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DOE OSTI2022

High-Entropy Borides under Extreme Environment of Pressures and Temperatures

The high-entropy transition metal borides containing a random distribution of five or more constituent metallic elements offer novel opportunities in designing materials that show crystalline phase stability, high strength, and thermal oxidation resistance under extreme conditions. We present a comprehensive theoretical and experimental investigation of prototypical high-entropy boride (HEB) materials such as (Hf, Mo, Nb, Ta, Ti)B2 and (Hf, Mo, Nb, Ta, Zr)B2 under extreme environments of pressures and temperatures. The theoretical tools include modeling elastic properties by special quasi-random structures that predict a bulk modulus of 288 GPa and a shear modulus of 215 GPa at ambient conditions. HEB samples were synthesized under high pressures and high temperatures and studied to 9.5 GPa and 2273 K in a large-volume pressure cell. The thermal equation of state measurement yielded a bulk modulus of 276 GPa, in excellent agreement with theory. The measured compressive yield strength by radial X-ray diffraction technique in a diamond anvil cell was 28 GPa at a pressure of 65 GPa, which is a significant fraction of the shear modulus at high pressures. The high compressive strength and phase stability of this material under high pressures and high temperatures make it an ideal candidate for application as a structural material in nuclear and aerospace fields.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Comparison of Biotite Elastic Properties Recovered by Spherical Nanoindentations and Atomistic Simulations — Influence of Nano-Scale Defects in Phyllosilicates

Phyllosilicate minerals, due to their sheets structure and morphology, are known to cause anisotropy in bulk rock properties and make the bulk rock more compliant. Accurately characterizing the micromechanical behavior of phyllosilicate minerals from laboratory observations, which eventually translates to the bulk rock behavior, is still challenging due to their fine-grained nature. Recent advances in atomistic simulations open the possibility of theoretically investigating such mineral mechanical behavior. We compare the elastic properties of biotites recovered by spherical nanoindentation with those predicted from density functional theory (DFT) simulations to investigate to what extent theoretical predictions reproduce actual phyllosilicate properties. Spherical nanoindentation was conducted using schist rocks from Poorman Formation, South Dakota, USA, to recover continuous indentation stress-strain curves. Loading in the layer-normal orientation shows an average indentation modulus (M) of about 35 GPa, while loading in the layer-parallel orientation gives a higher average of about 95 GPa. To facilitate comparison, the elastic stiffness constants (cij) determined from DFT were converted to indentation modulus (M) using solutions proposed in this study. The majority of the nanoindentation modulus results are below the values inferred from the simulation results representing ideal defect-free minerals. We suggest that crystal defects present at the nano-scale, potentially ripplocations, are the dominant cause of the lower indentation modulus recovered from nanoindentation compared to those inferred from DFT simulations. Results highlight the importance of acknowledging the defects that exist down to the nano-scale as it modifies the mechanical properties of phyllosilicates compared to its pure defect-free form.

58 GEOSCIENCES↗

DOE OSTI2025

The role of fast and slow dynamics in nonlinear resonant ultrasound spectroscopy of consolidated granular materials

Abstract Elastic nonlinearity observed in consolidated granular media can be attributed to the combination of slow and fast effects, which give rise to hysteresis and relaxation of both modulus and damping after the sample is perturbed. A consequence is a high level of complexity in the measurements of the sample linear and nonlinear elastic parameters. The results of experiments are dependent on the experimental protocol that is adopted to measure the relevant quantities and it is hard to quantify parameters with accuracy and repeatability. Here we focus on examining Nonlinear Resonant Ultrasound Spectroscopy, showing experimentally the role of slow dynamics in the process and quantifying/discussing its influence on the quantification of nonlinearity. We also propose a model to describe the process, which shows that different contributions to nonlinearity (e.g., classical and hysteretic) could be due to physical features (defects) relaxing with different relaxation times.

Science & Technology - Other Topics↗

DOE OSTI2025

Thick graded interfaces increase wear resistance in Ti/TiN nanolayered thin films

Multilayered composites with nanoscale layer thickness incorporating titanium and titanium nitride (Ti/TiN) are used as a model system to study the effects of heterophase interface structure on elastic and plastic deformation, as well as wear behavior. Here, in this work, hardness, modulus, and wear rate under dry reciprocating sliding contact are quantified as a function of Ti-TiN heterophase interfacial nitrogen gradient thickness for Ti/TiN multilayers with 10–80 nm layer thickness. Hardness and modulus are found to be inversely proportional to layer thickness and independent of interface gradient for most specimens. Wear rate is found to be inversely proportional to interface gradient thickness at constant layer thickness, demonstrating that control of nanoscale interface structure is a valid approach to enhancing wear behavior. The materials studied in this work wear comparably or slower than other Ti- and TiN-based composites in the literature, providing a promising avenue for engineering wear-resistant materials for use in industrially relevant applications.

Graded interfaces↗

DOE OSTI2021

A theory of localized excitations in supercooled liquids

Here, a new connection between the structure and dynamics in glass-forming liquids is presented. We show how the origin of spatially localized excitations, as defined by the dynamical facilitation (DF) theory, can be understood from a structure-based framework. This framework is constructed by associating excitation events in the DF theory to hopping events between energy minima in the potential energy landscape (PEL). By reducing the PEL to an equal energy well picture and applying a harmonic approximation, we develop a field theory to describe elastic fluctuations about inherent states, which are energy minimizing configurations of the PEL. We model an excitation as a shear transformation zone (STZ) inducing a localized pure shear deformation onto an inherent state. We connect STZs to T1 transition events that break the elastic bonds holding the local structure of an inherent state. A formula for the excitation energy barrier, denoted as J σ , is obtained as a function of inherent-state elastic moduli and the radial distribution function. The energy barrier from the current theory is compared to the one predicted by the DF theory where good agreement is found in various two-dimensional continuous poly-disperse atomistic models of glass formers. These results strengthen the role of structure and elasticity in driving glassy dynamics through the creation and relaxation of localized excitations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Empty perovskites as Coulomb floppy networks: Entropic elasticity and negative thermal expansion

Floppy networks (FNs) provide valuable insight into the origin of anomalous mechanical and thermal properties in soft matter systems, from polymers, rubber, and biomolecules to glasses and granular materials. Here, we use the same FN concept to construct a quantitative microscopic theory of empty perovskites, a family of crystals with ReO 3 structure, which exhibit a number of unusual properties. One remarkable example is ScF 3 , which shows a near-zero-temperature structural instability and large negative thermal expansion (NTE). Furthermore, we trace these effects to an FN-like crystalline architecture formed by strong nearest-neighbor bonds, which is stabilized by net electrostatic repulsion that plays a role similar to osmotic pressure in polymeric gels. NTE in these crystalline solids, which we conceptualize as Coulomb floppy networks, emerges from the tension effect of Coulomb repulsion combined with the FN's entropic elasticity and has the same physical origin as in gels and rubber. Our theory provides an accurate, quantitative description of phonons, thermal expansion, compressibility, and structural phase diagram, all in excellent agreement with experiments. The entropic stabilization of critical soft modes, which play only a secondary role in NTE, explains the observed phase diagram. Significant entropic elasticity resolves the puzzle of a marked, ≈50% discrepancy between the experimentally observed bulk modulus and ab initio calculations. The Coulomb FN approach is potentially applicable to other important materials with markedly covalent bonds, from perovskite oxides to iron chalcogenides, whose anomalous vibrational and structural properties are still poorly understood.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Achieving ultrahigh modulus of resilience and enhanced thermal stability in ZnO x /SU-8 interpenetrating network polymer nanocomposite nanopillars

The modulus of resilience, a mechanical property that quantifies the maximum strain energy density a material can store during elastic deformation, is a crucial parameter for materials used in flexible displays, micro/nano-electro-mechanical system (M/NEMS) actuators, and ultra-sensitive pressure sensors. In this study, ZnO x /SU-8 nanocomposite nanopillars with a diameter of 300 nm, fully infiltrated with a uniformly distributed, interpenetrating amorphous ZnO x filler network, were synthesized via vapor-phase infiltration (VPI). In-situ uniaxial nano-compression tests revealed that the modulus of resilience of ZnO x /SU-8 reaches ∼ 12 MJ/m 3 , which is an ultrahigh value among all engineering materials with comparable strength. In addition, the synthesis fidelity, inorganic infiltration depth, and mechanical performance were all significantly improved compared to VPI-synthesized AlO x nanocomposites. Thermal stability, another key requirement for M/NEMS device materials operating under extreme environments, was also notably enhanced. Furthermore, partial crystallization of the amorphous ZnO x fillers during annealing contributed to an additional increase in modulus of resilience, reaching up to ∼ 13.9 MJ/m 3 . This work presents an effective fabrication strategy for producing nanostructured organic–inorganic hybrid nanocomposites with ultrahigh modulus of resilience and superior thermal stability, paving the way for their integration into next-generation flexible displays and high-performance M/NEMS devices working under harsh environments.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Mechanical Properties of Functionally Graded Concrete Lining for Deep Underground Structures

With the mining depth of coal resources increasing, the thickness of traditional lining for deep mines becomes large. The bearing capacity of the outer lining cannot be fully utilized, so a new type of functionally graded lining structure (FGL) with radial Young’s modulus varying in gradient is proposed. In this study, through theoretical analysis and numerical simulation, the mechanical properties of the functionally graded lining were studied, including the characteristics of the elastic working state and the ultimate bearing state. The influences of the structural parameters of the functionally graded lining, including the inner radius, the thickness, Young’s modulus, the compressive strength of the concrete, Poisson’s ratio, and the number of layers on the mechanical properties were analyzed. The calculation formula of the ultimate bearing capacity of the lining and the calculation formula of the maximum tangential strain at the time of lining failure were put forward. The accuracy of the formula was verified by comparing with the numerical simulation results. The research results provide the basis for the construction of the design theory of a functionally graded lining structure and have great engineering significance for the construction of the kilometer-deep mines in the future.

Li, De-Chun↗

DOE OSTI2023

Molecular-Dynamics Analysis of the Mechanical Behavior of Plasma-Facing Tungsten

We report a systematic computational analysis of the mechanical behavior of plasma-facing component (PFC) tungsten focusing on the impact of void and helium (He) bubble defects on the mechanical response beyond the elastic regime. Specifically, we explore the effects of porosity and He atomic fraction on the mechanical properties and structural response of PFC tungsten, at varying temperature and bubble size. We find that the Young modulus of defective tungsten undergoes substantial softening that follows an exponential scaling relation as a function of matrix porosity and He atomic content. Beyond the elastic regime, our high strain rate simulations reveal that the presence of nanoscale spherical defects (empty voids and He bubbles) reduces the yield strength of tungsten in a monotonically decreasing fashion, obeying an exponential scaling relation as a function of tungsten matrix porosity and He concentration. Our detailed analysis of the structural response of PFC tungsten near the yield point reveals that yielding is initiated by emission of dislocation loops from bubble/matrix interfaces, mainly 1/2<111> shear loops, followed by gliding and growth of these loops and reactions to form <100> dislocations. Furthermore, dislocation gliding on the <111>{211} twin systems nucleates 1/6<111> twin regions in the tungsten matrix. These dynamical processes reduce the stress in the matrix substantially. Subsequent dislocation interactions and depletion of the twin phases via nucleation and propagation of detwinning partials lead the tungsten matrix to a next deformation stage characterized by stress increase during applied straining. Furthermore, our structural analysis reveals that the depletion of twin boundaries (areal defects) is strongly impacted by the density of He bubbles at higher porosities. After the initial stress relief upon yielding, increase in the dislocation density in conjunction with decrease in the areal defect density facilitates the initiation of dislocation-driven deformation mechanisms in the PFC crystal.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Elastic properties of the W 0.75 R e 0.25 alloy at high pressure up to 183 GPa

The high pressure equation of state for the W 0.75 R e 0.25 alloy is experimentally determined up to 183 GPa with synchrotron angle-dispersive powder x-ray diffraction in the diamond-anvil cell and to ∼925 GPa with density-functional theory. W-Re alloys are used in many industrial high-temperature applications and as a confining gasket material in high-pressure diamond-anvil cell research. The inclusion of 25 wt. % Re achieves the highest performance in terms of strength and ductility while also maintaining the body-centered-cubic (bcc) crystal structure, yet to date there has been no investigation into its elastic behavior at high pressure. We present the experimentally and theoretically determined volumetric and elastic pressure response and systematically compare these results to other W-Re alloys, finding that the bulk modulus of W-Re alloys varies nonlinearly with Re content and W 0.75 Re 0.25 becomes less incompressible than W at 85 GPa. Published by the American Physical Society 2025

Alloys↗

DOE OSTI2022

Effects of Microstructural Composition, Porosity, and Microcracks on the Elastic Moduli of Nuclear Graphites

The elastic responses of nuclear graphite not only depend on the graphitic content itself but are largely dictated by the microstructural constitution of the material. The types of raw materials combined with the manufacturing processes used to produce the graphite yield the microstructural content that primarily includes graphite filler, graphitized pitch binder, and voids/defects that typically occupy approximately 20% of the volume. Among these microstructural components, porosity and microcracking (considered to be part of voids/defects) heavily influence the overall properties of the material, including the elastic moduli. It is widely accepted that the primary effect of oxidation is to increase porosity, but the related effect on the moduli cannot be explained satisfactorily by simply noting changes to porosity. Models describing the elastic moduli of porous, polycrystalline graphite materials have been developed to interpret experimental determinations of Young's modulus and shear modulus in oxidized graphites. Beyond porosity, the moduli are heavily influenced by microcracks, and their effects can be assessed using physical property models based on orientation distribution coefficients and microcrack-modified, single-crystal moduli to represent the combined effects of crystallite orientation and microcracking. This work demonstrates how most modulus measurements in nuclear graphites can be understood using relatively simple models that describe the effects of porosity and microcracking. We also present directions to be pursued to account for microstructure-related effects that occur as a result of neutron irradiation.

Spicer, James B.↗

DOE OSTI2021

Preferred orientation of calcium aluminosilicate hydrate compacts: Implications for creep and indentation

Nano/micro-indentation has been extensively used to examine elastic properties and creep of cement-based materials. However, there have been inconsistencies in the measured elastic moduli and debate on the creep mechanism of calcium (alumino) silicate hydrates (C-(A-)S-H). To bring new insights, we examined the deviatoric stress-induced preferred orientation of calcium aluminosilicate hydrate (C-A-S-H), portlandite, and ettringite compacts, using synchrotron-based X-ray diffraction. Intense preferred orientations were observed in C-A-S-H compacts, and the c-axis of unit cells is highly aligned with the compression direction; weaker c-axis related fiber-type texture formed in portlandite and ettringite. Higher humidity, greater compacting pressure, and/or increased duration of the pressure intensified the C-A-S-H preferred orientation, which is facilitated by gel-pore water lubrication. This pressure-induced time-dependent preferential re-orientation of crystallites can contribute to the creep of cement-based materials, and it may cause overrepresentation of the soft c-axis of C-(A-)S-H unit-cell in nanoindentation experiments and underestimation of Young's modulus.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Assessment of mechanical, thermal properties and crystal shapes of monoclinic tricalcium silicate from atomistic simulations

The two most common polymorphs in industrial alite, M1 and M3, were characterized at the molecular scale. Different methods were employed and discussed to assess mechanical properties and specific heat of both polymorphs. The calculated homogenized elastic moduli and specific heat were found in good agreement with experimental measurements. A comparative analysis of spacial Youngs modulus reveal isotropic and anisotropic spacial distribution for M{sub 1} and M{sub 3} respectively. A more isotropic compressive strength is also reported for M{sub 1} when compared to M{sub 3} polymorph. Cleavage energies computation allowed to proposed equilibrium shapes for both polymorph, with significant differences. While the lowest cleavage energies were found along (100) and (001) for both polymorphs, the constructed M1 crystal possesses 3 independent facets, against seven for the M3 polymorph.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Woven ceramic matrix composite surrogate model based on physics-informed recurrent neural network

A recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear constitutive behavior of woven ceramic matrix composites (CMCs) driven by matrix damage at multiple length scales. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the multiscale generalized method of cells (MSGMC) approach coupled with a matrix damage model. This coupling permits simulating the nonlinear behavior of woven CMCs based on constituent response at the micro-, meso-, and macroscales. The multiscale repeating unit cell is loaded under non-monotonic conditions including multiple load / unload cycles and tension / compression. The fiber volume fraction as well as the intra- and intertow void volume fractions are also varied in the generation of training data. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input strain sequence and fiber and void volume fractions, the resulting stress versus strain response while satisfying physical constraints such as positive semi-definiteness of the tangent stiffness matrix and linear elastic unloading. Further, the trained surrogate model effectively matches the stress versus strain response and successfully predicts the tangent modulus throughout the loading regime. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex architectures, nonlinear multiaxial material response, and under non-monotonic loading conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Characterization of elastic mechanical properties of Tuscaloosa Marine Shale from well logs using the vertical transversely isotropic model

To avoid steep declines in the Tuscaloosa Marine Shale (TMS) production, wells are fracture-stimulated to release the hydrocarbons trapped in the matrix of the formation. An accurate estimation of Young’s modulus and Poisson’s ratio is essential for hydraulic fracture propagation. In addition, ignoring the highly heterogeneous and anisotropic character of TMS can lead to erroneous stress values, which subsequently affect hydraulic fracture width estimates and the overall hydraulic fracturing process. We have developed an empirical 1D geomechanical model that takes into account VTI anisotropy, and it is used to characterize the elastic mechanical properties of TMS in two wells. In the analyzed formation, the vertical Poisson’s ratio is less than the horizontal Poisson’s ratio, which suggests the necessity of an alternative to the ANNIE equations. The stiffness coefficients [Formula: see text] and [Formula: see text] were estimated using the relationships developed from the ultrasonic core data available for the two TMS. Further, correlations between the static and dynamic properties from laboratory tests were used to improve the minimum horizontal stress calculation. We compare VTI Young’s moduli, Poisson’s ratios, and minimum horizontal stress with the isotropic solution. VTI modeling improves the estimation of the elastic mechanical properties. The isotropic solution underestimates the minimum horizontal stress in the formation. Moreover, it was shown that the 20 ft shale interval below the TMS base is characterized by a low Young’s modulus (the vertical Young’s modulus is equal to 20 GPa, whereas the horizontal Young’s modulus is equal to 40 GPa) and may be a frac barrier.

Geochemistry & Geophysics↗

DOE OSTI2021

Anomalous elastic behavior of tantalum at high pressures: Experimental and theoretical studies

Elastic wave velocities of polycrystalline tantalum have been measured up to 13.6 GPa at room temperature using ultrasonic interferometry technique in a multi-anvil apparatus. The bulk and shear moduli, as well as their pressure derivatives are obtained using Eulerian 3rd order finite strain equations, yielding K S0 = 193.9(29) GPa, G 0 = 69.3(10) GPa, K S0' = 3.18(5) and G 0' = 0.88(1). Here the Steinberg-Guinan yield stress model is examined using the current shear modulus and its pressure derivative, where a slightly lower A 0 = 0.0127 GPa –1 compared to previous studies is obtained. First-principles calculations on the elasticity of tantalum have also been performed up to 200 GPa. Anomalous softening of the elastic shear constant C 44 and shear wave velocity V S is observed between 80– 180 GPa, whereas the anisotropy shows a softening-stiffening behavior with increasing pressure and reaches a minimum at around 150 GPa. Such anomalies might commonly originate from the nesting of Fermi surface for Group VB metals.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Ductile Glassy Polymer Networks Capable of Large Plastic Deformation and Heat-Induced Elastic Recovery

Many thermoplastic polymers are ductile by combining strength and large deformations. These deformations are irreversible - known as plastic deformation. Elastomers can deform reversibly but have low strength. To this end, we developed glassy and ductile polyamide networks capable of large plastic deformation (>200% strain) and high strength (~50 MPa tensile strength and ~1500 MPa Young’s modulus), similar to those of polyolefins and Nylon-66. We discovered that hydrogen bonding between meta-phthalamide groups was essential to the ductility. Since these polyamide networks are covalently bonded, we demonstrated their unique durability by repeatable elastic recovery at elevated temperatures, exhibiting indifferent tensile properties in each cycle. Furthermore, when we fixed the strain during the elastic recovery, these polyamide networks actuated stresses of 9–18 MPa, among the highest reported in shape-memory polymer actuators. Here, we envision these ductile, glassy polymer networks as promising alternatives to ductile thermoplastics, given the combined benefit of ductility and durability.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Probing the Mechanical Properties of 2D Materials via Atomic‐Force‐Microscopy‐Based Modulated Nanoindentation

Abstract As the field of low‐dimensional materials (1D or 2D) grows and more complex and intriguing structures are continuing to be found, there is an emerging need for techniques to characterize the nanoscale mechanical properties of all kinds of 1D/2D materials, in particular in their most practical state: sitting on an underlying substrate. While traditional nanoindentation techniques cannot accurately determine the transverse Young's modulus at the necessary scale without large indentations depths and effects to and from the substrate, herein an atomic‐force‐microscopy‐based modulated nanomechanical measurement technique with Angstrom‐level resolution (MoNI/ÅI) is presented. This technique enables non‐destructive measurements of the out‐of‐plane elasticity of ultra‐thin materials with resolution sufficient to eliminate any contributions from the substrate. This method is used to elucidate the multi‐layer stiffness dependence of graphene deposited via chemical vapor deposition and discover a peak transverse modulus in two‐layer graphene. While MoNI/ÅI has been used toward great findings in the recent past, here all aspects of the implementation of the technique as well as the unique challenges in performing measurements at such small resolutions are encompassed.

2D materials↗