Application Of Resonant Ultrasound Spectroscopy Research Articles

Elastic properties of single crystal Bi12SiO20 as a function of pressure and temperature and acoustic attenuation effects in Bi12MO20 (M = Si, Ge and Ti)

A comprehensive study of sillenite Bi12SiO20 single-crystal properties, including elastic stiffness and piezoelectric coefficients, dielectric permittivity, thermal expansion and molar heat capacity, is presented. Brillouin-interferometry measurements (up to 27 GPa), which were performed at high pressures for the first time, and ab initio calculations based on density functional theory (up to 50 GPa) show the stability of the sillenite structure in the investigated pressure range, in agreement with previous studies. Elastic stiffness coefficients c11 and c12 are found to increase continuously with pressure while c44 increases slightly for lower pressures and remains nearly constant above 15 GPa. Heat-capacity measurements were performed with a quasi-adiabatic calorimeter employing the relaxation method between 2 K and 395 K. No phase transition could be observed in this temperature interval. Standard molar entropy, enthalpy change and Debye temperature are extracted from the data. The results are found to be roughly half of the previous values reported in the literature. The discrepancy is attributed to the overestimation of the Debye temperature which was extracted from high-temperature data. Additionally, Debye temperatures obtained from mean sound velocities derived by Voigt-Reuss averaging are in agreement with our heat-capacity results. Finally, a complete set of electromechanical coefficients was deduced from the application of resonant ultrasound spectroscopy between 103 K and 733 K. No discontinuities in the temperature dependence of the coefficients are observed. High-temperature (up to 1100 K) resonant ultrasound spectra recorded for Bi12MO20 crystals revealed strong and reversible acoustic dissipation effects at 870 K, 960 K and 550 K for M = Si, Ge and Ti, respectively. Resonances with small contributions from the elastic shear stiffness c44 and the piezoelectric stress coefficient e123 are almost unaffected by this dissipation.

Application of resonant ultrasound spectroscopy to determine elastic constants of plasma-sprayed coatings with high internal friction

We present a novel modification of resonant ultrasound spectroscopy (RUS) for analysis of elastic constants of plasma-sprayed coatings in the ‘as sprayed’ state, i.e. without removing the substrate. This modification is suitable for coatings with high internal friction (Q−1≳10−2), which cannot be measured by RUS in the free-standing state due to strong damping. In combination with through-transmission measurements, this modification is able to provide full anisotropic tensor of elastic constants of the coating. As an illustrative example, the proposed methodology is applied to two steel coatings prepared by water-stabilized plasma (WSP) spraying. In addition to the moduli, also the internal friction parameters of the coatings are obtained. The results of RUS are compared to moduli determined by four-point bending tests, and it is shown that the anisotropic elasticity of both examined materials exhibits an elliptic form of transversal isotropy with four independent elastic coefficients.

Application of resonant ultrasound spectroscopy in diagnostics of rings

Resonant ultrasound spectroscopy (RUS) is a non-destructive technique originally developed for evaluating elastic constants of solids using resonance frequencies corresponding to the normal modes of vibration observed in samples with regular geometry. RUS can also be used for non-destructive evaluation of various metal or ceramic objects based on their resonance spectra. RUS can be used to detect deviations such as variations in dimensions and hardness or flaws in the inspected objects. This paper presents an application of RUS for monitoring the hardness of steel rings. Experimental results are presented that show a correlation between the shift of the resonant frequencies and the hardness of the inspected steel rings.

Elastic constants of chrome-diopside: application of resonant ultrasound spectroscopy to monoclinic single-crystals

The right-rectangular parallelepiped resonance (RPR) form of resonant ultrasound spectroscopy (RUS) is applied to monoclinic crystal symmetry to determine the 13 adiabatic elastic constants, C ij , of single-crystal chrome-diopside Di0.93Hd0.03Ur0.02 X 0.02 (Di, diopside; Hd, hedenbergite; Ur, ureyite; X, other or unknown). These data represent the first published values of the elastic tensor for a monoclinic single-crystal determined by the RPR method, thus demonstrating the feasibility of this method for studying elasticity of low-symmetry crystals. The lowest 62 modal frequencies of a gem-quality specimen were measured and identified at ambient temperature and pressure. Inverting the modal frequencies results in, respectively C 11, C 22, C 33, C 44, C 55, C 66, C 12, C 13, C 23, C 15, C 25, C 35, C 46 values (GPa) of 228.1(1.0), 181.1(0.6), 245.4(1.3), 78.9(0.3), 68.2(0.2), 78.1(0.2), 78.8(0.5), 70.2(0.7), 61.1(0.7), 7.9(0.5), 5.9(0.5), 39.7(0.4), and 6.4(0.2), where numbers in parentheses indicate experimental uncertainty. The corresponding isotropic bulk, K S , and shear, G, moduli are 116.5 (0.9) and 72.8(0.4) GPa, respectively. When comparing these results with other pyroxene data, we find systematic correlations between M2 site composition and C ij values for most, but not all, moduli. Unusual compositional dependence near end-member diopside is seen for a few moduli, and is propagated to the K S and G moduli, which should prompt a reexamination of some C ij values of end-member diopside.

Application of resonant ultrasound spectroscopy to geomaterials

Our objective is to apply resonant ultrasound spectroscopy (RUS) for obtaining the full elastic tensor of geomaterials. To our knowledge, RUS has never been successfully applied to complex materials such as rock: materials that are anisotropic and often inhomogeneous, and that contain grain-to-grain contacts, microcracks, etc. The fundamental problem with applying RUS to rock is high dissipation in the material, and the problem of coupling into all possible modes. The high dissipation limits the frequency band, and coupling into all modes controls the outcome of whether or not the full elastic tensor can be obtained. Our current experiment is operable in the frequency band of 3–30 kHz. Numerous sensor positions were tested in order to excite and detect different resonant modes. To date, the method has been applied to a rectangular brick sample. The comparison with theoretical calculation demonstrates that all modes (eigenfrequencies) of the sample were detected with high accuracy. Preliminary testing on cylindrical sandstone samples was also carried out. Duplicating the result from the brick in the rock sample is in progress. [This work is supported by the United States Industry Coalition, with the US DOE Contract W-7405-ENG-36, through the University of California.]

Cure monitoring of carbon epoxy composites: an application of resonant ultrasound spectroscopy

A novel method is applied to the monitoring of the degree of cure of a unidirectional panel of AS4/3501-6 carbon epoxy composite during cure. The composite panel to be cured is vacuum bagged on a steel caul plate. The resonance spectrum of the steel caul plate is measured periodically as the temperature is raised to the cure temperature and during the subsequent cure and cool-down periods. Because the curing composite acts to change the boundary conditions, the resonance spectrum changes as the composite cures. The spectrum at each temperature is compared with that obtained from the caul plate alone at the same temperature. Differences in amplitude, frequency and damping are related to the degree of cure of the composite.

Low temperature characterization of carbon epoxy composites: an application of resonant ultrasound spectroscopy

Abstract Resonant ultrasound spectroscopy is the study of spectra obtained by forced mechanical resonance of samples by swept frequency excitation. A novel apparatus is used to measure the amplitude/frequency resonance spectrum of a right rectangular parallelepiped specimen of AS4/3501-6 carbon epoxy composite material ([0, 60, 120] 192 lay-up) at 1 °C intervals between −177 °C and 25 °C. It is important to know the mechanical properties of this material at low temperatures for underwater, polar and space applications. The spectra indicate increasing stiffness with decreasing temperature and phase transitions. The damping decreases slightly with decreasing temperature. Analysis of the resonance spectrum, calculation of theoretical resonance spectrum, and computation of elastic stiffness tensor will be discussed.

Resonant ultrasound spectroscopy of single crystals

Electronics, transducer design, and computational procedures are described for the application of resonant ultrasound spectroscopy (RUS) to single crystal systems. The particular implementation of RUS described here can be used on samples without x-ray orientation of crystallographic axes and, because of the unique point-contact transducer design, works well from cryogenic temperatures to about 400 K. The power of the technique is illustrated with examples of studies on doped and stoichiometric single crystals and it is shown how the doped samples exhibit certain fundamental symmetry breaking effects only observable with RUS. [This work performed under the auspices of the U.S. Department of Energy.]

Application of resonant ultrasound spectroscopy to the study of small single crystal wafers

The study of acoustic waves in a solid can reveal many of its fundamental properties, such as the Debye temperature, the second derivatives of the free energy, and the strength of the electron–phonon coupling−but only if a specimen can be considered a single crystal with a minimum of defects and impurities. Such specimens tend to be extremely small and fragile, especially for newly discovered materials. Often, as the case with the high-temperature copper oxide superconductors, the samples can only be grown as wafers, typically 200×200×40 μm in size. These extremely small sizes and the ‘‘plate’’ proportions complicate the resonant ultrasound technique because stress on the sample from the transducers is more of a concern; second, only the ‘‘plate’’ modes, which have no dependence on the thin dimension, can be excited, and the overtones are widely spaced in frequency, so frequency-dependent mechanisms have to be considered; for example, measurements of the attenuation are of particular interest in high Tc materials. Applications to high Tc and TiB2 crystals will be discussed. [Work supported by NSF Grant No. DMR-9000549 and by the Office of Naval Research.]