Electronic Entropy Research Articles

Electronic Entropy as a Periodic Property of the Elements: A Theoretical Chemistry Approach

Periodicity in electronic molar entropy values has been shown on the basis of the electronic structures of the elements. Also, with the approximations discussed herein, one can estimate the electronic molar entropy without atomic spectroscopy results. All of this can be accomplished by showing the connection between the vector model of the atom and statistical thermodynamics in its quantum mechanical form.

Contribution of electronic entropy to the order-disorder transition of Cu3Au

The authors evaluate the electronic entropy change from transport measurements across the order-disorder transition in Cu${}_{3}$Au.

Effects of Ge substitution for Sn on the crystal structure, magnetization, and the magnetocaloric effect of Mn3SnC

The effects of a Ge substitution for 50% Sn on the crystal structure, magnetization and the magnetocaloric effect of Mn3SnC were investigated using high-resolution X-ray diffraction, magnetic and calorimetric measurements. Results show that the Ge substitution enlarges the magnetovolume effect, though it reduces the lattice parameter. On the other hand, the Ge substitution increases high field magnetization and reduces the Curie temperature. The Ge substitution also reduces latent heat during the ferrimagnetic transition and the magnetocaloric effect at the magnetic field change 0–5 T. It is suggested that the Ge substitution perhaps reduces the electronic entropy change via a change of the electronic structure and its stability against an external magnetic field. This effect is dominant over an increase of the magnetic entropy change leading to the reduction of the magnetocaloric effect.

Finite-temperature materials modeling from the quantum nuclei to the hot electron regime

Atomistic simulations provide insights into structure-property relations on an atomic size and length scale, that are complementary to the macroscopic observables that can be obtained from experiments. Quantitative predictions, however, are usually hindered by the need to strike a balance between the accuracy of the calculation of the interatomic potential and the modelling of realistic thermodynamic conditions. Machine-learning techniques make it possible to efficiently approximate the outcome of accurate electronic-structure calculations, that can therefore be combined with extensive thermodynamic sampling. We take elemental nickel as a prototypical material, whose alloys have applications from cryogenic temperatures up to close to their melting point, and use it to demonstrate how a combination of machine-learning models of electronic properties and statistical sampling methods makes it possible to compute accurate finite-temperature properties at an affordable cost. We demonstrate the calculation of a broad array of bulk, interfacial and defect properties over a temperature range from 100 to 2500 K, modeling also, when needed, the impact of nuclear quantum fluctuations and electronic entropy. The framework we demonstrate here can be easily generalized to more complex alloys and different classes of materials.

Entropic evidence for a Pomeranchuk effect in magic-angle graphene.

In the 1950s, Pomeranchuk1 predicted that, counterintuitively, liquid 3He may solidify on heating. This effect arises owing to high excess nuclear spin entropy in the solid phase, where the atoms are spatially localized. Here we find that an analogous effect occurs in magic-angle twisted bilayer graphene2-6. Using both local and global electronic entropy measurements, we show that near a filling of one electron per moiré unit cell, there is a marked increase in the electronic entropy to about 1kB per unit cell (kB is the Boltzmann constant). This large excess entropy is quenched by an in-plane magnetic field, pointing to its magnetic origin. A sharp drop in the compressibility as a function of the electron density, associated with a reset of the Fermi level back to the vicinity of the Dirac point, marks a clear boundary between two phases. We map this jump as a function of electron density, temperature and magnetic field. This reveals a phase diagram that is consistent with a Pomeranchuk-like temperature- and field-driven transition from a low-entropy electronic liquid to a high-entropy correlated state with nearly free magnetic moments. The correlated state features an unusual combination of seemingly contradictory properties, some associated with itinerant electrons-such as the absence of a thermodynamic gap, metallicity and a Dirac-like compressibility-and others associated with localized moments, such as a large entropy and its disappearance under a magnetic field. Moreover, the energy scales characterizing these two sets of properties are very different: whereas the compressibility jump has an onset at a temperature of about 30kelvin, the bandwidth of magnetic excitations is about 3kelvin or smaller. The hybrid nature of the present correlated state and the large separation of energy scales have implications for the thermodynamic and transport properties of the correlated states in twisted bilayer graphene.

Observation of inverse magnetocaloric effect in magnetic-field-induced austenite phase of Heusler alloys Ni50−xCoxMn31.5Ga18.5 (x=9 and 9.7)

Magnetocaloric effect (MCE), magnetization, specific heat, and magnetostriction measurements were performed in both pulsed and steady high magnetic fields to investigate the magnetocaloric properties of Heusler alloys Ni50-xCoxMn31.5Ga18.5 (x = 9 and 9.7). From direct MCE measurements for Ni41Co9Mn31.5Ga18.5 up to 56 T, a steep temperature drop was observed for magnetic-field-induced martensitic transformation (MFIMT), designated as inverse MCE. Remarkably, this inverse MCE is apparent not only with MFIMT, but also in the magnetic-field-induced austenite phase. Specific heat measurements under steady high magnetic fields revealed that the magnetic field variation of the electronic entropy plays a dominant role in the unconventional magnetocaloric properties of these materials. First-principles based calculations performed for Ni41Co9Mn31.5Ga18.5 and Ni45Co5Mn36.7In13.3 revealed that the magnetic-field-induced austenite phase of Ni41Co9Mn31.5Ga18.5 is more unstable than that of Ni45Co5Mn36.7In13.3 and that it is sensitive to slight tetragonal distortion. We conclude that the inverse MCE in the magnetic-field-induced austenite phase is realized by marked change in the electronic entropy through tetragonal distortion induced by the externally applied magnetic field.

Proximity to a critical point driven by electronic entropy in URu2Si2

The strongly correlated actinide metal URu2Si2 exhibits a mean field-like second order phase transition at To ≈ 17 K, yet lacks definitive signatures of a broken symmetry. Meanwhile, various experiments have also shown the electronic energy gap to closely resemble that resulting from hybridization between conduction electron and 5f-electron states. We argue here, using thermodynamic measurements, that the above seemingly incompatible observations can be jointly understood by way of proximity to an entropy-driven critical point, in which the latent heat of a valence-type electronic instability is quenched by thermal excitations across a gap, driving the transition second order. Salient features of such a transition include a robust gap spanning highly degenerate features in the electronic density of states, that is weakly (if at all) suppressed by temperature on approaching To, and an elliptical phase boundary in magnetic field and temperature that is Pauli paramagnetically limited at its critical magnetic field.

Energy, Entropy and Quantum Tunneling of Protons and Electrons in Brain Mitochondria: Relation to Mitochondrial Impairment in Aging-Related Human Brain Diseases and Therapeutic Measures.

Adult human brains consume a disproportionate amount of energy substrates (2–3% of body weight; 20–25% of total glucose and oxygen). Adenosine triphosphate (ATP) is a universal energy currency in brains and is produced by oxidative phosphorylation (OXPHOS) using ATP synthase, a nano-rotor powered by the proton gradient generated from proton-coupled electron transfer (PCET) in the multi-complex electron transport chain (ETC). ETC catalysis rates are reduced in brains from humans with neurodegenerative diseases (NDDs). Declines of ETC function in NDDs may result from combinations of nitrative stress (NS)–oxidative stress (OS) damage; mitochondrial and/or nuclear genomic mutations of ETC/OXPHOS genes; epigenetic modifications of ETC/OXPHOS genes; or defects in importation or assembly of ETC/OXPHOS proteins or complexes, respectively; or alterations in mitochondrial dynamics (fusion, fission, mitophagy). Substantial free energy is gained by direct O2-mediated oxidation of NADH. Traditional ETC mechanisms require separation between O2 and electrons flowing from NADH/FADH2 through the ETC. Quantum tunneling of electrons and much larger protons may facilitate this separation. Neuronal death may be viewed as a local increase in entropy requiring constant energy input to avoid. The ATP requirement of the brain may partially be used for avoidance of local entropy increase. Mitochondrial therapeutics seeks to correct deficiencies in ETC and OXPHOS.

Linear dielectric thermodynamics: A new universal law for optical, dielectric constants

AbstractThe thermodynamics of linear dielectric are formally developed to explore the isothermal and adiabatic temperature‐pressure dependence of dielectric constants. The refractive index of optical materials is widely measured in the literature: it is both temperature and pressure dependent. The argument to establish the dielectric constant's isentropic temperature dependence is a thermodynamic one and is thus applicable to all physical models that describe electron clouds and electronic resonances within materials. The isentropic slope of the displacement field vs the electric field at all temperatures is described by an adiabatic dielectric constant in an energy‐per‐unit mass system. This slope is shown through the electronic part of the entropy to be unstable at high temperatures due to the change in the curvature of the temperature dependence of the dielectric constant. The electronic entropy contribution for optical, thermo‐electro materials has negative heat capacities which are unacceptable. The dielectric constant's temperature and pressure dependence is predicted to be only dependent on the specific volume so isentropes are always positive. A new universal form for the dielectric constant follows from this hypothesis: the dielectric constant is proportional to the square root of the specific volume for fully dense solids.

Ligand dependent magnetism of the = 3/2 Mott insulator Cs2 MX 6 (M = Ta, Nb, X = Br, Cl)

Magnetic and structural properties of double perovskite type bromides Cs2 MBr6 (M = Ta, Nb), where Ta4+ (5d 1) and Nb4+ (4d 1) ions form the face centered cubic lattice, are investigated and compared with chlorides Cs2 MCl6. Cs2TaBr6 exhibits the effective magnetic moment of 0.24 μ B, which is much smaller than the spin only value of a d 1 ion, 1.73 μ B, and comparable to 0.25 μ B in Cs2TaCl6. On the other hand, the effective magnetic moment of Cs2NbBr6 is 0.7 μ B and is substantially smaller than 1.0 μ B in Cs2NbCl6. On cooling, successive structural and magnetic phase transitions accompanying the release of electronic entropy approximately Rln 4 in total as expected for the J eff = 3/2 state are observed. The type of the ligand changes the temperature dependence of magnetic susceptibility at low temperature as well as its magnitude. The role of the ligands on the magnetism of J eff = 3/2 Mott insulators are discussed in the light of metal–ligand hybridization and the electron–lattice coupling.

Ab initio theory of the impact of grain boundaries and substitutional defects on superconducting Nb3Sn

Grain boundaries play a critical role in superconducting applications of Nb3Sn: in dc applications, grain boundaries preserve the material’s inherently high critical current density by pinning flux, while in ac applications grain boundaries can provide weak points for flux entry leading to significant dissipation. We present the first ab initio study to investigate the physics of different grain boundary types in Nb3Sn and their impact on superconductivity using density-functional theory. We identify an energetically favorable selection of high-angle tilt and twist grain boundaries of distinct orientations. We find that clean grain boundaries free of point defects reduce the Fermi-level density of states by a factor of two, an effect that decays back to the bulk electronic structure ∼1–1.5 nm from the boundary. We further calculate the binding free-energies of tin substitutional defects to multiple boundaries, finding a strong electronic interaction that extends to a distance comparable to that of the reduction of density of states. Associated with this interaction, we discover a universal trend in defect electronic entropies near a boundary. We then probe the effects of defect segregation on grain boundary electronic structure and calculate the impact of substitutional impurities on the Fermi-level density of states in the vicinity of a grain boundary. We find that titanium and tantalum defects have little impact regardless of placement, whereas tin, copper, and niobium defects each have a significant impact but only on sites away from the boundary core. Finally, we introduce a model for a local superconducting transition temperature and consider how grain boundary composition affects as a function of distance from the boundary plane. The methodology established in this manuscript can be applied to other A15 superconductors in addition to Nb3Sn.

Field-dependent specific heat of the canonical underdoped cuprate superconductor hbox {YBa}_2hbox {Cu}_4hbox {O}_8

The cuprate superconductor hbox {YBa}_2hbox {Cu}_4hbox {O}_8, in comparison with most other cuprates, has a stable stoichiometry, is largely free of defects and may be regarded as the canonical underdoped cuprate, displaying marked pseudogap behaviour and an associated distinct weakening of superconducting properties. This cuprate ‘pseudogap’ manifests as a partial gap in the electronic density of states at the Fermi level and is observed in most spectroscopic properties. After several decades of intensive study it is widely believed that the pseudogap closes, mean-field like, near a characteristic temperature, T^*, which rises with decreasing hole concentration, p. Here, we report extensive field-dependent electronic specific heat studies on hbox {YBa}_2hbox {Cu}_4hbox {O}_8 up to an unprecedented 400 K and show unequivocally that the pseudogap never closes, remaining open to at least 400 K where T^* is typically presumed to be about 150 K. We show from the NMR Knight shift and the electronic entropy that the Wilson ratio is numerically consistent with a weakly-interacting Fermion system for the near-nodal states. And, from the field-dependent specific heat, we characterise the impact of fluctuations and impurity scattering on the thermodynamic properties.

Quantized thermoelectric Hall effect induces giant power factor in a topological semimetal

Thermoelectrics are promising by directly generating electricity from waste heat. However, (sub-)room-temperature thermoelectrics have been a long-standing challenge due to vanishing electronic entropy at low temperatures. Topological materials offer a new avenue for energy harvesting applications. Recent theories predicted that topological semimetals at the quantum limit can lead to a large, non-saturating thermopower and a quantized thermoelectric Hall conductivity approaching a universal value. Here, we experimentally demonstrate the non-saturating thermopower and quantized thermoelectric Hall effect in the topological Weyl semimetal (WSM) tantalum phosphide (TaP). An ultrahigh longitudinal thermopower S_{xx} sim 1.1 times 10^3 , mu , {mathrm{V}} , {mathrm{K}}^{ - 1} and giant power factor sim 525 , mu , {mathrm{W}} , {mathrm{cm}}^{ - 1} , {mathrm{K}}^{ - 2} are observed at ~40 K, which is largely attributed to the quantized thermoelectric Hall effect. Our work highlights the unique quantized thermoelectric Hall effect realized in a WSM toward low-temperature energy harvesting applications.

Mechanistic insights into efficient reversible hydrogen storage in ferrotitanium

Although FeTi is a well-known hydrogen storage material, producing FeTi on a commercial scale is quite challenging, and generally, one ends up with a multi-phase system consisting of Fe2Ti and FeTi. As Fe2Ti is inert towards hydrogen, it lowers the hydrogen storage efficacy of FeTi. However, there are some reports, which propose that the presence Fe2Ti in FeTi, primarily on the surface is inevitable and it helps in activation of FeTi. Here, we report results of targeted experiments together with first-principles density functional theory (DFT) based calculations to investigate the hydrogen storage properties of FeTi vis-à-vis origin of inertness of Fe2Ti towards hydrogen storage. The formation enthalpies, calculated using density functional theory, of FeTi–H system were found to be very close to the experimental values (−28.1 and −33.72 kJ/mol H2 for FeTiH and FeTiH2 respectively), and that of Fe2Ti–H systems was positive, indicating the inability to form stable intermetallic-hydrides. This corroborates well with the experimental observations, that the pure phase of Fe2Ti cannot store hydrogen. Further, the Gibbs free energy for FeTiH and FeTiH2 were evaluated at 298 K using first-principles quantum mechanics and statistical thermodynamics theories. The vibrational and electronic entropies were calculated using Debye theory of heat capacities. Gibbs free energy at 298 K for FeTiH and FeTiH2 were found to be −5.01 and −3.52 kJ/mol of H2, respectively. Our present study concludes that proper care must be taken to avoid or minimize the formation of Fe2Ti during the production of FeTi.

Electronic entropy contribution to the metal insulator transition in VO2

${\mathrm{VO}}_{2}$ experiences a metal-insulator transition at 340 K. Discontinuities in electronic transport properties, such as the Seebeck coefficient and the electronic conductivity, suggest that there is a significant change in the electronic structure upon metallization. However, the thermodynamic nature of this transformation remains difficult to describe using conventional computational and experimental methods. This has led to disagreement over the relative importance of the change in electronic entropy with respect to the overall transition entropy. A method is presented that links measurable electronic transport properties to the change in electronic state entropy of conduction electrons. The change in electronic entropy is calculated to be $9.2\ifmmode\pm\else\textpm\fi{}0.7$ J/mol K which accounts for 62%--67% of the total transition entropy. This compares favorably with some estimates of the vibrational entropy.

Evaluating the phase stability of binary titanium alloy Ti-X (X = Mo, Nb, Al, and Zr) using first-principles calculations and a Debye model

To realize bottom-up design of alloys based on theoretical calculations, the thermodynamic stabilities of phases in Ti binary alloys were estimated by a combination of density functional theory calculations for the internal enthalpy energy, the Bragg-Williams approximation for the mixing entropy contribution, the Debye model for the vibrational free energy, and the Sommerfeld model for the electronic excitation entropy. The special quasirandom structure (SQS) model was used to describe the disordered distribution of the alloying element in the solid solution state. We focused on Ti–Mo, Ti–Nb, Ti–Al, and Ti–Zr binary alloys, which have different phases, such as the α phase in the hexagonal close-packed (hcp) structure and the β phase in the body-centered cubic (bcc) structure, depending on the temperature and alloying element fraction. The elastic constants, bulk modulus, and Poisson's ratios were calculated using a strain energy method. Excitations from the vibrational contribution to the quasi-harmonic Debye approximation were added to the 0 K free energy originally derived from ab initio calculations. The effect of temperature up to 1000 K on phase stability was analyzed. Furthermore, to compare phase stabilities, the free energies of formation were calculated using the ground states of the constituent phases as references. The calculated elastic property indicated the mechanical instability of most bcc Ti–Al and bcc Ti–Zr alloys, hcp Ti–Mo and hcp Ti–Nb at high fraction range. The SQS supercell models showed good agreement in elastic constant, bulk modulus, and Poisson's ratio compared to the previous experimental and theoretical results. Free energy results showed that Mo and Nb are β-phase stabilizers, Al is an α-phase stabilizer, and Zr is a neutral element. As the fraction of the alloying element changed, stabilizing or destabilizing effects were observed under different temperatures. Moreover, the linear relationship between the filling of the d band and phase stability was identified in low temperature range. For the β phase, Mo had a stronger stabilizing effect than Nb; both Mo and Nb destabilized the α phase at low temperatures, whereas high temperatures increased the stability of the α phase and the temperature effect became more significant than the element effect. In the examined temperature range, the α phase Ti–Al alloys were stable at all Al fractions, where the thermal effect was negligible. All the α Ti–Zr alloys in this study had similar stabilities to their constituent phases (hcp Ti and hcp Zr) over a wide temperature range.

First-principles study of phase stability, elastic and thermodynamic properties of AlCrFeNi medium-entropy alloys

We have applied the first-principles method to predict the phase stability, elastic and thermodynamic properties of ternary (AlCrFe, AlCrNi, CrFeNi and AlFeNi) and quaternary (AlCrFeNi) medium-entropy alloys (MEAs). Both body-centered cubic (BCC) and face-centered cubic (FCC) disordered structures are described using the special quasi-random structures (SQSs) technique. AlCrFe, AlCrNi and AlCrFeNi are favorable in single BCC structures, while CrFeNi is likely to form a single FCC structure. Addition of Ni help stabilizes AlCrFeNi quaternary MEAs. Al and Cr addition are in favor of the formation of BCC AlCrFeNi. Addition of Al, Cr and Ni reduce the resistance to volume deformation for quaternary AlCrFeNi due to the effect of the average number of [Formula: see text]-electrons. The ternary MEAs have better resistance to shear deformation and elastic stiffness than quaternary AlCrFeNi. In addition, all the considered MEAs embody elastic anisotropy and AlCrFeNi are predicted to be ductile behavior. Finally, volumetric thermal expansion coefficient, constant volume heat capacity, vibrational and electronic entropy, and Helmholtz free energies of stable BCC AlCrFeNi, BCC AlCrFe, BCC AlCrNi and FCC CrFeNi are calculated using the Debye–Grüneisen model in temperature ranging from 0 to 1200 K to elucidate the relationships between thermodynamic parameters and temperature.

The Variation in the Standard Entropies of Aqueous Tripositive Lanthanide Ions.

Previous published entropies of solid lanthanide trichloride hydrates are reviewed and revised by taking account of the Kramers degeneracy of ground states with half-integral values of J. The revised values necessitate corrections to the standard entropies of the aqueous tripositive lanthanide ions which display an irregular variation with both atomic number and ionic radius. These irregularities can be smoothed out by taking account of contributions from the electronic or magnetic entropy, from structural changes in the coordination that have been revealed by EXAFS and XANES measurements and X-ray crystallography, and from an increasing intrusion of eight coordination across the series. When these contributions are removed, the entropies of the aqueous ions refer to a hypothetical nine-coordinate state in trigonal triprismatic coordination. Within experimental error, they then vary uniformly across the lanthanide series and there is a good linear correlation with the reciprocal of the metal-oxygen distance in the nine-coordinate aqua complexes.

Investigation on vibrational, electronic excitation entropy and magnetic moment contributions to phase stability of off-stoichiometric Ni50MnxIn50-x alloys at finite temperatures by first-principle calculations

The effects of Mn concentration and thermally excited contributions (including the vibrational, electronic excitation and magnetic contributions) on phase stability of austenite and martensite from 0 K to finite temperatures in Heusler typed Ni50MnxIn50-x shape memory alloys were studied by the first-principle calculations using exact muffin-tin orbitals with coherent potential approximation. Based on this, the martensitic transformation tendency was explored. Results show that at 0 K, the energy differences between the non-modulated martensite and the austenite become negative when extra Mn is added, indicating that the added Mn stabilizes the martensite and promotes martensitic transformation. The promoting effect increases with the increase of Mn content. At finite temperatures, the three thermal contributions (the vibrational, electronic excitation and magnetic contributions) were further calculated based on the equilibrium structure at 0 K. It was revealed that the vibrational entropies of the two phases increase with the increase of the temperature for all Mn contents. Under the two effects (temperature and Mn-content), the austenite has a larger vibrational entropy than the martensite, which indicates that the vibrational entropy contributes to promoting the martensitic transition. The Mn content and the temperature show a similar influence on the electronic entropies of the two phases. However, compared with the vibrational entropy, the contribution of the electronic entropy is much smaller. Furthermore, the influences of Mn content and temperature on the magnetic moment of both phases were simulated in their ferromagnetic state. The results show that the magnetic moments increase linearly with the Mn content, however, the influence of temperature is relatively small. Above 100 K, the magnetic moment of the austenite is higher than that of the martensite in ferromagnetic Ni50Mn29.25In20.75 alloy, suggesting that the magnetic entropy makes a similar contribution to promote the martensitic transformation, like the vibrational and electronic excitation entropies.

Configurational and communal entropies of formation of non-stoichiometric PdHx at the glass transition temperature and the critical temperature

Non-stoichiometric palladium hydride (PdHx) with vacancies for hydrogen exhibits a glass transition temperature (Tg), resulting in generation of both configurational and communal entropies. The communal entropy was evaluated under a given configurational entropy with a suitable hydrogen occupation of tetrahedral and octahedral sites of Pd using the standard molar entropy of formation (ΔfSm(exp.)°) calculated from the equilibrium pressures in pressure–composition–temperature (PCT) curves and the spectroscopic entropies of molecular hydrogen and PdHx.PCT curves with little hysteresis between hydrogenation and dehydrogenation processes were obtained just below the critical temperature Tc, at which the lattice volume mismatch between α and β phases of PdHx is almost negligible. The ΔfSm(exp.)° value calculated from the PCT curves was −83.4 ± 1.3 J/(K·molH2) in the hydrogenation process and −87.3 ± 1.7 J/(K·molH2) in the dehydrogenation process, showing only a relatively small discrepancy between the two.Based on data from the literature, we assumed that the α phase, with its lower hydrogen concentration, was PdH0.006, and that the β phase, with its higher hydrogen concentration, was PdH0.6 in the equilibrium hydrogenation reaction between α and β phases. We then estimated the difference in communal entropy (ΔScom.°) between PdH0.006 and PdH0.6 in terms of the ΔfSm(exp.)° value, the hydrogen molar entropy (Sm,H2°), the vibrational entropy (ΔSvib.°), the electronic entropy (ΔSele.°), and given configurational entropy (ΔSconf.°). We found that near Tc, H atoms occupied both the octahedral and tetrahedral sites in PdH0.6, with ΔScom.° approaching the value of the gas constant R. On the other hand, ΔScom.° approached 0 J/(K·molH) near the glass transition temperature Tg, with H atoms occupying only all the octahedral sites in PdH0.6.