P. Andreatch

Elastic Moduli of Diamond as a Function of Pressure and Temperature

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

Elastic Moduli of Silicon vs Hydrostatic Pressure at 25.0°C and − 195.8°C

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.

Third‐Order Elastic Coefficients of Quartz

All 14 third‐order elastic coefficients of quartz have been calculated from the measured transit times for small‐amplitude ultrasonic waves as functions of applied stress. Thirty‐four different experimental runs were made, ten under hydrostatic pressure, and 24 under uniaxial stress. The data permit calculation of the 14 coefficients with 20 crosschecks. Our recommended values at 25°C, based on a least‐squares fit, are as follows, all in 1012 dyn/cm2. CoefficientValueStandard errorC111−2.100.07C112−3.450.06C113+0.120.06C114−1.630.05C123−2.940.05C124−0.150.04C133−3.120.07C134+0.020.04C144−1.340.07C155−2.000.08C222−3.320.08C333−8.150.18C344−1.100.07C444−2.76 0.17.

Measurement of Third‐Order Moduli of Silicon and Germanium

Experimental techniques for determining third‐order moduli of single crystals by means of ultrasonic wave propagation are described. Results for silicon and germanium demonstrate a good degree of self‐consistency among the basic experimental data obtained with both hydrostatic and uniaxial pressure.In units of 1012 dyn/cm2 and for 25°C, the third‐order moduli are: ModulusValue for SiValue for GeC111−8.25±0.10−7.10±0.06C112−4.51±0.05−3.89±0.03C123−0.64±0.10−0.18±0.06C144+0.12±0.25−0.23±0.16C166−3.10±0.10−2.92±0.08C456−0.64±0.20−0.53±0.07 Thermodynamic definitions for the moduli (K. Brugger, Phys. Rev. 133, A1611 (1964)] have been used.

The Elastic Stiffness Moduli of Diamond

The elastic stiffness moduli of a 22‐carat Type II diamond have been measured at 25.0°C by the ultrasonic technique described by H. J. McSkimin. Basic wave velocities were obtained over a frequency range of 20–500 MHz in order to minimize errors due to diffraction and coupling effects. Moduli (in units of 1012 dyn/cm2) are as follows: c11=10.79±0.05, c12=1.24±0.05, c44=5.78±0.02. Comparison with literature values is made.

Third‐Order Elastic Moduli of Gallium Arsenide

The six third‐order moduli of GaAs have been determined by measurement of ultrasonic wave velocities (time delays) as a function of applied stress. The adiabatic values (in units of 1012 dyn/cm2) at 25°C and for zero electric field are very similar to those previously obtained for Si and Ge, as can be seen from the following table: ModulusGaAsGeSiC111−6.22±0.06−7.10−8.25C112−3.87±0.03−3.89−4.51C123−0.57±0.06−0.18−0.64C144+0.02±0.09−0.23+0.12C166−2.69±0.06−2.92−3.10C456−0.39±0.09−0.53−0.64.

Pressure dependence of ultrasonic wave velocities and elastic stiffness moduli for a TiO2‐SiO2 glass (Corning 7971)

A glass which is possibly useful as an optical and acoustical waveguide material was characterized. Ultrasonic wave velocities were measured as a function of hydrostatic pressure for Corning glass No. 7971, a TiO2‐doped silica, and also for an undoped‐specimen glass No. 7940. Pressure derivatives of the elastic stiffness moduli were determined.

Elastic Moduli of Cobalt‐Iron Single Crystals

Face‐centered‐cubic (fcc) Co–Fe alloys in the vicinity of 10 at. % Fe form the basis for an important class of semihard magnetic alloys used for memory and switching applications. The elastic properties are important in determining the magnitude of the internal and/or applied stresses resulting from device operation and processing. The work described was undertaken to evaluate the compositional dependence of the elastic stiffness moduli in the fcc range of stability. The elastic stiffness moduli for single crystals of 6, 12, and 14 at. % Fe were measured by an ultrasonic method previously described (Ref. 3). The results for the 6 at. % Fe alloy at 25°C were c11=2.340, c12=1.589, and c44=1.259×1012 dyn/cm2. The stiffness moduli were found to vary only slightly with composition.

Disk‐Loaded Torsional Wave Delay Line. I. Construction and Test

Torsional waves are propagated in a uniform diameter rod with the shear velocity (μ/ρ)12. On the other hand, the effective velocity is slower in a disk‐loaded rod with alternate large‐diameter and small‐diameter sections. Because of the slower velocity, a disk‐loaded rod will delay a signal longer than conventional ultrasonic delay lines of the same path length. This paper describes the construction of these disk‐loaded torsional wave delay lines, and of electromechanical transducers for generating and detecting the torsional waves. The method of testing and the results of tests on the lines are presented. For example, a brass line having the disk diameter five times the diameter of the sections between the disks provided a delay of 114 μsec/cm at 32 kc. For contrast, the delay of a uniform diameter brass rod is only 4.5 μsec/cm.

Elastic Moduli of Diamond and their Pressure Derivatives

The adiabatic elastic stiffness moduli of a 22‐carat type II diamond have been measured at 25.0°C by the ultrasonic technique described in IEEE Trans. Sonics Ultrasonics SU‐5, 25 (1957). Basic wave velocities were obtained over a frequency range 20–500 MHz in order to minimize errors due to diffraction and coupling effects. Variations with hydrostatic pressure were measured at 20 MHz using a pulse superposition technique [J. Acoust. Soc. Amer. 41, 1052 (1967)]. Values of moduli in units of 1012 dyn/cm2 and their respective pressure derivatives (dc/dP) are as follows: c11 = 10.79±0.05; c12 = 1.24±0.05; c44 = 5.78±0.02, 5.98±0.7, 3.06±0.7, and 2.98±0.3.