Chang, Y.-Y., S. D. Jacobsen, C. M. Holl, and C. R. Bina, Developments in GHz-ultrasonic interferometry for elasticity studies in geophysics and materials science: Application to diamond, Eos, Transactions of the American Geophysical Union, 90, Fall Meeting Supplement, MR13A-1661, 2009.
Elastic properties of solids are fundamentally important in Earth and materials science because they govern seismic wave propagation at the geophysical scale, but are controlled at the atomic scale by the nature of interatomic bonding. GHz-ultrasonic interferometry utilizes thin-film piezoelectric transducers driven by pulse modulated, microwave-range carrier frequencies at 0.5-2.0 GHz to measure sound wave travel times in sub-millimeter sized samples (Spetzler et al. 1993). Travel times are determined from the spacing of interference fringes produced by measuring the amplitude of overlapping echoes scanned in frequency (wavelength) from opposite polished faces of single crystals. The ultrasonic signals are near-optical in wavelength at 5-20 km/s in high-modulus materials, allowing study of samples as small as a few tens of micrometers in thickness, including micro-crystals loaded in diamond-anvil cells at high pressures and temperatures. Following Jacobsen et al. (2004), both longitudinal and shear-wave measurements are possible. Although relative changes in travel time on compression or heating are measured with standard deviation of about 0.02 nanoseconds out of 20-200 ns (depending on sample thickness), the absolute accuracy of ultrasonic measurements at standard conditions, required to anchor high P-T measurements, has been limited by our ability to measure sample thickness mechanically at STP, with only 1-2 micrometer accuracy out of 20-200 ým for typical samples. Thus, we have recently installed a commercial heterodyne optical interferometer to determine ultrasonic sample lengths at STP conditions. Using a double-pass laser interferometer we achieve λ/4 fundamental optical resolution with λ/128 (about 5 nm) system resolution through software-based interpolation. By adding real-time corrections for air temperature, humidity, and pressure applied to the laser wavelength, we achieve high accuracy with standard deviations of about 0.02 micrometers in the thickness measurements. Using this new setup, we determined the C11 and C44 elastic constants of natural type IIA single-crystal diamond with unprecedented precision: C11 = 1076.2(6) GPa and C44 = 575.8(4) GPa, improving the reported uncertainty in moduli of diamond by about one order of magnitude over previous ultrasonic measurements (e.g. McSkimin and Bond 1957). This technique will allow us to ascertain whether or not reported variability in elastic properties various forms of synthetic diamond are significant. We plan to use the instrument to study both natural and synthetic diamond elasticity and variations in equations of state with defect structure and pressure, as well as other superhard materials intended for use in future societal applications.Copyright © 2009 American Geophysical Union