling tower dynamics

A finite element method for analyzing accurately the free vibrations of cooling towers (with column-supports) is shown to give results that are in good agreement with the experimental data obtained on both a full scale cooling tower and the corresponding model structure, and as far as the author is aware, this agreement is appreciably better than that heretofore reported for comparable studies in the literature by other workers. The theoretical method is also used successfully to explain the apparent discrepancies between the respective experimental results obtained for both model and full scale structures. The effect of foundation elasticity can be included in the method and it is shown to have a significant effect on the lower modes of a cooling tower. The usefulness of the method as a design tool is demonstrated, and as an example, the effects of changing the dimensions of the cornice, ring-beam and column-supports are studied. The angle a column-support makes with the horizontal is shown to have a noticeable effect on the lowest mode of vibration. Varying the value of Poisson's ratio is shown to have only a small effect; this vindicates the use of material in a model cooling tower that does not have quite the same value of Poisson's ratio as the full scale structure. Whilst the free vibration of cooling towers is discussed in this paper, the method can be used to analyze other rotationally periodic structures such as chimneys, and can be extended to analyze the behaviour of rotationally periodic structures subjected to seismic disturbances, impacting missiles or wind-forces.     

Axisymmetric vibrations of an isotropic elastic non-homogeneous circular plate of linearly varying thickness

Free axisymmetric vibrations of an isotropic, elastic, non-homogeneous circular plate of linearly varying thickness have been studied on the classical theory of plates. The non-homogeneity of the material of the plate is assumed to arise due to the variation of Young's modulus and density with the radius vector whereas Poisson's ratio is assumed to remain constant. The governing differential equation of motion is solved by the method of Frobenius. The transverse displacement of the plate has been expressed as a power series in terms of the radial co-ordinate. The frequency parameters corresponding to the first two modes of vibration have been computed for different values of the non-homogeneity parameter and taper constant and for clamped and simply supported edge conditions of the plate. A comparison between the numerical results for homogeneous and non-homogeneous material of the plate is also made.     

Saturation of Electrostatic Potential: Exactly Solvable 2D Coulomb Models

We test the concepts of renormalized charge and potential saturation, introduced within the framework of highly asymmetric Coulomb mixtures, on exactly solvable Coulomb models. The object of study is the average electrostatic potential induced by a unique “guest” charge immersed in a classical electrolyte, the whole system being in thermal equilibrium at some inverse temperature β. The guest charge is considered to be either an infinite hard wall carrying a uniform surface charge or a charged colloidal particle. The systems are treated as two-dimensional; the electrolyte is modelled by a symmetric two-component plasma (TCP) of point-like ±e charges with logarithmic Coulomb interactions. Two cases are solved exactly: the Debye–Hückel limit β e²→ 0 and the Thirring free-fermion point β e²=2. The results at the free-fermion point can be summarized as follows: (i) The induced electrostatic potential exhibits the asymptotic behavior, at large distances from the guest charge, whose form is different from that obtained in the Debye–Hückel (linear Poisson–Boltzmann) theory. This means that the concept of renormalized charge, developed within the nonlinear Poisson–Boltzmann (PB) theory to describe the screening effect of the electrolyte cloud, fails at the free-fermion point. (ii) In the limit of an infinite bare charge, the induced electrostatic potential saturates at a finite value in every point of the electrolyte region. This fact confirms the previously proposed hypothesis of potential saturation.     

Pressure effect on structural,electronic and thermodynamic investigations of europium filled skutterudite EuFe4Sb12: LDA and LSDA approximations

Numerical calculations based on the full potential muffin-tin orbitals method (FP-LMTO) within the local density approximation (LDA) and the local spin-density approximation (LSDA) to investigate the structural, electronic and thermodynamic properties of filled skutterudite EuFe₄Sb₁₂ are presented. The electronic band structure and density of states profiles prove that this material is a conductor. The present investigation is also extended to the elastic constants, such as the bulk modulus B, anisotropy factor A, shear modulus G, young's modulus E, Poisson's ratio ν, and the B/G ratio with pressure in the range of 0–40 GPa. The sound velocities and Debye temperatures are also predicted from the above constants. The variations of the primitive cell volume, expansion coefficient α, bulk modulus B, heat capacity (C_p and C_v), Debye temperature θ_D, Helmholtz free energy A, Gibbs free energy G, entropy S, and internal energy U with pressure and temperature in the range 0–3000 K are calculated successfully.     

Approaches to a non-abelian antisymmetric tensor gauge field theory

Two distinct attempts at constructing a theory of non-abelian antisymmetric tensor gauge fields (ATGF's) are considered. First, a recently proposed geometry of abelian ATGF's is reviewed and then generalized to the non-abelian case. The resulting geometric action is non-local and is invariant under non-local gauge transformations; in the local limit the action describes free fields. Lattice actions for both the abelian and non-abelian ATGF theories are also presented. In the second approach, a lattice action for non-abelian ATGF's is constructed using a plaquette variables that carry four internal indices. The continuum limit is also a non-interacting theory.     

A study of the metal-ionic conductor interface capacitances. II. Capacitance versus surface potential

Using the experimental method described in the preceding paper to determine the interface capacitances, the influence of surface potential value on these capacitances is analysed on thin film samples elaborated with gold as electrodes and lead fluoride as ionic conductor. The experimental capacitance-surface potential curve is compared to the theoretical curve calculated from Poisson's equation and supposing a Boltzmann distribution of the ionic carriers. The results seem to show the presence of a saturation region obtained for negative values of the surface potential, and corresponding to a strong accumulation of fluorine vacancies.     

Relation between the parameters of the elasticity theory and averaged bulk modulus of solids

A relation between the elastic moduli and Poisson’s ratio of crystalline and vitreous solids is considered. The feasibility of introducing the averaged bulk modulus, which has the same attributes as other elastic moduli, is substantiated. A relationship between the Grüneisen parameter and Poisson’s ratio is discussed.     

Image charge potential at the interface of two semi-infinite media: Thomas-Fermi solution

The image charge potential is found for a parallel plate capacitor geometry in the infinite barrier Thomas—Fermi approximation to Poisson's equation. The material composition of the semi-infinite media are taken to be plasma-like although the jellium-dielectric interface is discussed in detail. Approximations such as single imaging (Newns) or that due to Gomer and Swanson are found to be reasonable in the center of large gaps but inaccurate for separations on the order of molecular dimensions. The dipole image potential is derived from the Green function solution for this geometry.     

Remarks on the Poisson equations of motion

In respect of Poisson's equations of motion, we give solutions of the form F_o(H)exp{iU(p, q)}, which have a physical significance and are of importance for the calculation of phase operators in quantum mechanics.     

Effects of Poisson's ratio on the band gaps and defect states in two-dimensional vacuum/solid porous phononic crystals

The effects of the Poisson’s ratio of the solid host on the band gaps and point defect states of the mixed elastic wave modes in two-dimensional vacuum/solid porous PNCs are studied by numerical simulations. Four typical systems are considered. The four systems are, respectively, (I) the system with a square lattice and circular pores, (II) the system with a hexagonal lattice and circular pores, (III) the system with a square lattice and square pores and (IV) the system with a hexagonal lattice and regular-hexagonal pores. In the latter two systems, with respect to the outer boundaries of the Wigner-Seitz unit cell, the pores rotate 45° and 30°, respectively. Some observable effects of the Poisson’s ratio are found in the numerical results. Especially, the variations of the band gap boundaries with the Poisson’s ratio exhibit relatively consistent behaviors. With the increase of the Poisson’s ratio, the normalized frequency of a band gap boundary generally increases, except that in system (III) the normalized frequency of the upper boundary of the first band gap remains almost unchanged. Detailed interpretations on this phenomenon are given.