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DOE OSTI2021

Strain Gradient Elasticity in SrTiO 3 Membranes: Bending versus Stretching

Young’s modulus determines the mechanical loads required to elastically stretch a material and also the loads required to bend it, given that bending stretches one surface while compressing the opposite one. Flexoelectric materials have the additional property of becoming electrically polarized when bent. The associated energy cost can additionally contribute to elasticity via strain gradients, particularly at small length scales where they are geometrically enhanced. Here, we present nanomechanical measurements of freely suspended SrTiO 3 crystalline membrane drumheads. In this work, we observe an unexpected nonmonotonic thickness dependence of Young’s modulus upon small deflections. Furthermore, the modulus inferred from a predominantly bending deformation is three times larger than that of a predominantly stretching deformation for membranes thinner than 20 nm. In this regime we extract a strain gradient elastic coupling of ~2.2 μN, which could be used in new operational regimes of nanoelectro-mechanics.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Graph neural networks predict energetic and mechanical properties for models of solid solution metal alloy phases

Here, we developed a PyTorch-based architecture called HydraGNN that implements graph convolutional neural networks (GCNNs) to predict the formation energy and the bulk modulus for models of solid solution alloys for various atomic crystal structures and relaxed volumes. We trained the GCNN surrogate model on a dataset for nickel–niobium (NiNb) generated by the embedded atom model (EAM) empirical interatomic potential for demonstration purposes. The dataset was generated by calculating the formation energy and the bulk modulus as a prototypical elastic property for optimized geometries starting from initial body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal compact packed (HCP) crystal structures, with configurations spanning the possible compositional range for each of the three types of initial crystal structures. Numerical results show that the GCNN model effectively predicts both the formation energy and the bulk modulus as function of the optimized crystal structure, relaxed volume, and configurational entropy of the model structures for solid solution alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Determination of single-crystal elastic moduli of Li RE F 4 ( RE =Y, Gd, and Tb) by resonant ultrasound spectroscopy

The tetragonal fluoro-scheelite Li RE F 4 compounds (RE = rare earth) have been shown to exhibit a variety of useful optical and magnetic properties. While LiYF 4 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 (C ij ) of single-crystalline LiYF 4 , LiTbF 4 , and LiGdF 4 using resonant ultrasound spectroscopy and density functional theory (DFT). Here we compare the results for LiYF 4 with prior experimental results using time-of-flight ultrasound methods. This is the first report, however, of the experimental elastic tensors of LiTbF 4 and LiGdF 4 . The present results point to a softening of the elastic moduli of the Li RE F 4 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 LiYF 4 , as compared to heavier LiTbF 4 and LiGdF 4 .

36 MATERIALS SCIENCE↗

DOE OSTI2022

Elastic properties of a Sc–Zr–Nb–Ta–Rh–Pd high-entropy alloy superconductor

Here, we report a comprehensive study on the elastic properties of a hexanary high-entropy alloy superconductor (ScZrNbTa) 0.685 [RhPd] 0.315 at room and cryogenic temperatures, by Resonant Ultrasound Spectroscopy experiments. The derived elastic constants are bulk modulus K=132.7 GPa, Young’s modulus E=121.0 GPa, shear modulus G=44.9 GPa, and Poisson’s ratio v= 0.348 for room temperature. The Young’s and shear moduli are ~ 10% larger than those in NbTi superconductor with similar T c , while the ductility is comparable. Moreover, the mechanical performance is further enhanced at cryogenic temperature. Our work confirms the advantageous mechanical properties of high-entropy alloy superconductors and suggests the application prospects.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Sound speed measurements in shock compressed cemented tungsten carbide: Evolution of elastic moduli with damage at pressures to 100 GPa

The motivation of the present study is to gain insights into the evolution of elastic properties of cemented tungsten carbides (WC) shock compressed to 100 GPa. Seven plate impact experiments—two front surface impact and five release wave overtake—are conducted to make simultaneous measurements of Hugoniot states and longitudinal sound speeds in shocked WC with 3.7wt.% cobalt binder. The sound speeds along with estimates for bulk sound speeds, obtained using the Birch–Murnaghan EoS, are analyzed to determine the elastic moduli—longitudinal, bulk, and shear—as a function of Hugoniot stress. The longitudinal and bulk sound speeds at Hugoniot states of interest are found to increase linearly with longitudinal stress. Consistent with the increase in sound speeds, the longitudinal and bulk moduli also increase with Hugoniot stress; however, the increase in longitudinal modulus is modest when compared to predictions of theoretical models that account for pressure and temperature dependence of elastic moduli, but with no damage. The shear moduli remain nearly constant at ~318 GPa over the range of Hugoniot states investigated. These values are, however, much lower than those predicted by the Steinberg–Guinan model with no damage. Poisson’s ratio decreases initially from its ambient value of 0.208 to ~0.199 for Hugoniot stress ≤10 GPa indicating consolidation of the WC microstructure with low initial stress; however, with an increase in Hugoniot stress to ~100 GPa, Poisson’s ratio increases to ~0.317, indicating degradation of shear moduli with increasing stress. The product of density and Grüneisen parameter (ρΓ), after an initial spike, remains nearly constant for volumetric strains ≥0.07. The maximum average temperature rise is estimated to be ~286°C at the highest Hugoniot stress employed in the study.

36 MATERIALS SCIENCE↗

DOE OSTI2023

AGC-2 Specimen Post Irradiation Data Package Report

This report documents results of the post-irradiation examination material property testing of the creep, control, and piggyback specimens from the irradiation creep capsule Advanced Graphite Creep (AGC)-2 are reported. This is the second of a series of six irradiation test trains planned as part of the AGC experiment to fully characterize the neutron irradiation effects and radiation creep behavior of current nuclear graphite grades. The AGC-2 capsule was irradiated in the Idaho National Laboratory Advanced Test Reactor at a nominal temperature of 600°C and to a peak dose of 5 dpa (displacements per atom). One half of the creep specimens were subjected to mechanical stresses (an applied stress of either 13.8, 17.2, or 20.7 MPa) to induce irradiation creep. All post-irradiation testing and measurement results are reported with the exception of the irradiation mechanical strength testing, which is the last destructive testing stage of the irradiation testing program. Material property tests were conducted on specimens from 15 nuclear graphite grades using a similar loading configuration as the first AGC capsule (AGC-1) to provide easy comparison between the two capsules. However, AGC-2 contained an increased number of specimens (i.e., 487 total specimens irradiated) and replaced specimens of the minor grade 2020 with the newer grade 2114. The data reported include specimen dimensions for both stressed and unstressed specimens to establish the irradiation creep rates, mass and volume data necessary to derive density, elastic constants (Young’s modulus, shear modulus, and Poisson’s ratio) from ultrasonic time of flight velocity measurements, Young’s modulus from the fundamental frequency of vibration, electrical resistivity, and thermal diffusivity and thermal expansion data from 100–500°C. No data outliers were determined after all measurements were completed. A brief statistical analysis was performed on the irradiated data and a limited comparison between pre- and post-irradiation properties is presented. A more complete evaluation of trends in the material property changes, as well as irradiation-induced creep due to irradiation, temperature, and applied load on specimens will be discussed in later AGC-2 post-irradiation examination analysis reports.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

AGC-4 Specimen Post-Irradiation Examination Data Interim Report

This interim report documents preliminary results of the post-irradiation examination material property testing from the fourth advanced graphite creep (AGC), AGC 4, capsule specimens. This is the fourth of a series of six irradiation test trains planned as part of the AGC experiment to fully characterize the neutron irradiation effects and radiation creep behavior of current nuclear graphite grades to moderate dose levels (=7 dpa). The AGC 4 capsule was irradiated in the Idaho National Laboratory Advanced Test Reactor at a nominal temperature of 800°C and to a peak dose of 8 dpa. Half of the AGC-4 specimens were subjected to compressive stresses to induce irradiation creep. Post-irradiation testing and measurement results are reported with the exception of thermal testing, which is still in progress, and irradiation mechanical strength testing. Additionally, some specimens initially deemed too hot to be examined in the ART Graphite laboratory may still be measured. The data reported includes specimen dimensions for both stressed and unstressed specimens to establish the irradiation creep rates, mass and dimensional data necessary to derive density, elastic constants (Young?s modulus, shear modulus, and Poisson?s ratio) from ultrasonic time of flight velocity measurements, Young?s modulus from the fundamental frequency of vibration, and electrical resistivity. A more complete evaluation of trends in the material property changes, as well as irradiation-induced creep due to the irradiation environment and applied load on the specimens, will be discussed later in AGC 4 post-irradiation examination analysis reports.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

AGC-4 Specimen Post-Irradiation Examination Data Interim Report

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Impact of microstructure on elastic properties in the alloy Ti-42Al-8.5 Nb

The microstructure of a γ-TiAl alloy containing niobium undergoes continuous transformations during annealing at 550 °C. These take place within the α 2 -phase of lamellar (α 2 +γ) colonies. We have characterized these changes by transmission electron microscopy and made a correlation to the elastic constants determined by resonant ultrasonic spectroscopy during in-situ annealing at the same temperature. Further, the results show a continuous increase of the E-modulus. This can be attributed to elastic strains acting within α 2 lamellae as a result of lattice transformations. After 5000h, a thermodynamic equilibrium was established with equal fractions of α 2 -phase and O-phase that differ only in lattice symmetry and Nb content. Generally, the presence of O-phase should contribute to lower elastic moduli, however in the present case the evolving microstructural characteristics were responsible for the observed increase in the E-modulus.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Micro-cantilever beam experiments and modeling in porous polycrystalline UO 2

Understanding the impact of microstructure on the thermo-mechanical behavior of oxide nuclear fuels is vital to predicting their performance through multiscale models. Evaluating the mechanical properties at the sub-grain length scale is key to developing these multiscale models. In this work, 3D finite element (FE) models were constructed to simulate the micrometer-scale bending of micro-cantilever beams fabricated using porous polycrystalline uranium dioxide (UO 2 ) and tested at room temperature. Here, the results showed that the porosity and elastic anisotropy of individual grains can play a significant role in determining the effective mechanical properties of the material deduced from the tests. Specifically, the porosity had a non-negligible effect, given that the pore size was of the same order of magnitude as the dimensions of the micro-beams. Correlations between load-deflection data, pore location, and elastic properties (effective Young's modulus) were investigated using UO 2 micro-beam FE models, where pore clusters were included and placed at different locations along the length of the beam. Results indicated that the presence of pore clusters near the substrate, i.e., the clamp of the micro-cantilever beam, has the strongest effect on the load-deflection behavior, with the porosity leading to a reduction of stiffness that is the largest for any location of the pore clusters. Furthermore, it was also found that pore clusters located towards the middle of the span and close to the end of the beam have a comparatively small effect on the load-deflection behavior. Therefore, it is concluded that accurate estimates of Young's modulus can be obtained from micro-cantilever experiments after accounting for porosity on the one third of the beam length close to the clamp. This, in turn, provides an avenue to improve microscale experiments and their analysis in porous, anisotropic elastic materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

First-principles investigation of elastic, vibrational, and thermodynamic properties of kagome metals CsM 3 Te 5 (M = Ti, Zr, Hf)

Kagome metals are a unique class of quantum materials characterized by their distinct atomic lattice arrangement, featuring interlocking triangles and expansive hexagonal voids. These lattice structures impart exotic properties, including superconductivity, interaction-driven topological many-body phenomena, and magnetism, among others. The kagome metal CsM 3 ⁢Te 5 (where M = Ti, Zr, or Hf) exhibits both superconductivity and nontrivial topological electronic properties, offering a promising platform for exploring topological superconductivity. This study employs first-principles density functional theory calculations to systematically analyze the elastic, mechanical, vibrational, thermodynamic, and electronic properties of CsM 3 ⁢Te 5 (M = Ti, Zr, Hf). Our calculations reveal that the studied compounds—CsTi 3 ⁢Te 5 , CsZr 3 ⁢Te 5 , and CsHf 3 ⁢Te 5 —are ductile metals with elastic properties akin to the hexagonal Bi and Sb, with average elastic constants, including a bulk modulus of 27 GPa, a shear modulus of 11 GPa, and Young's modulus of 29 GPa. We observe peculiar dispersionless, flat, phonon branches in the vibrational spectra of these metals. Additionally, we thoroughly analyze the symmetries of the zone-center phonon eigenvectors and predict vibrational fingerprints of the Raman- and infrared-active phonon modes. The analysis of thermodynamic properties reveals the Einstein temperature for CsTi 3 ⁢Te 5 , CsZr 3 ⁢Te 5 , and CsHf 3 ⁢Te 5 to be 66, 54, and 53 K, respectively. Our orbital-decomposed electronic structure calculations reveal significant in-plane steric interactions and multiple Dirac band crossings near the Fermi level. We further investigate the role of spin-orbit coupling effect on the studied properties. Furthermore, this theoretical investigation sheds light on the intriguing quantum behavior of kagome metals.

36 MATERIALS SCIENCE↗

DOE OSTI2023

LAVA 1.0: A general-purpose python toolkit for calculation of material properties with LAMMPS and VASP

Here, we introduce LAVA, a general-purpose python toolkit to provide user-friendly and high throughput calculations for material properties using both LAMMPS and VASP. It contains a set of classes as well as pre-processing and post-processing functions to prepare, execute and extract information from LAMMPS/VASP simulations. An overview of the program structure is provided. The current version contains modules to calculate elastic and mechanical properties such as lattice constant, cohesive energy, cold curve, elastic constants, bulk and shear modulus, volume conserving/non-conserving deformation path, vacancy/interstitial formation energy, surface energy, stacking fault energy, melting point, radial distribution function, and thermal expansion. These functionalities are demonstrated for different interatomic potentials and DFT calculations in Al.

36 MATERIALS SCIENCE↗

DOE OSTI2022

LAVA

We introduce LAVA, a general-purpose python toolkit to provide user-friendly and high throughput calculations for material properties using both LAMMPS and VASP. It contains a set of classes as well as pre-processing and post-processing functions to prepare, execute and extract information from LAMMPS/VASP simulations. An overview of the program structure is provided. The current version contains modules to calculate elastic and mechanical properties such as lattice constant, cohesive energy, cold curve, elastic constants, bulk and shear modulus, volume conserving/non-conserving deformation path, vacancy/interstitial formation energy, surface energy, stacking fault energy, melting point, radial distribution function, and thermal expansion.

Dang, Khanh↗

DOE OSTI2020

Determination of single crystal elastic moduli of KTb3F10 by resonant ultrasound spectroscopy

KTb3F10 (KTF) has been developed in recent years as a candidate Faraday rotator material because of its cubic symmetry, high figures of merit, and low absorption coefficient. While considerable efforts have focused on crystal growth and optical properties, investigations of fundamental thermodynamic behavior of KTF have been limited. Here, we report elastic moduli C11, C12, and C44 of single crystalline KTF measured by resonant ultrasound spectroscopy from 280 K up to 300 K and the obtained temperature derivatives of each modulus. We additionally report the single crystal elastic moduli of the rare-earth garnet Y3Al5O12 (YAG), yielding results that agree well with the prior literature. We found C11=135.62 GPa, C12=58.11 GPa, and C44=44.81 GPa for KTF and C11=332.43 GPa, C12=109.58 GPa, and C44=114.81 GPa for YAG at room temperature. The present results have been compared with previous experimental and theoretical results and with common oxide and fluoride optical materials, revealing the relative softness of KTF. The low elastic moduli of KTF are, in turn, responsible for its low thermal conductivity and low Debye frequency compared to other laser host materials.

Balodhi, Ashiwini (ORCID:0000000290496382)↗

DOE OSTI2024

Unconventional pressure-induced magnetic transitions and mechanical properties in non-magnetic LaFeSi

Here, this work demonstrates that two consecutive magnetic transitions occur in non-magnetic LaFeSi compound under negative hydrostatic pressure (small volume expansion). Electronic structure properties of LaFeSi were calculated using density functional theory (DFT) to understand the origin of these magnetic transitions. Mechanical properties of LaFeSi, especially elastic properties (shear and Young’s modulus, and Poisson’s ratio), were determined by DFT distortion calculations to elucidate lattice anisotropy and stability. The antiferromagnetic transition at –7.52 GPa, predicted in our work for LaFeSi, is consistent with the reported experimentally observed antiferromagnetic ground states in CeMnSi and LaMnSi compounds having similar crystal geometry. This finding of unexpected magnetic ordering predicts that layered non-magnetic materials, like LaFeSi, may become magnetically active with lattice expansion.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Extending the capillary wave model to include the effect of bending rigidity: X-ray reflectivity and diffuse scattering

The surface roughness of a thin film at a liquid interface exhibits contributions of thermally excited fluctuations. This thermal roughness depends on temperature (𝑇), surface tension (𝛾), and elastic material properties, specifically the bending modulus (𝜅) of the film. A nonzero 𝜅 suppresses the thermal roughness at small length scales compared to an interface with zero 𝜅, as expressed by the power spectral density of the thermal roughness. The description of the x-ray scattering of the standard capillary wave model (CWM), which is valid for zero 𝜅, is extended to include the effect of 𝜅. The extended CWM (eCWM) provides a single analytical form for both the specular x-ray reflectivity (XRR) and the diffuse scattering around the specular reflection, and recovers the expression of the CWM at its zero 𝜅 limit. This theoretical approach enables the use of single-shot grazing incidence x-ray off-specular scattering (GIXOS) measurements for characterizing the structure of thin films on a liquid surface. The eCWM analysis approach decouples the thermal roughness factor from the surface scattering signal, providing direct access to the intrinsic surface-normal structure of the film and its bending modulus. Moreover, the eCWM facilitates the calculation of reflectivity at any desired resolution (pseudo-XRR approach). The transformation into pseudo-XRR provides the benefit of using widely available XRR software to perform GIXOS analysis. The extended range of the vertical scattering vector (𝑄 𝑧 ) available with the GIXOS pseudo-XRR approach allows for a higher spatial resolution than with conventional XRR. Experimental results are presented for various lipid systems, showing strong agreement between conventional specular XRR and pseudo-XRR methods. This agreement validates the proposed approach and highlights its utility for analyzing soft, thin films.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Kohn anomaly and elastic softening in body-centered cubic molybdenum at high pressure

Transition metals in body-centered cubic (bcc) structures under compression can display several novel physical properties because of their complex electronic structures and electron-phonon interactions. Here, we used inelastic x-ray scattering experiments in a diamond-anvil cell up to ∼45 GPa and density-functional theory calculations up to 210 GPa to investigate the phonon dispersions, and electronic and elastic properties of single-crystal molybdenum (Mo). Our results show a pressure-induced Kohn anomaly at 𝑞∼0.5 along the [ξ00] direction in the longitudinal acoustic mode at ∼45 GPa; this anomaly is triggered by the pressure-enhanced Fermi-surface nesting effect. Theoretical calculations show that electron redistributions in the 𝑠-to-𝑑 orbitals of bcc-Mo contribute to the shear modulus anomaly at ∼50 GPa. In contrast, the Young's modulus anomaly in bcc-Mo at ∼210 GPa results from a Lifshitz-type electronic topological transition. In conclusion, our results shed light on the complex electronic behaviors that are associated with macroscopic elastic properties in typical bcc 𝑑-block transition metals under compression.

3-dimensional systems↗

DOE OSTI2022

Effect of Cr and Al on Elastic Constants of FeCrAl Alloys Investigated by Molecular Dynamics Method

The FeCrAl alloy system is recognized as one of the candidate materials for accident-tolerant fuel (ATF) cladding in the nuclear power industry due to its high oxidation resistance under irradiation and high-temperature environments. The concentrations of Cr and Al have a significant effect on elastic properties of the FeCrAl alloy. In this work, elastic constants C 11 , C 12 , C 44 , bulk modulus and shear modulus of FeCrAl alloy were calculated with molecular dynamics methods. We explored compositions with 1–15 wt.% Cr and 1–5 wt.% Al at temperatures from 0 K to 750 K. The results show that the concentrations of Al and Cr have different effects on the elastic constants. When the concentration of Al was fixed, a decrease in bulk modulus and shear modulus with increasing Cr content was observed, consistent with previous experimental results. The dependence of elastic constants on temperature was also the same as in the experiments. Investigations into elastic properties of defect-containing alloys have shown that vacancies, voids, interstitials and Cr-rich precipitations have different effects on elastic properties of FeCrAl alloys. Investigations of elastic properties of defect-containing alloys have shown that vacancies, void, interstitials and Cr-rich precipitations have different effects on elastic properties of FeCrAl alloys. Therefore, the present results indicate that both the Cr and Al concentrations and radiation defects should be considered to develop and apply the FeCrAl alloy in ATF design.

36 MATERIALS SCIENCE↗