Values of wave velocities and elastic moduli at 25°C were measured for hydrostatic pressures to 20 000 psi (excess over 1 atm). Variations of velocities and moduli at 1 atm were obtained over a temperature range of +50°C to −195.8°C. Adiabatic stiffness moduli (units of 1012 dyn/cm2), their pressure derivatives, and their temperature coefficients (units of 10−5/C), are shown below for 1 atm and 25°C. ModulusValuePressure derivativesTemperature coefficientc1110.79±0.055.98±0.7−1.37±0.2c12 1.24±0.053.06±0.7−5.70±1.5c44 5.78±0.022.98±0.3−1.25±0.1

Ultrasonic waves (shear or longitudinal) in the 10–30 mc range are transmitted down a fused silica rod, through a polystyrene or silicone one-quarter wavelength seal, and into the solid specimen. Measurement of reflections within the specimen yields values for velocities of propagation and elastic constants. Data obtained over a temperature range of 78° to 300°K for silicon and germanium single crystals, and 1.6° to 300°K for fused silica are listed. For the latter, a high loss is noted, with an indicated maximum near 30°K.

Ultrasonic wave velocities and elastic moduli for high purity silicon (resistivity ∼400 Ω-cm) have been measured as a function of hydrostatic pressure and temperature in the ranges 0–30 000 psi (0–2100 kg/cm2) and − 195.8° to 25°C. Variations of moduli with pressure are found to be nearly independent of temperature in the range listed. For 25°C(Δc11/Δp)=4.33, (Δc12/Δp)=4.19, (Δc44/Δp)=0.80, (ΔK/Δp)=4.24. For − 195.8°C(Δc11/Δp)=4.29, (Δc12/Δp)=4.20, (Δc44/Δp)=0.75, (ΔK/Δp)=4.23.

Ultrasonic wave velocities in single-crystal quartz have been measured as a function of temperature and pressure by means of a pulse superposition method described in J. Acoust. Soc. Am. 33, 12 (1961). In order to make good use of all the experimental data, a set of "adjusted" velocities and initial pressure derivatives was obtained which satisfies all the cross-checks exactly, while minimizing a weighted sum of the squares of the adjustments from the measured values. These adjusted values were then used to calculate the elastic moduli as functions of temperature and pressure. Values of "zero-field" moduli at zero pressure and the initial pressure derivatives determined in this way are shown below.

It has long been suspected that if liquids were sheared sufficiently rapidly they would exhibit a shear elastic effect as well as a viscous effect. This supposition was verified recently by one of the writers (see reference 8) by employing a torsionally vibrating crystal and measuring the mechanical loading for the shear wave by observing the increased resistance at resonance and the change in the resonant frequency. By this method it was shown that long chain polymer liquids had shear configurational elasticities in the order of 10 7 dynes/cm 2 .The use of a torsional crystal is limited in frequency to about 2 to 3 X10 5 cycles on account of the small sizes needed. In the present paper the range of shear wave measurements in liquids has been extended up to 60 megacycles by observing the effect, on a series of shear waves in a fused quartz rod, of terminating the rod by a thin layer of a liquid. The shear wave in the rod is altered in magnitude and phase by the boundary layer impedance of the liquid. By observing the reflection loss and the change in phase caused by the liquid layer, a measure is obtained of the shear impedance of the liquid. By employing a fused quartz rod for which the shear wave strikes the reflecting surface at an angle from the normal of about 79 degrees, the effect of the shear wave impedance on the boundary is greatly enhanced and a more accurate measurement obtained.Both the torsional crystal and high frequency shear wave techniques applied to polyisobutylene and poly-a-methylstyrene liquids, show that there are two main relaxation frequencies in these liquids. At frequencies under 100 kc, the shear stiffness is in the order of 3X10 7 dynes/cm 2 , while in the high megacycle range it has increased to 5 X10 9 dynes/cm 2 . The low shear elasticity appears to be associated with a composite motion of molecular rotation and translation that allows a configurational change to occur from the most probable chain shape. When the shear stress is removed, the molecule quickly returns to its most probable shape. This results in a low shear stiffness. At high frequencies this motion cannot take place, and the shear stiffness is determined by motions within single potential wells, and the value approaches that for a crystal. It is shown that the dispersion for longitudinal waves measured recently (see reference 11) is primarily due to the shear mechanisms investigated. L INTRODUCTIONI T HAS long been suspected that if liquids were sheared sufficiently rapidly, they would exhibit a shear elastic effect as well as a viscous effect. In fact, Maxwell, 1 on the basis of a gas model, predicted that an instantaneous shear distortion would have a relaxation time r and a relaxation frequency jv given by the formulas T = r}/n\ / r ==l/(27rr)=M/(27n?),(1) where t\ is the shear viscosity and \x the shear elasticity. A similar result has recently been obtained by Frenkel 2 by assuming that a liquid has a short range order similar to a solid, and identifying the relaxation time r as the mean life in a sedentary stat...