Elastic modulus sound absorption

Grayish metal hexagonal close-packed crystal system, lattice constant, a=2.286 A and c=3.584 A density 1.85 g/cm permeable to x-rays highly ductile modulus to weight ratio very high, elastic modulus 44.5 x 10 at 25°C (for hot-pressed block and sheet) melting point 1,287°C vaporizes at 2,471°C sound transmission velocity 12,600 m/sec reflectivity (white hght) 55% thermal neutron absorption cross-section 0.0090 barns/atom electrode potential, Be/Be2+(aq) 1.85 V electrical resistivity 3.36 x 10-i° ohm.m (at 20°C). 

Techniques for measuring the complex sound speeds and moduli of polymers are described in the section on test methods. The data shows that the real and imaginary components of the elastic moduli are frequency dependent. The frequency dependence is strongest for materials with high values of the loss factor r. Materials with frequency-dependent elastic moduli are called dispersive, and measurements and theory show that sound absorption mechanisms lead to dispersion. The real and imaginary part of an elastic modulus are related by the Kramers-Kronig relations, which are presented in the next section. 

Soft white, ductile metal high-purity metal is very ductile at ordinary temperatures occurs in three allotropic forms (i) body-centered cubic form, alpha iron stable up to 910°C, (ii) face-centered cubic form, gamma iron occurring between 910 to 1,390°C, and (iii) body-centered delta iron allotrope forming above 1,390°C. Density 7.873 g/cm at 20°C melting point 1,538°C vaporizes at 2,861°C hardness (Brinell) 60 electrical resistivity 4.71 microhm-cm at 0°C tensile strength 30,000 psi Poisson s ratio 0.29 modulus of elasticity 28.5 X 10 psi thermal neutron absorption cross-section 2.62 bams velocity of sound 5,130 m/s at 20°C. 

Grayish-white metal hody-centered cubic crystalline structure density 19.3 g/cm3 melts at 3,422°C vaporizes at 5,555°C vapor pressure 1 torr at 3,990°C electrical resistivity 5.5 microhm-cm at 20°C modulus of elasticity about 50 to 57 x lO psi (single crystal) Poisson s ratio 0.17 magnetic sus-ceptibilty +59 x 10-6 thermal neutron absorption cross section 19.2 + 1.0 barns (2,200m/sec) velocity of sound, about 13,000 ft/sec insoluble in water practically insoluble in most acids and alkabes dissolves slowly in hot concentrated nitric acid dissolves in saturated aqueous solution of sodium chlorate and basic solution of potassium ferricyanide also solubibzed by fusion with sodium hydroxide or sodium carbonate in the presence of potassium nitrate followed by treatment with water... 

In equations (5)-(8), i is the molecule s moment of Inertia, v the flow velocity, K is the appropriate elastic constant, e the dielectric anisotropy, 8 is the angle between the optical field and the nematic liquid crystal director axis y the viscosity coefficient, the tensorial order parameter (for isotropic phase), the optical electric field, T the nematic-isotropic phase transition temperature, S the order parameter (for liquid-crystal phase), the thermal conductivity, a the absorption constant, pj the density, C the specific heat, B the bulk modulus, v, the velocity of sound, y the electrostrictive coefficient. Table 1 summarizes these optical nonlinearities, their magnitudes and typical relaxation time constants. Also included in Table 1 is the extraordinary large optical nonlinearity we recently observed in excited dye-molecules doped liquid... 

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