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NASA NTRS1993

Computing Properties Of Pure And Mixed Fluids

GASPLUS created as two-part code: first designed for use with pure fluids and second designed for use with mixtures of fluids and phases. Offers routines for mathematical modeling of conditions of fluids in pumps, turbines, compressors and other machines. Other routines for calculating performance of para/ortho-hydrogen reactor and heat of para/normal-hydrogen reaction as well as unique convergence routine demonstrates engineering flavor of GASPLUS. Written in FORTRAN 77.

Fowler, J. R.↗

NASA NTRS1999

Coherence between QPOs in X-Ray Pulsars

Rossi X-ray Timing Explorer (RXTE) observations of Cen X-3 and 4U 1626 have shown that when a low frequency (upsilon(sub qpo) approx. 50 mHz) Quazi-Periodic Oscillation (QPO) is presented in the power spectrum of these sources, smaller QPOs also appear in the upper and lower sidebands of the spin frequency upsilon(sub s), and in the sidebands of the spin frequency harmonics. This is expected if the QPO is a modulation in the accretion rate.However, the QPO in the lower sideband of the spin frequency (upsilon = upsilon(sub s) - upsilon(sub qpo)) is stronger than the QPO in the upper sideband (upsilon = upsilon(sub s) + upsilon(sub qpo)), which is not consistent with pure acretion rate modulation. I will present a method for measuring the phase coherent between the main QPO and any of the sideband QPOs, and apply this to RXTE observations. Preliminary results for Cen X-3 show that the QPO in the lower sideband of the spin frequency is highly coherent with the main QPO, while the QPO in the upper sideband is not. Implications for possible QPO mechanisms will be discussed.

Finger, Mark H.↗

NASA NTRS2003

Creep Resistance of ZrO2 Ceramic Improved by the Addition of a Small Amount of Er2O3

Zirconia (ZrO2) has great technological importance in structural, electrical, and chemical applications. It is the crucial component for state-of-the art thermal barrier coatings and an enabling component as a solid electrolyte for solid-oxide fuel cell systems. Pure ZrO2 is of limited use for industrial applications because of the phase transformations that occur. Upon the addition of stabilizers, cubic (c-ZrO2) and tetragonal (t-ZrO2) forms can be preserved. It is the stabilized and partially stabilized forms of zirconia that function as thermal barrier coatings, solid electrolytes, and oxygen sensors and that have numerous applications in the electrochemical industry. The cubic form of ZrO2 is typically stabilized through Y2O3 additions. However, Y2O3-stabilized zirconia is susceptible to deformation at high temperatures (greater than 900 C) because of the large number of slip systems and the high oxygen diffusion rates, which result in high creep rates at high temperatures. Successful use of ZrO2 at high temperatures requires that new dopant additives be found that will retain or enhance the desirable properties of cubic ZrO2 and yet produce a material with lower creep rates. At the NASA Glenn Research Center, erbium oxide (Er2O3) was identified as a promising dopant for improving the creep resistance of. ZrO2. The selection of Er2O3 was based on the strong interactions of point defects and dislocations. Single crystals of 5 mol% Er2O3- doped ZrO2 rods (4 mm in diameter) and monofilaments (200 to 300 mm in diameter and 30 cm long) were grown using the laser-heated float zone technique, and their creep behavior was measured as a function of temperature. The addition of 5 mol% Er2O3 to single-crystal ZrO2 improved its creep resistance at high temperatures by 2 to 3 orders of magnitude over state-of-the-art Y2O3-doped crystals. Detailed microstructural characterization of ZrO2-Er2O3 single crystals has identified new mechanisms for improving the creep resistance of this class of materials. Adding Er2O3 to ZrO2 results in microstructure of stable and metastable tetragonal precipitates that with thermal treatment evolve to a tweed structure of nanosize tetragonal lamellae. The superior high-temperature creep resistance of Er2O3-doped ZrO2 is attributed to nanoscale precipitation hardening. Doping with Er2O3 will significantly increase the upper-use temperature limit of ZrO2. Potential applications include using Er2O3-doped ZrO2 as a high-temperature fiber for structural applications and adding Er2O3 to reduce the sintering rates of ZrO2 thermal barrier coatings. This work was conducted at Dpto. de F sica de la Materia Condensada, Universidad de Sevilla, Spain, and at NASA Glenn.

Martinez-Fernandez, Julian↗

NASA NTRS2012

Numerical Simulation of Rocket Exhaust Interaction with Lunar Soil

This technology development originated from the need to assess the debris threat resulting from soil material erosion induced by landing spacecraft rocket plume impingement on extraterrestrial planetary surfaces. The impact of soil debris was observed to be highly detrimental during NASA s Apollo lunar missions and will pose a threat for any future landings on the Moon, Mars, and other exploration targets. The innovation developed under this program provides a simulation tool that combines modeling of the diverse disciplines of rocket plume impingement gas dynamics, granular soil material liberation, and soil debris particle kinetics into one unified simulation system. The Unified Flow Solver (UFS) developed by CFDRC enabled the efficient, seamless simulation of mixed continuum and rarefied rocket plume flow utilizing a novel direct numerical simulation technique of the Boltzmann gas dynamics equation. The characteristics of the soil granular material response and modeling of the erosion and liberation processes were enabled through novel first principle-based granular mechanics models developed by the University of Florida specifically for the highly irregularly shaped and cohesive lunar regolith material. These tools were integrated into a unique simulation system that accounts for all relevant physics aspects: (1) Modeling of spacecraft rocket plume impingement flow under lunar vacuum environment resulting in a mixed continuum and rarefied flow; (2) Modeling of lunar soil characteristics to capture soil-specific effects of particle size and shape composition, soil layer cohesion and granular flow physics; and (3) Accurate tracking of soil-borne debris particles beginning with aerodynamically driven motion inside the plume to purely ballistic motion in lunar far field conditions. In the earlier project phase of this innovation, the capabilities of the UFS for mixed continuum and rarefied flow situations were validated and demonstrated for lunar lander rocket plume flow impingement under lunar vacuum conditions. Applications and improvements to the granular flow simulation tools contributed by the University of Florida were tested against Earth environment experimental results. Requirements for developing, validating, and demonstrating this solution environment were clearly identified, and an effective second phase execution plan was devised. In this phase, the physics models were refined and fully integrated into a production-oriented simulation tool set. Three-dimensional simulations of Apollo Lunar Excursion Module (LEM) and Altair landers (including full-scale lander geometry) established the practical applicability of the UFS simulation approach and its advanced performance level for large-scale realistic problems.

Liever, Peter↗

NASA NTRS1976

Products of the reaction of chlorine atoms and ozone

Preliminary matrix-isolation infrared spectroscopic studies of the gas-phase reaction of chlorine atoms and ozone are reported. It was shown that the major product of the reaction is the symmetric OClO radical, while very little of the asymmetric ClOO radical is produced. It was also shown that the presence of O2 enhances the OClO production and the ClOO is the primary product in the reaction of Cl atoms and pure O2. The radical ClO was observed for the first time in a gas-phase reaction of Cl and O3. A mechanism for these observations is proposed.

Hall, J. H., Jr.↗

DOE OSTI2021

Effect of Polyphenylsulfone and Polysulfone Incompatibility on the Structure and Performance of Blend Membranes for Ultrafiltration

This study deals with the modification of polyphenylsulfone ultrafiltration membranes by introduction of an incompatible polymer polysulfone to the polyphenylsulfone casting solution to improve the permeability. The correlation between properties of the blend polyphenylsulfone/polysulfone solutions and porous anisotropic membranes for ultrafiltration prepared from these solutions was revealed. The blend polyphenylsulfone/polysulfone solutions were investigated using a turbidity spectrum method, optical microscopy and measurements of dynamic viscosity and turbidity. The structure of the prepared blend flat sheet membranes was studied using scanning electron microscopy. Membrane separation performance was investigated in the process of ultrafiltration of human serum albumin buffered solutions. It was found that with the introduction of polysulfone to the polyphenylsulfone casting solution in N-methyl-2-pyrrolidone the size of supramolecular particles significantly increases with the maximum at (40–60):(60:40) polyphenylsulfone:polysulfone blend ratio from 76 nm to 196–354 nm. It was shown that polyphenylsulfone/polysulfone blend solutions, unlike the solutions of pristine polymers, are two-phase systems (emulsions) with the maximum droplet size and highest degree of polydispersity at polyphenylsulfone/polysulfone blend ratios (30–60):(70–40). Pure water flux of the blend membranes passes through a maximum in the region of the most heterogeneous structure of the casting solution, which is associated with the imposition of a polymer-polymer phase separation on the non-solvent induced phase separation upon membrane preparation. The application of polyphenylsulfone/polysulfone blends as membrane-forming polymers and polyethylene glycol (Mn = 400 g·mol -1 ) as a pore-forming agent to the casting solutions yields the formation of ultrafiltration membranes with high membrane pure water flux (270 L·m -2 ·h -1 at 0.1MPa) and human serum albumin rejection of 85%.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Gas-Phase Composition as a Predictive Metric for Calendar Life Behavior of Next-Generation Silicon Anodes

The expansion of renewable technologies and electrification of the transportation sector is driving increased demand for next-generation battery materials that provide higher power and energy density with superior cycling and calendar life stability. Silicon (Si) has a theoretical capacity nearly 10x that of graphite, and is therefore a promising anode material candidate to meet these rigorous performance demands. While leading Si anode battery demonstrations are approaching target metrics for cycle life, a series of complex and interrelated modes of reactivity lead to reduced calendar life and therefore challenge practical adoption of these materials. Deconvoluting the degradation processes that impact Si calendar life is critical to informing the rational and accelerated design of improved Si materials. In the present work, we employ novel sampling techniques and GC-MS-FID characterization to measure gas-phase composition during initial Si cycling, which we tie to selective mechanisms of Si passivation. We utilize a tiered analysis approach to identify and quantify the gas-phase reaction products associated with three advanced Si material candidates under practical operating conditions. Ex situ analysis of Si powders (pure chemical reactivity) is coupled with nondestructive in situ sampling of Si electrodes in a practical pouch-cell format (coupled chemical and electrochemical reactivity). We link the observed gas-phase species evolution to electrochemical behavior and measured calendar life of the three Si materials. Further, we evaluate the voltage-resolved evolution of gas-phase species for one such Si nanomaterial, where nonmonotonic gas generation implies competition between passivating reaction pathways. The measured gas-phase compositional data serves as a critical input for our advanced electrochemical SEI models to identify favorable vs unfavorable reaction pathways to stabilize Si. In addition to bolstering a fundamental understanding of Si reactivity, the present approach informs specific and quantifiable gas-phase metrics tied to calendar life improvements in Si, which can streamline and accelerate the process of next-generation material development.

DIRECT ENERGY CONVERSION,ENERGY STORAGE↗

DOE OSTI2026

A structural and electrochemical study of perfluoropolyether-poly(ethylene oxide) solid polymer electrolytes

Solid polymer electrolytes offer attractive safety, processability, and interfacial adhesion for enabling high–energy solid-state lithium batteries, but they are often limited by narrow oxidative stability windows and low lithium-ion transference numbers. In an attempt to broaden the electrochemical stability window and increase lithium-ion transference number of poly(ethylene oxide) (PEO)-based solid polymer electrolytes, we produce an optically clear, crosslinked membrane of PEO and perfluoropolyether (PFPE) using a mixed solvent method and subsequently infuse the membrane with a lithium salt. Structural and thermal analyses reveal nanoscale phase separation between fluorocarbon and hydrocarbon domains with characteristic spacings of 7–8 nm and an elevated glass transition for the hydrocarbon phase. Consistent with this, PFPE-containing membranes exhibit substantially lower ionic conductivity than PEO analogs (dry and plasticized). The transference number and electrochemical stability are similar to pure PEO. These results demonstrate that fluorination implemented as segregated nanoscale domains does not deliver the anticipated transport or stability benefits; instead, phase separation increases tortuosity and suppresses hydrocarbon-phase dynamics. The work underscores the importance of fluorine placement and morphology control, guiding the design of partially fluorinated solid polymer electrolytes toward architectures that avoid detrimental nanoscale phase separation.

Carden, Peyton [ORNL] (ORCID:0000000162296538)↗

NASA NTRS2000

Thermal Control and Enhancement of Heat Transport Capacity of Two-Phase Loops With Electrohydrodynamic Conduction Pumping

There are three kinds of electrohydrodynamics (EHD) pumping based on Coulomb force: induction pumping, ion-drag pumping, and pure conduction pumping. EHD induction pumping relies on the generation of induced charges. This charge induction in the presence of an electric field takes place due to a non-uniformity in the electrical conductivity of the fluid which can be caused by a non-uniform temperature distribution and/or an inhomogeneity of the fluid (e.g. a two-phase fluid). Therefore, induction pumping cannot be utilized in an isothermal homogeneous liquid. In order to generate Coulomb force, a space charge must be generated. There are two main mechanisms for generating a space charge in an isothermal liquid. The first one is associated with the ion injection at a metal/liquid interface and the related pumping is referred to as ion-drag pumping. Ion-drag pumping is not desirable because it can deteriorate the electrical properties of the working fluid. The second space charge generation mechanism is associated with the heterocharge layers of finite thickness in the vicinity of the electrodes. Heterocharge layers result from dissociation of the neutral electrolytic species and recombination of the generated ions. This type of pumping is referred to as pure conduction pumping. This project investigates the EHD pumping through pure conduction phenomenon. Very limited work has been conducted in this field and the majority of the published papers in this area have mistakenly assumed that the electrostriction force was responsible for the net flow generated in an isothermal liquid. The main motivation behind this study is to investigate an EHD conduction pump for a two-phase loop to be operated in the microgravity environment. The pump is installed in the liquid return passage (isothermal liquid) from the condenser section to the evaporator section. Unique high voltage and ground electrodes have been designed that generate sufficient pressure heads with very low electric power requirements making the EHD conduction pumping attractive to applications such as two-phase systems (e.g. capillary pumped loops and heat pipes). Currently, the EHD conduction pump performance is being tested on a two-phase loop under various operating conditions in the laboratory environment. The simple non-mechanical and lightweight design of the EHD pump combined with the rapid control of performance by varying the applied electric field, low power consumption, and reliability offer significant advantages over other pumping mechanisms; particularly in reduced gravity applications.

Seyed-Yagoobi, J.↗

DOE OSTI2020

Recovering Gardner restacking with purely diffusive operations

The maximum particle kinetic energy that can be extracted from an initial six-dimensional phase space distribution motivates the concept of free or available energy. The free energy depends on the allowed operations that can be performed. A key concept underlying the theoretical treatment of plasmas is the Gardner free energy, where the exchange of the contents of equal phase volumes is allowed. Further, a second free energy concept is the diffusive free energy, in which the contents of volumes are instead averaged. For any finite discretization of phase space, the diffusive free energy is known to be less than the Gardner free energy. However, despite the apparent fundamental differences between these free energies, it is demonstrated here that the Gardner free energy may be recovered from the continuous limit of the diffusive free energy, leading to the surprise that macroscopic phase-space conservation can be achieved by ostensibly entropy-producing microscopic operations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Compositional heterogeneity in Cs y FA 1- y Pb(Br x I 1- x ) 3 perovskite films and its impact on phase behavior

Hybrid organic inorganic lead halide perovskite semiconductors of the form Cs y FA 1-y Pb(Br x I 1-x ) 3 are promising candidate materials for high-efficiency photovoltaics. Notably, cation and anion substitution can be used to tune the band gaps to optimize performance and improve stability. However, multi-component materials can be prone to compositional and structural inhomogeneity and the extent, length scale and impact of this heterogeneity on lead halide perovskite properties are not well understood. Here we use synchrotron X-ray diffraction to probe the evolution of crystal structure across the tetragonal-to-cubic phase transition for a series of Cs y FA 1-y Pb(Br x I 1-x ) 3 thin films with x = 0.05 to 0.3 and y = 0.17 to 0.40. We find that the transition occurs across a broad temperature range of approximately 40 °C, much larger than for pure compounds such as MAPbI 3 and MAPbBr 3 . Finally, we hypothesize that this smearing of the phase transition is due to compositional inhomogeneities that give rise to a distribution of local transition temperatures and we estimate the composition varies by about 10% to 15% with likely greater heterogeneity for the halide anion than the cation. This approach of mapping the transition is a simple and effective method of assessing heterogeneity, enabling evaluation of its impact.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Galactic echoes

Gaia has revealed a variety of substructures in the phase space of stars in the Solar neighbourhood, including the vertical ‘Snail’ $(z, v_z)$ in space. Such substructures are often interpreted as the incompletely phase-mixed response of the disc stars to a single perturbation, such as an impulsive encounter with a satellite galaxy. In this paper, we consider the possibility that such structures contain manifestations of phase-space echoes. First established in plasma physics in the 1960s, echoes arise when a collisionless system is perturbed twice: the macroscopic responses to both perturbations mix to small scales in phase space, whereupon they couple non-linearly, producing a third macroscopic ‘echo’ response without the need for a third perturbation. We derive the galactic analogue of the plasma echo theory using angle-action variables and apply it to a one-dimensional model of vertical motion in the Milky Way. We verify the predicted echo behaviour using idealized test particle simulations, both with and without the inclusion of diffusion through orbital scattering off molecular clouds. While we conclude that the Gaia Snail itself is unlikely a (pure) echo effect, the basic physics we uncover is sufficiently generic that we expect phase-space echoes to be common in disc galaxies.

Galaxy: evolution↗

DOE OSTI2022

Phase Transitions of Cu and Fe at Multiscales in an Additively Manufactured Cu–Fe Alloy under High-Pressure

A state of the art, custom-built direct-metal deposition (DMD)-based additive manufacturing (AM) system at the University of Michigan was used to manufacture 50Cu–50Fe alloy with tailored properties for use in high strain/deformation environments. Subsequently, we performed preliminary high-pressure compression experiments to investigate the structural stability and deformation of this material. Our work shows that the alpha (BCC) phase of Fe is stable up to ~16 GPa before reversibly transforming to HCP, which is at least a few GPa higher than pure bulk Fe material. Furthermore, we observed evidence of a transition of Cu nano-precipitates in Fe from the well-known FCC structure to a metastable BCC phase, which has only been predicted via density functional calculations. Finally, the metastable FCC Fe nano-precipitates within the Cu grains show a modulated nano-twinned structure induced by high-pressure deformation. The results from this work demonstrate the opportunity in AM application for tailored functional materials and extreme stress/deformation applications.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Erosion and cathodic arc plasma of Nb–Al cathodes: composite versus intermetallic

Many properties of cathodic arcs from single-element cathodes show a correlation to the cohesive energy of the cathode material. For example, the burning voltage, the erosion rate, or, to a lesser extent, plasma properties like electron temperatures or average ion energy and charge states. For multi-element cathodes, various phases with different cohesive energies can initially be present in the cathode, or form due to arc exposure, complicating the evaluation of such correlations. To test the influence of morphology and phase composition of multi-element cathodes on cathodic arc properties, a Nb–Al cathode model system was used that includes: pure Nb and Al cathodes; intermetallic Nb 3 Al, Nb 2 Al and NbAl 3 cathodes; and three composite Nb–Al cathodes with atomic ratios corresponding to the stoichiometric ratios of the intermetallic phases. Pulsed cathodic arc plasmas from these cathodes were examined using a mass-per-charge and energy-per-charge analyzer, showing that charge-state-resolved ion energy distributions of plasmas from the intermetallic and corresponding composite cathodes are nearly identical. An examination of converted layers of eroded cathodes using x-ray diffraction and scanning electron microscopy indicates the formation of a surface layer with similar phase composition for intermetallic and their corresponding composite cathode types. The average arc voltages do not follow the trend of cohesive energies of Nb, Al and intermetallic Nb–Al phases, which have been calculated using density functional theory. Possible reasons for this effect are discussed based on the current knowledge of multi-element arc cathodes and their arc plasma available in literature.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Solar neutrino measurements using the full data period of Super-Kamiokande-IV

An analysis of solar neutrino data from the fourth phase of Super-Kamiokande (SK-IV) from October 2008 to May 2018 is performed and the results are presented. The observation time of the dataset of SK-IV corresponds to 2970 days and the total live time for all four phases is 5805 days. For more precise solar neutrino measurements, several improvements are applied in this analysis: lowering the data acquisition threshold in May 2015, further reduction of the spallation background using neutron clustering events, precise energy reconstruction considering the time variation of the PMT gain. The observed number of solar neutrino events in 3.49–19.49 MeV electron kinetic energy region during SK-IV is 65,443 − 388 + 390 ( stat . ) ± 925 ( syst . ) events. Corresponding B 8 solar neutrino flux is ( 2.314 ± 0.014 ( stat . ) ± 0.040 ( syst . ) ) × 10 6 cm − 2 s − 1 , assuming a pure electron-neutrino flavor component without neutrino oscillations. The flux combined with all SK phases up to SK-IV is ( 2.336 ± 0.011 ( stat . ) ± 0.043 ( syst . ) ) × 10 6 cm − 2 s − 1 . Based on the neutrino oscillation analysis from all solar experiments, including the SK 5805 days dataset, the best-fit neutrino oscillation parameters are sin 2 θ 12 , solar = 0.306 ± 0.013 and Δ m 21 , solar 2 = ( 6.1 0 − 0.81 + 0.95 ) × 10 − 5 eV 2 , with a deviation of about 1.5 σ from the Δ m 21 2 parameter obtained by KamLAND. The best-fit neutrino oscillation parameters obtained from all solar experiments and KamLAND are sin 2 θ 12 , global = 0.307 ± 0.012 and Δ m 21 , global 2 = ( 7.5 0 − 0.18 + 0.19 ) × 10 − 5 eV 2 . Published by the American Physical Society 2024

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Understanding the phase transformation mechanisms that affect the dynamic response of Fe-based microstructures at the atomic scales

Large-scale molecular dynamics (MD) simulations were carried out to investigate the shock-induced evolution of microstructure in Fe-based systems comprising single-crystal and layered Cu/Fe alloys with a distribution of interfaces. The shock compression of pure single-crystal Fe oriented along [110] above a threshold pressure results in a BCC (α)→HCP (ε) phase transformation behavior that generates a distribution of ε phase variants in the phase transformed region of the microstructure behind the shock front. The propagation of the release wave through a phase transformed ε phase causes a reverse ε→α phase transformation and renders a distribution of twins for the [110] oriented Fe that serve as void nucleation sites during spall failure. The simulations reveal that the α→ε→α transformation-induced twinning for shock loading along the [110] direction is due to a dominant ε phase variant formed during compression that rotates on the arrival of the release wave followed by a reverse phase transformation to twins in the α phase. The modifications in the evolution of the ε phase variants and twins in Fe behavior are also studied for Cu–Fe layered microstructures due to the shock wave interactions with the Cu/Fe interfaces using a newly constructed Cu–Fe alloy potential. Here, the MD simulations suggest that interfaces affect the observed variants during shock compression and, hence, distributions of twins during shock release that affects the void nucleation stresses in the Fe phase of Cu/Fe microstructures.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Tusas: A fully implicit parallel approach for coupled phase-field equations

In this study, we develop a fully-coupled, fully-implicit approach for phase-field modeling of solidification in metals and alloys. Predictive simulation of solidification in pure metals and metal alloys remains a significant challenge in the field of materials science, as microstructure formation during the solidification process plays a critical role in the properties and performance of the solid material. Our simulation approach consists of a finite element spatial discretization of the fully-coupled nonlinear system of partial differential equations at the microscale, which is treated implicitly in time with a preconditioned Jacobian-free Newton-Krylov method. The approach is algorithmically scalable as well as efficient due to an effective preconditioning strategy based on algebraic multigrid and block factorization. We implement this approach in the open-source Tusas framework, which is a general, flexible tool developed in C++ for solving coupled systems of nonlinear partial differential equations. The performance of our approach is analyzed in terms of algorithmic scalability and efficiency, while the computational performance of Tusas is presented in terms of parallel scalability and efficiency on emerging heterogeneous architectures. We demonstrate that modern algorithms, discretizations, and computational science, and heterogeneous hardware provide a robust route for predictive phase-field simulation of microstructure evolution during additive manufacturing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Thermodynamic stability of elemental boron allotropes with varying numbers of interstitial atoms

Elemental boron exists in multiple allotropes, each characterized by structures containing icosahedral subunits. These structures have interstitial sites between the icosahedral subunits that are partially occupied. The number of atoms in the unit cell varies depending on the occupancy of these interstitial sites. Here we have investigated the thermodynamic stability of boron allotropes for different numbers of atoms in the unit cell by calculating the free energies, including the contribution of phonons. It has been found that β-rhombohedral boron is most stable with 107 atoms/cell at low temperatures, while it becomes most stable with 105 atoms/cell above 1700 K. This suggests the occurrence of a phase transition at this temperature, which could account for the large variation in the number of atoms in the unit cell for β-rhombohedral boron samples. α-tetragonal boron is consistently most stable with 52 atom/cell and becomes unstable with more than 52 atoms/cell. Similar to β-rhombohedral boron, β-tetragonal boron may undergo a phase transition between 192 and 190 atoms/cell configurations. However, the thermodynamic stability of pure β-tetragonal boron has been questioned in comparison with other allotropes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗