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The Homrit Akarem granitic intrusion (HAGI) outcrops near the western edge of the south Eastern Desert basement exposure in Egypt. It is a composite of two cogenetic intrusive bodies: an early albite granite phase shallowly emplaced at the apex of a magmatic cupola, and a later subjacent pink granite phase with a marginal zone of muscovite granite and better preservation of magmatic features. Mineral chemistry of primary biotite and garnet, together with whole-rock chemistry, identify the HAGI as a highly fractionated A-type peraluminous intrusion. The chemistry of F-dominant, Li-bearing, Fe3+-rich primary magmatic mica in the pink granite resembles that typically found in highly evolved Nb-Y-F pegmatites. The HAGI is the evolved product of a primary magma generated by partial melting of juvenile crust of the Arabian-Nubian Shield (ANS), emplaced along a regional strike-slip fault system that promoted its ascent. The main emplacement mechanism and evolutionary sequence of the HAGI was magmatic, although secondary minerals and textures resulting from hydrothermal fluid interactions are observed, especially at its margins. Primary columbite-(Mn) crystallized from melt and was partly replaced by secondary fluorcalciomicrolite. The high fluorine content of magmatic fluids exsolved from the intrusion is indicated by quartz-fluorite veins, greisenization, albitization, and F-bearing secondary oxide minerals. The magmatic derivation of this fluid is demonstrated by the F-dominant primary mica, a siderophyllite-polylithionite solid solution commonly known as zinnwaldite. The chemistry of zinnwaldite constrains the F/OH activity ratio and oxygen fugacity of its parental melt and thereby resolves the ambiguity between pressure and the effects of F in controlling the normative quartz content of rare-metal granites. The HAGI is less mineralized than the post-collisional rare-metal granites found further east in the south Eastern Desert, replicating a trend observed previously in the central Eastern Desert and suggesting that east-west zoning in rare metal enrichment is a persistent feature across latitudes at the western edge of the ANS.

We report that a porous, electron-rich, covalent, organonitridic framework (PECONF-4) exhibits an unusually high hydrogen uptake at 77 K, relative to its specific surface area. Chahine’s rule, a widely cited heuristic for hydrogen adsorption, sets a maximum adsorptive uptake of 1 wt % hydrogen at 77 K per 500 m^2 of the adsorbent surface area. High-pressure hydrogen adsorption measurements in a Sieverts apparatus showed that PECONF-4 exceeds Chahine’s rule by 50%. The Brunauer–Emmett–Teller (BET) specific surface area of PECONF-4 was measured redundantly with nitrogen, argon, and carbon dioxide and found to be between 569 ± 2 and 676 ± 13 m^2 g^(–1). Furthermore, hydrogen on PECONF-4 has a high heat of adsorption, in excess of 9 kJ mol^(–1).

A quantum Langevin model, like models from optomechanics, was developed for phonons. It predicts intermodulation phonon sidebands (IPSs) in anharmonic crystals. Ab initio calculations of anharmonic phonons in rock-salt NaBr showed these spectral features as many-body effects. Modern inelastic neutron scattering measurements on a crystal of NaBr at 300 K revealed diffuse intensity at high phonon energy from a predicted upper IPS. The transverse optical (TO) part of the new features originates from phonon intermodulation between the transverse acoustic (TA) and TO phonons. The longitudinal optical spectral features originate from three-phonon coupling between the TA modes and the TO lattice modes. The partner lower IPS proves to be an intrinsic localized mode. Interactions with the thermal bath broaden and redistribute the spectral weight of the IPS pair. These sidebands are a probe of the anharmonicity and quantum noise of phonons in NaBr and suggest novel interactions between photons and phonons.

Hydriding and dehydriding transitions in bulk and nanocrystalline binary metal hydrides were studied using the Pd-H model system by measuring pressure-composition isotherms with in situ x-ray diffractometry. Nanocrystalline Pd showed a smaller pressure hysteresis, solvus hysteresis, and hysteresis in lattice parameter, compared to bulk Pd. The time-dependence of pressure equilibration was measured after dosing with aliquots of hydrogen, giving equilibration times that were much faster in the single-phase regions than in the two-phase plateaus. In the broad two-phase plateaus, the pressure relaxations were exponential functions of time. An explanation of hysteresis is developed that is based on a dissipative potential barrier that impedes the motion of the interface due to interactions between lattice defects and the two-phase interface. The exponential pressure relaxations and hysteresis are consistent for this mechanism. For a simple model of the pinning potential, the potential barrier maximum is an order of magnitude less than typical grain boundary energies. These pinning effects are substantially different in the nanocrystalline Pd, suggesting differences in the hydriding mechanism.

Inelastic neutron scattering on a single crystal of silicon was performed at temperatures from 100 to 1500 K. These experimental data were reduced to obtain phonon spectral intensity at all wave vectors $\stackrel{P\vec}{Q}$ and frequencies $\ensuremath{\omega}$ in the first Brillouin zone. Thermal broadenings of the phonon peaks were obtained by fitting and by calculating with an iterative ab initio method that uses thermal atom displacements on an ensemble of superlattices. Agreement between the calculated and experimental broadenings was good, with possible discrepancies at the highest temperatures. Distributions of phonon widths versus phonon energy had similar shapes for computation and experiment. These distributions grew with temperature but maintained similar shapes. Parameters from the ab initio calculations were used to obtain the thermal conductivity from the Boltzmann transport equation, which was in good agreement with experimental data. Despite the high group velocities of longitudinal acoustic phonons, their shorter lifetimes reduced their contribution to the thermal conductivity, which was dominated by transverse acoustic modes.

The heat capacities of nanocrystalline ${\mathrm{Ni}}_{3}\mathrm{Fe}$ and control materials with larger crystallites were measured from $0.4--300\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The heat capacities were integrated to obtain the enthalpy, entropy, and Gibbs free energy and to quantify how these thermodynamic functions are altered by nanocrystallinity. From the phonon density of states (DOS) measured by inelastic neutron scattering, we find that the Gibbs free energy is dominated by phonons and that the larger heat capacity of the nanomaterial below 100 K is attributable to its enhanced phonon DOS at low energies. Besides electronic and magnetic contributions, the nanocrystalline material has an additional contribution at higher temperatures, consistent with phonon anharmonicity. The nanocrystalline material shows a stronger increase with temperature of both the enthalpy and entropy compared to the bulk sample. Its entropy exceeds that of the bulk material by 0.4 ${k}_{\mathrm{B}}$/atom at 300 K. This is insufficient to overcome the enthalpy of grain boundaries and defects in the nanocrystalline material, making it thermodynamically unstable with respect to the bulk control material.

The phonons of wurtzite and zinc blende GaAs were calculated at simultaneously elevated temperature and pressure, and elastic constants were calculated as functions of pressure. Pressure caused instabilities of shorter-wavelength transverse acoustic modes in both wurtzite and zinc blende GaAs, causing them to fall to zero at 18 and 20 GPa, respectively. The Born stability criteria, which depend on elastic constants and only long wavelength phonons, therefore overestimated the pressure needed to induce instability at 0 K. At elevated temperatures, explicit anharmonicity pushes the onset of instability to higher pressures in both wurtzite and zinc blende GaAs. Phonon linewidth and densities of states data showed that the quasiharmonic approximation failed to account for temperature-induced phonon frequency shifts, and the quasiharmonic approximation became less reliable at elevated pressure. In general, the number of three-phonon processes increased with pressure, thereby increasing the temperature-driven broadening of phonon spectral lineshapes.

Offering a fresh viewpoint on phase changes and the thermodynamics of materials, this textbook covers the thermodynamics and kinetics of the most important phase transitions in materials science, spanning classical metallurgy through to nanoscience and quantum phase transitions. Clear, concise and complete explanations rigorously address transitions from the atomic scale up, providing the quantitative concepts, analytical tools and methods needed to understand modern research in materials science. Topics are grouped according to complexity, ensuring that students have a solid grounding in core topics before they begin to tackle more advanced material, and are accompanied by numerous end-of-chapter problems. With explanations firmly rooted in the context of modern advances in electronic structure and statistical mechanics, and developed from classroom teaching, this book is the ideal companion for graduate students and researchers in materials science, condensed matter physics, solid state science and physical chemistry.

First-principles calculations were used to study the Fermi surface of body-centered cubic vanadium at elevated temperatures. Supercell calculations accounted for effects of thermal atom displacements on band energies, and band unfolding was used to project the spectral weight of the electron states into the Brillouin zone of a standard bcc unit cell. An electronic topological transition (ETT, or Lifshitz transition) occurred near the $\mathrm{\ensuremath{\Gamma}}$ point with increasing temperature, but the large thermal smearings from the atomic disorder and the Fermi-Dirac distribution reduced the effect of this ETT on the electron-phonon interactions. The phonon dispersions showed thermal stiffening of their Kohn anomalies near the $\mathrm{\ensuremath{\Gamma}}$ point and of the longitudinal N phonon mode. In general the effects of the ETT were overcome by the thermal smearing of the Fermi surface that reduces the spanning vector densities for anomalous phonon modes.

While most solids expand when heated, some materials show the opposite behavior: negative thermal expansion (NTE). In polymers and biomolecules, NTE originates from the entropic elasticity of an ideal, freely-jointed chain. The origin of NTE in solids has been widely believed to be different. Our neutron scattering study of a simple cubic NTE material, ScF3, overturns this consensus. We observe that the correlation in the positions of the neighboring fluorine atoms rapidly fades on warming, indicating an uncorrelated thermal motion constrained by the rigid Sc-F bonds. This leads us to a quantitative theory of NTE in terms of entropic elasticity of a floppy network crystal, which is in remarkable agreement with experimental results. We thus reveal the formidable universality of the NTE phenomenon in soft and hard matter., 6 pages, 4 figures. Work reported at 2019 APS March meeting (http://meetings.aps.org/Meeting/MAR19/Session/B33.8)

We report the successful development of Ti_(29)V_(62−x)Ni_9Cr_x (x = 0, 6, 12) body centered cubic metal hydride (MH) electrodes by addressing vanadium corrosion and dissolution in KOH solutions. By identifying oxygen as the primary source of corrosion and eliminating oxygen with an Ar-purged cell, the Cr-free Ti_(29)V_(62)Ni_9 alloy electrode achieved a maximum capacity of 594 mAh g^(-1), double the capacity of commercial AB_5 MH electrodes. With coin cells designed to minimize oxygen evolution, the cycle stability of a Ti_(29)V_(62)Ni_9 alloy electrode was greatly improved with either vanadate ion additions to the electrolyte or Cr-substitution in the alloy. Together, both approaches resulted in a reversible capacity of around 500 mAh g^(−1) for at least 200 cycles. We performed energy density calculations for a 100 W h MH–air cell utilizing the high capacity Ti_(29)V_(62−x)Ni_9Cr_x electrodes and found that these cells are comparable in energy density to state-of-the-art Li-ion batteries.

All phonons in a single crystal of NaBr were measured by inelastic neutron scattering at temperatures of 10, 300 and 700 K. Even at 300 K the phonons, especially the longitudinal-optical (LO) phonons, showed large shifts in frequencies, and showed large broadenings in energy owing to anharmonicity. Ab initio computations were first performed with the quasiharmonic approximation (QHA), in which the phonon frequencies depend only on $V$, and on $T$ only insofar as it alters $V$ by thermal expansion. This QHA was an unqualified failure for predicting the temperature dependence of phonon frequencies, even 300 K, and the thermal expansion was in error by a factor of four. Ab initio computations that included both anharmonicity and quasiharmonicity successfully predicted both the temperature dependence of phonons and the large thermal expansion of NaBr. The frequencies of LO phonon modes decrease significantly with temperature owing to the real part of the phonon self-energy from explicit anhamonicity, originating from the cubic anharmonicity of nearest-neighbor Na-Br bonds. Anharmonicity is not a correction to the QHA predictions of thermal expansion and thermal phonon shifts, but dominates the behavior., 3 figures, 1 table, and the Supplementary Material appended

In order to determine a material's hydrogen storage potential, capacity measurements must be robust, reproducible, and accurate. Commonly, research reports focus on the gravimetric capacity, and often times the volumetric capacity is not reported. Determining volumetric capacities is not as straight-forward, especially for amorphous materials. This is the first study to compare measurement reproducibility across laboratories for excess and total volumetric hydrogen sorption capacities based on the packing volume. The use of consistent measurement protocols, common analysis, and figure of merits for reporting data in this study, enable the comparison of the results for two different materials. Importantly, the results show good agreement for excess gravimetric capacities amongst the laboratories. Irreproducibility for excess and total volumetric capacities is attributed to real differences in the measured packing volume of the material.

The Law of Corresponding States for classical gases is well established. Recent attempts at developing an analogous Law of Corresponding States for gas physisorption, however, have had limited success, in part due to the omission of relevant adsorption considerations such as the adsorbate volume and cooperative adsorbate-adsorbate interactions. In this work, we modify a prior Law of Corresponding States for gas physisorption to account for adsorbate volume, and test it with experimental data and a generalized theoretical approach. Furthermore, we account for the recently-reported cooperative adsorbate-adsorbate interactions on the surface of zeolite-templated carbon (ZTC) with an Ising-type model, and in doing so, show that the Law of Corresponding States for gas physisorption remains valid even in the presence of atypically enhanced adsorbate-adsorbate interactions.

The interplay between sodium ordering and electron mobility in NaxFePO4 was investigated using a combination of synchrotron X-ray diffraction and Mossbauer spectrometry. Synchrotron X-ray diffraction measurements were carried out for a range of temperatures between 298 and 553 K. Rietveld analysis of the diffraction patterns was used to determine the temperature of sodium redistribution on the lattice. This diffraction analysis also gives new information about the phase stability of the system. Mossbauer spectra were collected in the same temperature range. An analysis of the temperature evolution of the spectral shapes was used to identify the onset of fast electron hopping and determine the polaron hopping rate. The temperature evolution of the iron site occupancies from the Mossbauer measurements, combined with the synchrotron diffraction results, shows a relationship between the onset of fast electron dynamics and the loss of local order on the sodium sublattice.

Inelastic neutron scattering was used to measure phonon dispersions in a single crystal of FeGe_2 with the C16 structure at 300, 500, and 635 K. Phonon densities of states (DOS) were also measured on polycrystalline FeGe_2 from 325 to 1050 K, and the Fe partial DOS was obtained from polycrystalline ^(57)FeGe_2 at 300 K using nuclear resonant inelastic x-ray scattering. The dominant feature in the temperature dependence of the phonon spectrum is thermal broadening of high-energy modes. The energy shifts of the low- and high-energy parts of the spectrum were almost the same. DFT calculations performed with the quasiharmonic approximation gave results in moderate agreement with the experimental thermal energy shifts, although the isobaric Gruneisen parameter calculated from the quasiharmonic model was smaller than that from measurements. The thermal broadening of the phonon spectrum and dispersions, especially at high energies, indicates a cubic anharmonicity to second order that should also induce phonon shifts. We show that different anharmonic contributions cancel out, giving average phonon shifts in moderate agreement to calculations with the quasiharmonic approximation. The different parts of the large phonon contribution to the entropy are separated for FeGe_2, showing modest but interpretable anharmonic contributions.

A thermodynamic study of carbon dioxide adsorption on a zeolite-templated carbon (ZTC), a superactivated carbon (MSC-30) and an activated carbon (CNS-201) was carried out at temperatures from 241 to 478 K and pressures up to 5.5•10^6 Pa. Excess adsorption isotherms were fitted with generalized Langmuir-type equations, allowing the isosteric heats of adsorption and adsorbed-phase heat capacities to be obtained as a function of absolute adsorption. On MSC-30, a superactivated carbon, the isosteric heat of carbon dioxide adsorption increases with occupancy from 19 to 21 kJ•mol^(−1), before decreasing at high loading. This increase is attributed to attractive adsorbate-adsorbate intermolecular interactions as evidenced by the slope and magnitude of the increase in isosteric heat and the adsorbed-phase heat capacities. An analysis of carbon dioxide adsorption on ZTC indicates a high degree of binding-site homogeneity. A generalized Law of Corresponding States analysis indicates lower carbon dioxide adsorption than expected.

Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.

The effects of temperature and pressure on the phonons of GaN were calculated for both the wurtzite and zinc-blende structures. The quasiharmonic approximation (QHA) gave reasonable results for the temperature dependence of the phonon DOS at zero pressure but unreliably predicted the combined effects of temperature and pressure. Pressure was found to change the explicit anharmonicity, altering the thermal shifts of phonons and more notably qualitatively changing the evolution of phonon lifetimes with increasing temperature. These effects were largest for the optical modes, and phonon frequencies below approximately 5 THz were adequately predicted with the QHA. The elastic anisotropies of GaN in both wurtzite and zinc-blende structures were calculated from the elastic constants as a function of pressure at 0 K. The elastic anisotropy increased with pressure until reaching elastic instabilities at 40 GPa (zinc blende) and 65 GPa (wurtzite). The calculated instabilities are consistent with proposed transformation pathways to rocksalt GaN and place upper bounds on the pressures at which wurtzite and zinc-blende GaN can be metastable. Funding Agencies|Office of Science of the U.S. Department of Energy [DE-AC02-05CH11231]; Department of Energy through the Carnegie-DOE Alliance Centers Stewardship Sciences Academic Alliance Program; Department of Energy through Office of Science Graduate Fellowship Program (DOE SCGF) [DE-AC05-06OR23100]

Krypton adsorption was measured at eight temperatures between 253 and 433 K on a zeolite-templated carbon and two commercial carbons. The data were fitted using a generalized Langmuir isotherm model and thermodynamic properties were extracted. Differing from that on commercial carbons, krypton adsorption on the zeolite-templated carbon is accompanied by an increasing isosteric enthalpy of adsorption, rising by up to 1.4 kJ mol^(–1) as a function of coverage. This increase is a result of enhanced adsorbate–adsorbate interactions promoted by the ordered, nanostructured surface of the adsorbent. An assessment of the strength and nature of these adsorbate–adsorbate interactions is made by comparing the measured isosteric enthalpies of adsorption (and other thermodynamic quantities) to fundamental metrics of intermolecular interactions of krypton and other common gases.

Ethane adsorption was measured on zeolite-templated carbon (ZTC) and compared to superactivated carbon MSC-30. Isotherms measured at temperatures between 252 and 423 K were fitted using a superposition of two Langmuir isotherms, and thermodynamic properties were assessed. Unlike typical carbon adsorbents, the isosteric heat of adsorption on ZTC increases by up to 4.6 kJ/mol with surface coverage. This increase is attributed to strong adsorbate–adsorbate intermolecular interactions, a hypothesis that is shown to be consistent with fundamental estimates of intermolecular interactions. Furthermore, the molar entropy of the adsorbed phase was measured and compared to an estimate derived from statistical mechanics. While the measured and estimated entropies of the adsorbed phase of ethane on MSC-30 are in agreement, they differ significantly on ZTC at high coverage, indicative of the atypical properties of ethane adsorption on ZTC.

A combination of operando X-ray diffraction, pair distribution function (PDF) analysis coupled with electrochemical measurements and Mossbauer spectroscopy elucidates the nature of the phase transitions induced by insertion and extraction of sodium ions in P2-Na0.67[NiyMn0.5+yFe0.5−2y]O2 (y = 0, 0.10, 0.15). When phase transitions are avoided, the optimal cathode material – P2-Na0.67Fe0.2Mn0.65Ni0.15O2 – delivers 25% more energy than the unsubstituted material, sustaining high specific energy (350 Wh kg−1) at moderate rates and maintains 80% of the original energy density after 150 cycles – a significant improvement in performance vs. the unsubstituted analogue. The crystal structure of the high voltage phase is solved for the first time by X-ray PDF analysis of P2-Na0.67−zFe0.5Mn0.5O2 (where z ∼ 0.5), revealing that migration of the transition metals – particularly Fe3+ – into tetrahedral sites in the interlayer space occurs at high potential. This results in new short range order between two adjacent layers. Although the transition metal migration is reversible as proven by electrochemical performance, it induces a large disfavourable cell polarization. The deleterious high voltage transition is mitigated by substitution of Fe3+ by Mn4+/Ni2+, giving rise to better cycling performance. Moreover, as demonstrated by 57Fe Mossbauer spectroscopy, the much lower ratio of Fe4+O6 to Fe3+O6 observed systematically across the range of Ni content – compared to the values expected from a purely ionic model – suggests redox activity involves the O-2p orbitals owing to their overlap with the transition metal-3d orbitals.

Glassy materials exist in nature and play a critical role in technology, but key differences between the glass, liquid and crystalline phases are not well understood. Over several decades there has been controversy about the specific heat absorbed as a glass transforms to a liquid—does this originate from vibrational entropy or configurational entropy? Here we report direct in situ measurements of the vibrational spectra of strong and fragile metallic glasses in the glass, liquid and crystalline phases. For both types of material, the measured vibrational entropies of the glass and liquid show a tiny excess over the crystal, representing less than 5% of the total excess entropy measured with step calorimetry. These results reveal that the excess entropy of metallic glasses is almost entirely configurational in origin, consistent with the early theories of Gibbs and co-workers describing the glass transition as a purely configurational transition.

Raman spectroscopy was used to measure the frequencies of phonons in Si_(24) with an open clathrate structure at temperatures from 80 to 400 K with simultaneous pressures of 0 to 8 GPa. The frequency shifts of the different phonons were substantially different under either temperature or pressure. The quasiharmonic behavior was isolated by varying pressure at low temperatures, and the anharmonic behavior was isolated by varying temperature at low pressures. Phonon modes dominated by bond bending were anomalous, showing stiffening with temperature and softening with pressure. Both the quasiharmonic behavior and the anharmonic behavior changed markedly with simultaneous changes in temperature ΔT and pressure ΔP. With ΔT = 320 K and ΔP = 8 GPa, some frequency shifts that scaled with the product ΔT ΔP were as large as the shifts from ΔT and ΔP alone. The thermodynamic entropy of this material likely has a dependence on ΔT and ΔP that cannot be obtained by adding effects from quasiharmonicity and phonon-phonon anharmonicity.

Phonon partial densities of states (pDOS) of ^(57)Fe_3 C were measured from cryogenic temperatures through the Curie transition at 460 K using nuclear resonant inelastic x-ray scattering. The cementite pDOS reveal that low-energy acoustic phonons shift to higher energies (stiffen) with temperature before the magnetic transition. This unexpected stiffening suggests strongly nonharmonic vibrational behavior that impacts the thermodynamics and elastic properties of cementite. Density functional theory calculations reproduced the anomalous stiffening observed experimentally in cementite by accounting for phonon-phonon interactions at finite temperatures. The calculations show that the low-energy acoustic phonon branches with polarizations along the [010] direction are largely responsible for the anomalous thermal stiffening. The effect was further localized to the motions of the Fe_(II) site within the orthorhombic structure, which participates disproportionately in the anomalous phonon stiffening.

The cycle lives for cathodes of nanocrystalline iron trifluoride (FeF_3) were measured in rechargeable lithium batteries at different depths of discharge. When the discharge was limited to less than one Li^+ ion per FeF_3, both the cycle life and energy efficiency were considerably greater than when converting FeF_3 into Fe and LiF in deep discharge. An in situ X-ray diffractometry (XRD) study of the FeF_3 cathode during its initial discharge to LiFeF_3 showed a continuous change of the FeF_3 diffraction pattern, indicating Li^+ insertion into the rhombohedral FeF_3 causing distortion of its lattice parameters. Electrochemical cycling is most reversible when this mechanism occurs in the absence of other changes in the crystal structure.

In-situ exploration of Venus is challenging due to its severe environment, which is benign (25oC) at an altitude of 55 km, but rapidly becoming more hostile at lower altitudes. The temperature increases at ~7oC/km to ~465°C, with the pressure reaching 90 bars at the surface.1 These challenging conditions have limited in-situ exploration missions to high altitude balloons at 55 km (above the clouds) that lasted for 48 h, or even shorter duration surface missions that survived for two hours.2,3 The high-altitude (55-65km) balloon missions are stymied by the opaqueness of the Venusian clouds, which underlines the need for more long-duration in-situ missions for a better understanding of the Venus atmosphere across the cloud layers and below, as recommended by the Venus science community, Venus Exploration Analysis Group (VEXAG).4 Long-duration variable-altitude balloons (VABs) extending below the clouds have gained particular interest. Durable VABs would allow i) long-term measurements across Venus clouds, ii) determination of chemical species and isotopes underneath the clouds, iii) transport to different longitudes on the planet and measure atmospheric flow patterns, especially with the altitude control, iv) probing the interior structure through close-range imaging, and v) investigation of the seismic activity from acoustic measurements at various altitudes. For these missions, conventional power technologies are inadequate. For example, the performance of photovoltaics (PV) is hampered by the decreasing solar flux deeper in the clouds, the selective loss of short wavelength radiation, and the performance loss from the high temperatures.5 An energy storage system tolerant to high temperatures is needed to compensate for the reduced power generation of PVs at low altitudes, and to support nighttime operations for the VABs. In this paper, we will describe a novel ‘Venus Interior Probe using in-situ Power and Propulsion (VIP-INSPR) architecture we have been developing under NASA-NIAC (Novel Innovative and Advanced Concepts) program for sustained Venus atmospheric exploration. The probe concept utilizes: i) PV as a power source to the probe at high altitudes, and to electrolyze water carried from ground using regenerative solid oxide fuel/ electrolysis cell (SOEC), ii) Solid oxide fuel cell (SOFC)6 to provide power at low altitudes, iii) hydrogen storage bed for on-demand storage or release of hydrogen,7 iv) and a balloon filled with hydrogen and with hydrogen buoyancy-based altitude control system. Both H2 and O2 would be regenerated through electrolysis of the water produced in the fuel cell (a closed–system) at high altitudes. Acknowledgments: This work presented here was carried out at the Jet Propulsion Laboratory, California Institute of Technology under a contract with National Aeronautics and Space Administration and supported NASA-NIAC. References: 1) T. Basilevsky, J. W. Head, "The surface of Venus". Rep. Prog. Phys. 66, 1699 (2003); 2) R. Z. Sagdeev, et al., The VEGA Venus balloon experiment, Science, 231, 1407, 1986; 3) M. Wade, "Venera 1VA". Encyclopedia Astronautica. Retrieved 28 July 2010; 4) “Aerial Platforms For the Scientific Exploration of Venus”, The Venus Aerial Platforms Study Team Summary Report, August 2018; 5) G. A. Landis and T. Vo, "Photovoltaic Performance in the Venus Environment," 34th IEEE Photovoltaic Specialists Conference, Philadelphia PA, June 7-12, 2009; 6) A. B. Stambouli and E. Traversa, Renewable and Sustainable Energy Reviews, 6 (2002) 433-455, 7) G. Sandrock, S. Suda and L. Schlapbach, “Applications,” in Hydrogen in Intermetallic Compounds II, Topics in Appl. Phys. V. 67, Springer-Verlag 1992, ISBN 3-540-54668-5.

Progress in materials science through thermodynamic modelling may rest crucially on access to a database, such as that developed by Scientific Group Thermodata Europe (SGTE) around 1990. It gives the Gibbs energy G(T)of the elements in the form of series as a function of temperature, i.e. essentially a curve fitting to experimental data. In the light of progress in theoretical understanding and first-principles calculation methods, the possibility for an improved database description of the thermodynamics of the elements has become evident. It is the purpose of this paper to provide a framework for such work. Lattice vibrations, which usually give the major contribution to G(T), are treated in some detail with a discussion of neutron scattering studies of anharmonicity in aluminium, first-principles calculations including ab initio molecular dynamics (AIMD), and the strength and weakness of analytic model representations of data. Similarly, electronic contributions to G(T) are treated on the basis of the density of states N(E) for metals, with emphasis on effects at high T. Further, we consider G(T) below 300 K, which is not covered by SGTE. Other parts in the paper discuss metastable and dynamically unstable lattices, G(T) in the region of superheated solids and the requirement on a database in the calculation of phase diagrams.

A nanocrystalline face-centered cubic (fcc) solid solution of 6% Fe in Cu was prepared by high-energy ball milling, and annealed at temperatures from 200 to 360 °C to induce chemical unmixing. The chemical state of the material was characterized by three-dimensional atom probe microscopy, Mossbauer spectrometry and X-ray powder diffractometry. The unmixing was heterogeneous, with iron atoms forming iron-rich zones that thicken with further annealing. The phonon partial density of states (pDOS) of ^(57)Fe was measured by nuclear resonant inelastic X-ray scattering, showing the pDOS of the as-prepared material to be that of an fcc crystal. The features of this pDOS became broader in the early stages of unmixing, but only small changes in average phonon frequencies occurred until the body-centered cubic (bcc) phase began to form. The vibrational entropy calculated from the pDOS underwent little change during the early stage of annealing, but decreased rapidly when the bcc phase formed in the material.

A thermodynamic study of the enthalpy of adsorption of methane on high surface area carbonaceous materials was carried out from 238 to 526 K. The absolute quantity of adsorbed methane as a function of equilibrium pressure was determined by fitting isotherms to a generalized Langmuir-type equation. Adsorption of methane on zeolite-templated carbon, an extremely high surface area material with a periodic arrangement of narrow micropores, shows an increase in isosteric enthalpy with methane occupancy; i.e., binding energies are greater as adsorption quantity increases. The heat of adsorption rises from 14 to 15 kJ/mol at near-ambient temperature and then falls to lower values at very high loading (above a relative site occupancy of 0.7), indicating that methane/methane interactions within the adsorption layer become significant. The effect seems to be enhanced by a narrow pore-size distribution centered at 1.2 nm, approximately the width of two monolayers of methane, and reversible methane delivery increases by up to 20% over MSC-30 at temperatures and pressures near ambient.

Ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M_{5}^{-} phonon mode in B2-ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topological transition, in which new features of the Fermi surface arise at elevated temperatures. The thermally induced electronic topological transition causes an increased electronic screening for the atom displacements in the M_{5}^{-} phonon mode and an adiabatic electron-phonon interaction with an unusual temperature dependence.

Inelastic neutron scattering was used to measure the phonon density of states in fcc palladium and platinum metal at temperatures from 7 K to 1576 K. Both phonon-phonon interactions and electron-phonon interactions were calculated by methods based on density functional theory (DFT) and were consistent with the measured shifts and broadenings of phonons with temperature. Unlike the longitudinal modes, the characteristic transverse modes had a nonlinear dependence on temperature owing to the requirement for a population of thermal phonons for upscattering. Kohn anomalies were observed in the measurements at low temperature and were reproduced by calculations based on DFT. Contributions to the entropy from phonons and electrons were assessed and summed to obtain excellent agreement with prior calorimetric data. The entropy from thermal expansion is positive for both phonons and electrons but larger for phonons. The anharmonic phonon entropy is negative in Pt, but in Pd it changes from positive to negative with increasing temperature. Owing to the position of the Fermi level on the electronic DOS, the electronic entropy was sensitive to the adiabatic electron-phonon interaction in both Pd and Pt. The adiabatic EPI depended strongly on thermal atom displacements.

Zeolite-templated carbon (ZTC) materials were synthesized, characterized, and evaluated as potential hydrogen storage materials between 77 and 298 K up to 30 MPa. Successful synthesis of high template fidelity ZTCs was confirmed by X-ray diffraction and nitrogen adsorption at 77 K; BET surface areas up to ~3600 mT2 g^(–1) were achieved. Equilibrium hydrogen adsorption capacity in ZTCs is higher than all other materials studied, including superactivated carbon MSC-30. The ZTCs showed a maximum in Gibbs surface excess uptake of 28.6 mmol g–1 (5.5 wt %) at 77 K, with hydrogen uptake capacity at 300 K linearly proportional to BET surface area: 2.3 mmol g^(–1) (0.46 wt %) uptake per 1000 m^2 g^(–1) at 30 MPa. This is the same trend as for other carbonaceous materials, implying that the nature of high-pressure adsorption in ZTCs is not unique despite their narrow microporosity and significantly lower skeletal densities. Isoexcess enthalpies of adsorption are calculated between 77 and 298 K and found to be 6.5–6.6 kJ mol^(–1) in the Henry’s law limit.

Methane adsorption at high pressures and across a wide range of temperatures was investigated on the surface of three porous carbon adsorbents with complementary structural properties. The measured adsorption equilibria were analyzed using a method that can accurately account for nonideal fluid properties and distinguish between absolute and excess quantities of adsorption, and that also allows the direct calculation of the thermodynamic potentials relevant to adsorption. On zeolite-templated carbon (ZTC), a material that exhibits extremely high surface area with optimal pore size and homogeneous structure, methane adsorption occurs with unusual thermodynamic properties that are greatly beneficial for deliverable gas storage: an enthalpy of adsorption that increases with site occupancy, and an unusually low entropy of the adsorbed phase. The origin of these properties is elucidated by comparison of the experimental results with a statistical mechanical model. The results indicate that temperature-dependent clustering (i.e., reduced configurations) of the adsorbed phase due to enhanced lateral interactions can account for the peculiarities of methane adsorbed on ZTC.

Two-phase mixtures of Li_(0.5)FePO_4 with crystal sizes as small as 25 nm were prepared by solid-state reaction, ball milling, and chemical delithiation. Mssbauer spectra of nanocrystalline Li_(0.5)FePO_4 found evidence for a thin layer of Fe^(3+) at the crystal surfaces. Spectra acquired at temperatures from 25 to 225 °C showed thermally driven electronic relaxations, where the electric field gradients (EFG) of the main Fe^(3+) and Fe^(2+) spectral components decreased with temperature. The isomer shifts (IS) of Fe^(3+) and Fe^(2+) showed similar thermal trends, indicative of valence fluctuations caused by small polaron hopping. The activation energies obtained from the temperature dependence of the EFG were 410 meV for Fe^(3+) and 330 meV for Fe^(2+), and an activation energy of 400 meV was obtained for the IS of both. The rapid valence electron hopping between Fe sites is intrinsic to electronic conductivity in Li_(x)FePO_4, which is calculated to be higher than most reports for bulk material.

Raman spectra of monoclinic zirconia (ZrO_2) were measured at temperatures of up to 950 K. Temperature-dependent Raman peak shifts and broadenings were reported and compared with prior results on hafnia (HfO_2). Lattice dynamics calculations were performed with both shell model and density functional theory to obtain Raman frequencies, and the total and partial phonon density of states. These calculations were also used to identify the individual motions of metal and oxygen atoms in the different Raman modes. By correlating these motions to the thermal peak shifts and broadenings, it was confirmed that modes involving changes in oxygen-oxygen bond length were the most anharmonic. The metal-dominated modes were found to be more quasiharmonic, and thus showed less broadening with temperature. Mass effects were evident by comparing the mode softening and shifting between zirconia and hafnia.

The literature on vibrational thermodynamics of materials is reviewed. The emphasis is on metals and alloys, especially on the progress over the last decade in understanding differences in the vibrational entropy of different alloy phases and phase transformations. Some results on carbides, nitrides, oxides, hydrides and lithium-storage materials are also covered. Principles of harmonic phonons in alloys are organized into thermodynamic models for unmixing and ordering transformations on an Ising lattice, and extended for non-harmonic potentials. Owing to the high accuracy required for the phonon frequencies, quantitative predictions of vibrational entropy with analytical models prove elusive. Accurate tools for such calculations or measurements were challenging for many years, but are more accessible today. Ab initio methods for calculating phonons in solids are summarized. The experimental techniques of calorimetry, inelastic neutron scattering, and inelastic X-ray scattering are explained with enough detail to show the issues of using these methods for investigations of vibrational thermodynamics. The explanations extend to methods of data analysis that affect the accuracy of thermodynamic information. It is sometimes possible to identify the structural and chemical origins of the differences in vibrational entropy of materials, and the number of these assessments is growing. There has been considerable progress in our understanding of the vibrational entropy of mixing in solid solutions, compound formation from pure elements, chemical unmixing of alloys, order–disorder transformations, and martensitic transformations. Systematic trends are available for some of these phase transformations, although more examples are needed, and many results are less reliable at high temperatures. Nanostructures in materials can alter sufficiently the vibrational dynamics to affect thermodynamic stability. Internal stresses in polycrystals of anisotropic materials also contribute to the heat capacity. Lanthanides and actinides show a complex interplay of vibrational, electronic, and magnetic entropy, even at low temperatures. A “quasiharmonic model” is often used to extend the systematics of harmonic phonons to high temperatures by accounting for the effects of thermal expansion against a bulk modulus. Non-harmonic effects beyond the quasiharmonic approximation originate from the interactions of thermally-excited phonons with other phonons, or with the interactions of phonons with electronic excitations. In the classical high temperature limit, the adiabatic electron–phonon coupling can have a surprisingly large effect in metals when temperature causes significant changes in the electron density near the Fermi level. There are useful similarities in how temperature, pressure, and composition alter the conduction electron screening and the interatomic force constants. Phonon–phonon “anharmonic” interactions arise from those non-harmonic parts of the interatomic potential that cannot be accounted for by the quasiharmonic model. Anharmonic shifts in phonon frequency with temperature can be substantial, but trends are not well understood. Anharmonic phonon damping does show systematic trends, however, at least for fcc metals. Trends of vibrational entropy are often justified with atomic properties such as atomic size, electronegativity, electron-to-atom ratio, and mass. Since vibrational entropy originates at the level of electrons in solids, such rules of thumb prove no better than similar rules devised for trends in bonding and structure, and tend to be worse. Fortunately, the required tools for accurate experimental investigations of vibrational entropy have improved dramatically over the past few years, and the required ab initio methods have become more accessible. Steady progress is expected for understanding the phenomena reviewed here, as investigations are performed with the new tools of experiment and theory, sometimes in integrated ways.

LixFePO4 solid solutions with different lithium concentrations, x, were investigated by Mössbauer spectrometry at temperatures between 25° and 210°. The Mössbauer spectra show a temperature dependence of their isomer shifts (EIS) and electric quadrupole splittings (EQ), typical of thermally-activated, electronic relaxation processes involving 57Fe ions. The activation energies for the fluctuations of EQ and EIS do not have a measurable dependence on the concentration of lithium, but varies between Fe3+ and Fe2+. Typically, for the Fe2+ components of the spectra, the fluctuations of EQ occurred at lower temperatures than the fluctuations of EIS, with activation energy of 512 meV for EQ and 551 meV for EIS. The more facile fluctuations of EQ for Fe2+ are evidence for local motions of neighboring Li+ ions.

Samples of nanostructured Li_(x)FePO_4 with characteristic crystal sizes of 26 nm, and compositions of x = 0.35 and 0.65, were synthesized by ball-milling and chemical delithiation. X-ray powder diffraction showed that the solid solution phase started to form whenever two-phase materials were heated above 200 °C. The solid solution phase of nanocrystalline Li_(0.65)FePO_4 was quick to form above 200 °C but did not unmix at lower temperatures. Unmixing below 200 °C was found after long-time annealing of nanocrystalline Li_(0.35)FePO_4, however, consistent with the equilibrium phase diagram of bulk Li_(x)FePO_4. The stability of the solid solution of nanocrystalline Li_(x)FePO_4 is kinetic in origin, perhaps originating with effects of crystal surfaces.

The solid solution phase of Li_xFePO_4 with different Li concentrations, x, was investigated by Mossbauer spectrometry at temperatures between 25 and 210 °C. The Mossbauer spectra show a temperature dependence of their isomer shifts (E_(IS)) and electric quadrupole splittings (E_Q), typical of thermally activated, electronic relaxation processes involving ^(57)Fe ions. The activation energies for the fluctuations of E_Q and E_(IS) for Fe^(3+) are nearly the same, 570 ± 9 meV, suggesting that both originate from charge hopping. For the Fe^(2+) components of the spectra, the fluctuations of E_Q occurred at lower temperatures than the fluctuations of E_(IS), with an activation energy of 512 ± 12 meV for E_Q and one of 551 ± 7 meV for E_(IS). The more facile fluctuations of E_Q for Fe^(2+) are evidence for local motions of neighboring Li^+ ions. It appears that the electron hopping frequency is lower than that of Li^+ ions. The activation energies of relaxation did not have a measurable dependence on the concentration of lithium, x.

The hydrogen storage reaction ScH_2 + 2LiBH_4 → ScB_2 + 2LiH + 4H_2 (8.91 wt %), based on the thermodynamic destabilization of LiBH_4, is predicted to have a reaction enthalpy of ΔH_(300K) = 34.1 kJ/mol H_2. The isothermal kinetic desorption behavior in this system was measured. At temperatures up to 450 °C, less than 5 wt % H_2 is released, which is only half of the theoretical capacity. Powder X-ray diffraction data indicate that LiBH_4 has decomposed into LiH in the final desorption product, but the data provide no evidence that ScH_2 has participated in the reaction. Magic angle spinning NMR (MAS NMR) results do not show that the expected ScB_2 equilibrium product phase has formed during desorption. While the addition of 2 mol % TiCl_3 catalyst does improve desorption kinetics at 280 °C, it does not otherwise assist the destabilization reaction. The calculated reaction enthalpy suggests that this system should be of interest at moderate temperatures, but the large heats of formation of the reactant phases in this system appear to play a critical role in determining overall kinetics. Furthermore, the formation of a Li_2B_(12)H_(12) intermediate phase was determined by MAS NMR, which is an undesirable stable product if reaction reversibility is to be accomplished.