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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.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Lower Temperature Annealing of Vapor Diffused Nb₃Sn for Accelerator Cavities

Nb₃Sn is a next-generation superconducting material for the accelerator cavities with higher critical temperature and superheating field, both twice compared to Nb. It promises superior performance and higher operating temperature than Nb, resulting in significant cost reduction. So far, the Sn vapor diffusion method is the most preferred and successful technique to coat niobium cavities with Nb₃Sn. Although several post-coating techniques (chemical, electrochemical, mechanical) have been explored to improve the surface quality of the coated surface, an effective process has yet to be found. Since there are only a few studies on the post-coating heat treatment at lower temperatures, we annealed Nb₃Sn-coated samples at 800 C - 1000 C to study the effect of heat treatments on surface properties, primarily aimed at removing surface Sn residues. This paper discusses the systematic surface analysis of coated samples after annealing at temperatures between 850 C and 950 C.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Characterization of Losses in Superconducting Radio-Frequency Cavities by Combined Temperature and Magnetic Field Mapping

Superconducting radio-frequency (SRF) cavities are one of the fundamental building blocks of modern particle accelerators. To achieve the highest quality factors (10 10 -10 11 ), SRF cavities are operated at liquid helium temperatures. Magnetic flux trapped on the surface of SRF cavities during cool-down below the critical temperature is one of the leading sources of residual RF losses. Instruments capable of detecting the distribution of trapped flux on the cavity surface are in high demand in order to better understand its relation to the cavity material, surface treatments and environmental conditions. We have designed, developed, and commissioned two novel diagnostic tools to measure the distribution of trapped flux at the surface of SRF cavities. One is a magnetic field scanning system (MFSS) which uses cryogenic Hall probes and anisotropic magnetoresistance sensors that fit the contour of a 1.3 GHz cavity. The second setup is a stationary, combined magnetic and temperature mapping system which uses AMR sensors and carbon resistor temperature sensors, covering the surface of a 3 GHz SRF cavity. The MFSS system revealed a non-uniform distribution of trapped flux on the cavities' surface, dependent on the magnitude of the applied magnetic field during field-cooling below the critical temperature. The MFSS shows that magnetic field scanning as a function of the RF field indicates redistribution of trapped flux at some locations. About ~ 33% of hot-spots observed by temperature mapping during high power RF tests overlapped with the high B-field spots. Almost all high B-field spots observed after field-cool were found to be overlapped on grain boundaries. A clear correlation between the hot- spot formed after quench and local trapped flux was found, providing insight on the RF dissipation of trap vortices. The combined B&T map system showed that the T-map system is capable of detecting hot-spots and quench location on the surface of the 3 GHz SRF cavity. Different distribution of trapped flux was measured after different cool-down and residual B-field, but, no variation in magnetic field distribution was observed during quench, possibly due to magnetic sensors being far from the quench location.

Parajuli, Ishwari↗
DOE OSTI2024

Mild-Temperature Supercritical Water Confined in Hydrophobic Metal–Organic Frameworks

Fluids under extreme confinement show characteristics significantly different from those of their bulk counterpart. This work focuses on water confined within the complex cavities of highly hydrophobic metal–organic frameworks (MOFs) at high pressures. A combination of high-pressure intrusion–extrusion experiments with molecular dynamic simulations and synchrotron data reveals that supercritical transition for MOF-confined water takes place at a much lower temperature than in bulk water, ~250 K below the reference values. This large shifting of the critical temperature (T c ) is attributed to the very large density of confined water vapor in the peculiar geometry and chemistry of the cavities of Cu 2 tebpz (tebpz = 3,3',5,5'-tetraethyl-4,4'-bipyrazolate) hydrophobic MOF. This is the first time the shift of Tc is investigated for water confined within highly hydrophobic nanoporous materials, which explains why such a large reduction of the critical temperature was never reported before, neither experimentally nor computationally.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

High resolution diagnostic tools for superconducting radio frequency cavities

Superconducting radio-frequency (SRF) cavities are one of the fundamental building blocks of modern particle accelerators. To achieve the highest quality factors (10 10 –10 11 ), SRF cavities are operated at liquid helium temperatures. Magnetic flux trapped on the surface of SRF cavities during cool-down below the critical temperature is one of the leading sources of residual RF losses. Instruments capable of detecting the distribution of trapped flux on the cavity surface are in high demand in order to better understand its relation to the cavity material, surface treatments and environmental conditions. We have designed, developed, and commissioned two high-resolution diagnostic tools to measure the distribution of trapped flux at the surface of SRF cavities. One is a magnetic field scanning system, which uses cryogenic Hall probes and anisotropic magnetoresistance sensors that fit the contour of a 1.3 GHz cavity. This setup has a spatial resolution of ~ 13 μm in the azimuthal direction and ~ 1 cm along the cavity contour. The second setup is a stationary, combined magnetic and temperature mapping system, which uses anisotropic magnetoresistance sensors and carbon resistor temperature sensors, covering the surface of a 3 GHz SRF cavity. This system has a spatial resolution of 5 mm close to the iris and 11 mm at the equator. Initial results show a non-uniform distribution of trapped flux on the cavities’ surfaces, dependent on the magnitude of the applied magnetic field during field-cooling below the critical temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Intrinsic thermal conductivity of ZrC from low to ultrahigh temperatures: A critical revisit

Current phonon transport theory based on ground-state calculations has been successful in predicting thermal conductivity at room and medium temperatures but may misrepresent behavior at high temperatures. Here, in this work, we predict the thermal conductivity (κ) of ZrC including electronic and phonon contributions from 300 to 3500 K, by including high-order phonon scattering; lattice expansion; temperature-dependent (TD) second-, third-, and fourth-order force constants (2FC, 3FC, and 4FC); and interband phonon conduction by using first principles. For the phonon transport, we find that four-phonon scattering (4ph) significantly reduces the phonon thermal conductivity (κ ph ), by as much as ~75% at 3500 K. After including 4ph scattering and all other factors, κ ph shows a ~T –1.5 rather than ~T –1 dependence. TD 2FC decreases three-phonon scattering rates but increases 4ph rates by decreasing and increasing the scattering phase spaces, respectively. For 4ph phase space, the TD 2FC flattens phonon bands, and allows more redistribution-4ph processes (1 + 2 → 3 + 4) to happen. The combination effect of TD 2FC and TD 4FC reduces 4ph rates of acoustic modes but increases those of optical modes. The TD 3FC and 4FC decrease the phonon scattering cross section and increase the κ ph significantly (by 52% at 3500 K). The contribution from interband (Wigner) phonon conduction is small, even at ultrahigh temperatures. For electronic thermal transport, we find that it is sensitive to and can be changed by 20% by the TD lattice constants. The Lorenz number varies from 1.6 to 3.3 × 10 –8 WΩK –2 at different temperatures. The theoretical prediction in the literature overpredicts κph (e.g., ~28%) and underpredicts the κ el (e.g., ~38%), resulting in an overall underprediction of κ (~26% at 1500 K). The impacts of grain size and defects are found to be strong, leading to the lower observed thermal conductivity in experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1972

The thermodynamic properties of oxygen and nitrogen. Part 2: Thermodynamic properties of oxygen from 100 R to 600 R with pressure to 5000 psia

An equation of state is presented for liquid and gaseous oxygen for temperatures from 100 R to 600 R and pressures to 5000 psia. The pressure-density-temperature data available from the published literature have been reviewed, and appropriate corrections have been applied to bring experimental temperatures into accord with the International Practical Temperature Scale of 1968. Representative comparisons of property values calculated from the equation of state to measured values are included to illustrate the accuracy of the equation of state. The coefficients of the equation of state were determined by a weighted least squares fit to selected published data, and simultaneously to isochoric heat capacity data, and to data which define the phase equilibrium for the saturated liquid and saturated vapor. The equation of state is estimated to be accurate for the liquid to within 0.1 percent in density, to within 0.2 percent for the vapor below the critical temperature and for states above the critical temperatures to 250 K, and within 0.1 percent for supercritical states at temperatures from 250 K to 300 K. The vapor pressure equation is accurate to within + or - 0.01 K between the triple point and the critical point.

Stewart, R. B.↗
NASA NTRS1984

Supercritical solvent coal extraction

Yields of soluble organic extract are increased up to about 50% by the supercritical extraction of particulate coal at a temperature below the polymerization temperature for coal extract fragments (450 C.) and a pressure from 500 psig to 5,000 psig by the conjoint use of a solvent mixture containing a low volatility, high critical temperature coal dissolution catalyst such as phenanthrene and a high volatility, low critical temperature solvent such as toluene.

Compton, L. E.↗
NASA NTRS1994

Impact of stratospheric aircraft on calculations of nitric acid trihydrate cloud surface area densities using NMC temperatures and 2D model constituent distributions

A parameterization of NAT (nitric acid trihydrate) clouds is developed for use in 2D models of the stratosphere. The parameterization uses model distributions of HNO3 and H2O to determine critical temperatures for NAT formation as a function of latitude and pressure. National Meteorological Center temperature fields are then used to determine monthly temperature frequency distributions, also as a function of latitude and pressure. The fractions of these distributions which fall below the critical temperatures for NAT formation are then used to determine the NAT cloud surface area density for each location in the model grid. By specifying heterogeneous reaction rates as functions of the surface area density, it is then possible to assess the effects of the NAT clouds on model constituent distributions. We also consider the increase in the NAT cloud formation in the presence of a fleet of stratospheric aircraft. The stratospheric aircraft NO(x) and H2O perturbations result in increased HNO3 as well as H2O. This increases the probability of NAT formation substantially, especially if it is assumed that the aircraft perturbations are confined to a corridor region.

Considine, David B.↗
DOE OSTI2024

A variational method for the sheath potential of hypersonic leading edges with space-charge limitations

Electron transpiration cooling for the leading edges (LE) of hypersonic aircraft utilizes thermionic emission; however, space-charge effects limit the electron emission rate, potentially diminishing the efficiency of this cooling mechanism. We develop a variational weak form of the Poisson equation that describes the sheath potential and then numerically solve it using the finite element method. This formulation has two main benefits: (1) the space-charge limit condition can be incorporated as a constraint and (2) it allows for the analysis of three-dimensional geometries with complex boundary conditions. We demonstrate that the current emitted from the surface of an LE is generally a small fraction of the Child–Langmuir limit due to space charge. We then propose several methods to enhance the emitted current from the surface and to boost the cooling effect of thermionic emission. These include increasing the plasma density, applying a negative surface potential, and using fringe fields under suitable geometric conditions. For a LaB6 emitting LE, the total emitted current is shown to be minimal and independent of the temperature of a surface with floating potential. However, when a negative potential is applied and the surface is heated, the emitted current follows the Richardson–Dushman relationship up to a critical temperature, beyond which it remains constant. At an applied surface potential of −5 V, the critical temperature is around 1700 K.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Properties of Nb3Sn films fabricated by magnetron sputtering from a single target

Superconducting Nb3Sn films were fabricated on sapphire and fine grain Nb substrates by magnetron sputtering from a single stoichiometric Nb3Sn target. The structural, morphological and superconducting properties of the films annealed for 24 h at temperatures of 800-1000 {\deg}C were investigated. The effect of the annealing time at 1000 {\deg}C was examined for 1, 12, and 24 h. The film properties were characterized by X-ray diffraction, scanning electron microscopy, atomic force microscopy, energy dispersive X-ray spectroscopy, and Raman spectroscopy. The DC superconducting properties of the films were characterized by a four-point probe measurement down to cryogenic temperatures. The RF surface resistance of films was measured over a temperature range of 6-23 K using a 7.4 GHz sapphire-loaded Nb cavity. As-deposited Nb3Sn films on sapphire had a superconducting critical temperature of 17.21 K, which improved to 17.83 K when the film was annealed at 800 {\deg}C for 24 h. For the films annealed at 1000 {\deg}C, the surface Sn content was reduced to ~11.3 % for an annealing time of 12 h and to ~4.1 % for an annealing time of 24 h. The Raman spectra of the films confirmed the microstructural evolution after annealing. The RF superconducting critical temperature of the as-deposited Nb3Sn films on Nb was 16.02 K, which increased to 17.44 K when the film was annealed at 800 {\deg}C for 24 h.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Experimental Investigation of Polymer Induced Fouling of Heater Tubes in the First-Ever Polymer Flood Pilot on Alaska North Slope

Mineral fouling in heat exchangers has been extensively investigated by researchers in recent times. The oil and gas industry has a long history of fouling issues in production systems as a result of produced fluids treatment. Due to decline in production rates in oilfields new technologies are being developed and field tested in pilots. Polymer flooding is one such technology that involves addition of polymers to injection fluids to enhance oil production. A polymer flood pilot has been set up in the Schrader Bluff viscous oil reservoir at Milne Point field on the Alaska North Slope (ANS). The results from the pilot are encouraging, however a major concern of the operator is the influence of polymer on the production system after breakthrough, especially the fouling in heat exchangers. This study investigates the propensity of polymer fouling on the heater tubes as a function of different variables, with the ultimate goal of determining safe and efficient operating conditions. This work applies a multi-experimental approach to study the severity of polymer-induced fouling in both dynamic and static states of produced fluids as well as studying the stability of polymer solutions at different temperatures. A unique experimental setup was designed and developed in-house to simulate the fouling process on the heating tube. The influence of heating tube skin temperature, tube material, and polymer concentration on fouling tendency was investigated. Each test was run five times with the same tube, and in each run, the freshly prepared synthetic brine and polymer solution was heated from 77°F to 122°F to mimic field-operating conditions. The heating time and fouling amount were recorded for each run. Dynamic Scale Loop (DSL) tests were conducted to study fouling due to polymer at different temperatures (165°F to 350°F) in a dynamic state of fluid flow where the fluids mimic the residence time of fluids in the heat exchanger on the field pilot. Cloud point measurement has also been conducted to find the critical temperature at which the polymer in solution becomes unstable and precipitates out. The morphology and composition of the deposit samples were analyzed by environmental scanning electron microscopy (ESEM) and X-ray diffraction (XRD), respectively. It was found that the presence of polymer in produced fluids would aggravate the fouling issues on both carbon steel and stainless-steel surfaces at all tested skin temperatures. Only higher skin temperatures of 250°F and 350°F could cause polymer-induced fouling issues on the copper tube surface, and the fouling tendency increased with polymer concentration. At the lower skin temperatures of 165°F, no polymer-induced fouling was identified on the copper tube. A critical temperature that is related to the cloud point of the polymer solution was believed to exist, below which polymer-induced fouling would not occur, and only mineral scale was deposited but above which the polymer would aggravate the fouling issue. The cloud point of the tested polymer solution was determined to be between 220°F and 230°F. In the DSL tests it was found that at higher skin temperatures of 250°F and 350°F tube blocking was observed in the DSL tests whereas the tests at 165°F and 200°F did not show any tube blocking in the same time period. These experiments also manifested the influence of cloud point of the solution as deposit rate increased significantly in both carbon steel and stainless-steel tubes when the skin temperature was higher than the solution cloud point. The results of this study have provided guidance to the operator for the field-operations.

Dhaliwal, Anshul↗
DOE OSTI2026

Structural Phase Transitions in the van der Waals Ferromagnets Fe x Pd y Te 2

Two-dimensional van der Waals (vdW) magnets are attracting significant attention, both as platforms for studying fundamental magnetic interactions and for the exciting possibility of utilizing them as building blocks in devices and heterostructures, which may lead to new physical phenomena and functionalities. Here, we provide a detailed study of the crystal structure and physical properties of the recently discovered vdW ferromagnet FePd 2 Te 2 . We find this compound has a relatively wide width of formation, and grow single crystals with compositions Fe x Pd y Te 2 where x ranges from 0.9 to 1.1 and y from 1.8 to 2.5, respectively. Temperature-dependent X-ray diffraction and transport measurements reveal that a first-order structural transition occurs in the range of T = 360–420 K, where the critical temperature, modulation wave vector, and corresponding room-temperature crystal structures all depend on chemical composition. Above the transition, the compounds with Pd fraction y > 2 adopt a disordered derivative of the tetragonal FeTe structure, with the Fe layer showing mixed Fe/Pd occupancy and the extra Pd atoms partially occupying interstitial sites. Below 370 K, the structure is incommensurately modulated, likely associated with the complex ordering of Pd/Fe atoms in the metal layers or the interstitial Pd in the vdW gaps. For y < 2, the composition Fe 1.1 Pd 1.8 Te 2 has monoclinic symmetry at room temperature that is consistent with the reported structure of FePd 2 Te 2 . This phase undergoes a structural transition at 420 K for which the high temperature structure is yet to be determined; however, based on the similarities with the y > 2 compounds, we speculate that its T > 420 K structure is also tetragonal. Importantly, the high temperature, symmetry-breaking structural transition observed here provides a likely explanation for the origin of the structural domains previously observed in FePd 2 Te 2 . All compounds investigated in the Fe x Pd y Te 2 series show metallic behavior, with magnetic characterization indicating that they are easy-plane, hard, ferromagnets with T C spanning 98–180 K. Both the critical temperature for the structural transition and the Curie temperature are moderately suppressed with increasing Pd fraction y and corresponding decreasing Fe fraction x, indicating that synthetic control over x and y paves way for the further exploration of these compounds.

crystal structure↗
DOE OSTI2020

Hole-doped room-temperature superconductivity in H 3 S 1-x Z (Z=C, Si)

We examine the effects of the low-level substitution of S atoms by C and Si atoms on the superconductivity of H 3 S with the Im3¯m structure at megabar pressures. The hole doping can fine-tune the Fermi energy to reach the electronic density-of-states peak maximizing the electron-phonon coupling. This can boost the critical temperature from the original 203 K to 289 K and 283 K, respectively, for H 3 S 0.962 C 0.038 at 260 GPa and H 3 S 0.960 Si 0.040 at 230 GPa. The former may provide an explanation for the recent experimental observation of room-temperature superconductivity in a highly compressed CeSeH system. Our work opens a new avenue for substantially raising the critical temperatures of hydrogen-rich materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Stretched exponential magnetic relaxation dynamics in artificial square ice revealed through x-ray photon correlation spectroscopy

X-ray photon correlation scattering measurements are undertaken on a thermally active artificial spin ice based on the square lattice, referred to as artificial square ice, to probe the fluctuation timescales as a function of temperature as the system passes through the paramagnetic-antiferromagnetic phase transition, which belongs to the two-dimensional Ising universality class. In the paramagnetic regime, a single exponential timescale is seen, whereas at and below the critical temperature, a stretched exponential decorrelation is observed, with the stretching exponent decreasing from unity down to below one-half as the temperature reduces. This trend is confirmed by kinetic Monte Carlo simulations of a simplified point-dipolar square ice system, and is in agreement with past theoretical work on the kinetic Ising model where stretched exponential relaxation due to equilibrium domain wall dynamics below the critical temperature was found.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Theoretical Analysis of a Single-Stage Gas-Fired Ejector Heat Pump Water Heater

Ejector driven systems have the ability to operate at high efficiencies, utilizing recycled thermal energy as a power source. For a typical ejector heat pump system, the increase of the condenser temperature reduces the coefficient of performance (COP). In addition, if the condenser temperature is higher than the critical temperature, the ejector may not function. In this situation, the condenser temperature must be reduced, and an additional heater will be utilized to heat the production water from the condenser temperature to the desired temperature. In this investigation, a single-stage gas-fired ejector heat pump (EHP) is investigated and thermodynamically modeled in order to optimize the system COP for the purpose of heating water by utilizing the thermal energy from the ambient air. The effects of the high-temperature evaporator (HTE) and low-temperature evaporator (LTE) temperatures on the ejector critical back pressure and the EHP system performance are examined for a HTE temperature range of 120–180 °C and LTE temperatures of 15.5, 17.5, and 19.5 °C. Results show that an optimized COP of the EHP system exists which depends on HTE and LTE temperatures, primary nozzle throat diameters. In addition, it is found that the EHP COP is independent of the ejector COP. From this investigation a maximum EHP COP of 1.31 is able to be achieved for a HTE temperature of 160 °C and a LTE temperature of 19.5 °C with a total heat capacity of 15.98 kW.

Spitzenberger, Jeremy↗
DOE OSTI2024

Nb$^{3}$Sn Technology for Low-beta linacs

Nb3Sn is the most advanced potential successor for niobium in superconducting RF accelerator cavities. Nb3Sn has a significantly higher critical temperature (18.3 K) compared to that of niobium (9.2 K). This has a large effect on the BCS surface resistance, and therefore, on the dynamic RF losses at 4.5 K. The higher critical temperature allows two important changes for cavity and cryomodule design. First, the lower BCS losses allow the designer to use a higher frequency, translating to physically smaller cavities and cryomodules. Second, the low dynamic losses allow the use of stand-alone cryocoolers instead of complex helium refrigerators and distribution systems. Fabrication of a prototype 218 MHz cavity, test results, and continuing challenges are discussed.

43 PARTICLE ACCELERATORS↗
NASA NTRS2009

The New Weather Radar for America's Space Program in Florida: A Temperature Profile Adaptive Scan Strategy

A new weather radar is being acquired for use in support of America s space program at Cape Canaveral Air Force Station, NASA Kennedy Space Center, and Patrick AFB on the east coast of central Florida. This new radar replaces the modified WSR-74C at Patrick AFB that has been in use since 1984. The new radar is a Radtec TDR 43-250, which has Doppler and dual polarization capability. A new fixed scan strategy was designed to best support the space program. The fixed scan strategy represents a complex compromise between many competing factors and relies on climatological heights of various temperatures that are important for improved lightning forecasting and evaluation of Lightning Launch Commit Criteria (LCC), which are the weather rules to avoid lightning strikes to in-flight rockets. The 0 C to -20 C layer is vital since most generation of electric charge occurs within it and so it is critical in evaluating Lightning LCC and in forecasting lightning. These are two of the most important duties of 45 WS. While the fixed scan strategy that covers most of the climatological variation of the 0 C to -20 C levels with high resolution ensures that these critical temperatures are well covered most of the time, it also means that on any particular day the radar is spending precious time scanning at angles covering less important heights. The goal of this project is to develop a user-friendly, Interactive Data Language (IDL) computer program that will automatically generate optimized radar scan strategies that adapt to user input of the temperature profile and other important parameters. By using only the required scan angles output by the temperature profile adaptive scan strategy program, faster update times for volume scans and/or collection of more samples per gate for better data quality is possible, while maintaining high resolution at the critical temperature levels. The temperature profile adaptive technique will also take into account earth curvature and refraction when geo-locating the radar beam (i.e., beam height and arc distance), including non-standard refraction based on the user-input temperature profile. In addition to temperature profile adaptivity, this paper will also summarize the other requirements for this scan strategy program such as detection of low-level boundaries, detection of anvil clouds, reducing the Cone Of Silence, and allowing for times when deep convective clouds will not occur. The adaptive technique will be carefully compared to and benchmarked against the new fixed scan strategy. Specific environmental scenarios in which the adaptive scan strategy is able to optimize and improve coverage and resolution at critical heights, scan time, and/or sample numbers relative to the fixed scan strategy will be presented.

Carey, L. D.↗
NASA NTRS1991

Thermal stress analysis of a silicon carbide/aluminum composite

Thermal deformations and stresses were studied in a silicon-carbide/aluminum filamentary composite at temperatures up to 370 C (700 F). Longitudinal and transverse thermal strains were measured with strain gages and a dilatometer. An elastoplastic micromechanical analysis based on a one-dimensional rule-of-mixtures model and an axisymmetric two-material composite cylinder model was performed. It was established that beyond a critical temperature thermal strains become nonlinear with decreasing longitudinal and increasing transverse thermal-expansion coefficients. This behavior was attributed to the plastic stresses in the aluminum matrix above the critical temperature. An elastoplastic analysis of both micromechanical models was performed to determine the stress distributions and thermal deformation in the fiber and matrix of the composite. While only axial stresses can be determined by the rule-of-mixtures model, the complete triaxial state of stress is established by the composite cylinder model. Theoretical predictions for the two thermal-expansion coefficients were in satisfactory agreement with experimental results.

Gdoutos, E. E.↗