Resonant ultrasound spectroscopy provides for an experimental determination of the elastic moduli of a solid sample. The moduli are extracted by matching a theoretically computed resonant spectrum to the experimental vibrational spectrum. To determine the pressure dependence of the moduli, the vibrational spectrum can be taken with the sample in a pressurizing gas. Then the extraction of the intrinsic, pressure dependent moduli requires a theoretical treatment which permits removal of the perturbation of the spectrum due to the surface loading by the pressure and shear waves in the gas. In order to illustrate a treatment which accomplishes this removal, the theoretically computed frequency shifts and the quality factors are reported for two single-crystal parallelepiped pressurized by noble gases.
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Resonant ultrasound spectroscopy applications: Elastic moduli computation with x-ray computed tomography input for irregularly shaped objects.
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University of Dayton Research Institute, Dayton, Ohio 45469, USA.
Resonant ultrasound spectroscopy is a technique that uses a combination of experimentally measured resonant frequencies and physics-based computation of these frequencies to determine the entire set of single crystal elastic moduli of the material. Computation of the resonances is most often accomplished using the Rayleigh-Ritz energy minimization technique, and a basis function that requires sample with canonical geometry, such as a cylinder or a rectangular parallelepiped. Any deviation from canonical geometry can have a significant impact on the calculated resonance frequencies and the inverted elastic moduli.
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Department of Chemistry, University of Minnesota, Minneapolis, NY 55455, USA.
Treatment of tetraethylammonium hexacarbonyltantalate, [EtN][Ta(CO)], with 1.1 equivalents of molecular iodine (I) in tetrahydrofuran (THF) at 200 K, followed by the addition of 6.0 equivalents of 2,6-diisopropylphenyl isocyanide (CNDipp) and slow warming to 293 K over a 24 h period gave the tantalum(I) iodide derivative hexakis(2,6-diisopropylphenyl isocyanide-κC)iodidotantalum(I), [TaI(CHN)] or TaI(CNDipp), 1.
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Materials Department, University of California, Santa Barbara, California 93106-5050, USA.
Bayesian modeling and Hamiltonian Monte Carlo (HMC) are utilized to formulate a robust algorithm capable of simultaneously estimating anisotropic elastic properties and crystallographic orientation of a specimen from a list of measured resonance frequencies collected via Resonance Ultrasound Spectroscopy (RUS). Unlike typical optimization procedures which yield point estimates of the unknown parameters, computing a Bayesian posterior yields probability distributions for the unknown parameters, and HMC is an efficient way to compute this posterior. The algorithms described are demonstrated on RUS data collected from two parallelepiped specimens of structural metal alloys.
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Ultrasonics
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Department of Physics and Astronomy, University of Hawaii-Manoa, Honolulu, HI 96822, United States.
Resonant ultrasound spectroscopy provides for an experimental determination of the elastic moduli of a solid sample. The moduli are extracted by matching a theoretically computed resonant spectrum to the experimental vibrational spectrum. To determine the pressure dependence of the moduli, the vibrational spectrum can be taken with the sample in a pressurizing gas.
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Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany.
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