Resonant Ultrasound Spectroscopy Research Articles

High temperature mechanical properties of fluorite crystal structured materials (CeO2, ThO2, and UO2) and advanced accident tolerant fuels (U3Si2, UN, and UB2)

The mechanical interaction between the fuel and cladding that occurs during operation of a nuclear reactor is important to understand as it can lead to cladding failures and release of radioactive material into the coolant. In order to develop better models of the pellet-clad mechanical interactions , the mechanical properties of the fuel at relevant operating temperatures, like the elastic moduli, are needed for current and advanced accident tolerant fuels (ATFs). In this work, elevated temperature nanoindentation and resonant ultrasound spectroscopy were used to measure the moduli and hardness of several fluorite materials (CeO 2 , ThO 2 , UO 2 ) and several ATF candidates (ATF) (U 3 Si 2 , UN, UB 2 ). In addition, a comparison of the two techniques was performed in this study to independently validate the mechanical properties.

Variations of Classical and Nonclassical Ultrasound Nonlinearity Parameters during Heat-Induced Microstructural Evolution in an Iron-Copper Alloy

This research demonstrates and compares the potential of two nonlinear ultrasound techniques, second harmonic generation (SHG) and nonlinear resonant ultrasound spectroscopy (NRUS). This research examines a set of thermally aged iron-copper (Fe-1.0% Cu) alloy specimens, which are used as surrogate specimens for radiation damage. It is found that both SHG and NRUS are sensitive to the growth of the copper precipitates, while the changes in the respective nonlinearity parameters are due to different mechanisms. This research demonstrates the potential use of both of these nonlinear ultrasound techniques.

Full Set of Material Properties of Lead-Free PIC 700 for Transducer Designers.

The impact of Pb on the environment and human health and recent restrictions on its use in electronic devices are generating demand for Pb-free piezoelectric materials. Examples are now available commercially, but the full elastic-piezoelectric-dielectric (EPD) matrices needed for device design, including over a range of operating conditions, have not yet been published. The standard IEEE EPD matrix measurement method needs four sample geometries, making it inconvenient and increasing errors. Here, we present an alternative method combining resonant ultrasound spectroscopy with optimization algorithms to measure the EPD matrix from a single exact cube sample. The Levenberg-Marquardt (LM) and Nelder-Mead (NM) optimizations are compared in refining the independent parameters. Both give convergent solutions, but the LM algorithm is more accurate and efficient. The single-sample approach was used to obtain results from Pb-free Na1/2Bi1/2TiO3 (PIC 700, PI Ceramics, Lederhose, Germany) piezoceramic ( ∞ mm sample symmetry) characterized with the standard IEEE method at ambient temperature and with the single-sample method at ambient temperature and additionally up to 80 °C. The results are validated with the laser Doppler vibrometry via mode shape reconstruction and comparison with finite-element analysis (FEA). They demonstrate that convenient measurement of the EPD matrix of Pb-free materials with temperature dependence is possible, providing a crucial capability for the adoption of these materials in devices.

A new elastic characterization method for anisotropic bilayer specimens via Bayesian resonant ultrasound spectroscopy

A novel nondestructive method for complete elastic characterization of substrate-coating bilayer specimens with distinct anisotropic layers via resonant ultrasound spectroscopy (RUS) and Bayesian inversion is developed here. Bayesian formulations of the RUS inversion problem—of quantifying elastic properties given a measured list of resonance frequencies recorded from a single, typically small, precisely fabricated, macroscopically homogeneous, linear-elastic specimen—are a recent development. Here we report the first Bayesian formulation of the bilayer problem, and through a series of practical examples, demonstrate novel parameter estimation capabilities of our open-source CmdStan-RUS code. Finding specimen geometry and the number of resonance modes used for inversion strongly govern the ability to retrieve individual elastic moduli. The concept of “invertability” is explored for a range of relevant geometries using virtual specimens that resemble experimental bilayers of plasma sprayed ceramic coatings on single crystal metallic substrates. A range of Bayesian posterior evaluation methods are addressed, particularly considering the large computational cost of the bilayer forward model. Laplace approximation methods are thus developed and implemented for bilayer geometry design space modeling and expedient estimates of parameter uncertainties. Ideal specimen design, different noise models, the influence of prior distributions, dual-likelihood fits incorporating measurements of the bare substrate, and how Bayesian RUS methods differ from traditional RUS optimization are discussed.

Single-crystal elastic and thermodynamic properties of γ-LiAlO2

The elastic properties of γ-LiAlO2 were reinvestigated with the aid of resonant ultrasound spectroscopy (RUS) at ambient conditions. A strong discrepancy of the elastic coefficients derived by RUS can be found from the experimental results from the literature, where c12 and c13 deviate from our results by up to 60% (46 GPa). In contrast to the experimental cij from the literature, we can recognize a good agreement between the elastic coefficients derived from RUS and the values using density functional theory. The dielectric permittivity was measured on large plane-parallel plates, and the piezoelectric stress coefficient e123=0.14Cm−2 was derived from RUS measurements at ambient conditions. The heat capacity between 4 and 398 K has been obtained by microcalorimetry using a relaxation calorimeter. The Debye temperature was derived from heat capacity measurements (ΘCp=676 K) and RUS measurements (Θelastic=688 K).

Determining the full elastic tensor using resonant ultrasound spectroscopy in extreme environments

Elastic moduli are fundamental thermodynamic susceptibilities that connect directly to thermodynamics, electronic structure and mechanic properties. Thus, determining the changes of elastic moduli as a function of time and temperature is a powerful tool to study a variety of phenomena. The Resonant Ultrasound Spectroscopy (RUS) technique is based on the measurement of mechanical resonance frequencies that can be made with extreme precision and used to compute the elastic moduli without corrections. In this talk, I will give show several examples of the use of RUS in different systems, ranging from magnetic phase transition, determining very small degrees of elastic anisotropy in metals as well as changes in time product of radioactive decay. I will discuss the latest advances made at Los Alamos on measuring and determination of elastic constants. This allow to track the resonance position with high precision, obtaining moduli with an absolute precision of 0.5% and relative changes smaller than part per 10 million.

In situ resonant ultrasound spectroscopy for neutron scattering

Resonant ultrasound spectroscopy (RUS) is an efficient nondestructive technique to study the elastic properties of solid materials. In principle, the full elastic tensor can be determined for regularly shaped solids (e.g., sphere, cuboid, cylinder). Here, we report our progress in developing RUS probes for in situ neutron scattering at beamlines of the Spallation Neutron Source at Oak Ridge National Laboratory. A low-temperature (2–300 K) probe has been assembled and tested at the NOMAD and SEQUOIA beamlines to assess the probe’s neutronics, data acquisition system, and compatibility with the existing sample environment. Our discussion will include how the probe and data acquisition system operate as well as results for two measurements: bulk metallic glass (La65Cu20Al10Co5) and bismuth-antimony (Bi0.89Sb0.11 [1]). Assembly of a high-temperature (300–875 K) probe is currently underway and both probes are scheduled to be available to users by late-2021. Our aim is to provide users with live monitoring of an intrinsic variable at the neutron scattering beamlines, in addition to existing controls, to monitor the state of their samples and make informed decisions in real time. The probe developments are accompanied by developments of data acquisition and analysis software. 1. D. Vu et al., arXiv: 1906.02248 [cond-mat.mtrl-sci] (2019).

Ultrasonic Characterization of Nanoparticle-Based Ceramics Fabricated by Spark-Plasma Sintering

Resonant ultrasound spectroscopy was used to determine elastic constants and internal friction parameters of bulk nanoparticle-based ceramic materials compacted by spark plasma sintering. Boron nitride-based and boron carbon nitride-based materials were studied, and the results were compared with similar bulk materials prepared from graphene nanoplatelets. The results showed that such nanoparticle-based materials can be strongly anisotropic, and can have very different elastic constants depending on the nanoparticles used. From the temperature dependence of the internal friction parameters, the activation energy for sliding of the individual monolayers along each other was determined for each material. Very similar values of the activation energy were obtained for boron nitride, boron carbon nitride, and graphene, ranging from 15 to 17 kJ/mol.

Strain relaxation dynamics of multiferroic orthorhombic manganites

Resonant ultrasound spectroscopy has been used to characterise strain coupling and relaxation behavior associated with magnetic/magnetoelectric phase transitions in GdMnO3, TbMnO3 and TbMn0.98Fe0.02O3 through their influence on elastic/anelastic properties. Acoustic attenuation ahead of the paramagnetic to colinear-sinusoidal incommensurate antiferromagnetic transition at ∼41 K correlates with anomalies in dielectric properties and is interpreted in terms of Debye-like freezing processes. A loss peak at ∼150 K is related to a steep increase in electrical conductivity with a polaron mechanism. The activation energy, E a, of ≳0.04 eV from a loss peak at ∼80 K is consistent with the existence of a well-defined temperature interval in which the paramagnetic structure is stabilised by local, dynamic correlations of electric and magnetic polarisation that couple with strain and have relaxation times in the vicinity of ∼10−6 s. Comparison with previously published data for Sm0.6Y0.4MnO3 confirms that this pattern may be typical for multiferroic orthorhombic RMnO3 perovskites (R = Gd, Tb, Dy). A frequency-dependent loss peak near 10 K observed for TbMnO3 and TbMn0.98Fe0.02O3, but not for GdMnO3, yielded E a ⩾ ∼0.002 eV and is interpreted as freezing of some magnetoelastic component of the cycloid structure. Small anomalies in elastic properties associated with the incommensurate and cycloidal magnetic transitions confirm results from thermal expansion data that the magnetic order parameters have weak but significant coupling with strain. Even at strain magnitudes of ∼0.1–1‰, polaron-like strain effects are clearly important in defining the development and evolution of magnetoelectric properties in these materials. Strains associated with the cubic–orthorhombic transition due to the combined Jahn–Teller/octahedral tilting transition in the vicinity of 1500 K are 2–3 orders of magnitude greater. It is inevitable that ferroelastic twin walls due to this transition would have significantly different magnetoelectric properties from homogeneous domains due to magnetoelastic coupling with steep strain gradients.

Rejuvenation of Directionally Solidified and Single-Crystal Nickel-Base Superalloys

During service, superalloy turbine components degrade over time by creep and fatigue deformation mechanisms due to a complex combination of stresses at high temperatures. The high cost of fabricating Ni-base superalloy components and, consequently, replacement components has encouraged the development of rejuvenation (restoration) procedures to extend useful service life. The processes that limit repeated rejuvenation of directionally solidified GTD444 and single-crystal Rene N5(SX) alloys have been studied in detail. A rejuvenation cycle includes a rejuvenation heat treatment and/or small-scale material removal, followed by creep or fatigue testing. With the application of multiple rejuvenation cycles, the total creep rupture life of Rene N5(SX) tested at 982 °C and 206 MPa was extended by a factor of 2.8 over the baseline rupture life. To produce this increase in rupture life, creep strains were limited to 2 or 3 pct prior to application of a rejuvenation cycle, involving solutioning at 28 °C below the $$\gamma ^{\prime }$$ solvus temperature for 2 hours and aging at 1079 °C for 4 hours. Rejuvenation of compressive hold-time fatigue damage was also successful with the use of small-scale material removal. Due to the tortuosity of the grain boundaries in GTD444(DS), some boundaries are initially oriented transverse to the growth direction. The enhanced plasticity near these grain boundaries may be the primary reason why the initially single-crystal Rene N5(SX) specimens were more amenable to rejuvenation than GTD444(DS). For both alloys, recrystallization after multiple rejuvenation cycles was responsible for early failure during the subsequent creep test. Resonant ultrasound spectroscopy was successfully implemented to detect the presence of recrystallized grains.

Determining material properties of components with complex shapes using Resonant Ultrasound Spectroscopy

In this paper, Resonance Ultrasound Spectroscopy (RUS) is used to invert the elastic properties of components with complex shapes from a limited selection of mode matched frequencies. RUS is based on the unique relationship between the vibrational resonance response (resonance frequencies and mode shapes) of a component and its set of material properties, geometry, and boundary conditions. The study is conducted on 3 nominally identical components that have geometric imperfections due to the manufacturing process. The study reveals that an accurate characterization of the shape is critical to the success of the RUS process. The RUS process presented in this paper also relies on matching measured and computed vibrational mode shapes, in addition to the resonance frequencies. This strategy enables using high-order modes with complex modal information, in a frequency range with high modal density where modal identification based on the resonance frequencies alone would be challenging. This approach contrasts with the traditional approach of matching a number of resonance frequencies in sequential order. With the proposed approach, the elastic constants for the three components are similar, consistent with values found in the literature, and lead to small error of the RUS inversion, despite variations in the shapes and the resulting changes in the resonance response of the components.

Refractive index gas thermometry between 13.8 K and 161.4 K

We have measured the refractive index of helium using a quasi-spherical copper microwave resonator at five different temperatures in the interval between the triple point of hydrogen at 13.8 K and the triple point of xenon at 161.4 K for pressures up to 380 kPa. From these results and additional measurements of the refractive index of neon near 54.4 K, 83.8 K and 161.4 K we determine the differences (T − T 90) between the thermodynamic temperature T and its approximation T 90 by the International Temperature Scale of 1990 (ITS-90). We have estimated the isothermal compressibility of copper and the effective compressibility of our microwave resonator by different methods including resonant ultrasound spectroscopy (RUS) and microwave measurements with helium at 273.16 K. We compare the results of these compressibility estimates and discuss the associated uncertainty. From the refractive index measurements, we estimate the second density virial coefficient of helium and neon which are found in good agreement with the ab initio calculations of the same properties.

Thermoelastic properties of zircon: Implications for geothermobarometry

Abstract A thermal-pressure equation of state has been determined for zircon (ZrSiO4) that characterizes its thermoelastic behavior at metamorphic conditions. New pressure-volume (P-V) data from a “Mud Tank” zircon have been collected from 1 bar to 8.47(1) GPa using X-ray diffraction, and elastic moduli were measured from room temperature up to 1172 K by resonance ultrasound spectroscopy. These data were fitted simultaneously with temperature-volume (T-V) data from the literature in EosFit7c using a new scaling technique. The parameters of a third-order Birch-Murnaghan EoS with a Mie-Grüneisen-Debye model for thermal pressure have compressional EoS parameters K0T = 224.5(1.2) GPa, K0T′ = 4.90(31) with a fixed initial molar volume V0 = 39.26 cm3/mol and thermal parameters γ0 = 0.868(15), q = 2.37(80), and ΘD = 848(38) K. EoS parameters that describe the variation of unit-cell parameters with pressure and temperature were determined using an isothermal-type EoS. This new EoS confirms that zircons are stiffer than garnets and exhibit a much lower thermal expansion. This results in steep isomekes between zircon and garnets, which makes zircon trapped as inclusions in garnets at metamorphic conditions a good piezothermometer.

Determining elastic anisotropy of textured polycrystals using resonant ultrasound spectroscopy

Polycrystalline materials can have complex anisotropic properties depending on their crystallographic texture and crystal structure. In this study, we use resonant ultrasound spectroscopy (RUS) to nondestructively quantify the elastic anisotropy in extruded aluminum alloy 1100-O, an inherently low-anisotropy material. Further, we show that RUS can be used to indirectly provide a description of the material’s texture, which in the present case is found to be transversely isotropic. By determining the entire elastic tensor, we can identify the level and orientation of the anisotropy originated during extrusion. The relative anisotropy of the compressive (c11/c33) and shear (c44/c66) elastic constants is 1.5% ± 0.5% and 5.7% ± 0.5%, respectively, where the elastic constants (five independent elastic constants for transversely isotropic) are those associated with the extrusion axis that defines the symmetry of the texture. These results indicate that the texture is expected to have transversely isotropic symmetry. This finding is confirmed by two additional approaches. First, we confirm elastic constants and the degree of elastic anisotropy by direct sound velocity measurements using ultrasonic pulse echo. Second, neutron diffraction (ND) data confirm the symmetry of the bulk texture consistent with extrusion-induced anisotropy, and polycrystal elasticity simulations using the elastic self-consistent model with input from ND textures and aluminum single-crystal elastic constants render similar levels of polycrystal elastic anisotropy to those measured by RUS. We demonstrate the ability of RUS to detect texture-induced anisotropy in inherently low-anisotropy materials. Therefore, as many other common materials have intrinsically higher elastic anisotropy, this technique should be applicable for similar levels of texture, providing an efficient general diagnostic and characterization tool.

Anisotropic elasticity drives negative thermal expansion in monocrystalline SnSe

Negative thermal expansion (NTE) materials have been at the center of attention for the past few decades as thermal expansion compensators in the fields of engineering, photonics, electronics, and medicine. Numerous crystalline materials exhibit NTE, wherein a combination of positive and negative linear thermal expansion coefficients results from their highly anisotropic elasticity. In this study, we selected SnSe, an anisotropic uniaxial NTE material as a model system where theoretical studies have linked its NTE along the $c$ direction to transverse phonons and to positive Gr\uneisen parameters along all crystallographic axes. However, the fundamental origin of NTE in SnSe have not been experimentally resolved. Here we performed temperature-dependent resonant ultrasound spectroscopy (between 295--773 K) on single-crystalline SnSe to experimentally measure all nine independent elastic constants (${C}_{11}, {C}_{22}, {C}_{33}, {C}_{44}, {C}_{55}, {C}_{66}, {C}_{12}, {C}_{13}, {C}_{23}$). Our data revealed a high degree of anisotropy in the temperature-dependent elastic constants with shear anisotropic factors show a contrasting pattern with increasing temperature. From this data we also deduced its material compressibility and negative Poisson's ratios in the major crystallographic directions that could explain its colossal linear thermal expansion coefficient along the $c$ direction, reaching $\ensuremath{\sim}--12\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at 773 K as reported in this study. Furthermore, we confirmed positive Gr\uneisen parameters along all the crystallographic axes and observe that SnSe behaves like a semicompressible parallelepiped with elastically coupled $a$ and $b$ axes, with the NTE being driven by the displacement of Sn atoms in the $c$ direction.

Cortical bone viscoelastic damping assessed with resonant ultrasound spectroscopy reflects porosity and mineral content

Viscoelasticity is an essential property of bone related to fragility, which is altered in aging and bone disease. Bone viscoelastic behavior is attributed to several mechanisms involving collagen and mineral properties, porosities, and bone hierarchical tissue organization. We aimed to assess the relationships between cortical bone viscoelastic damping measured with Resonant Ultrasound Spectroscopy (RUS), microstructural and compositional characteristics. We measured 52 bone specimens from the femur of 26 elderly human donors. RUS provided a shear damping coefficient at a frequency of the order of 150 kHz. The characteristics of the structure of the vascular pore network and tissue mineral density were measured using synchrotron radiation high-resolution computed tomography (SR-μCT). Fourier transformed infrared microspectroscopy (FTIRM) was used to quantify mineral-to-organic phase ratio, mineral maturity, crystallinity, and collagen maturity. Cross-links were quantified from biochemistry. Viscoelastic damping was found to increase with vascular porosity (r=0.68), to decrease with the degree of mineralization of the extravascular matrix (r=−0.68), and was marginally affected by collagen. We built a multilinear model suggesting that when porosity is controlled, the variation of mineral content explains a small additional part of the variability of damping. The work supports the consideration of viscoelasticity measurement as a potential biomarker of fragility and provides a documentation of bone viscoelastic behavior and its determinants in a frequency range rarely investigated.

Elastic and thermodynamic properties of cerium‐doped yttrium aluminum garnets

AbstractCerium‐doped yttrium aluminum garnets (Y3‐xCexAl5O12, Ce:YAGs) are promising yellow light‐emitting components of solid‐state white light‐emitting diodes. Although there have been numerous studies examining the effects of Ce concentrations on the luminescent properties of Y3‐xCexAl5O12, the impacts of Ce dopant on the elastic and thermodynamic properties are not well understood. In this work, we used resonant ultrasound spectroscopy (RUS) to determine the effects of Ce doping (0.025, 0.1, 1 at. %) on the elastic and thermodynamic properties of Y3‐xCexAl5O12. The elastic moduli calculated via the Voigt–Reuss–Hill (VRH) method demonstrated that low Ce dopant concentrations (≤0.1 at. %) induced negligible effects on the elasticity of the YAG host matrix, while a high Ce concentration (1 at. %) yielded significant softening. RUS spectral analysis and SEM images suggested that the elastic softening originated from microstructural differences induced at higher Ce dopant concentrations. In addition, we demonstrated an increase in elastic anisotropy at higher Ce concentrations, which further elucidated the correlations between structure and elasticity of Y3‐xCexAl5O12. Debye temperatures (θD), heat capacities (Cp), and thermal conductivities (κ) were calculated for Ce:YAGs through the relations of RUS‐derived parameters (sound velocities, elastic moduli) and previously determined thermal expansion coefficients. Ce:YAG was found to have a significant reduction in θD, Cp, and κ at Ce concentrations ≥1 at. %. Lastly, extrapolation of Cp and κ to higher temperatures allowed the modeling of thermal stress experienced by Y3‐xCexAl5O12 disks up to 1073.15 K.

Thermoelastic properties and \u03b3\u2019-solvus temperatures of single-crystal Ni-base superalloys

The present work shows that thermal expansion experiments can be used to measure the γʼ-solvus temperatures of four Ni-base single-crystal superalloys (SX), one with Re and three Re-free variants. In the case of CMSX-4, experimental results are in good agreement with numerical thermodynamic results obtained using ThermoCalc. For three experimental Re-free alloys, the experimental and calculated results are close. Transmission electron microscopy shows that the chemical compositions of the γ- and the γʼ-phases can be reasonably well predicted. We also use resonant ultrasound spectroscopy (RUS) to show how elastic coefficients depend on chemical composition and temperature. The results are discussed in the light of previous results reported in the literature. Areas in need of further work are highlighted.Graphical abstract

A non-destructive resonant acoustic testing and defect classification of additively manufactured lattice structures

Additive manufacturing enables the fabrication of lattice structures which are of particular interest to fabricate medical implants and lightweight aerospace parts. Product integrity is critical in these applications. This requests very challenging quality control for such complex geometries, particularly on detecting internal defects. It is important not only to detect whether there are missing struts for a product with a large size of lattices, but also to identify the number of missing struts for safety-critical applications. Resonant ultrasound spectroscopy is a promising method for fast and cost-effective non-destructive testing of complex geometries but data analytics methods are needed to systematically analyze resonant ultrasound signals for defect identification and classification. This study utilizes resonant acoustic method to obtain resonant frequency spectrum of test lattice structures. In addition, regularized linear discriminant analysis, combined with adaptive sampling and normalization, is developed to classify the number of missing struts. The result shows 80.95% testing accuracy on validation study, which suggests that the resonant acoustic method combined with machine learning is a powerful tool to inspect lattices.

2Pa1-2 Anelastic properties of gallium nitride studied by resonant ultrasound spectroscopy at elevated temperatures

2Pa1-2 Anelastic properties of gallium nitride studied by resonant ultrasound spectroscopy at elevated temperatures