Resonant Ultrasound Spectroscopy Research Articles

The effects of Fe and Al on the phase transformations and mechanical behavior of β-Ti alloy Ti-11at.%Cr

Alloy composition is important for developing desired microstructures in beta-titanium (β-Ti) alloys during thermomechanical processing. In this work, the relatively low-cost alloying elements iron (Fe) and aluminum (Al) were added to a base Ti-11at.%chromium (Cr) alloy and in-situ and ex-situ examination of the microstructural evolution and mechanical properties during tension, hardness, elevated temperature X-ray diffraction (XRD) and resonance ultrasound spectroscopy (RUS) were performed. The 400 °C XRD revealed that Ti-11at.%Cr underwent β-to-ω and β-to-α transformations. Adding 0.85 at.% Fe reduced the volume fraction of the ω- and α-phases, and adding 5.3 at.% Al inhibited the β-to-ω transformation. The 400 °C RUS showed that the alloys containing the ω phase exhibited an increase in shear modulus of ∼140%, while the ω-free alloys exhibited an increase of only ∼102%. The hardness and strength values of the ω-containing Ti–11Cr and Ti–11Cr-0.85Fe increased with increased ω-phase volume fraction when the ω/α ratio was greater than 0.25. The relationship between ω/α volume fraction ratio and mechanical properties is discussed.

Nonlinear/linear resonance ultrasound spectroscopy (N/RUS) of additively manufactured 316L stainless steel samples using in-contact and non-contact excitation

Due to their sensitivities to defects and microstructural changes, the linear and nonlinear parameters measured with nonlinear resonance ultrasound spectroscopy (NRUS) have the potential to evaluate the quality of additively manufactured parts. Here, NRUS with in-contact and non-contact excitation configurations is used to test a set of 316L stainless steel samples manufactured by laser powder bed fusion. Subgroups of the samples are heat treated to three temperatures to alter the samples' microstructure and mechanical performance. Results show that the hysteretic nonlinearity parameter measured with in-contact NRUS demonstrates sensitivity to heat-treatment-induced microstructural changes. However, due to the unwanted nonlinearity introduced by the bonding, variations in the repeated in-contact measurements of a single sample are almost as large as the differences between the heat treatment subgroups. The non-contact configuration allows measurement of two linear parameters (resonance frequency and damping) with exceptional repeatability, and results show clear distinction between samples in different heat treatment groups. The non-contact NRUS configuration could not produce a sufficient dynamic strain amplitude to allow a reliable measurement of the samples’ nonlinear response. In-contact and non-contact NRUS results are analyzed in relation to independently measured mechanical properties and microstructural information to investigate the feasibility of NRUS for the nondestructive evaluation of additively manufactured metals.

Asymptotic behavior of resonant frequencies in resonant ultrasound spectroscopy.

Resonance ultrasound spectroscopy is a non-destructive technique used to assess materials' elastic and anelastic properties. It involves measuring the frequencies of free vibrations in a carefully prepared sample to extract material properties. In this paper, we investigate the asymptotic behavior of eigenfrequencies. Our primary focus is on analyzing the asymptotic behavior of eigenfrequencies, aiming to understand their rate of growth and convergence. We also make observations regarding the impact of elastic constants on eigenfrequencies.

Implementation of Non Destructive Testing and in-line monitoring techniques on extra-large structures printed with WAAM technology

Grade2XL is a European project funded by the H2020 program that gathers 21 academic and industrial partners. Started in March 2020 for 4 years, the principal objective is to print extra-large structures using the WAAM (Wire Arc Additive Manufacturing) method with a complete control of the fabrication process. Since WAAM is a relatively new technology for printing large specimens, it is important to develop quality assurance methods that can be used during the fabrication and once the structure has been built, which is the focus of CEA List in the project. Regarding methods applied built structures, CEA List has investigated Resonant Ultrasound Spectroscopy (RUS) for the material characterization and more specifically the evaluation of the elastic constants or more conventional ones for the inspection with phased-array ultrasonic techniques (PAUT) or eddy current (EC) for the detection of indications are implemented and optimised them for the inspection of the final structures. Concerning the development of in-line monitoring methods, CEA List has been working on laser Doppler vibrometry (LDV) and X-ray fluorescence (XRF) spectrometry, in order to get structural information during the printing but also detect the appearance of abnormal events and correlate them to the appearance of defects generated during the WAAM process. This proceeding presents the advantages of those methods for the inspection of extra-large structures made by WAAM and discusses the first results obtained in the framework of the project. Keywords: Additive Manufacturing, NDT, Imaging techniques, Eddy current, In-line monitoring, laser vibrometry, X-ray fluorescence spectrometry, Resonant Ultrasound Spectroscopy.

Multiscale static and dynamic mechanical study of the Turritella terebra and Turritellinella tricarinata seashells.

Marine shells are designed by nature to ensure mechanical protection from predators and shelter for molluscs living inside them. A large amount of work has been done to study the multiscale mechanical properties of their complex microstructure and to draw inspiration for the design of impact-resistant biomimetic materials. Less is known regarding the dynamic behaviour related to their structure at multiple scales. Here, we present a combined experimental and numerical study of the shells of two different species of gastropod sea snail belonging to the Turritellidae family, featuring a peculiar helicoconic shape with hierarchical spiral elements. The proposed procedure involves the use of micro-computed tomography scans for the accurate determination of geometry, atomic force microscopy and nanoindentation to evaluate local mechanical properties, surface morphology and heterogeneity, as well as resonant ultrasound spectroscopy coupled with finite element analysis simulations to determine global modal behaviour. Results indicate that the specific features of the considered shells, in particular their helicoconic and hierarchical structure, can also be linked to their vibration attenuation behaviour. Moreover, the proposed investigation method can be extended to the study of other natural systems, to determine their structure-related dynamic properties, ultimately aiding the design of bioinspired metamaterials and of structures with advanced vibration control.

Resonant ultrasound spectroscopy measurement and modeling of additively manufactured octet truss lattice cubes

In this work, the elastic characteristics of additively manufactured Ti-5553 octet truss lattice cubes were examined using resonant ultrasound spectroscopy (RUS) techniques and correlated to X-ray computed tomography measurements of strut continuity. RUS models and measurements identified an outlier lattice possessing lower effective modulus despite larger effective density. Experimental measurements of density and effective Young's modulus were treated as input parameters in a homogenous anisotropic continuum model. The continuum model exhibited good agreement with experimental RUS measurements, thus confirming the potential for a simplified approximation of the octet truss lattice.

Employment of Fracture Mechanics Criteria for Accurate Assessment of the Full Set of Elastic Constants of Orthorhombic/Tetragonal Mono-Crystalline YBCO

The effect of elastic constants, cij, on the nature (easy or difficult) of a cleavage system in mono-crystalline YBa2Cu3O7−δ is investigated by employing a novel three-dimensional eigenfunction expansion technique, based in part on the separation of the thickness variable and partly on a modified Frobenius-type series expansion technique in conjunction with Eshelby–Stroh formalism. Out of the three available, complete sets of elastic constants, only the experimental measurements using resonant ultrasound spectroscopy merit serious attention, despite reported values of c12 and, to a lesser extent, c66 being excessively high. The present investigation considers six through-thickness crack systems weakening orthorhombic mono-crystalline Yttrium barium copper oxide (YBCO) plates. More importantly, the present investigation establishes sufficient conditions for crack path stability/instability, which entail a cleavage system being easy or difficult, i.e., whether a crack would propagate in its original plane/direction or deflect to a different one. This criterion of fracture mechanics is then employed for accurate determination of the full set of elastic constants of superconducting mono-crystalline YBCO. Finally, heretofore unavailable results pertaining to the through-thickness variations of stress intensity factors and energy release rates for a crack corresponding to symmetric and skew-symmetric hyperbolic cosine loads, which also satisfy the boundary conditions on the plate surfaces, bridge a longstanding gap.

Theory of nematic charge orders in kagome metals

Kagome metals $A$V$_3$Sb$_5$ ($A=$K, Rb, Cs) exhibit an exotic charge order (CO), involving three order parameters, with broken translation and time-reversal symmetries compatible with the presence of orbital currents. The properties of this phase are still intensely debated, and it is unclear if the origin of the CO is mainly due to electron-electron or electron-phonon interactions. Most of the experimental studies confirm the nematicity of this state, a feature that might be enhanced by electronic correlations. However, it is still unclear whether the nematic CO becomes stable at a temperature equal to ($T_{\text{nem}} = T_\text{C}$) or lower than ($T_{\text{nem}} < T_\text{C}$) the one of the CO itself. Here, we systematically characterize several CO configurations, some proposed for the new member of the family ScV$_6$Sn$_6$, by combining phenomenological Ginzburg-Landau theories, valid irrespective of the specific ordering mechanism, with mean-field analysis. We find a few configurations for the CO that are in agreement with most of the experimental findings to date and that are described by different Ginzburg-Landau potentials. We propose to use resonant ultrasound spectroscopy to experimentally characterize the order parameters of the CO, such as the number of their components and their relative amplitude, and provide an analysis of the corresponding elastic tensors. This might help understand which mean-field configuration found in our study is the most representative for describing the CO state of kagome metals, and it can provide information regarding the nematicity onset temperature $T_\text{nem}$ with respect to $T_\text{C}$.

A modulated fingerprint assisted machine learning method for retrieving elastic moduli from resonant ultrasound spectroscopy

We used deep-learning-based models to automatically obtain elastic moduli from resonant ultrasound spectroscopy (RUS) spectra, which conventionally require user intervention of published analysis codes. By strategically converting theoretical RUS spectra into their modulated fingerprints and using them as a dataset to train neural network models, we obtained models that successfully predicted both elastic moduli from theoretical test spectra of an isotropic material and from a measured steel RUS spectrum with up to 9.6% missing resonances. We further trained modulated fingerprint-based models to resolve RUS spectra from yttrium–aluminum-garnet (YAG) ceramic samples with three elastic moduli. The resulting models were capable of retrieving all three elastic moduli from spectra with a maximum of 26% missing frequencies. In summary, our modulated fingerprint method is an efficient tool to transform raw spectroscopy data and train neural network models with high accuracy and resistance to spectra distortion.

Relaxing free boundary conditions in resonant ultrasound spectroscopy for extreme environments

Elastic constants are thermodynamic susceptibilities, which provide symmetry-resolved insight into phase transitions and material anisotropy. Therefore, their importance spans basic to applied science and engineering. Resonant ultrasound spectroscopy (RUS) is a powerful method to determine elastic constants, because RUS simultaneously measures all elastic constants in small, low symmetry samples with high precision and accuracy. Conventionally, elastic constants in RUS are obtained from resonant frequencies assuming the sample freely resonates. However, achieving free resonance is often incompatible with experimental situations, because such configurations are inherently unstable. This limitation has hindered utilizing RUS to study phases arising in extreme environments like strong magnetic fields. To overcome these obstacles, we introduce a variation of RUS in which small, finite-area contact is maintained between the sample and ultrasonic transducers using an adhesive. First, we establish the conditions under which this clamped point contact can be treated as a small perturbation to free resonance. After comparing predictions from this modelling with experiment, we then experimentally demonstrate the ability to extract elastic constants, and their temperature dependence, with comparable accuracy and precision to conventional RUS. Finally, we show we can reproducibly map phase boundaries in temperature and magnetic fields using our new approach.

Accurate determination of elastic anisotropy to detect internal microstructures using resonant ultrasound spectroscopy

Elastic constants are of great significance, because they are fundamental thermodynamic susceptibilities that connect directly to thermodynamics and electronic structure, as well as to mechanical properties. Resonant ultrasound spectroscopy (RUS) measures non-destructively all fundamental elastic properties by determining the natural frequencies at which a 3D object resonates when is mechanically excited (normal modes). By using an inversion scheme, it is possible to extract the entire elastic tensor of a material with extreme sensitivity in a single frequency sweep using only one, small sample. This makes RUS particularly advantageous to study physical properties of low-symmetry single crystals and textured bulk materials. I will present recent RUS measurement examples of its applications to thermodynamic and materials science problems. I will focus on the effect of texture in elastic constants as a result of mechanical or growth processes and the robustness of results obtained by RUS. In materials such as aluminum that is often considered isotropic but shows clear anisotropy when it is extruded, or 3D printed. Similar but much larger effect is found in additive manufactured stainless steel where the growth process leads to a large anisotropy with a softening of 40%–50% along the build direction.

Elastic behavior of additively manufactured 316L stainless steel with changing laser power and speed

Ultrasonic investigations of additively manufactured 316L stainless steel were performed to reveal correlations between properties and printing parameters. The laser power and scanning speed of the selective-Laser-Melting printing process were varied systematically: 40–100 W in 20-W steps, and 600 mm/s to 1200 mm/s in 200-mm/s steps. Resonant ultrasound spectroscopy and pulse-echo measurements were performed. The extensive data allow for observations of specific behaviors in the elastic properties of the material as a function of VED, the volumetric energy density (VED ∝ power/speed). An increase in the values of c11 and c44 with increasing VED is confirmed, followed by saturation in the expected complete-fusion zone. The saturation values are comparable to those of the wrought (∼250 GPa for c11 and ∼75 GPa for c44). At low VED, c11 is quite small (∼100 GPa). Furthermore, an interesting behavior appears in the incomplete-fusion zone. At a fixed VED, the laser power level affects the elastic properties. As power increases, the porosity decreases, the mass density increases, and both elastic constants increase. The details observed in the material’s elastic properties are important for its correct usage in space and biomechanical applications.

Modeling and characterizing the dynamic response of Octet-Truss lattice structures using elastic parameters determined from Resonant Ultrasound Spectroscopy

Modeling and characterization of additively manufactured materials and structures is a critical stage in the design process. This presentation will present an approach using Resonant Ultrasound Spectroscopy to determine the elastic tensor of an additively manufactured Octet Truss lattice structure. The lattice structures are fabricated from an alloy of Titanium using a laser powder bed fusion process. Material characterization begins by applying resonance techniques on simple regular parallelepiped shapes. Solid and lattice samples are measured to obtain estimates for the elastic properties of the bulk material and the effective elastic properties of the lattice structure. The measured elastic properties are then incorporated into structural models representing continuum approximations of several test parts. Comparisons between the continuum models and the experimental measurements indicate agreement over a wide frequency range within a long wavelength approximation defined for the lattice. The measurements also suggest that there is additional physics and geometrical effects accounted for in the RUS continuum approximations of the lattice that are not completely captured by the full finite model utilizing only base material properties.

Nondestructive quantification of single crystal elasticity for additively manufactured SB-CoNi-10C, IN625, and Ti64

Resonant ultrasound spectroscopy (RUS) is capable of determining the single crystal elastic constants from polycrystalline specimens with known crystallographic texture. However, the calculated single crystal elastic constants vary with the measured texture, resulting in inconsistent estimates for additively manufactured (AM) specimens with heterogeneous texture regions. In this work, the accuracy of the determined single crystal elastic constants is improved by incorporating the uncertainty of the texture in the determination of single crystal elasticity, and requiring only small quantities of electron backscatter diffraction data (EBSD) to do so. The single crystal elastic constants are determined by Bayesian inference with parallelized sequential Monte Carlo (SMC), enabling an order of magnitude reduction in computational cost. AM specimens of a cobalt-nickel-base superalloy (SB-CoNi-10C) demonstrate that the incorporation of texture variability enables the single crystal elastic constants to converge to the reported literature values within one standard deviation, avoiding any dependence on the initial texture values. The single crystal elastic constants of nickel-base-superalloy Inconel 625 (IN625) and Ti-6Al-4V (Ti64) are determined from AM specimens, using only RUS and EBSD data. The determined single crystal elastic constants of IN625 agree between two different texture conditions (induced by AM raster strategy), as well as with the literature values, within one standard deviation. The single crystal elastic constants determined from three AM Ti64 specimens, printed with different beam powers, agree with the range of literature values within two standard deviations but demonstrate variability between AM specimens, indicating that the frequencies may be susceptible to the effects of secondary phases.

Perspective: Machine learning in experimental solid mechanics

Experimental solid mechanics is at a pivotal point where machine learning (ML) approaches are rapidly proliferating into the discovery process due to significant advances in data storage and processing capabilities. Much of the ML that is being adopted by the mechanics community was initially developed for application outside of science and engineering, and has the potential to produce results of questionable physical validity. To ensure that these data-driven approaches are trustworthy, there is a clear need to embed physical principles into their architectures, to evaluate and compare ML frameworks against benchmark datasets, and to test their broader extensibility. Frameworks must be grounded in a clear objective, quantifiable error, and a well-defined scope of extensibility. These principles enable ML models with a wide range of architectures to be meaningfully categorized, compared, evaluated, and extended to broader experimental and computational frameworks. Application of these principles are demonstrated through an investigation of ML models in two different use cases, acoustic emission and resonant ultrasound spectroscopy, along with a discussion of outlooks for the future of trustworthy ML in experimental mechanics.

Study of elastic anisotropy for 1, 3, 5-trinitro-1, 3, 5-triazacyclohexane by supramolecular structural unit

The relation between elastic property and crystal structure provides a foundation for designing new materials with desired properties and understanding the chemical decomposition and explosion of energetic materials. The supramolecular structural unit is proposed as the smallest chemical unit to quantitatively characterize the elastic anisotropy of 1, 3, 5-trinitro-1, 3, 5-triazacyclohexane (RDX). The supramolecular structural unit refers to the nearest-neighbor coordination polyhedron of one molecule. The supramolecular structural unit of RDX is composed of 15 molecules, and analyzed by the total molecular number density and the density of intermolecular interactions. The elastic modulus model is established on the assumption that 1) the RDX molecule is of sphere and rigid-body; 2) the intermolecular interaction is regarded as a linear spring, i.e. it is described by a bond-spring model; 3) the molecules are close-packed in the series mode. The elastic modulus model based on the supramolecular structural unit demonstrates that the elastic modulus is intrinsically determined by the total molecular number, the equilibrium distance of the molecular pair, the intermolecular force constant, and the angle between the intermolecular non-bonding interaction and the normal to crystal face. The intermolecular force constant is calculated as the second derivative of the intermolecular interaction with respect to the equilibrium centroid distance. The intermolecular interaction is expressed as the summation of van der Waals and electrostatic interactions calculated by COMPASS (condensed-phase optimized molecular potentials for atomistic simulation studies) II forcefield. The calculated elastic moduli are 21.7, 17.1, 20.1, 19.1, and 15.3 GPa for RDX (100), (010), (001), (210), and (021) crystal faces, respectively. The calculation results are consistent with the theoretical values computed by the density functional theory. Excluding RDX(001), the calculated elastic moduli accord with the experimental results measured by the resonant ultrasound spectroscopy (RUS), impulsive stimulated thermal scattering, Brillouin spectroscopy, and nanoindentation methods. The theoretical value (20.1 GPa) of RDX(001) overestimates the experimental values in a range of 15.9–16.6 GPa. The reason can be attributed to the rigid-body approximation for flexible molecules, in which are ignored the motion and deformation of the ring and NO&lt;sub&gt;2&lt;/sub&gt; groups when the external loads are applied to RDX(001). The results suggest that the supramolecular structural unit can be the smallest chemical unit to quantitatively characterize the elastic anisotropy of RDX and the elastic anisotropy is mainly due to the angle between the intermolecular interaction and the normal to crystal face.

Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method

Ultrasonic attenuation coefficients of ceramic and inorganic materials were determined for the longitudinal and transverse wave modes. Sample materials included hard and soft ceramics, common ceramics, ceramic-matrix composites, mortars, silicate glasses, rocks, minerals and crystals. For ceramic attenuation measurements, a standardized method has existed, but this method based on a buffer-rod arrangement was found to be inconsistent, producing vastly different results. Resonant ultrasound spectroscopy was also found to be unworkable from its sample preparation requirements. Experimental reevaluation of the buffer-rod method showed its impracticality due to unpredictable reflectivity parameters, yielding mostly negative attenuation coefficients. In this work, attenuation tests relied on a through-transmission method, which incorporated a correction procedure for diffraction losses. Attenuation exhibited four types of frequency (f) dependence, i.e., linear, linear plus f4 (called Mason-McSkimin relation), f2 and f3. The first two types were the most often observed. Elastic constants of tested materials were also tabulated, including additional samples too small for attenuation tests. Observed levels of attenuation coefficients will be useful for designing test methods for ultrasonic nondestructive evaluation and trends on ultrasonic attenuation are discussed in terms of available theories. However, many aspects of experimental findings remain unexplained and require future theoretical developments and detailed microstructural characterization. This study discovered a wide range of attenuation behaviors, indicating that the attenuation parameter can aid in characterizing the condition of intergranular boundaries in combination with imaging studies.

Classification of metal PBF-LB parts manufactured with different process parameters using resonant ultrasound spectroscopy

To face the challenges raised by the qualification of metallic additively manufactured (AM) complex shaped and rough finish parts, non-destructive testing (NDT) volumetric methods are required. X-ray computed tomography (XCT) is presently the favored technique; however, alternative methods are needed to overcome the requirement of technical skills and the high cost of the technique. XCT also has limitations regarding the size and density of parts. Here, we propose an easy to use, fast, and efficient global NDT volumetric method based on resonant ultrasound spectroscopy (RUS) which basic principle relies on the comparative analysis of natural resonant frequency spectra of similar parts from the same family, both of which vibrating as free as possible. The methods have already proven to have the ability to sort parts with defects from flawless parts. In the present study, we demonstrate that RUS can also segregate metallic parts manufactured with different AM system process parameters. Eleven sets of three parts were manufactured, using a metal laser-powder bed fusion process, with different wall thicknesses, laser powers, scanning speeds, and scanning strategies. These parts were tested by RUS and then analyzed using the Z-score statistical method. The AM process parameter changes clearly influenced the resonance responses of the parts, and thus, the method is able to classify the different groups of parts according to their process parameters. Hence, the RUS methods can provide industries convenient tools to not only identify defective parts but to also configure AM machine parameters according to the expected and desired material properties.

Magnetoelastic coupling behaviour of nanocrystalline ε-Fe2O3

Preparation of a ceramic sample which preserved the nanoscale grain sizes of ∼10–30 nm has allowed elastic and anelastic properties of ε-Fe2O3 to be investigated as functions of temperature and magnetic field strength by Resonant Ultrasound Spectroscopy in the frequency range ∼0.1–1 MHz. Formal analysis of spontaneous strains, e, from previously obtained high resolution lattice parameter data confirmed that magnetic ordering below ∼500 K is accompanied by strains of up to ∼±0.002 due to coupling with the order parameter, m, according to λem2. However, this coupling does not result in elastic softening that would be expected if the order parameter relaxed in response to an induced strain on the timescale of the acoustic resonances. Stiffening or softening during heating through ∼450–480 K of the initial as prepared material, which acquired a distinct magnetisation parallel to the stress applied during Spark Plasma Sintering, is attributed to changes in magnetic domain configurations involving preferred local alignments of individual moments of monodomain crystals. The crystallographic space group, Pna21, and magnetic space group at room temperature, Pna'21', allow ε-Fe2O3 to be both piezoelectric and piezomagnetic. It is postulated that changes in the effective coefficients of these properties for bulk samples are responsible for the observed variations in acoustic resonance frequencies according to the magnetic domain structure present. No elastic or anelastic anomalies were observed at the commensurate-incommensurate transition near 110 K. Instead, acoustic resonance frequencies changed in response to an applied magnetic field, consistent with viscous motion of magnetic domain walls and the effect of poling on piezo coefficients. Ceramic samples of ε-Fe2O3 could have potentially functional piezoelectric and/or piezomagnetic properties that are tunable by choice of magnetic and thermal history.

Determination of single-crystal elastic moduli of LiREF4 (RE = Y, Gd, and Tb) by resonant ultrasound spectroscopy

The tetragonal fluoro-scheelite LiREF4 compounds (RE=rareearth) have been shown to exhibit a variety of useful optical and magnetic properties. While LiYF4 has been widely studied, many of the fundamental thermodynamic properties of other members of this family remain unknown. Here, we report the complete elastic tensors (Cij) of single-crystalline LiYF4, LiTbF4, and LiGdF4 using resonant ultrasound spectroscopy and density functional theory (DFT). We compare the results for LiYF4 with prior experimental results using time-of-flight ultrasound methods. This is the first report, however, of the experimental elastic tensors of LiTbF4 and LiGdF4. The present results point to a softening of the elastic moduli of the LiREF4 system when Y is replaced by the larger ionic radius of Tb or Gd. Furthermore, we find that just 0.3% doping with Nd on the Y site also leads to a slight softening of the moduli. The variation of the elastic moduli as a function of temperature up to 216°C was also measured. A nearly linear softening of all seven independent elastic moduli was observed with increasing temperature. Phonon dispersions and phonon density of states obtained by DFT support the experimental finding of a significantly higher sound velocity due to lighter Y atoms in LiYF4, as compared to heavier LiTbF4 and LiGdF4.