Resonant Ultrasound Spectroscopy Research Articles

Stress-Induced Domain Wall Motion in a Ferroelastic Mn3+ Spin Crossover Complex.

Domain wall motion is detected for the first time during the transition to a ferroelastic and spin state ordered phase of a spin crossover complex. Single‐crystal X‐ray diffraction and resonant ultrasound spectroscopy (RUS) revealed two distinct symmetry‐breaking phase transitions in the mononuclear Mn3+ compound [Mn(3,5‐diBr‐sal2(323))]BPh4, 1. The first at 250 K, involves the space group change Cc→Pc and is thermodynamically continuous, while the second, Pc→P1 at 85 K, is discontinuous and related to spin crossover and spin state ordering. Stress‐induced domain wall mobility was interpreted on the basis of a steep increase in acoustic loss immediately below the the Pc‐P1 transition

Stress‐Induced Domain Wall Motion in a Ferroelastic Mn3+ Spin Crossover Complex

AbstractDomain wall motion is detected for the first time during the transition to a ferroelastic and spin state ordered phase of a spin crossover complex. Single‐crystal X‐ray diffraction and resonant ultrasound spectroscopy (RUS) revealed two distinct symmetry‐breaking phase transitions in the mononuclear Mn3+ compound [Mn(3,5‐diBr‐sal2(323))]BPh4, 1. The first at 250 K, involves the space group change Cc→Pc and is thermodynamically continuous, while the second, Pc→P1 at 85 K, is discontinuous and related to spin crossover and spin state ordering. Stress‐induced domain wall mobility was interpreted on the basis of a steep increase in acoustic loss immediately below the the Pc‐P1 transition

Anisotropic elastic properties of human cortical bone tissue inferred from inverse homogenization and resonant ultrasound spectroscopy

Bone extravascular matrix (EVM) elasticity at several tens micrometer scale plays a key role in the mechanical behavior of bone at different length scales with implications on bone biology through mechanotransduction. The elastic properties of cortical bone EVM have been evaluated by several experimental methods, including nanoindentation, scanning acoustic microscopy (SAM) and mechanical testing on µm sized bone specimens. Nevertheless, these methods hardly give access to elastic anisotropy. In this work, we propose a novel inverse homogenization method to evaluate the anisotropic elastic properties of cortical bone EVM based on the transverse isotropic elastic tensor of millimeter-sized bone specimens measured by using resonant ultrasound spectroscopy and Fast Fourier Transform homogenization method. With the inverse homogenization method, the anisotropic EVM stiffness constants were evaluated on 50 human femoral cortical bone specimens from an elderly group. To our knowledge, this is the first time that the whole set of the EVM stiffness tensor is evaluated on the same specimen and on a large number of samples. Further comparison with the results from SAM and the degree of mineralization of bone (DMB) showed the potential of this method. Empirical laws between DMB and EVM anisotropic stiffness constants were also provided for the first time. With the anisotropic elasticity evaluated by the proposed method, more accurate models can be developed to better understand bone mechanics and biology, such as mechanotransduction.

Elastic and thermal properties of W7Re13B and synthesis of a new ternary phase W1.3Re2.7B2

We synthesized phase pure samples of W7Re13B via arc-melting and subsequent annealing and a new compound W1.3(2)Re2.7(2)B2, which crystallizes in the Mg2Cu structure type. Based on pressure-dependent synchrotron X-ray diffraction (XRD), the bulk modulus of W7Re13B is B0,X−ray = 333(6) GPa. Resonant ultrasound spectroscopy was used to determine the elastic stiffness coefficients c11 = 507(3) GPa and c12 = 283(2) GPa and to derive B0,RUS = 358(2) GPa, c44 = 112(2) GPa, Young's modulus E = 672(7) GPa, shear modulus G = 112(2) GPa, a Poisson ration ν = 0.19 and a Debye temperature θD,elastic = 182(2) K. The linear coefficient of thermal expansion is α93K−773K = 5.5(2) 10−6 K−1 and was determined by dilatometry. Microhardness measurements at varying loads were employed to obtain the hardness, which is HV (W7Re13B) ≈ 19 GPa at high loads. Microcalorimetry gave Cp,298 (W7Re13B) = 517(10) J/mol, ΔH2980 (W7Re13B) = 109(2) kJ/mol, S2980 (W7Re13B) = 766(8) J/mol K and θD,298 (W7Re13B) = 259(3) K. The structure of W1.3Re2.7B2 was solved and refined by single-crystal X-ray diffraction. W1.3Re2.7B2 crystallizes in the orthorhombic space group Fddd with a = 4.5286(3) Å, b = 7.9660(5) Å, c = 15.632(2) Å and Z = 8. X-ray photoelectron spectroscopy and energy dispersive X-ray spectroscopy were employed to constrain the chemical composition. Microcalorimetry gave Cp,298 (W1.3Re2.7B2) = 132(1) J/mol, ΔH2980 (W1.3Re2.7B2) = 24.74(20) kJ/mol, S2980 (W1.3Re2.7B2) = 160(2) J/mol K and θD,298 (W1.3Re2.7B2) = 317(3) K. The bulk modulus of this phase from pressure-dependent diffraction studies up to 42 GPa is B0,X−ray (W1.3Re2.7B2) = 335(5) GPa. The data obtained here were used to evaluate models for predicting the hardness of materials, and we show that, for the compounds studied here, often used approaches are unsatisfactory.

Carbon deficiency-induced changes of structure and magnetism of Mn3SnC

Crystal structure, magnetoelastic coupling, magnetization and magnetocaloric effects of Mn3SnC0.94 and Mn3SnC0.81 were investigated. Temperature-dependent high-resolution X-ray diffraction measurements showed that a larger carbon deficiency of Mn3SnC0.81 reduces lattice distortions more significantly than it reduces the lattice parameter. Resonant ultrasound spectroscopy measurements showed that the larger carbon deficiency has no effect on the lattice stiffening across a ferromagnetic transition, whereas it reduces the lattice softening across a low-temperature transition. Magnetic measurements showed that the larger carbon deficiency doubles high-field magnetization and improves the refrigeration capacity. It is suggested that the larger carbon deficiency of Mn3SnC0.81 weakens antiferromagnetic interactions more significantly than it enhances ferromagnetic interactions. However, the magnetocaloric effect of each sample includes a contribution from the lattice entropy change, which is not sensitive to the carbon deficiency.

Characterization of bonding quality of a cold-sprayed deposit by laser resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy was utilized to determine the mechanical properties of a planar interface between a cold-sprayed iron deposit and an aluminum alloy substrate. The measurements were done at room temperature and with a thermal cycle from room temperature to 500 °C. The properties of the interface were assessed by analyzing the resonant frequencies of a sandwich-like sample by means of a numerical model. While the as-sprayed deposit at the room temperature exhibited a perfect adhesion to the substrate, the thermal cycle led to deterioration of the properties due to precipitation of FeAl3 along the interface and subsequent cracking. The modal analysis enabled localization of the damage zone along the interfaces and simulating its temperature evolution during the cooling run.

An ultrasonic study of relaxation processes in pure and mechanically alloyed tungsten

High-temperature internal friction in a pure tungsten single crystal, polycrystals with different grain sizes, and mechanically alloyed tungsten polycrystals was studied. Positron annihilation spectroscopy was used to prove that all studied materials contain a detectable amount of dislocations. Then, resonant ultrasound spectroscopy was applied to determine the internal friction evolution with temperature from room temperature up to 740 °C. For the pure tungsten samples, a sharp increase of internal friction was observed for temperatures above 470 °C (for the single crystal) or above 400 °C (for the polycrystals); the activation energy corresponding to this increase was the same as the activation energy for the ductile-to-brittle transition in tungsten reported in the literature. For the alloyed materials, direct observation of the onset of this relaxation mechanism was impossible due to additional effects resulting from the secondary phases in the material.

Switching the soft shearing mode orientation in Ni–Mn–Ga non-modulated martensite by Co and Cu doping

Resonant ultrasound spectroscopy measurements and density functional theory calculations were used to analyze the effect of Co and Cu doping (3–6 at. %) on elastic constants of non-modulated martensite of the Ni–Mn–Ga ferromagnetic shape memory alloy. Due to the doping, the studied alloys exhibited decreased tetragonal ratios c/a ≈ 1.14. Both the experiments and the calculations revealed that the lowering of the c/a ratio resulted in a change of the orientation of the softest shearing modes of the tetragonal lattice. The newly appearing softest shearing modes for the doped materials have approximately orientations and indicate a lattice instability directly related to the particularly low twinning stress for compound twins, needed for the magnetically induced reorientation.

One-component order parameter in URu2Si2 uncovered by resonant ultrasound spectroscopy and machine learning.

The unusual correlated state that emerges in URu2Si2 below T HO = 17.5 K is known as "hidden order" because even basic characteristics of the order parameter, such as its dimensionality (whether it has one component or two), are "hidden." We use resonant ultrasound spectroscopy to measure the symmetry-resolved elastic anomalies across T HO. We observe no anomalies in the shear elastic moduli, providing strong thermodynamic evidence for a one-component order parameter. We develop a machine learning framework that reaches this conclusion directly from the raw data, even in a crystal that is too small for traditional resonant ultrasound. Our result rules out a broad class of theories of hidden order based on two-component order parameters, and constrains the nature of the fluctuations from which unconventional superconductivity emerges at lower temperature. Our machine learning framework is a powerful new tool for classifying the ubiquitous competing orders in correlated electron systems.

AN ALTERNATIVE TO PERIODIC HOMOGENIZATION FOR DENTIN ELASTIC STIFFNESS

Dentin, the main tissue of the tooth, is made of tubules surrounded by peri-tubular dentin (PTD), embedded in a matrix of inter-tubular dentin (ITD). The PTD and the ITD have different relative fractions of collagen and hydroxyapatite crystals. The ITD is typically less rigid than the PTD, which can be seen as a set of parallel hollow cylindrical reinforcements in the ITD matrix. In this paper, we extend Hashin and Rozen’s homogenization scheme to a nonuniform distribution of hollow PTD cylinders, determined from image analysis. We relate the transverse isotropic elastic coefficients of a Representative Elementary Volume (REV) of dentin to the elastic and topological properties of PTD and ITD. The model is calibrated against experimental data. Each sample tested is consistently characterized by Environmental Scanning Electron Microscopy (ESEM), nanoindentation and Resonant Ultrasound Spectroscopy (RUS), which ensures that macroscopic mechanical properties measured are correlated with microstructure observations. Despite the high variability of microstructure descriptors and mechanical properties, statistical analyses show that Hashin’s bounds converge and that the proposed model can be used for back-calculating the microscopic Poisson’s ratios of dentin constituents. Three-point bending tests conducted in the laboratory were simulated with the Finite Element Method (FEM). Elements were assigned transverse isotropic elastic parameters calculated by homogenization. The tubule orientation and the pdf of the ratio inner/outer tubule radius were determined in several zones of the beams before testing. The remainder of the micro-mechanical parameters were taken equal to those calibrated by RUS. The horizontal strains found experimentally by Digital Image Correlation (DIC) were compared to those found by FEM. The DIC and FEM horizontal strain fields showed a very good agreement in trend and order of magnitude, which verifies the calibration of the homogenization model. By contrast with previous studies of dentin, we fully calibrated a closed form mechanical model against experimental data and we explained the testing procedures. In elastic conditions, the proposed homogenization scheme gives a better account of microstructure variability than micro–macro dentin models with periodic microstructure.

Cover Picture: Nonlinear Resonant Ultrasound Spectroscopy for Predicting Sensitivity to Initiation in Granular High Explosives (Prop., Explos., Pyrotech. 3/2020)

Cover Picture: Nonlinear Resonant Ultrasound Spectroscopy for Predicting Sensitivity to Initiation in Granular High Explosives (Prop., Explos., Pyrotech. 3/2020)

Investigation on the Crack Effect in the Cylinder and Matrix on the Backscattering Field Frequency Specifications using the Finite Element Method

A novel method to determine the health of the industrial parts is using the ultrasound scattering waves. Any changes in the structure of the scattering object or in the boundary conditions will cause a change in the scattering field. The frequency spectrum of the scattering time signal has valuable information, which is studied by resonant ultrasound spectroscopy (RUS). Since any defect, property changes, or changes in boundary conditions can affect the scattering field. Therefore, the possible defects in the piece are detected using the response of the scattering field. One possible defect in the fiber-reinforced composites is the existence of a crack in the matrix or fibers. In the present study, the effect of crack on the far-field backscattering amplitude spectrum is investigated using the finite element method (FEM). To this end, the effect of the crack’s direction in the cylinder and matrix on the form function is scrutinized. The results show that the Rayleigh frequency modes are more sensitive to the cracks existing in the epoxy matrix than the Whispering-gallery frequency modes. Also, the existence of the crack in the aluminum cylinder has the most effect on the Whispering-gallery frequency modes. Besides, the existence of a horizontal crack in the aluminum cylinder leads to a significant reduction in these frequency modes. The validation of the research is determined by comparing the steel cylinder form function obtained from the finite element method’s information and the analytical and experimental form functions in addition to the comparison of the aluminum cylinder form function and reference form function.

Estimation and Determination of Isotropic Elastic Constants in Resonant Ultrasound Spectroscopy

Accurate measurement of elastic constants in resonant ultrasound spectroscopy (RUS) depends on a perfect matching in the calculated and measured mode frequencies of free vibration of the solid specimen under study. Calculation of these frequencies requires estimated values of the elastic constants of the material. The present work proposes and demonstrates a method to derive initial guess values of the essential parameters for an isotropic and homogeneous material from the acquired RUS spectra itself. Specimen samples are prepared in the shape of rectangular parallelepiped having nearly same cross-sectional dimension but with different lengths. For particular compression (shear) mode corresponding to length l, the frequency f is inversely proportional to l. The slope m of f versus 1/l plot equals half of the compression (shear) velocity and this in turn gives an estimate of $$ c_{11} $$ ($$ c_{44} $$). With these parameters as the input guess parameters, RUS fitting method is executed to find out the best fit results. $$ c_{44} $$ obtained in this way is a good estimate close to its actual value. Further refinement of the parameter values is achieved by identifying volume oscillation mode frequencies for various sample lengths from the best fit frequency table of RUS output. The slope m of f versus 1/l plot for these modes corresponds to the bulk modulus (K). $$ c_{11} $$ calculated from K and $$ c_{44} $$ is a better estimate and a second step fitting method with these parameters as the input values gives final output values with improved accuracy. Elastic constants of commercially available specimens of aluminum, copper, lead, steel and brass are measured in this method assuming macroscopic homogeneity. Results are compared and found to be in good agreement with available literature values.

Large Non-ergodic Magnetoelastic Damping in Ni–Mn–Ga Austenite

Resonant ultrasound spectroscopy was used to analyze magnetoelastic damping in Ni–Mn–Ga single crystals in austenite and premartensite phases. Crystals with different treatment were studied, exhibiting different density of antiphase boundaries (APBs), as confirmed by magnetic force microscopy, and different magnetic behavior. For a quenched single crystal with high density of APBs, extremely strong damping was observed in a broad temperature range in the austenite phase. It was shown that this damping is history-dependent, i.e., non-ergodic, appearing only during heating runs preceded by a premartensite → austenite transition. We suggest that this non-ergodicity results from the pinning of the fine magnetic domain structure on APBs and other defects.

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.

Comparison of changes in nonclassical (α) and classical (β) acoustic nonlinear parameters due to thermal aging of 9Cr–1Mo ferritic martensitic steel

The objective of this research is to demonstrate the sensitivity of the hysteretic, nonclassical acoustic nonlinear parameter, α to track changes in the microstructure of 9Cr–1Mo ferritic martensitic steel due to thermal aging. The α parameter is measured with a non-contact nonlinear resonance ultrasound spectroscopy (NRUS) system with an air-coupled source and a laser Doppler vibrometer (LDV) receiver. This NRUS setup is used to track changes in multiple 9Cr–1Mo specimens subjected to different aging times at the same 650∘C temperature. These α results are shown to be highly sensitive to the associated changes in the microstructure of the 9Cr–1Mo specimens, and are then compared to three different parameters – Rockwell hardness, Young's modulus, E and the classical acoustic nonlinear parameter, β – all measured in the same specimens. These results are then combined to infer microstructure changes such as the removal of dislocations and the formation of carbide precipitates occurring in the 9Cr–1Mo specimens during thermal aging.

Elastic moduli of high-density, sintered monoliths of yttrium dihydride

Yttrium dihydride has been considered as potential nuclear reactor moderator for micro-reactors operating in the thermal energy spectrum due to their ability to retain hydrogen to high temperatures while having a relatively low impact on neutron economy. Despite these advantages, it is difficult to prepare yttrium dihydride in high-density, near net-shape monoliths for moderator applications due to volume expansion upon hydriding and the pyrophoric nature of the material. In this work, high-density monoliths of yttrium dihydride were prepared by direct hydriding and using powder metallurgical methods. Resonant ultrasound spectroscopy was used to measure the elastic moduli of the sintered monoliths, while nanoindentation was used to determine the Young’s modulus and hardness of the directly-hydrided yttrium and the sintered monoliths. Single crystal elastic constants and related properties of yttrium dihydride were also determined using density functional theory (DFT) for comparison. Mechanical properties of materials produced by both methods were observed to be consistent with the values from literature for yttrium dihydride. Due to the novelty of producing yttrium dihydride by powder metallurgy, this result indicated that the monoliths produced by powder metallurgy were of high quality. To that end, powder metallurgy is believed to be a viable method for large-scale production of yttrium dihydride monoliths for nuclear reactor moderator applications.

Particle Swarm Optimization-Based Identification of the Elastic Properties in Resonant Ultrasound Spectroscopy.

Resonant ultrasound spectroscopy (RUS) is an experimental measurement method for obtaining elastic constants of an anisotropic material from the free resonant frequencies of a sample. One key step of the method is to adjust elastic constants to minimize the difference between calculated and experimental frequencies. The method has been widely used in the determination of elastic constants of solid materials with high Q value, such that the resonant frequencies can be easily extracted from the measured spectrum. However, for materials with high damping, the identification of the resonant modes becomes difficult due to the overlap of resonant peaks and the absence of some modes. Thus, the success of RUS depends largely on initial guessing of elastic constants. In this article, these limitations are addressed with a new RUS approach. First, the identification of resonant modes is transformed into a linear assignment problem solved by the Hungarian algorithm. Second, the inversion of the elastic tensor is achieved using the particle swarm optimization (PSO) algorithm. This method, having the ability of global optimization in the search space, is less sensitive to the initial guess of the elastic constants. The PSO algorithm was successfully applied for the first time to RUS data, providing estimates of elastic constants that were in good agreement with reference values. First, simulated data for a transversely isotropic sample of enamel of rectangular parallelepiped shape were used to validate the proposed RUS method. Second, the proposed RUS approach was validated using experimental data collected on a sample of transversally isotropic bone-mimicking material.

Thermal damage evaluation in nickel plate by nonlinear electromagnetic acoustic resonance technique

Nickel and nickel-based composites are of vital importance in many fields, while temperature loading can greatly influence the strength and performance of the materials. Nondestructive evaluation and characterization of such thermal damage can be used to predict the failure of metallic structures, thermal barrier coatings and so on, especially in a non-contact way under certain strict circumstances, such as testing at high temperature or in radiative environment. Herein, a contactless ultrasonic technique employing electromagnetic acoustic transducers (EMATs) combined with the resonance ultrasound spectroscopy is applied to make up the low energy transition efficiency of EMATs and enhance the signal-to-noise ratio of ultrasonic testing signals. The method is adopted to assess the thermal damages of different levels in artificially heat loaded nickel plates. The damage sensitivity of third order harmonics generated from shear waves is discussed, along with linear ultrasonic features including wave velocity and attenuation. Experimental results show that the proposed nonlinear electromagnetic acoustic resonance (EMAR) technique can be used to evaluate the thermal damage in ferromagnetic material with improved reliability and sensitivity over linear ones.

In-situ characterization of growth of isothermal ω phase in metastable β-Ti alloy TIMETAL LCB

Metastable β-Ti alloys exhibit various solid-solid phase transitions. Our study is focused on the characterization of the diffusion controlled β→ωiso phase transition. The particles of ω phase play an important part in thermomechanical treatment since they serve as heterogeneous nucleation sites for precipitation of finely dispersed particles of hexagonal α phase. The in-situ observation of the growth of particles of ω phase could be difficult by conventional techniques. However, it was shown recently that the ω phase significantly influences the elastic constants of the material, and the different forms of ω phase have different effects on the elastic anisotropy, as well as on the internal friction coefficients. Therefore, the β→ω phase transformation could be in-situ observed by the precise measurement of the tensor of elastic constants. In this contribution, we present the study of the kinetics of the β→ωiso phase transformation by resonant ultrasound spectroscopy. The polycrystalline samples of TIMETAL LCB alloy were in-situ examined by this technique during isothermal and non-isothermal ageing at temperatures up to 300 °C.