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DOE OSTI2022

Analysis of sparse recovery for Legendre expansions using envelope bound

We provide novel sufficient conditions for the uniform recovery of sparse Legendre expansions using ℓ 1 minimization, where the sampling points are drawn according to orthogonalization (uniform) measure. So far, conditions of the form m ≳ Θ 2 s x log factors have been relied on to determine the minimum number of samples m that guarantees successful reconstruction of s-sparse vectors when the measurement matrix is associated to an orthonormal system. However, in case of sparse Legendre expansions, the uniform bound Θ of Legendre systems is so high that these conditions are unable to provide meaningful guarantees. Here, in this paper, we present an analysis which employs the envelop bound of all Legendre polynomials instead, and prove a new recovery guarantee for s-sparse Legendre expansions, m ≳ Θs 2 x log factors, which is independent of Θ. Arguably, this is the first recovery condition established for orthonormal systems without assuming the uniform boundedness of the sampling matrix. The key ingredient of our analysis is an extension of chaining arguments, recently developed in Bourgain and Chkifa et al., to handle the envelope bound. Furthermore, our recovery condition is proved via restricted eigenvalue property, a less demanding replacement of restricted isometry property which is perfectly suited to the considered scenario. Along the way, we derive simple criteria to detect good sample sets. Our numerical tests show that sets of uniformly sampled points that meet these criteria will perform better recovery on average.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Coefficient of Thermal Expansion Evolution during Ratchet Growth of PBX 9502 and Neat TATB

The Plastic-Bonded Explosive (PBX) 9502 is comprised of the insensitive high explosive TATB (triamino trinitrobenzine) crystals coated in FK-800 polymer binder and isostatically pressed. The TATB crystals have a graphitic, plate-like morphology and possess significant thermal and mechanical anisotropy. Compactions of neat TATB or TATB-based composites (like PBX 9502) have been shown to have TATB crystals that are oriented during the pressing process giving rise to TATB texture and resulting in micro- and macro-scale anisotropy of the compaction. Thermal cycling of the compactions results in irreversible volume expansion (or ratchet growth) likely by creating stress points on the microscale. However, the actual mechanism behind this expansion is not fully understood. Previous characterization of the ratchet growth phenomenon has focused on the magnitude of the irreversible strain as measured before and after a thermal cycle. In the work presented here, we analyze the evolving thermal expansion behavior during the ascending and descending temperature ramps and compare differences observed due to the presence/absence of binder in the compaction.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2024

Negative thermal expansion coefficient and amorphization in defective 4H-SiC

This paper presents thermal expansion coefficient (TEC) and amorphization in 4H-SiC containing point defects at different concentrations. We considered vacancy defects, interstitial defects, and Frenkel pair defects and investigated the thermomechanical response of the lattice over a wide range of temperatures using classical molecular dynamics simulations. The results show that 4H-SiC with vacancy defects exhibits a negative TEC above a critical defect density of around 9% (irrespective of the temperature). With interstitial defects, it exhibits a positive TEC (regardless of the defect density), and with Frenkel pair defects it shows a transition from positive TEC to negative TEC for a defect density greater than 8%. The coupling between temperature-induced expansion and defect-introduced stress in the lattice forms the mechanistic basis for the observed variation in TEC. Furthermore, the specific heat decreases rapidly with an increase in defect density at room temperature, with the highest sensitivity of the lattice observed for the Frenkel pair defects followed by interstitial defects and then by vacancy defects. Finally, these findings highlight the critical implications of defects on thermal expansion behavior of 4H-SiC with applications in radiation environments.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Calcium nitrate: A chemical admixture to inhibit aggregate dissolution and mitigate expansion caused by alkali-silica reaction

Alkali-silica reaction (ASR) is a significant cause of the degradation of concrete structures. ASR results from the dissolution of reactive silicate aggregates and the subsequent formation of damaging, expansive ASR gels. Despite the prevalence of ASR, so far only lithium-based chemical admixtures have been shown to be successful in mitigating its deleterious effects. Herein, dissolved calcium nitrate (Ca(NO 3 ) 2 : CN) is demonstrated to reduce ASR-induced expansion caused by the use of sodium borosilicate (NBS) glass as a model reactive aggregate. The significance of reductions of NBS-glass dissolution and mortar-bar expansion rates is discussed, with special focus on highlighting the mechanism by which calcium nitrate mitigates ASR, i.e., by the inhibition of aggregate dissolution. This study reveals a new and cost-effective pathway to suppress aggregate dissolution and ASR in concrete based on the dosage of soluble alkaline-earth additives.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Modeling brittle fracture due to anisotropic thermal expansion in polycrystalline materials

Here, this work investigated brittle fracture of polycrystalline materials due to thermal stresses arising from anisotropic thermal expansion. We used phase-field fracture simulations with the properties of alpha-uranium (α-U) and assumed a linear elastic mechanical response. Three-dimensional simulations were used to predict fracture for various conditions and crystallographic textures. We found that fracture was more pronounced during cooling than during heating because the anisotropy increased with temperature. We also found that the total crack surface area increased with increasing average misorientation, while the net shape change of the material decreased with increasing misorientation. Two-dimensional simulations in which one crystallographic coefficient of thermal expansion (CTE) was set to zero indicated that the expansion behavior in the crystallographic direction with the smallest CTE was the primary cause of fracture.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Gapped-filtering for efficient Chebyshev expansion of the density projection operator

In this paper, we develop the gapped-filtering method, whereby a short Chebyshev expansion accurately represents the density-matrix operator. The method optimizes the Chebyshev coefficients to give the correct density matrix at all energies except within the gapped region where there are no eigenstates. Gapped filtering reduces the number of required terms in the Chebyshev expansion compared to traditional expansion methods, as long as one knows or can determine efficiently the HOMO and LUMO positions. The reduction is especially noticeable (factors of 2-3) when high accuracy is sought. To exemplify the method, we use gapped-filtering to increase the efficiency of stochastic-GW calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Parallel computing for power system climate resiliency: Solving a large-scale stochastic capacity expansion problem with mpi-sppy

Here we propose a nodal stochastic generation and transmission expansion planning model that incorporates the output from high-resolution global climate models through load and generation availability scenarios. We implement our model in Pyomo and perform computational studies on a realistically-sized test case of the California electric grid in a high performance computing environment. We propose model reformulations and algorithm tuning to efficiently solve this large problem using a variant of the Progressive Hedging Algorithm. We utilize the parallelization capabilities and overall versatility of mpi-sppy, exploiting its hub-and-spoke architecture to concurrently obtain inner and outer bounds on an optimal expansion plan. Initial results show that instances with 360 representative days on a system with over 8,000 buses can be solved to within 5% of optimality in under 4 h of wall clock time, a first step towards solving a large-scale power system expansion planning problem across a wide range of climate-informed operational scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Discrete versus continuous: Enhancing battery optimization in capacity expansion models

This study compares two battery modeling approaches for capacity expansion models: discrete-duration and continuous-duration formulations. In the discrete approach, battery duration is fixed, and power capacity is optimized. In the continuous approach, both power and energy capacities are decision variables, allowing storage duration to be optimized endogenously. Although both discrete-duration and continuous-duration battery formulations are used in long-term power system planning models, the literature has provided limited direct, systematic comparisons of their implications within a common modeling framework. To address this gap, this study implements both approaches in the Regional Energy Deployment System (ReEDS TM ) capacity expansion model using two resource adequacy methods, across a range of future system conditions, and with varying battery cost projections. Results show continuous-duration and high-resolution discrete approaches produce similar capacity expansion outcomes. The continuous formulation achieves faster runtimes compared to discrete-duration runs with many discrete-duration options. However, the discrete-duration approach allows users to choose to have limited fidelity for storage duration options, which in some cases can outperform the continuous formulation. The continuous formulation has the lowest overall system costs, indicating its ability to fine-tune storage duration to better meet specific system needs. This study's findings provide a side-by-side evaluation of discrete and continuous battery modeling approaches and offer guidance for improving the representation of real-world systems, flexibility, and computational efficiency for representing energy storage in long-term power system planning models.

25 ENERGY STORAGE↗

DOE OSTI2025

High-temperature stability and thermal expansion behavior of equi-atomic refractory multi-principal element alloys based on MoNbTi system for Gen IV reactor applications

The present study investigates the thermal stability and thermal expansion behavior of seven equi-atomic refractory multi-principal element alloys (MPEAs) based on the MoNbTi ternary system composed of low neutron absorption cross section elements. Through an integrated approach utilizing in-situ high-temperature X-ray diffraction (HT-XRD) in conjunction with differential scanning calorimetry (DSC), dilatometry and ageing heat treatment, the thermal stability of the MPEAs was comprehensively analyzed. In-situ HT-XRD experiment confirmed the stability of the room temperature phases up to 1000 °C with no peaks observed corresponding to additional phases in the HT-XRD patterns at 500, 800 and 1100 °C. DSC thermograms showed the absence of peaks up to 1000 °C, while peaks and valleys corresponding to exothermic and endothermic events were observed above 1000 °C. Coefficient of thermal expansion (CTE) derived from second order polynomial fitting of linear thermal expansion data from the dilatometry experiment showed linear increment up to 1000 °C for all the alloys except those containing Zr. The Cr containing alloys exhibited notably higher CTE values, particularly the Al containing alloy exhibited the highest value. Ageing heat treatment at 800 and 1000 °C for 96 h and subsequent microstructural analysis revealed significant precipitation of secondary phases in MoNbTiZr, MoNbTiZrV and MoNbTiCrAl. In conclusion, a substantial increase in hardness was observed in MoNbTiZr and MoNbTiCrAl due to secondary phase precipitation, while the other alloys maintained hardness values comparable to their as-cast and homogenized states.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Enhanced negative thermal expansion of boron-doped Fe 43 Mn 28 Ga 28.97 B 0.03 alloy

Enhanced negative thermal expansion (NTE) properties are achieved by introducing a little amount of boron in the Fe 43 Mn 28 Ga 28.97 B 0.03 alloy. As a result, this alloy shows a giant NTE coefficient of alpha(1) = -79.7 x 10 -6 K -1 in a wide temperature range from 277 K to 136 K. Compared to the NTE characteristics in Fe 43 Mn 28 Ga 29 , the NTE operation temperature window has expanded by 74% with the corresponding coefficient of thermal expansion increased by 57% within the NTE temperature window for the boron-doped Fe 43 Mn 28 Ga28.97B0.03. Additionally, in-situ synchrotron high-energy X-ray diffraction results suggest that by boron substitution, the large unit cell volume change across martensitic transformation and the wide phase transition temperature interval are responsible for the pronounced NTE behavior in Fe 43 Mn 28 Ga 28.97 B 0.03 . Moreover, for the Fe 43 Mn 28 Ga 28.97 B 0.03 NTE material, the compressive strength and strain are significantly improved compared with that of Fe 43 Mn 28 Ga 29 . The present study indicates that Fe 43 Mn 28 Ga 28.97 B 0.03 with enhanced NTE across martensitic transformation may be used for practical application as thermal-expansion compensators.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Towards new zero-thermal-expansion materials: Li-free quartz solid solutions stuffed with transition metal cations

Stuffed aluminosilicate quartz solid solutions (Qss) represent the main functional component of state-of-the-art zero-thermal-expansion glass-ceramics. For the first time, we present the synthesis of Li-, Mg- and Zn-free Qss solely stuffed with transition metal cations (Fe 2+ , Ni 2+ , Co 2+ ); partial Li + co-doping enables also significant Mn 2+ incorporation. Further, they were obtained by glass powder crystallization; Qss crystals exhibit compositionally tunable coefficients of thermal expansion (CTEs), from - 2 × 10 -6 K -1 to ~10 × 10 -6 K -1 in the range 30–300 °C. Co 2+ -bearing crystals exhibit the closest-to-zero CTE value (0.2 ×10 -6 K -1 ) and the most isotropic behavior in the whole Qss family, opening up new perspectives for the development of Li-free low-expansion materials. From a structural point of view, we identified the unit cell volume (and not the pseudo-hexagonality of the aluminosilicate framework) as the key structural parameter leading to low or negative CTEs in Qss, with a linear correlation extending to non-stuffed non-silicate quartz-like phases.

36 MATERIALS SCIENCE↗

DOE OSTI2023

High-temperature chemical expansion of Pr0.1Ce0.9O2-δ thin films determined by Differential Laser Doppler Vibrometry

The chemical expansion of thin-film praseodymium-cerium oxide solid solutions (Pr 0.1 Ce 0.9 O 2-δ , PCO10) is investigated at temperatures ranging from 500 °C to 800 °C and oxygen activities down to about 10 -22 . Differential Laser Doppler Vibrometry (D-LDV) in combination with periodic electrochemical pumping of oxygen is used to detect very small displacements of the sample surface. With decreasing pumping frequency, the film approaches chemical equilibrium, which is nearly reached at 700 °C below 0.01 Hz. D-LDV enables direct measurement of film thickness changes as well as the bending of the underlying substrates due electrochemically induced lateral mechanical stress. The substrate bending is found to be more than an order of magnitude larger than the film thickness change, increasing the detection limit by the same factor. The thickness change of the thin film is calculated from the measured displacement of the sample surface and compared with directly measured values. Thin-film literature data available for low oxygen activities up to 650 °C agree with our measurements. In addition, the thickness change of the film is determined from the displacement at different sample positions, which validates previous measurements. Finally, thin film chemical expansion is found to be larger by a factor of about 2 than the corresponding bulk value in agreement with predictions from a mechanical model that the out-of-plane expansion of a constrained film is increased.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Bayesian-based response expansion and uncertainty quantification using sparse measurement sets

Systems subjected to dynamic loads often require monitoring of their vibrational response, but limitations on the total number and placement of the measurement sensors can hinder the data-collection process. Here, we present an indirect approach to estimate a system’s full-field dynamic response, including all uninstrumented locations, using response measurements from sensors sparsely located on the system. This approach relies on Bayesian inference that utilizes a system model to estimate the full-field response and quantify the uncertainty in these estimates. By casting the estimation problem in the frequency domain, this approach utilizes the modal frequency response functions as a natural, frequency-dependent weighting scheme for the system mode shapes to perform the expansion. This frequency-dependent weighting scheme enables an accurate expansion, even with highly correlated mode shapes that may arise from spatial aliasing due to the limited number of sensors, provided these correlated modes do not have natural frequencies that are closely spaced. Furthermore, the inherent regularization mechanism that arises in this Bayesian-based procedure enables the utilization of the full set of system mode shapes for the expansion, rather than any reduced subset. This approach can produce estimates when considering a single realization of the measured responses, and with some modification, it can also produce estimates for power spectral density matrices measured from many realizations of the responses from statistically stationary random processes. A simply supported beam provides an initial numerical validation, and a cylindrical test article excited by acoustic loads in a reverberation chamber provides experimental validation.

42 ENGINEERING↗

DOE OSTI2021

Computation of the Thermal Expansion Coefficient of Graphene with Gaussian Approximation Potentials

Direct experimental measurement of thermal expansion coefficient without substrate effects is a challenging task for two-dimensional (2D) materials, and its accurate estimation with large-scale ab initio molecular dynamics is computationally very expensive. Machine learning-based interatomic potentials trained with ab initio data have been successfully used in molecular dynamics simulations to decrease the computational cost without compromising the accuracy. In this work, we investigated using Gaussian approximation potentials to reproduce the density functional theory-level accuracy for graphene within both lattice dynamical and molecular dynamical methods, and to extend their applicability to larger length and time scales. Two such potentials are considered, GAP17 and GAP20. GAP17, which was trained with pristine graphene structures, is found to give closer results to density functional theory calculations at different scales. Further vibrational and structural analyses verify that the same conclusions can be deduced with density functional theory level in terms of the reasoning of the thermal expansion behavior, and the negative thermal expansion behavior is associated with long-range out-of-plane phonon vibrations. Thus, it is argued that the enabled larger system sizes by machine learning potentials may even enhance the accuracy compared to small-size-limited ab initio molecular dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Guest-Induced Large and Tunable Negative Thermal Expansion in Soft Microporous Carbon

Materials that exhibit negative thermal expansion (NTE) are of fundamental interest due to their rarity and counterintuitive behavior. While research in this area has been directed toward the discovery of materials that display NTE and explaining its origin, there has been less attention to describing the complexities of a secondary phase or other guests that could influence the magnitude and mechanism of NTE. We report herein that zeolite-templated carbon (ZTC), a soft carbonaceous framework solid with ordered microporosity, exhibits a large and widely tunable thermal expansion in the presence of adsorbed guests. For ZTC in the presence of CO 2 at 1 bar, the largest coefficient of isotropic NTE ever observed (−8.4 × 10 –4 K –1 ) is measured between 200 and 220 K. These results comprise a tunable mechanism of thermal expansion based on the interaction between two independent, positively expanding phases that together give rise to an anomalous guest-induced NTE under certain conditions.

03 NATURAL GAS↗

DOE OSTI2023

Interplanar Ferromagnetism Enhanced Ultrawide Zero Thermal Expansion in Kagome Cubic Intermetallic (Zr,Nb)Fe 2

A cubic metal exhibiting zero thermal expansion (ZTE) over a wide temperature window demonstrates significant applications in a broad range of advanced technologies but is extremely rare in nature. Here, enabled by high-temperature synthesis, we realize tunable thermal expansion via magnetic doping in the class of kagome cubic (Fd-3m) intermetallic (Zr,Nb)Fe 2 . A remarkably isotropic ZTE is achieved with a negligible coefficient of thermal expansion (+0.47 x 10 -6 K -1 ) from 4 to 425 K, almost wider than most ZTE in metals available. A combined in situ magnetization, neutron powder diffraction, and hyperfine Mössbauer spectrum analysis reveals that interplanar ferromagnetic ordering contributes to a large magnetic compensation for normal lattice contraction upon cooling. Trace Fe-doping introduces extra magnetic exchange interactions that distinctly enhance the ferromagnetism and magnetic ordering temperature, thus engendering such an ultrawide ZTE. Finally, this work presents a promising ZTE in kagome metallic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Experimental demonstration of the reduced expansion of a laser-heated surface using a low density foam layer, pertaining to advanced hohlraum designs with less wall-motion

The ablative expansion of laser-heated materials is important for determining how hohlraum cavities can be utilized for inertial confinement fusion. The utility of a low-density foam layer to reduce the density of the expanding heated hohlraum wall is demonstrated here in a series of experiments on the National Ignition Facility. X-ray radiography measurements of the expanding foam-lined Au wall in low aspect-ratio cylindrical geometry are used to compare the impact of Au-doped CH and Ta 2 O 5 foams between 10 and 40 mg/cc on the wall expansion. HYDRA Simulations are used to estimate the x-ray transmission at the 1/4 nc surface, which is important in understanding the absorption of laser light by the plasma. These demonstrate for the first time that a foam layer reduces the expansion of a hohlraum-like target and illustrate that the interplay between the expanding foam plasma and the shock reflected by the hohlraum wall is critical in optimizing foam-liner parameters to achieve the maximum time for a symmetric drive on a capsule.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Thermal expansion of LaB 6 from 298 to 998 K

We propose LaB 6 as a temperature calibration standard for high-temperature (HT) X-ray diffractometry owing to its high temperature stability. Such HT applications require a reliable HT lattice parameter or, equivalently, peak position data, which have not been readily accessible to the diffraction community to date. As such, the thermal expansion behavior of NIST SRM 660a LaB6 was assessed in the temperature range 298–998 K using HT Bragg–Brentano parafocusing θ:θ X-ray diffractometry in conjunction with Rietveld analysis. Data were collected in the 2θ range 20–150° at a data collection rate of 0.5° θ min −1 in air and at 1 atm. The temperature was stepped in 50 K increments. The cubic unit-cell lattice parameter [a(T)] of LaB 6 in Å was found to vary as a(T) = 4.15678 (±0.00001) + Ξ(T − 298 K) + Ψ(T − 298 K) 2 , where Ξ = 2.4645 × 10 −5 (±4.8904 × 10 −8 ) Å K −1 and Ψ = 1.0325 × 10 −8 (±6.7376 × 10 −11 ) Å K −1 . The isobaric volume thermal expansion coefficient (TEC) was obtained as α V P = (5.9291 × 10 −6 ) + (4.9680 × 10 −9 )(T − 298 K) K −1 , from which the corresponding linear TEC was obtained as α L P = (1.9764 × 10 −6 ) + (1.6560 × 10 −9 )(T − 298 K) K −1 . The 3 × 3 matrix representations of the single-crystal isobaric linear TEC and the volume expansivity were obtained for the cubic crystal class to which LaB 6 belongs. Also, the temperature dependence of the lattice parameter data of this study was compared with past landmark studies on LaB 6 by Dutchak et al. [Inorg. Mater. (1972), 8, 1877–1880] and Aivazov et al. [Inorg. Mater. (1979), 15, 1015–1016].

LaB6 standard material↗