Schock of the Lawrence Livermore Laboratory of the University of California generously lent the author an optical cell for measuring the pressure dependence. The temperature dependence of single-crystal elastic constants of synthetic stoichiometric MgA1 204 spinel was measured using the light-acoustic scattering technique in the Raman-Nath region. In general, the effect is considered to be negligible compared to. other disturbing effects due to rotation, ellipticity and lateral inhomogeneities.
Temperature dependence of single crystal spinel (MgA1 20 . 4) Elastic constants from 293K to 423K Measured by light-sound scattering in the Raman-Nath region. TEMPERATURE DEPENDENCE OF SINGLE CRYSTAL SPINEL (MgA'204) ELASTIC CONSTANTS FROM 293K TO 423K MEASURED BY SOUND BREAKING IN THE RAMAN-NATH REGION. The present work is an attempt to use an independent method, the method of light-sound scattering in the Raman-Nath region, to.
The cross-section of the furnace assembly through the two thermocouples is shown in Figure 1.3-9. A Uniblitz model 225-0 closer (Vincent Associates, Rochester, N.V.) is secured to the inside of one of the flanges with screws. Another rotating flange is welded to a bellows section and a photographic plate holder is welded to the other end.
The sample is gold plated in a configuration shown in Figure 1;3~18 to provide grounding of the transducer through the sample holder half. This reflected beam is used to guide the adjustment of the plate holder orientation screws. After evacuating the optical path between the crystal and the photographic plate, the OPDT switch is thrown and the photographic plate is exposed to the diffracted rays.
GOLD COATED FOR CONDUCT IV ITY
LESS THAN 5 OHMS AROUND CORNER
The photographic plate is placed on the microdensitometer table with its lower edge pushed against the lower edge of the recessed table. The angle between the direction defined by the spots and the lower edge of the photographic plate y is read from the rotation table of the table. Positioning the protractor angle sets the scale divisions on the step micrometer perpendicular to the direction of travel of the microdensitometer.
The purpose of the stage micrometer is to place fiducial marks on the microdensitometer readout card for distance measurement. An example of the microdensitometer readout with this arrangement is shown in Figure I.S-2a and Figure I.S-2b. There are two pencil marks on Figure I.5-2a because the two density profiles are not identical, and there is a latitude in which "fit" of the.
A measure of the reproducibility of the microdensitometer reading is provided by repeated readings of the optical density of the sections on the stage micrometer used as a fiducial. Consider now the problem of the difference in two density profiles on the same photographic plate. In summary, the errors discussed in measuring the distance between two dots on photographic plates from a microdensitometer reading are:
Figures 1.5-10 to 1.5-13 are plots of the relationship between transducer drive frequency and spot separation vs. The method is to minimize the sum of the distance from the center of each error bar to the straight line squared. However, the error bars in the present case represent, as explained earlier, the latitude in the matching of the two density profiles and the probability distribution.
Each temperature reading listed in Tables 1.5-1 through 1.5-4 is an average of the temperatures at both locations on the thermocouple. The third thermocouple is glued to the middle of the output surface (face to shutter) with Sauereisen cement. Matching one density profile of a D-9 photographic plate to the mirror image of another density profile.
RADIUS OF CURVATURE7
Therefore, the results of the present work are consistent with the measurements obtained by Chang and Barsch (1973). Under a pressure load, the window deforms in the following way: the two surfaces become curved. -axis of the indicatrix at the entry point, the refractive index seen by this ray through the window can be written as 1.7-l), where p' is the angle between the polarization vector and the optical axis of the uniaxial indicatrix before elastic deformation.
-1) is the first three terms of the expansion in r in the axisymmetric medium of the expression. Verification of the validity state also waits for a numerical calculation of the indicators inside the window. Ignoring for the moment we consider the solution of the ray equation in medium of varying index of refraction in one dimension only.
Since the change in refractive index within a stressed window is two orders of magnitude small compared to the refractive index, the indicatrix used to calculate the equivalent focal length of the window curvature can be approximated by a uniaxial indicatrix in the absence of stress. The focal length f2', however, depends on the internal elastic tension of the window and on the individual beam that travels through the window. From the three intensity profiles, equation (1.7-46) can be solved for 0 as a quadratic function of the distance along.
The cause of the wide scatter in the data is suspected to be the fluctuating index of refraction in the pressure medium. The thickness of the spacer block between the sample and the window should be reduced as much as possible in order to reduce the effect of the refractive index fluctuation in the pressurized fluid. Some difficulties, which limit the accuracy of the measurement, are (1) The resonance point of the transducer is not sharp and deteriorates with temperature and pressure, which makes it difficult to determine the constant phase shift of the transducer. 2) The connection impedance (most commonly used is Nonag stop grease) varies with pressure and temperature and this is usually not allowed.
The only error introduced by the boundaries of the sample, as discussed in the section on data and data reduction, is profile distortion of the diffracted light intensities. The sound wave emitted by the transducer is absorbed at the far end of the crystal. A separate experiment to determine the temperature and pressure dependence of the refractive index of the solid whose velocities are measured is necessary to determine the elastic constants from Brillouin scattering.
TRANSDUCER
CRYSTAL
SOFT METAL ABSORBER
The temperature dependence of the elastic constants of a single crystal of synthetic stoichiometric MgA1 204, spinel, has been measured by sound-light scattering in the Raman-Nath region. The crystal is set into forced vibration by a single crystal LiNb03 transducer attached to one face of the crystal. The temperature dependence of the adiabatic elastic constants and bulk and shear moduli (average VRH) is calculated using the density and the literature value of the coefficient of thermal expansion.
The results of the present work agree with measurements obtained by Chang and Barsch (1973) by pulse superposition method while they do not agree with the results obtained by O'Conne1 and Graham (1971) by ultrasonic interferometry through a buffer rod. An attempt was also made to measure the pressure dependence of elastic constants of spinel using the same technique. It failed because of the large spurious diffraction introduced by the fluctuation in refractive index of the pressurized fluid.
Finally, the present method is evaluated with its possibilities for further improvements as a new method for measuring temperature and pressure dependence of elastic constants. Sammis, Brillouin scattering-- a new geophysical tool, in The Application of Modern Physics to the Earth and Planetary Interiors, S. Jordan, Composition of the Mantle and Core, in The Nature of the Solid Earth, Eugene C.
Barsch, Measurement of the elastic constants of bronzite as a function of pressure and temperature, J. Krischner, C., Measurement of sound velocities in crystals using Bragg diffraction of light and application to lanthanum fluoride, App1. Andreatch, Analysis of the pulse superposition method for measuring ultrasonic wave velocities as a function of temperature and pressure, J.
Schacher, Determination of elastic constants from sound velocity measurements in crystals of general symmetry, J.
PART II
The anesthetic nature of the Earth's interior causes a series of important phenomena in solid earth geophysics. The mechanisms responsible for the inelastic behavior of the Earth's interior are largely controlled by the defect structure of the crystals that make up the stony minerals. The reported resolution of basic oTt toroidal modes ranges from 0.031% to 0.262% and is generally around 0.1% for higher frequency oTt toroidal modes where anesthetic drift becomes significant.
This has been discussed by Saito (1971) and the additional operator H of the operator H has been constructed by him. However, as the number of zeros in Wki(r) increases with k, the first term of the series is also the largest. Two laterally homogeneous Earth models are used in the calculations, one characteristic of the Basin and Range mantle province.
Two of them are frequency independent with their low Q region corresponding to the low speed Earth channel. The phase and group velocities of the two Earth models are shown in Figure 11.3-7. Longer-period free oscillations of oT~ have most of their displacement field outside the low-speed region.
For free oscillations of much shorter periods oT~ the displacement field does not sample much of the low-velocity zone. The resolution of the fundamental toroidal modes reported by them varies between 0.031% and 0.262%, and is generally around 0.1% for the higher frequency toroidal modes where the aneasticity shift becomes important. The percentage shifts in the period of the multiplet central line (m=O) due to ellipticity alone na~Ea ', as calculated by Dahlen (1968), are plotted in Figure 11.3-6, together with percentage shifts caused by anelasticity.
The numerical calculation of the present study is performed only for toroidal oscillations of the Earth. However, Dziewonski and Gilbert (1972) reported that the observation accuracy of spheroidal free oscillation periods is generally two orders of magnitude higher than that of the toroidal modes. Press, F., Long-periodic waves and free oscillations of the Earth in Research in Geophysics, Vol.
