Elastic constants of natural quartz

The elastic constants of a natural-quartz sphere using resonance-ultrasound spectroscopy (RUS) are measured. The measurements of the near-traction-free vibrational frequencies of the sphere are matched with the predicted frequencies from the dynamic theory of elasticity, with optimized estimates for the elastic constants driving the differences between these sets of frequencies to a minimal value. The present computational model, although based on earlier approaches, is the first application of RUS to trigonal-symmetry spheres. Quartz shows six independent elastic constants, and our estimates of these constants are close to those computed by other means. Except for C14, after a 1% mass-density correction, natural quartz and cultured quartz show the same elastic constants. Natural quartz shows higher internal frictions.     

Elastic constants of lead-bismuth alloys

A study of ultrasonic velocities and internal friction has been carried out in Pb-Bi alloys in the concentration range of 0 to 49.5 atomic % Bi using the composite oscillator technique. From the velocity and density data a set of elastic constants namely, Young’s modulus, rigidity modulus, bulk modulus and Poisson’s ratio are estimated. The results are interpreted in terms of the phase changes occurring in the alloy system. Internal friction is found to be more sensitive than the elastic constants to the phase changes.     

Elastic constants of antiferromagnetic chromium-vanadium alloys

Single crystals of chromium alloys containing 0.67 and 1.5% vanadium were prepared by the floating-zone technique. Elastic constants and attenuation were measured by the pulse-echo method between 77 and 300 K. The changes of the elastic properties in the paramagnetic and antiferromagnetic states and in particular at the magnetic transition are described and discussed.     

Elastic constants of mixed ammonium halides

In the present communication a method based on the three body forces for the evaluation of second and third order elastic constants of mixed ammonium halides has been described. The Lundqvist three body potential is used along with long range Coulombian and short-range overlap repulsive potentials. The latter is taken of the Born-Mayer type and effective up to first neighbours only. It has been assumed that the charge transfer and short-range parameters depend linearly on the composition of solid solutions. Theoretical results obtained, for the entire range of compositions of mixed NH₄Cl and NH₄Br, have been compared with the recently measured experimental values and the theoretical results of other workers, whenever these are available.The authors are thankful to Dr. J. Shanker, Department of Physics, Agra University, Agra, for helpful discussions.     

Elastic constants of nonionic anharmonic crystals

Taking into account the entire anharmonicity of the crystal an exact relation between the long-wavelength limit of the static self-energy and the isothermal elastic constants is established. The result can be reformulated as a sum rule for the displacement correlation function. The diagram technique is also employed to discuss the equation for the elastic constants in the pseudoharmonic approximation as well as to derive the integral equations for the quasiparticle parameters.     

Elastic constants of sodium chlorate from 77 K to 350 K

The elastic constantsC ₁₁,C ₁₂ andC ₄₄ of sodium chlorate single crystal have been evaluated using 10 MHz ultrasonic pulse echo superposition technique. The values areC ₁₁=4.90,C ₁₂=1.39,C ₄₄=1.17 (× 10¹⁰ N/m ²) at 298 K and 6.15, 2.16, 1.32 (×10¹⁰ N/m ²) at 77 K. The data agree well with the values measured earlier up to 223 K. Brief mention is also made of the low temperature bonding problems in these soft crystals.     

Elastic scattering of light from quantum-well exciton-polarization fluctuations in a microcavity

A model of exciton polarization fluctuations in a quantum well of a randomly variable lateral width is proposed. The stochastic part of the nonlocal susceptibility of quasi-two-dimensional excitons is expressed through random functions of the shape of quantum well boundaries. A theory of elastic light scattering from a quantum well placed in a Fabry-Perot cavity or a semiconductor microcavity is constructed in the lowest (Born) approximation in interface roughness height. The scattering cross section is calculated for an arbitrary statistics of interface roughness. The spectral and angular dependences of the intensity of light scattered by a quantum well have been studied using Gaussian correlation functions of the interface shape. It follows from numerical estimates that elastic resonant scattering in quantum wells should be observed at an rms roughness height of the order of the atomic monolayer thickness.     

A potential for Th from inversion of cohesive energy: Elastic constants

An interatomic pair potential for Th was derived by using the Chen–Mobius lattice inversion of cohesive energy for fcc Th as a starting point to develop a free-parameter potential suitable to be used in molecular dynamic calculations for predicting microstructure evolution and thermal properties in multicomponent nuclear fuel. The cohesive energy versus lattice parameter of Th was computed from first principles electronic structure calculations. The elastic constants for fcc Th were calculated by applying different types of strain to the starting crystal. Based on this information, the shear modulus, the Youngs modulus and the Poissons ratio were obtained. The computed elastic constants of fcc Th are found to be in a good agreement with experiments and previous theoretical results.     

Elastic and elasto-optic constants of ammonium perchlorate

Using Brillouin scattering, the elastic and elasto-optic constants of ammonium perchlorate have been measured at room temperature. The polarized Brillouin scattering spectra yielded the nine elastic constants (in the units of $\text{10}{}^{11}\text{dynes}\text{cm}{}^2\text{)}$ as follows: C₁₁ = 2.51, C₂₂ = 2.46, C₃₃ = 3.15, C₄₄ = 0.66, C₅₅ = 0.47, C₆₆ = l.03, C₁₂ = 1.63, C₂₃ = 1.15, C₂₃ = 0.76; as well as the absolute value of nine elasto-optic constants. In the light of these results, some thermodynamic properties of the crystal are discussed.     

Elastic constants of an aluminum-alumina unidirectional composite

The five independent second-order elastic constants of a transversely isotropic aluminum/alumina fiber composite have been measured for the first time using a resonant ultrasound spectroscopy technique. These data were used to deduce the elastic constants and engineering moduli for off-axis loading conditions.     

Elastic constants of solids at high pressures

The isothermal and adiabatic nth-order (n ?? 2) elastic constants of a loaded crystal are defined. These constants fully determine the behavior of solids at an arbitrary load and are controlled by both an interatomic interaction and an applied load. Expressions that relate these constants (of the second, third, and fourth order) to Brugger elastic constants of the corresponding order, which are only determined by an inter-atomic interaction, are found for cubic symmetry crystals under hydrostatic pressure. These expressions are used to calculate the equation of state and the second- and third-order elastic constants of bcc tantalum at T = 0 K over a wide pressure range (0?C600 GPa) using an electron density functional method. The results of calculating the equation of state and the second-order elastic constants agree with available experimental data and the calculation results obtained in other works.     

Elastic constants of layers in isotropic laminates

The individual laminae elastic constants in multilayer laminates composed of dissimilar isotropic layers were determined using ultrasonic-resonance spectroscopy and the linear theory of elasticity. Ultrasonic resonance allows one to measure the free-vibration response spectrum of a traction-free solid under periodic vibration. These frequencies depend on pointwise density, laminate dimensions, layer thickness, and layer elastic constants. Given a material with known mass but unknown constitution, this method allows one to extract the elastic constants and density of the constituent layers. This is accomplished by measuring the frequencies and then minimizing the differences between these and those calculated using the theory of elasticity for layered media to select the constants that best replicate the frequency-response spectrum. This approach is applied to a three-layer, unsymmetric laminate of WpCu, and very good agreement is found with the elastic constants of the two constituent materials.     

Elastic constants of a plate from impact-echo resonance and Rayleigh wave velocity

A new method is proposed for calculating the dynamic elastic constants of an isotropic plate from measurements of the impact-echo resonance and Rayleigh wave velocity. Poisson's ratio is shown to be a single-valued function of the ratio between thickness frequency and Rayleigh wave velocity. This dependence is derived theoretically from the condition of resonance at the minimum frequency of the first-order symmetric Lamb mode. A finite element model is developed to determine how this frequency varies with Poisson's ratio. The results obtained by modal analysis and the power-spectral density technique are in good agreement with those calculated as the solution of the S1 Lamb mode equation. The method is verified by impact-echo tests on concrete and methacrylate plates. A laser interferometer is used to detect the vibration. Thickness frequencies are accurately identified by applying the multicross-spectral density to the signals detected at several points close to the impact point. In a separate experiment, Rayleigh waves are generated by the mediator technique. The wave velocities are determined from the arrival times of the surface wave at several points. Finally, the main sources of uncertainty are evaluated.