Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Nuclear Fusion”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,441 records · Page 80
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Tritium Breeder Composites for Fusion Applications

Due to the short half-life of tritium, all fusion reactors planned for long-term operation using a deuterium-tritium fuel cycle must produce sufficient tritium from reactions outside the core to maintain reactor operation. Typically, the core is surrounded by a tritium breeder blanket filled with lithium-containing materials which react under a neutron flux to form tritium that can then be collected. Here, reactor designers are forced to choose between using chemically reactive liquid breeders (e.g., Pb-Li, FLiBe, Li) or solid breeders, which often have lower lithium concentrations and questionable mechanical integrity under irradiation (e.g., Li4SiO4, Li2TiO3). To expand this pool of options, this work has sought to produce composite tritium breeder materials using lithium-containing ceramics and metal reinforcements. The resultant composite tritium breeders simultaneously feature higher lithium densities and improved mechanical integrity, including tensile strength and toughness, compared to other tritium breeders previously reported in literature.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Low latency optical-based mode tracking with machine learning deployed on FPGAs on a tokamak

Active feedback control in magnetic confinement fusion devices is desirable to mitigate plasma instabilities and enable robust operation. Optical high-speed cameras provide a powerful, non-invasive diagnostic and can be suitable for these applications. Here, in this study, we process high-speed camera data, at rates exceeding 100 kfps, on in situ field-programmable gate array (FPGA) hardware to track magnetohydrodynamic (MHD) mode evolution and generate control signals in real time. Our system utilizes a convolutional neural network (CNN) model, which predicts the n = 1 MHD mode amplitude and phase using camera images with better accuracy than other tested non-deep-learning-based methods. By implementing this model directly within the standard FPGA readout hardware of the high-speed camera diagnostic, our mode tracking system achieves a total trigger-to-output latency of 17.6 μs and a throughput of up to 120 kfps. This study at the High Beta Tokamak-Extended Pulse (HBT-EP) experiment demonstrates an FPGA-based high-speed camera data acquisition and processing system, enabling application in real-time machine-learning-based tokamak diagnostic and control as well as potential applications in other scientific domains.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

The Vacuum Cherenkov Detector (VCD) for γ-ray measurements in inertial confinement fusion experiments

Inertial confinement fusion experiments at both the National Ignition Facility (NIF) and the Laboratory for Laser Energetics OMEGA laser facility currently utilize Cherenkov detectors, with fused silica as the Cherenkov medium. At the NIF, the Quartz Cherenkov Detectors improve the precision of neutron time-of-flight measurements; and at OMEGA, the Diagnostic for Areal Density provides measurements of capsule shell areal densities. An inherent property of fused silica is the radiator’s relatively low energy threshold for Cherenkov photon production (E threshold < 1 MeV), making it advantageous over gas-based Cherenkov detectors for experiments requiring low-energy γ detection. The Vacuum Cherenkov Detector (VCD) has been specifically designed for efficient detection of low energy γ’s. Its primary use is in implosion experiments, which will study reactions relevant to stellar and big-bang nucleosynthesis, such as T( 4 He,γ) 7 Li, 4 He( 3 He,γ) 7 Be, and 12 C(p,γ) 13 N. Further, the VCD is compatible with LLE’s standard Ten-Inch Manipulator diagnostic insertion module. This work will outline the design and characterization of the VCD as well as provide results from recent experiments conducted at the OMEGA laser facility.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Satellite Enveloped with STITCHED Engineering Sensors for Detection of Approaching Objects

Today as well as tomorrows spaceborne assets impact almost all areas of national and nuclear security. Spaceborne assets can not only collect and disseminate valuable data, well beyond just the visual, but also track terrestrial-based mobile assets in real-time, and active spaceborne platforms potentially pose serious risk to vulnerable earth-based systems and infrastructures. The capability to defend national spaceborne assets from attack/interference is critical for security interests. This effort supports this mission through the cost-effective preeminent detection of approaching threats to our nation’s vital resources, in order to help secure and trust these high-value assets against the threats of tomorrow. This project develops novel fabrication techniques for conformal, low-profile and lightweight leakywave antenna (LWA) detection/imaging systems, which fuses technical embroidery (TE) and laser ablation (LA) processes with LWA design. Technical embroidery is an emerging field in additive textile manufacturing where flexible materials and functionalized fabrics are created for a wide variety of uses and purposes, while laser ablation is the process of removing material from a solid surface by irradiating it with a laser beam. Here, thin, conformal antenna designs are designed, modeled and fabricated using both TE and LA, to create lightweight, flexible and conformal object detection and imaging radars. This novel development ensures our nation’s ability to field advanced lightweight and conformal technologies to protect spaceborne assets.

42 ENGINEERING↗
DOE OSTI2023

Experimental study of the S 38 excited level scheme

Information on the 38 S level scheme was expanded through experimental work utilizing a fusion-evaporation reaction and in-beam γ-ray spectroscopy. Prompt γ-ray transitions were detected by the Gamma-Ray Energy Tracking Array (GRETINA) and recoiling 38 S residues were selected by the Fragment Mass Analyzer (FMA). Tools based on machine-learning techniques were developed and deployed for the first time in order to enhance the unique selection of 38S residues and identify any associated γ-ray transitions. The new level information, including the extension of the even-spin yrast sequence through J π =8( + ), was interpreted in terms of a basic single-particle picture as well shell-model calculations which incorporated the empirically derived FSU interaction. A comparison between the properties of the yrast states in the even-Z, N = 22 isotones from Z = 14 to 20, and for 36 Si– 38 S in particular, was also presented with an emphasis on the role and influence of the neutron 1 p 3/2 orbital on the structure in the region.

20 ≤ A ≤ 38↗
DOE OSTI2023

Anomaly Detection in Liquid Sodium Cold Trap Operation with Multisensory Data Fusion Using Long Short-Term Memory Autoencoder

Sodium-cooled fast reactors (SFR), which use high temperature fluid near ambient pressure as coolant, are one of the most promising types of GEN IV reactors. One of the unique challenges of SFR operation is purification of high temperature liquid sodium with a cold trap to prevent corrosion and obstructing small orifices. We have developed a deep learning long short-term memory (LSTM) autoencoder for continuous monitoring of a cold trap and detection of operational anomaly. Transient data were obtained from the Mechanisms Engineering Test Loop (METL) liquid sodium facility at Argonne National Laboratory. The cold trap purification at METL is monitored with 31 variables, which are sensors measuring fluid temperatures, pressures and flow rates, and controller signals. Loss-of-coolant type anomaly in the cold trap operation was generated by temporarily choking one of the blowers, which resulted in temperature and flow rate spikes. The input layer of the autoencoder consisted of all the variables involved in monitoring the cold trap. The LSTM autoencoder was trained on the data corresponding to cold trap startup and normal operation regime, with the loss function calculated as the mean absolute error (MAE). The loss during training was determined to follow log-normal density distribution. During monitoring, we investigated a performance of the LSTM autoencoder for different loss threshold values, set at a progressively increasing number of standard deviations from the mean. The anomaly signal in the data was gradually attenuated, while preserving the noise of the original time series, so that the signal-to-noise ratio (SNR) averaged across all sensors decreased below unity. Results demonstrate detection of anomalies with sensor-averaged SNR < 1.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Contactless Position Measurement System for Remote Alignment of Highly Reflective Objects

The Contactless Position Measurement System (CPMS) permits automatic alignment of highly-reflecting components that cannot or should not be touched by human hands, such as those used in SRF cavities. CPMS also has application during maintenance of fusion reactors, when the components in the reactor are radioactive. The length of time for which humans can handle the components in order to carry out maintenance or repairs is limited. We would like to measure the relative positions of such objects so we can bring them into alignment with motorized stages, thus eliminating the need for human contact. The CPMS is a computer vision system that measures the location of highly reflective components to within a fraction of a millimeter by finding the edges of silhouette images. This is done by placing a uniform, infrared backlight behind the components, and viewing each component with two low-aberration, infrared cameras. Each of these stereoscopic cameras are located within a coordinate system we set up with reference platforms, light sources, and survey cameras distributed around the perimeter of the string assembly room, or fusion reactor. We obtain stereoscopic silhouette images of each component, and we use these to determine the position of the component within our string assembly coordinate system. The CPMS combines the silhouette images with knowledge of the dimensions of the objects to obtain the relative positions of components in its field of view. These position measurements then allow us to mechanically maneuver the components into contact. Once we know where they are, we can move the components to where they are supposed to be with motorized stages or other mechanical means, check they are in the right place, and bolt them together. In Phase I, we built a prototype infrared backlights and cameras, tested it, wrote an analysis program to fit the images. At a range of 50 cm, we are able to measure the relative positions of two stainless steel flanges with an accuracy of 150 μm rms. The next steps are to test the analysis program with motorized stages, build a full-size prototype, and implement it in an cleanroom with SRF cavity assembly. This can be done in a cost effective way given the materials with which the system is designed. As Open Source Instruments achieved more in Phase I than anticipated, despite not receiving a Phase II SBIR grant, we hope to move forward with product development and sales with a testing partner.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Sodium Chemistry Assessment and Initiation of Sodium Exposure Experiment on A709 Commercial Heats and LPBF 316H SS

This report documents sodium chemistry characterization and the initiation of forced‑convection sodium exposure experiments for two structural materials for sodium‑cooled fast reactors (SFRs): Alloy 709 (solution‑annealed and with an additional 775 °C/10 h precipitation treatment) and laser powder bed fusion (LPBF) 316H stainless steel tensile specimens printed with an as‑built surface condition. The sodium exposure experiment was conducted in a forced‑convection sodium loop with two vessels operated at 550 °C and 600 °C, and a cold trap maintained at <130 °C. Carbon activity in sodium was quantified using a nickel‑foil equilibration method. Initial post‑exposure evaluation after ~1,000 h indicates negligible thickness change for Alloy 709 and a small but measurable mass decrease. To isolate thermal effects from sodium effects, parallel thermal‑aging experiments were performed on Alloy 709 at 550 °C and 600 °C. Baseline tensile tests at room temperature, 550 °C, and 600 °C show expected reduction in strength with increasing temperature and serration tensile curves at elevated temperatures, consistent with dynamic strain aging. After 3,000 h thermal aging, Alloy 709 exhibits modest strengthening and reduced ductility at 550 °C. Together, these results establish the loop chemistry conditions and provide the initial corrosion and mechanical property results for ongoing long‑duration sodium exposure of Alloy 709 and LPBF 316H stainless steel.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Precision measurements of Higgs hadronic decay modes at the FCC-ee

The expected precision at the FCC-ee on the product $σ$ x $\mathcal{B} \large{(}H → b\bar{b}, c\bar{c}, s\bar{s}, gg\large{)}$ of Higgs boson production cross sections times branching ratios of hadronic decays is presented. This study provides the first comprehensive determination of all major hadronic Higgs decay modes in a combined fit at future $e^+e^−$ colliders, using both Higgs-strahlung $(ZH)$ and Vector boson fusion $(v\bar{v}H)$ production processes, with a full treatment of interference effects in the $v\bar{v}jj$ final state. It assumes four identical IDEA detectors collecting $e^+e^−$ collisions at $\sqrt{s}$ = 240 and 365 GeV. The combination of all channels across both energies, with full covariance between production and decay modes, yields a production cross-section times branching-ratio precision at the percent to per-mil level for the dominant hadronic final states $(b\bar{b}, c\bar{c}, gg)$. These results provide a comprehensive input to the determination of Higgs coupling projections at the FCC-ee, and they establish for the first time sensitivity to the rare decay $H → s\bar{s}$, demonstrating that FCC-ee has the potential to provide evidence of the strange-quark Yukawa coupling.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Divertor shaping with neutral baffling as a solution to the tokamak power exhaust challenge

Exhausting power from the hot fusion core to the plasma-facing components is one fusion energy’s biggest challenges. The MAST Upgrade tokamak uniquely integrates strong containment of neutrals within the exhaust area (divertor) with extreme divertor shaping capability. By systematically altering the divertor shape, this study shows the strongest evidence to date to our knowledge that long-legged divertors with a high magnetic field gradient (total flux expansion) deliver key power exhaust benefits without adversely impacting the hot fusion core. These benefits are already achieved with relatively modest geometry adjustments that are more feasible to integrate in reactor designs. Benefits include reduced target heat loads and improved access to, and stability of, a neutral gas buffer that ‘shields’ the target and enhances power exhaust (detachment). Analysis and model comparisons shows these benefits are obtained by combining multiple shaping aspects: long-legged divertors have expanded plasma-neutral interaction volume that drive reductions in particle and power loads, while total flux expansion enhances detachment access and stability. Containing the neutrals in the exhaust area with physical structures further augments these shaping benefits. These results demonstrate strategic variation in the divertor geometry and magnetic topology is a potential solution to one of fusion’s power exhaust challenge.

magnetically confined plasmas↗
DOE OSTI2022

Spectroscopic signatures and oxidation characteristics of nanosecond laser-induced cerium plasmas

Improving technologies related to the wide area environmental sampling of nuclear materials supports the nuclear nonproliferation mission of preventing the proliferation of nuclear weapons by monitoring nuclear weapons tests and detecting undeclared nuclear fuel cycle activities. Standoff, laser-based detection techniques such as laser-induced breakdown spectroscopy have the potential to offer robust, field-deployable methods that provide rapid element-specific and phase identifiable measurements over a wide range of materials. This work aims to elucidate the effects of atmospheric conditions and oxidation reactions on the highly complex and transient spectroscopic signatures of laser-induced plutonium surrogate plasmas. Time-resolved spectra of nanosecond laser ablation cerium plasmas were measured using laser-induced breakdown spectroscopy in a range of atmospheres containing low to high concentrations of oxygen. Here, the growth of strong CeO molecular emission bands was observed in the visible spectrum, where it was shown that the persistence of CeO is reduced from around 60 μs to 50 μs in oxygen rich atmospheric environments. To further investigate the growth and depletion of CeO in the laser-produced plasma, ratios of CeO-to-Ce emission were generated using integrated intensities corresponding to the Q-branch of the CeO D 1 -X 1 transitions and numerous strong atomic Ce peaks. It was determined that the fastest rate of formation of CeO in argon occurred for moderate oxygen mass fractions between 0.10 and 0.15 while the ratios were reduced at higher oxygen mass fractions (i.e., Y O 2 = 0.20) due to competing oxidation reactions and lower plasma temperatures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Onset of band structure in 70 Ga

Excited states in the odd-odd nucleus 70 Ga were studied using the 62 Ni( 14 C, αpn) fusion-evaporation reaction at the John D. Fox Superconducting Accelerator Laboratory at Florida State University with a 50 MeV beam. Depopulating γ rays were measured in coincidence with a Compton-suppressed Ge array consisting of three Clover detectors and seven single-crystal detectors. Analysis of γ–γ coincidences led to the addition of 16 new transitions to the 70 Ga level scheme, including transitions associated with the onset of a new positive-parity band structure likely based on the πg 9/2 ⊗ νg 9/2 configuration. Spins and parities were assigned using directional correlation of oriented nuclei (DCO) ratios and linear polarization measurements. Shell-model calculations with the JUN45 effective interaction reproduce the excitation energies of the positive-parity states reasonably well but predict negative-parity states that are typically 400–500 keV lower than observed. Furthermore, total Routhian surface calculations for the lowest positive-parity configuration with signature α = 0 indicate significant triaxiality (γ ≈ −20°) and the development of competing non-collective excitations at J = 8, corresponding to the experimentally observed onset of the positive-parity band. Similar features are found in the calculated surfaces for the lowest negative-parity states with α = 0.

59 ≤ A ≤ 89↗
DOE OSTI2024

Impact of gas injection location and divertor surface material on ITER fusion power operation phase divertor performance assessed with SOLPS-ITER *

Abstract The ITER divertor design and performance assessment, primarily based on the SOLPS-4.3 burning plasma database (Pitts R. et al 2019 Nucl. Mater. Energy 20 100696), assumes the use of beryllium (Be) as the divertor surface material and the injection of gas from the main chamber top. However, the current ITER baseline favors gas injection from the more toroidally symmetric sub-divertor region. This paper evaluates the implications of these assumptions for divertor performance in the ITER fusion power operation phase. The impact of the divertor surface material and the gas injection location on the main ions mirrors the hydrogen only low power phase scenario shown in Park J.-S. et al (2020 Nucl. Fusion 61 016021). However, during burning plasma operation, extrinsic impurity seeding will be required. In the case of neon (Ne), studied here, impurity retention is influenced by both the divertor surface material and the fueling location. Neon leakage increases due to more energetic reflection from tungsten than beryllium, but equivalent divertor performance can be achieved by adjusting the neon seeding rate. While the impurity seeding location does not affect the distributions of impurity or radiation, the fueling location does. Top fueling provides local ionization sources mainly in the mid-SOL under detached conditions, enhancing divergences of the flux there (source-driven flow), bringing stagnation points close to the fueling location, and equilibrating flows towards both targets. In contrast, the global flow pattern (in the absence of fluid drifts) in the case of sub-divertor fueling is biased towards the inner target. Impurity flows, driven by force balance, largely mirror those of the main ion flow, including the stagnation point. The case with top fueling enhances Ne retention and corresponding radiation in the outer divertor, effectively reducing the total and peak target heat fluxes by 20%–40%, compared to the case with divertor fueling. Meanwhile, the case with outer target fueling also achieves similar reductions by enhancing plasma-neutral interactions. These results suggest the possibility that the selection of the fueling location and throughput can be used as an actuator to control impurity divertor retention and divertor radiation asymmetry.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

From MAST-U to STEP: Power exhaust control challenges and opportunities

This work explores the challenges and opportunities for power exhaust control in STEP, informed by dedicated MAST-U experiments. The STEP system primarily relies on hydrogenic and argon gas injection into the divertors, compensating for transients originating in the plasma core. Fast transients (>10 Hz) that evolve too quickly for actuators to compensate must be absorbed passively; the enhanced transient buffering of the foreseen long-legged divertor provides a clear advantage over conventional geometries, as demonstrated in the MAST-U Super-X divertor. Experiments further indicate that STEP’s tight divertor baffling enables near-independent control of the upper and lower divertors. The most challenging transients are expected from power-sharing fluctuations, as MAST-U experiments observed extremely fast dynamics. Fluctuations from core pellet fuelling remain relatively benign due to the small pellet size according to simulations. Exhaust control in a reactor like STEP requires an integrated approach befitting its machine-critical nature. A predictive control element, integrated with core plasma control, allows pre-emptive preparation of the divertor for incoming transients. An observer-based diagnostic approach is foreseen to monitor the divertor in the challenging reactor environment, supported by an extended diagnostic set in the non-nuclear phase to validate the required dynamic models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Synergies between H, He and radiation damage in dual and triple ion irradiation of candidate fusion blanket materials

Three ferritic/martensitic alloys were studied to understand the synergistic effect between single ion beam (Fe 2+ ), dual ion beam (Fe 2+ +He 2+ and Fe 2+ +H + ), and triple ion beam (Fe 2+ +He 2+ +H + ) irradiations on cavity evolution. A commercial alloy, F82H, a castable nanostructured alloy, CNA3, and a high purity model alloy, Fe8Cr2W, were irradiated at 400°C to 600°C to a damage level of 50 dpa at a damage rate of 1 × 10 –3 dpa/s with He and H injection rates of 10 and 40 appm/dpa, respectively. Post-irradiation characterization via bright field transmission electron microscopy and high-angle annular dark-field scanning transmission electron microscopy was performed on all irradiated conditions to characterize the cavity size distribution and determine the effects of H/He injection on cavity microstructure. In all three alloys, hydrogen co-injection with helium resulted in an increased cavity number density and maximum cavity size, producing an increase in swelling over that from helium injection alone. Swelling in F82H appears to peak between 450°C and 500°C. At 600°C, swelling was minimal and cavities of high density and small size were confined to grain boundaries and dislocations while at 400°C, swelling is also low with a nearly homogeneous, high density, distribution of very small cavities throughout. Swelling was least in the commercial alloy F82H due to the high sink strength. The CNA3 alloy underwent dissolution of precipitates that lowered the sink strength and resulted in higher swelling than F82H, but less than the model alloy. Electron energy loss spectroscopy (EELS) elemental mapping revealed hydrogen forming a halo-like structure about the periphery of the cavities and helium residing within the cavities themselves. Finally, this observation suggests that hydrogen reduces the surface energy of helium-filled cavities which results in both increased cavity number density and cavity size in triple beam irradiation over dual beam irradiation.

36 MATERIALS SCIENCE↗
DOE OSTI2026

MCNP® Code Version 6.3.2 Theory & User Manual (Rev. 1)

This document acts as a repository of knowledge for the Monte Carlo N-Particle (MCNP) transport computer code. It is maintained alongside the source code and attempts to introduce new users and re-familiarize experienced users with the theory and practices of using the MCNP code for the wide range of particle transport analyses that it is appropriate for. The latest version of the MCNP code, version 6.3.2, provides the Monte Carlo particle transport community with the latest feature developments and bug fixes in the MCNP code. The MCNP code version 6.0 and later is also known as the MCNP6 code.

42 ENGINEERING↗
DOE OSTI2024

Observation of collective modes of excitations in 59 Co, 59 Ni, and 61 Co and the influence of the $g_{9/2}$ orbital

High-spin states in 59 Co (Z = 27), 59 Ni (Z = 28), and 61 Co have been populated by the fusion evaporation reactions, 48 Ti( 14 C, p2n ) 59 Co, 48 Ti( 14 C, 3 n ) 59 Ni, and 50 Ti( 14 C, p2n ) 61 Co. The 9 MV tandem accelerator at the John D. Fox Laboratory, Florida State University (FSU) was used to accelerate the 14 C beam and the deexciting γ rays were detected by the FSU detector array consisting of six high-purity germanium (HPGe) clover detectors and three single crystals. Directional correlation of the $γ$ rays deexciting oriented states (DCO ratios) and polarization asymmetry measurements helped to establish spin and parities of the excited states whenever possible. The level scheme of 59 Co has been expanded with the inclusion of positive-parity states up to 31/2 + at around 11 MeV. The 59 Ni positive-parity states known from previous study were verified with modifications to some of the spins and parities. On the other hand, the negative-parity states were extended to 31/2 at an excitation energy of 12 MeV. No new transition was observed for 61 Co, but one of the major bands has been reassigned as consisting of positive-parity states by reason of this study. Importantly, excitations observed within the f 7/2 , p 3/2 , f 5/2 , and p 1/2 orbitals, and also across the N = 40 subshell closure into the g 9/2 orbital was established by comparison with large-scale shell-model calculations for the three nuclei studied.

59 ≤ A ≤ 89↗
DOE OSTI2025

Solid structure of Li 2 BeF 4 (FLiBe) from room temperature to melting studied by neutron and X-ray diffraction

Molten fluoride salts such as Li 2 BeF 4 (FLiBe) are used in molten salt reactors, fluoride-salt-cooled high-temperature reactors and fusion reactors as a fuel solvent, coolant and/or tritium breeding medium. In engineered systems that use molten salt, solid-state material will be present during melting and freezing scenarios, and therefore the temperature-dependent properties of the solid and solid/liquid phase transition merit investigation. To observe the behavior of the solid state of Li 2 BeF 4 from room temperature to melting, this work used neutron and X-ray diffraction to measure the changes in the lattice parameters and volume of the crystalline unit cell and compared the results with prior low-temperature data for solid Li 2 BeF 4 . From neutron diffraction data it is also possible to identify anisotropy: centimetre-scaled crystals align preferentially with the a axes parallel to the direction of freezing front propagation, and the c axes expand 54% more than the a axes. This work provides the lattice constants as a function of temperature, quantifies the thermal expansion, and determines the equation describing the change in density for solid Li 2 BeF 4 from room temperature to 459°C to be ρ solid (kg m −3 ) = 2182 (3) − 0.115 (2) T (°C) and the volume expansion upon melting to be less than 5%. This density changes depending on molecular weight and enrichment.

36 MATERIALS SCIENCE↗