Methods-A Potential-Dependent Thiele Modulus to Quantify the Effectiveness of Porous Electrocatalysts
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Wan, Charles Tai-Chieh↗
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Low frequency bulk modulus of partially molten peridotite, KLB-1
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Weidner, Donald J.↗
Full-Field Strain Measurement Integrated with Two Dimension Regression Analysis to Evaluate the Bi-Modulus Elastic Properties of Isotropic and Transversely Isotropic Materials
Background: Measuring the physical properties of shale is critical for optimizing engineering activities such as geothermal energy generation and hydraulic fracturing. Shale is a transversely isotropic material. Furthermore, this material can also include micro and macro cracks at different locations and orientations that cause it to behave differently under tensile or compressive loading. Objective: In this work, a combined experimental–numerical approach is proposed to evaluate the bi-modulus elastic properties of isotropic and transversely isotropic materials. Methods: Full-field strain measurements for a circular disk under diametral compression are integrated with a regression analysis technique to evaluate the elastic properties of bi-modulus materials subjected to tensile and compressive loads using two loading configurations on the same specimen. Digital Image Correlation (DIC) is used to measure the full-field strains. Subsequently, in the case of an isotropic material, a linear least-squares approach is utilized to process the experimentally determined strains in conjunction with analytical expressions of the stress fields (in terms of far-field loading) to determine the elastic modulus E, the shear modulus G, and the Poisson’s ratio $v$. In the case of a transversely isotopic material, such as shale, a finite element model is implemented to determine the stress fields (again in terms of far-field loading), which is followed by repeating the previous regression analysis in an iterative process to estimate the elastic parameters. Results: The results show that the proposed technique successfully provides a complete set of elastic properties as a function of both the loading condition and the principal material directions. The technique is validated by measurements on a known isotropic material and then applied to determine the properties of shale. Conclusion: In this work, the proposed approach is successfully used to calculate the bi-modulus elastic response of poly(methyl meth- acrylate) (PMMA) and shale. As expected, PMMA exhibits an isotropic response with no bi-modulus effect, however, shale exhibits both transverse isotropy and a bi-modulus effect. Therefore, this approach holds promise for investigating the elastic properties of materials like rocks and fiber-reinforced composite laminates as functions of the principal material directions and the loading conditions.
42 ENGINEERING↗
Improved Calculation of the Young’s Modulus of Rectangular Prisms from Their Resonant Frequency Overtones by Identifying Appropriate Shear Constants
Young’s modulus is an important parameter for characterizing the strength of, and wave propagation through, a given material. This study improves the estimation of Young’s modulus using the impulse excitation technique based on an experimental analysis of 19 borosilicate glass bars. Analysis of the frequency equations relating Young’s modulus to the out-of-plane and in-plane flexural resonant frequencies of rectangular prisms has been conducted for both the fundamental frequency and its overtones at higher orders of vibration. Furthermore, the Young’s moduli of three novaculite rocks with various porosities were then measured up to the seventh order of vibration to validate the optimum shear constant equation for estimating Young’s modulus. Young’s modulus was found to be nearly frequency independent for these rock samples.
Impulse excitation↗
Experimental evaluation of shear modulus scaling of dynamic strength at extreme pressures
Recent progress in the development of dynamic strength experimental platforms is allowing for unprecedented insight into the assumptions used to construct constitutive models operating in extreme conditions. In this work, we make a quantitative assessment of how tantalum strength scales with its shear modulus to pressures of hundreds of gigapascals through a cross-platform examination of three dynamic strength experiments. Specifically, we make use of Split–Hopkinson pressure bar and Richtmyer–Meshkov instability experiments to assess the low-pressure strain and strain rate dependence. Concurrent examination of magnetically driven ramp-release experiments up to pressures of 350GPa allows us to examine the pressure dependence. In this work, using a modern description of the shear modulus, validated against both ab initio theory and experimental measurements, we then assess how the experimentally measured pressure dependence scales with shear modulus. Furthermore, we find that the common assumption of scaling strength linearly with the shear modulus is too soft at high pressures and offer discussion as to how descriptions of slip mediated plasticity could result in an alternative scaling that is consistent with the data.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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↗
Direct measurement and calculation of rubber bulk modulus by piston-cylinder method using conventional mechanical testing equipment
This article describes a method to directly measure the bulk modulus of rubber using a piston-cylinder type apparatus. The function of the testing apparatus is to reliably transfer load to the water inside the vessel and allow for the accurate and continuous measurement of volumetric displacement as the contents are compressed. During the test, load is applied to a piston-cylinder containing the rubber test sample and water using a conventional mechanical testing load frame. Load and the travel of the piston are recorded by a load cell and extensometer, respectfully. A brass or stainless steel plug of the same dimensions as the test sample is tested as a control sample to isolate the compliance of the system, including the compressibility of water and compliance of the piston-cylinder. The results from this control test are used to disincorporate the compliance of the system from the sample test results. Load-linear displacement data are mathematically converted to pressure-volumetric displacement data, from which bulk modulus is calculated. The test apparatus and method are validated using the known bulk modulus of water. Finally, the bulk modulus for two similar rubbers is evaluated. The validity of the results and limitations of the device are discussed.
36 MATERIALS SCIENCE↗
Interfacial Strength in Hierarchical Carbon Fiber Composites: Interplay of Interphase Modulus and Roughness
A facile, direct deposition approach that exploits van der Waals interactions between carbonaceous materials is utilized to create unidirectional hybrid carbon fiber composites. Two small molecule crosslinkers, a trifunctional aromatic (TL) and a difunctional aliphatic (DL) acyl chloride, are first utilized to create a crosslinked interphase with a softer and stiffer modulus respectively. TL crosslinked interphase with a higher modulus improved the tensile strength by 50%, despite non-covalent linking between fiber and matrix, elucidating the critical role of the interphase in alleviating modulus mismatch between the high modulus carbon fiber and the rubbery matrix. Fractional quantities of carbon nanotubes are additionally dispersed in the small molecule crosslinkers which behaved as a dispersant, helping introduce nanoasperities on the carbon fiber surface. Strong “pi-pi” interactions between CNTs and CF contributed to tensile properties, which are increased by 66% compared to the control. A cohesive zone model suggests that a stiffer interphase is better able to exploit surface heterogeneities and roughness on the fiber, synergistically enhancing interfacial strength.
36 MATERIALS SCIENCE↗
Atom-in-jellium predictions of the shear modulus at high pressure
Atom-in-jellium calculations of the Einstein frequency in condensed matter and of the equation of state were used to predict the variation of shear modulus from zero pressure to ~10 7 g/cm 3 , for several elements relevant to white dwarf stars and other self-gravitating systems. This is by far the widest range reported electronic structure calculation of shear modulus, spanning from ambient through the one-component plasma to extreme relativistic conditions. The predictions were based on a relationship between the Debye temperature and shear modulus, which we assess to be accurate at the o(10%) level, and is the first known use of atom-in-jellium theory to calculate a shear modulus. Finally, we assessed the overall accuracy of the method by comparing with experimental measurements and more detailed electronic structure calculations at lower pressures.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Analytic fits to atom-in-jellium shear modulus predictions
Fits to AJ shear modulus calculations from ρ0 to the limit of the corresponding AJ EOS table (usually 1000 ρ0), adjusted to reproduce STP shear modulus where possible. Fitting minimized the fractional difference, so low-pressure points would be reproduced accurately despite the wide-ranging tabulation. AJ calculations were at T=0. Isochoric variation G(T) has been small for all cases spot-tested so far, and may have either sign. The fitted equation usually matches the AJ data to within a few percent. Between numerical noise in the AJ calculation and probably-physical structure not captured by the equation, the deviation could be up to 20% in some places in most models, and 30% in a few. AJ does not capture structural phase transitions or phases stabilized by directional bonds, where the shear modulus may vary by a greater amount. Where possible, STP ρ,G were used as parameters, and low pressure AJ points were de-weighted or removed if necessary. Otherwise, such as where AJ fails to capture solid phases with a significantly different shear modulus, the AJ data were fitted as far down in pressure as possible, G0 was also fitted if necessary, and ρ0 was also adjusted if needed to keep G0>0. The resulting models are not intended for use at low pressure, though some are probably adequate for practical purposes
36 MATERIALS SCIENCE↗
Electrode Elastic Modulus as the Dominant Factor in the Capping Effect in Ferroelectric Hafnium Zirconium Oxide Thin Films
The discovery of ferroelectricity in hafnia based thin films has catalyzed significant research focused on understanding the ferroelectric property origins and means to increase stability of the ferroelectric phase. Prior studies have revealed that biaxial tensile stress via an electrode “capping effect” is a suspected ferroelectric phase stabilization mechanism. This effect is commonly reported to stem from a coefficient of thermal expansion (CTE) incongruency between the hafnia and top electrode. Despite reported correlations between ferroelectric phase fraction and electrode CTE, the thick silicon substrate dominates the mechanics and CTE-related stresses, negating any dominant contribution from an electrode CTE mismatch toward the capping effect. In this work, these discrepancies are reconciled, and the origin of these differences deriving from electrode elastic modulus, not CTE, is demonstrated. Pt/M/TaN/Hf 0.5 Zr 0.5 O 2 /TaN/Si devices, where M is platinum, TaN, iridium, tungsten, and ruthenium, were fabricated. Sin 2 (ψ)-based X-ray diffraction measurements of biaxial stress in the HZO layer reveal a strong correlation between biaxial stress, remanent polarization, and electrode elastic modulus. Conversely, a low correlation exists between the electrode CTE, HZO biaxial stress, and remanent polarization. A higher elastic modulus enhances the resistance to electrode elastic deformation, which intensifies the capping effect during crystallization, and culminates in the tandem restriction of out-of-plane hafnia volume expansion and preferential orientation of the polar c-axis normal to the plane. These behaviors concomitantly increase the ferroelectric phase stability and polarization magnitude. This work provides electrode material selection guidelines toward the development of high-performing ferroelectric hafnia into microelectronic devices, such as nonvolatile memories.
36 MATERIALS SCIENCE↗
Electronically driven collapse of the bulk modulus in δ -plutonium
Plutonium metal exhibits an anomalously large softening of its bulk modulus at elevated temperatures that is made all the more extraordinary by the finding that it occurs irrespective of whether the thermal expansion coefficient is positive, negative, or zero—representing an extreme departure from conventional Grüneisen scaling. We show here that the cause of this softening is the compressibility of plutonium’s thermally excited electronic configurations, which has thus far not been considered in thermodynamic models. We show that when compressible electronic configurations are thermally activated, they invariably give rise to a softening of the bulk modulus regardless of the sign of their contribution to the thermal expansion. The electronically driven softening of the bulk modulus is shown to be in good agreement with elastic moduli measurements performed on the gallium-stabilized δ phase of plutonium over a range of temperatures and compositions and is shown to grow rapidly at small concentrations of gallium and at high temperatures, where it becomes extremely sensitive to hydrostatic pressure.
36 MATERIALS SCIENCE↗
Predicting the tensile and compressive modulus of electrospun fiber mat‐reinforced hydrogels using the Halpin–Tsai equations
Abstract The reinforcement of mechanically‐weak hydrogels to yield composites with increased stiffness, strength, or toughness is a well‐established approach. In particular, introducing electrospun nanofibers into hydrogels is a common strategy for biomedical applications, as the resulting hierarchical structure mimics biology and allows for control over fiber diameter and alignment and tuning of mechanical properties. However, further study of the link between the constituent materials and the mechanical properties of the composite is uncommon. One potential model to understand the mechanical properties of fiber‐reinforced hydrogels involves the Halpin–Tsai equations, which relate the modulus values of the fibers and hydrogel matrix and the fiber volume fraction, to the modulus of the composite. To assess the application of this model to fiber‐reinforced hydrogels, predicted values were compared with experimental values from mechanical testing of a poly(ethylene glycol) (PEG) matrix reinforced with an electrospun polycaprolactone (PCL) fiber mat. Although the equations described these systems well in tension, providing a facile approach to identify a fiber volume fraction that will achieve a desired modulus, the Halpin–Tsai approach was less successful under compression. This study motivates additional investigation of the role of structural features of hydrogel composites in determining mechanical properties to enable design of materials for specific applications.
Polymer Science↗
Dark matter and dark radiation from the early universe with a modulus coupled to the PQMSSM
The supersymmetrized DFSZ axion model is especially compelling in that it contains 1. the SUSY solution to the gauge hierarchy problem, 2. the Peccei-Quinn (PQ) solution to the strong CP problem and 3. the Kim-Nilles solution to the SUSY μ problem. In a string setting, where a discrete R-symmetry ($Z$$^{R}_{24}$ for example) may emerge from the compactification process, a high-quality accidental axion (accion) can emerge from the accidental, approximate remnant global U(1) PQ symmetry where the decay constant f a is linked to the SUSY breaking scale, and is within the cosmological sweet zone. In this setup, one also expects the presence of stringy remnant moduli fields Φ i . Here, we consider the situation of a single light modulus Φ coupled to the PQMSSM in the early universe, with mixed axion plus higgsino-like WIMP dark matter. We evaluate dark matter and dark radiation production via nine coupled Boltzmann equations and assess the severity of the cosmological moduli problem (CMP) along with dark matter and dark radiation production rates. We find that typically the light modulus mass should be m Φ ≳ 10 4 TeV to avoid the moduli-induced dark matter overproduction problem. If one is able to (anthropically) tune the modulus field amplitude, we find a value of Φ 0 ≲ 10 –7 m P would be required to solve the overall CMP.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
In Situ Synchrotron X-ray Diffraction Investigations of the Nonlinear Deformation Behavior of a Low Modulus β -Type Ti36Nb5Zr Alloy
The low modulus β-type Ti alloys usually have peculiar deformation behaviors due to their low phase stability. However, the study of the underlying mechanisms is challenging since some physical mechanisms are fully reversible after the release of the load. In this paper, the deformation behavior of a low modulus β-type Ti36Nb5Zr alloy was investigated with the aid of in situ synchrotron X-ray diffraction (SXRD) during tensile loading. The evolution of lattice strains and relative integrated diffraction peak intensities of both the β and α” phases were analyzed to determine the characteristics of the potential deformation mechanisms. Upon loading, the α” diffraction spots appeared at specific azimuth angles of the two-dimensional SXRD patterns due to the <110> fiber texture of original β grains and the selection of favorable martensitic variants. The nonlinear deformation behavior originated from a reversible stress-induced martensitic transformation (SIMT). However, the SIMT contributed a little to the large recoverable strain of over 2.0%, which was dominated by the elastic deformation of the β phase. Various deformation mechanisms were activated successively at different applied strains, including elastic deformation, SIMT and plastic deformation. Our investigations provide in-depth understandings of the deformation mechanisms in β-type Ti alloys with low elastic modulus.
36 MATERIALS SCIENCE↗
A Solution-Processable High-Modulus Crystalline Artificial Solid Electrolyte Interphase for Practical Lithium Metal Batteries
The solid electrolyte interphase (SEI) has been identified as a key challenge for Li metal anodes. The brittle and inhomogeneous native SEI generated by parasitic reactions between Li and liquid electrolytes can devastate battery performance; therefore, artificial SEIs (ASEIs) have been proposed as an effective strategy to replace native SEIs. Herein, as a collaboration between academia and industrial R&D teams, a multifunctional (crystalline, high modulus, and robust, Li + ion conductive, electrolyte-blocking, and solution processable) ASEI material, LiAl-FBD (where “FBD” refers to 2,2,3,3-tetra-fluoro-1,4-butanediol), for improving Li metal battery performance is designed and synthesized. The LiAl-FBD crystal structure consists of Al 3+ ions bridged by FBD 2– ligands to form anion clusters while Li + ions are loosely bound at the periphery, enabling an Li + ion conductivity of 9.4 × 10 –6 S cm –1 . Further, the fluorinated, short ligands endow LiAl-FBD with electrolyte phobicity and high modulus. The ASEI is found to prevent side reactions and extend the cycle life of Li metal electrodes. Specifically, pairing LiAl-FBD coated 50 μm thick Li with industrial 3.5 mAh cm –2 NMC811 cathode and 2.8 μL mAh –1 lean elec-trolyte, the Li metal full cells show superior cycle life compared to bare ones, achieving 250 cycles at 1 mA cm –2 .
25 ENERGY STORAGE↗
Ultrafine-grained Fe-TiB 2 high-modulus nanocomposite steel with high strength and isotropic mechanical properties by laser powder bed fusion
Fe-TiB 2 metal matrix composite, also called high-modulus steels (HMSs), are of great interest for applications in fuel-efficient transportation infrastructure, aerospace, and wear industries due to their high specific stiffness and yield strength. However, conventional cast Fe-TiB 2 HMSs often contain coarse and sharp-edged TiB 2 particles which easily trigger premature cracking during loading. Here, we synthesized a Fe-TiB 2 nanocomposite HMS via laser powder bed fusion (LPBF) additive manufacturing of mixed micro-sized powders of Fe, Ti, and Fe 2 B. We investigated the microstructure formation and mechanical behavior of the Fe-TiB 2 HMS. We found that in situ chemical reaction of Ti and Fe 2 B enables the formation of TiB 2 particles at nanoscale during rapid solidification of LPBF. These nanoscale TiB 2 particles can serve as heterogeneous nucleation sites and promote the formation of ultrafine and equiaxed α-Fe grains with random crystallographic textures, which differ from many other additively manufactured (AM) metal alloys characteristic of strong crystallographic textures. As such, isotropic mechanical properties were achieved in the AM Fe-TiB 2 nanocomposite HMS with a high elastic modulus of ~ 240 GPa, an exceptional yield strength of ~ 1450 MPa, and a large plasticity of ~ 20% under compression. Quantitative analysis reveals that the high yield strength primarily originates from strengthening contributions of the ultrafine grains with an average grain size of ~450 nm, the nanoscale TiB 2 reinforcing particles of 20–180 nm, and a high density of printing-induced dislocations of the order of 10 15 m –2 . In situ synchrotron high-energy X-ray diffraction unveils the load partitioning from the softer α-Fe matrix to the stiffer and stronger TiB 2 nanoparticles, contributing to the sustained strain hardening during compression. Our work not only provides a general pathway for achieving high-performance metal matrix nanocomposites by in situ chemical reaction and precipitation of ceramic nanoparticles during additive manufacturing, but also offers mechanistic insights into the deformation mechanism of nanoparticle-reinforced HMS composites.
36 MATERIALS SCIENCE↗
A combined machine learning and density functional theory study of binary Ti-Nb and Ti-Zr alloys: Stability and Young’s modulus
The multicomponent Ti alloys, specifically the -phase, have experienced a strong growth over the last decades, due to their outstanding properties of ultra-high strength and low Young’s modulus. These properties play a significant role in many aerospace and biomedical applications. Selection and optimization of multicomponent alloys is challenging due to the vast chemical and compositional space. Here we investigate the use of machine learning techniques informed by density functional calculations to guide the selection of Nb- and Zr-based Ti binary alloys. From the cubic structures obtained from high throughput calculations and literature, we identify several structures with Young’s moduli below 40 GPa. The multivariant decision tree methods provide efficient surrogate models to identify structure variables have high influences on the energetic stability and Young’s modulus. Furthermore, we implement a workflow of incorporating DFT provided results and machine learning method to explore the chemical and composition space of other binary and multicomponent alloys, to eventually accelerate the material design via taking advantages of identified key variables.
36 MATERIALS SCIENCE↗