Part I. Temperature Dependence of Single Crystal Spinel (MgAl₂O₄) Elastic Constants from 293K to 423K Measured by Light-Sound Scattering in the Raman-Nath Region. Part II. Effect of Anelasticity on Periods of Earth's Free Oscillation (Toroidal Modes)

Citation

Liu, Hsi-Ping (1974) Part I. Temperature Dependence of Single Crystal Spinel (MgAl₂O₄) Elastic Constants from 293K to 423K Measured by Light-Sound Scattering in the Raman-Nath Region. Part II. Effect of Anelasticity on Periods of Earth's Free Oscillation (Toroidal Modes). Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/QYWT-AK53. https://resolver.caltech.edu/CaltechTHESIS:01132011-114814151

Abstract

Part I:

The temperature dependence of single-crystal elastic constants of synthetic stoichiometric MgAl_2O_4 spinel has been measured by the light-sound scattering technique in the Raman-Nath region. The crystal is set into forced vibration by a single crystal LiNbO_3 transducer coupled to one crystal face. A He-Ne laser beam is diffracted by the stress-induced birefringence inside the crystal. The diffraction angle is determined from the distance of two spots exposed on a photographic plate by the first order diffracted beams as measured by a microdensitometer. The sound wavelength inside the crystal is then inferred from the laser diffraction angle. Combining the sound wavelength with the measured transducer driving frequency, the velocity inside the crystal is determined typically to a precision of 0.05%. In this method, the measurement of velocity is not dependent on either the determination of sample length or on phase shifts at sample-transducer interface. Velocities of four pure modes, L//[001], T//[001], L//[110], and T//[110] (P//[1^-_10]) are measured in the temperature range between 293K and 423K. A linear temperature dependence is fit to the data by a least square method. Values obtained at 25°C from this linear fit are V_p[001] = 8.869 ± 0.013 km/sec, (∂V/∂T)_p = -(3.14 ± 0.13) x 10^(-4)km/sec-K; V_s[001] = 6.5666 ± 0.0055 km/sec, (∂V/∂T)_p = -(1.47 ± 0.10) x 10^(-4)km/sec-K; V_p[110] = 10.199 ± 0.011 km/sec, (∂V/∂T)_p = -(3.20 ± 0.15) x 10^(-4)km/sec-K; V_s[110][P//[110]) = 4.2101 ± 0.0043 km/sec, (∂V/∂T)_p = -(2.07 ± 0.06) x 10^(-4)km/sec-K. The temperature dependence of the adiabatic elastic constants and bulk and shear (VRH average) moduli is computed using the density and literature value of thermal expansion coefficient. Values obtained are: C^s_(11) = 2814 ± 8 kb, (∂C^s_(11)/∂T)_p = -0.258 ± 0.018 kb/K; C^s_(12) = 1546 ± 9 kb, (∂C^s_(12)/∂T)_p = -0.107 ± 0.019 kb/K; C^s_(44) = 1543 ± 3 kb, (∂C^s_(44)/∂T)_p = -0.101 ± 0.010 kb/k; K_s = 1969 ± 6 kb, (∂K^s_/∂T)_p = -0.157 ± 0.014 kb/K; µ_(VRH) = 1080 ± 5 kb, (∂µ_(VRH)/∂T)_p = -0.094 ± 0.008 kb/K. A comparison with previous measurements by pulse superposition and ultrasonic interferometry methods is made. Disagreement, when present, is discussed in terms of the separate measuring techniques. An attempt has also been made to measure the pressure dependence of elastic constants of spinel with the same technique. It failed because of the large spurious diffraction introduced by the fluctuation in index of refraction of the pressure fluid. A method to eliminate this spurious effect is discussed. An optical interferometry method is devised to measure the pressure window distortion effect in the pressure dependence measurement. Finally, the present method with its possibility for further improvement is evaluated as a new method to measure temperature and pressure dependence of elastic constants. Other methods using light-sound scattering to measure sound velocities are also reviewed.

Part II:

It is known that the anelastic properties of the earth characterized by a "Q" structure will affect the periods of free oscillation. It is generally considered that the effect is negligible compared to the other perturbing effects due to rotation, ellipticity, and lateral inhomogeneities. Nevertheless, it is of some interest to investigate the precise magnitude of this effect for the observed free oscillation modes since it could provide us with another constraint in the determination of the Q structure of the Earth. An application of perturbation theory provides us with a good estimate of the magnitude of the changes in the periods of an elastic model due to inclusion of anelastic effects. Calculations based on currently accepted elastic and anelastic models for the Earth show that the shift in period due to anelasticity is at most 0.023 percent for the toroidal modes from _oT_2 to o_T_(99) the maximum occurring near _oT_(60) This is smaller by a factor of five than the present observational accuracy. Compared to the other perturbing effects, the anelastic effect, when important, is larger than the effect of ellipticity considered alone but smaller by an order of magnitude when compared with ellipticity and rotational effects coupled together or with the continent-ocean lateral inhomogeneity. Since the frequency shift due to anelasticity is scaled by (1/Q)^2, the anelastic effect can be within observational accuracy and comparable to other perturbing effects for more extreme, yet acceptable, Q models.

Thesis Files