Electronic Entropy Research Articles

Effect of electronic entropy on temperature peculiarities of the frequency characteristics of two interacting anharmonic vibrational modes inβ−Zr

A two-dimensional temperature-dependent effective potential is calculated for the interacting longitudinal and transverse $L$ phonons of $\ensuremath{\beta}$ zirconium in the frozen-phonon model. The effective potentials obtained for different temperatures are used for the numerical solution of a set of stochastic differential equations with a thermostat of the white-noise type. Analysis of the spectral density of transverse vibrations allows one to determine the temperature at which $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Zr}$ becomes unstable with respect to the longitudinal $L$ vibrations. The obtained temperature value practically coincides with the experimental temperature of the $\ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\alpha}$ structural transition in zirconium. The role of electronic entropy in the $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Zr}$ stability is discussed.

Thermoelectric Power in Nonstoichiometric Orthorhombic Titanium Oxides

Nonstoichiometric orthorhombic titanium oxides (TiOx; x=1.86–1.94) prepared by reducing the anatase titanium oxide in H2 at 950°C are found to show large thermoelectric power. Their Seebeck coefficients are in the range −0.060 to −0.518 mV/K, and theoretical discussions are made based on the assumption that the electronic spin entropy dominating the entropy current is a main factor of the thermoelectric power. The figure of merit for TiO1.94 at 70°C is estimated at 0.195. The nonstoichiometric orthorhombic titanium oxides, containing no hazardous elements, are promising materials for thermoelectric power generation.

Electron-vibration approximation method for hydrogen isotope compounds TiH2,TiD2 and TiT2

The ground states of TiH2,TiD2 and TiT2 are determined as 3A2 based on atomic and molecular statics and ground theory. The energy E, heat capacity Cv and entropy S of hydrogen isotopic molecules and its titanium compounds have been calculated using density functional theory (DFT) with basis set 6-311G**. The electronic and vibrational energy and entropy of single molecules TiH2,TiD2 and TiT2 are used as the energy and entropy in their solid states approximately, which is called the electron-vibration motion approximation theory(EVMAT). The calculated results of hydrogenation (and of its isotopes) thermodymical functions ΔH0, ΔS0, ΔG0 and equilibrium pressure of metallic titanium changing with temperature are in good agreement with experimental data, which confirms EVMAT theory further.

Vibrational spectrum of the spin crossover complex [Fe(phen)2(NCS)2] studied by IR and Raman spectroscopy, nuclear inelastic scattering and DFT calculations

The vibrational modes of the low-spin and high-spin isomers of the spin crossover complex [Fe(phen)(2)(NCS)(2)] (phen = 1,10-phenanthroline) have been measured by IR and Raman spectroscopy and by nuclear inelastic scattering. The vibrational frequencies and normal modes and the IR and Raman intensities have been calculated by density functional methods. The vibrational entropy difference between the two isomers, DeltaS(vib), which is--together with the electronic entropy difference DeltaS(el)--the driving force for the spin-transition, has been determined from the measured and from the calculated frequencies. The calculated difference (DeltaS(vib) = 57-70 J mol(-1) K(-1), depending on the method) is in qualitative agreement with experimental values (20-36 J mol(-1) K(-1)). Only the low energy vibrational modes (20% of the 147 modes of the free molecule) contribute to the entropy difference and about three quarters of the vibrational entropy difference are due to the 15 modes of the central FeN(6) octahedron.

Thermally driven low-spin∕high-spin phase transitions in solids

A microscopic model of low-spin∕high-spin transitions in solids containing transition metal ions with ${d}^{6}$ configuration is described. The underlying physics of the transition is related to the large totally symmetric relaxation of ligands accompanying the two electron promotion from the ${t}_{2}$ to $e$ orbitals. The electron distribution function, the electronic entropy, and the heat capacity are determined from the analysis of the free energy. The qualitative estimation of the relaxation is in agreement with x-ray determination. The electronic and lattice entropies are comparable because of the large lattice relaxation. The stepwise low-spin∕high-spin transition of ${\mathrm{Fe}}^{2+}$ with temperature is demonstrated and, hence, the temperature induced abrupt changes in the properties of solids. The weak long-range intermolecular interaction is not excluded but it is not necessary for the explanation of a variety of experimental observations.

Application of entropy calculations to the determination of transition temperature in zirconium

AbstractThe Helmholtz free energy is determined in order to calculate the bcc–hcp phase transition temperature in zirconium. The molecular dynamics method is employed to calculate the vibrational entropy which comprises both the harmonic and anharmonic vibrational entropy. Electronic effects are estimated and taken into account. The anharmonic vibrational entropy is determined from the anharmonic free energy and the electronic entropy is calculated via the electronic density of states. By considering the Helmholtz free energy, the bcc–hcp transition temperature from our simulations is 1047 ± 210 K compared to 1135 K from experimental results. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Temperature dependence of the charge-density-wave energy gap onIn∕Cu(001)

A charge-density-wave (CDW) phase transition on $\mathrm{In}∕\mathrm{Cu}(001)$ with In coverage of 0.63 ML has been studied with angle-resolved photoelectron spectroscopy. Because of the quasi-two-dimensional electronic structure, the upper and lower bands of the CDW ground state were observed at a $k$ point slightly offset from ${k}_{\mathrm{F}}$ of the high-temperature phase. The two bands transformed to a metallic band at 405 K. Tracing the upper-band minimum and the lower-band maximum, we determined the temperature dependence of the CDW order parameter. The dependence indicates that the electronic entropy plays an important role in the transition. We discuss the enhanced contribution of electronic entropy to the free energy due to underlying bulk metallic states.

Pressure-Induced Colossal Magnetocaloric Effect in MnAs

To present day, the maximum magnetocaloric effect (MCE) at room temperature for a magnetic field change of 5 T is 40 J/(kg K) for MnAs. In this Letter we present colossal MCE measurements on MnAs under pressure, reaching values up to 267 J/(kg K), far greater than the magnetic limit arising from the assumption of magnetic field independence of the lattice and electronic entropy contributions. The origin of the effect is the contribution to the entropy variation coming from the lattice through the magnetoelastic coupling.

Entropy ofLiintercalation inLixCoO2

The entropy of lithiation of LixCoO2 for 0.5 < x less than or equal to 1.0 was determined from measurements of the temperature dependence of equilibrated voltages of electrochemical cells. Measured changes in the entropy of the lithiation reaction were as large as 9.0 k(B)/atom, and as large as 4.2 k(B)/atom within the layered hexagonal structure of LixCoO2. Three contributions to the entropy of lithiation for the O3 phase were assessed by experiment and calculation. The phonon entropy of lithiation was determined from measurements of inelastic neutron scattering. Phonon entropy can account for much of the negative entropy of lithiation, but its changes with lithium concentration were found to be small. Electronic structure calculations in the local density approximation gave a small electronic entropy of lithiation of the O3 phase. The configurational entropy from lithium-vacancy disorder was large enough to account for most of the compositional trend in the entropy of lithiation of the O3 phase if ordered structures exist at lithium concentrations of x=1/2 and x=5/6. The electrochemical measurements showed the existence of a two-phase region in the composition range between x=5/6 and 0.95. Electronic structure calculations gave evidence that these phases were metallic and insulating, respectively. Changes of the electronic and configurational entropy were found to be of comparable importance for this metal-insulator transition.

Superconducting high-temperature pairing–theoretical considerations on an unusual phenomenon

In the theoretical framework of a recently developed first-order mechanism for the superconducting pairing an inverted temperature dependence for the transition between the unpaired and a paired state has been observed. We suggest the existence of a paired state at high temperatures T emerging from an unpaired low-temperature state. The entropy driven stabilization of paired states is the outcome of a T-dependent competition between the electronic energy and the electronic configuration entropy. With increasing T the entropy admixtures to the free energy of a given quantum ensemble can exceed energetic effects. The unusual T-dependence of superconductivity has been derived by cluster calculations in the two-parameter Hubbard approximation. The clusters chosen are of the four-electron-four-center type.

Superconducting first‐order pairing: Finite‐temperature simulations

AbstractA recently developed first‐order mechanism for superconducting pairing has been extended from T = 0 K to finite temperatures. On the basis of quantum statistical considerations, we have suggested a direct pairing interaction that does not necessarily involve second‐order elements, such as the electron–phonon coupling or specific magnetic interactions submitted by spin fluctuations. The driving force for the (energy‐driven) first‐order pairing is an attenuation of the destabilizing influence of the Pauli antisymmetry principle (PAP). Only the moves of unpaired fermions are controlled by the PAP, while the moves of superconducting Cooper pairs are not. The quantum statistics of Cooper pairs is of a mixed type, as it combines fermionic on‐site and bosonic intersite properties. The strong correlation between the strength of PAP constraints and system topology in combination with the electron number has been discussed for some larger clusters. Detailed finite‐temperature simulations on first‐order pairing have been performed for four‐center–four‐electron clusters with different topologies. A canonical ensemble statistics has been employed to derive the electronic energy, the electronic configuration entropy, and the free energy of paired and unpaired states in thermal equilibrium. The simulations show that pairing can be caused by either the electronic energy or the electronic configuration entropy. The coexistence of two different sets of quantum particles in paired states (i.e., the Cooper pairs and the unpaired electrons) can lead to an enhanced configuration entropy. In this context, we discuss the possibility of an entropy‐driven high‐temperature superconductor emerging from a low‐temperature unpaired state. The charge and spin degrees of freedom of the four‐center–four‐electron systems have been studied with the help of the charge and spin fluctuations. The spin fluctuations are helpful in judging the validity of pairing theories based on magnetic interactions. The charge fluctuations are a measure for the carrier delocalization in unpaired and paired states. The well‐known proximity between Jahn–Teller activity and superconductivity is analyzed in the zero‐temperature limit. It is demonstrated that both processes compete in their ability to reduce PAP constraints. All theoretical results have been derived within the framework of the simple Hubbard Hamiltonian. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

The phase diagram of high- Tc superconductors

The phase behavior of hole-doped HTS cuprates is summarized particularly with respect to the normal-state pseudogap in the underdoped regime. At a critical doping state p = 0.19 holes/Cu there is an abrupt change in the ground superconducting state and in the normal state centered on a possible quantum glass transition. Maps are presented of the electronic entropy and spin susceptibility with and without superconducting pairing. These reveal much information about the electronic state and in particular suggest an electronically homogeneous intrinsic state for p > 1/8. They also suggest that inhomogeneity sets in for p ⩽ 0.11 possibly associated with freezing out of fluctuating spin-charge stripes.

Stochastic-based descriptors studying peptides biological properties: modeling the bitter tasting threshold of dipeptides

MARCH-INSIDE methodology was applied to the prediction of the bitter tasting threshold of 48 dipeptides by means of pattern recognition techniques, in this case linear discriminant analysis (LDA), and regression methods. The LDA models yielded a percentage of good classification higher than 80% with the two main families of descriptor generated by this methodology (95.8% for self return probability and 83.3% using electronic delocalization entropy). The regression models can explain more than 80% of the experimental variance of the independent variable. Two regression models were obtained with R2 values of 0.82 and 0.88 for the whole data and the data without two outliers, respectively; having a standard deviation of 0.27 and 0.23. The predictive power of the obtained equations was assessed by the Leave-One-Out cross validation procedures, giving the same percentages of good classification as in the training set, in the LDA models, and yielding values of q2 of 0.78 and 0.86 in the regression model, respectively. The validation of this methodology was also carried out by comparison with previous reports modeling this data with other well-known methodologies, even 3-D molecular descriptors.

Superfluid density in cuprate high-Tcsuperconductors: A new paradigm

We show that the Uemura relation, namely ${T}_{c}$ proportional to superfluid density ${\ensuremath{\rho}}_{s},$ is not generally satisfied in high-${T}_{c}$ superconductors. Instead, a modified plot of ${T}_{c}/{\ensuremath{\Delta}}_{0}$ versus ${\ensuremath{\rho}}_{s}$ where ${\ensuremath{\Delta}}_{0}$ is the maximum d-wave gap at $T=0,$ exhibits universal features that point to an alternative interpretation of the underlying physics. In the underdoped region this plot exhibits the canonical negative curvature expected when a ground-state correlation competes with superconductivity (SC) by opening up a gap (the pseudogap) in the normal-state density of states. Moreover we observe simple linear relations between ${T}_{c}{\ensuremath{\rho}}_{s},$ the electronic entropy at ${T}_{c},$ and the critical impurity concentration for suppressing SC. These relations confirm that the pseudogap persists to $T=0,$ strongly modifying the SC ground state.

Dual nature of a charge-density-wave transition on In/Cu(001)

A surface phase transition on In/Cu(001) with In coverage of 0.63 was studied. The structural analysis shows that the reversible phase transition at 405 K between the high-temperature $(2\ifmmode\times\else\texttimes\fi{}2)$ and the low-temperature $(2\sqrt{2}\ifmmode\times\else\texttimes\fi{}2\sqrt{2})R45\ifmmode^\circ\else\textdegree\fi{}$ phases belongs to an order-disorder type. The angle-resolved photoemission experiment shows that the low-temperature phase is stabilized by the partial gap formation at the Fermi surface, indicating that the transition is due to the Peierls-type Fermi-surface nesting. While the above observations point to a strong-coupling charge-density-wave (SCDW) scenario, the temperature-dependent behavior of the gap is in better agreement with the weak-coupling CDW theory. Thus, the results serve the first experimental characterization of the CDW transition driven cooperatively by electronic and lattice entropies.

Spin entropy as the likely source of enhanced thermopower in Na(x)Co2O4.

In an electric field, the flow of electrons in a solid produces an entropy current in addition to the familiar charge current. This is the Peltier effect, and it underlies all thermoelectric refrigerators. The increased interest in thermoelectric cooling applications has led to a search for more efficient Peltier materials and to renewed theoretical investigation into how electron-electron interaction may enhance the thermopower of materials such as the transition-metal oxides. An important factor in this enhancement is the electronic spin entropy, which is predicted to dominate the entropy current. However, the crucial evidence for the spin-entropy term, namely its complete suppression in a longitudinal magnetic field, has not been reported until now. Here we report evidence for such suppression in the layered oxide Na(x)Co2O4, from thermopower and magnetization measurements in both longitudinal and transverse magnetic fields. The strong dependence of thermopower on magnetic field provides a rare, unambiguous example of how strong electron-electron interaction effects can qualitatively alter electronic behaviour in a solid. We discuss the implications of our finding--that spin-entropy dominates the enhancement of thermopower in transition-metal oxides--for the search for better Peltier materials.

Thermal quenching of electronic shells and channel competition in cluster fission.

Experimental and theoretical studies of fission of doubly charged Li, Na, and K clusters in the low-fissility regime reveal the strong influence of electronic shell effects on the fission products. The electronic entropy controls the quenching of the shell effects and the competition between magic-fragment channels, leading to a transition from favored channels of higher mass symmetry to the asymmetric channel involving the trimer cation at elevated temperatures.

Theoretical exploration of electronic structure in cuprates from electronic entropy

The electronic entropy of superconducting cuprates includes crucial information on the metallic state. In this context the electronic entropy of cuprates is calculated for the ${\mathrm{CuO}}_{2}$ layer in order to clarify the features of metallic states. It is shown that the observed peculiar doping dependence of electronic entropy can be explained by the Kamimura-Suwa model without introducing the pseudogap concept, while an ordinary band structure gives too small values even in the overdoped region. It is also shown that the observed anomalous behaviors in normal-state properties of cuprates such as resistivity and the Hall effect are explained by the Kamimura-Suwa model. From these results it is suggested that the hole carriers in cuprates form a metallic state by taking the Zhang-Rice singlet and Hund's coupling triplet alternately in the presence of the local antiferromagnetic ordering.

Vibrational and electronic entropy of β-cerium and γ-cerium measured by inelastic neutron scattering

Time-of-flight (TOF) inelastic neutron-scattering spectra were measured on \ensuremath{\beta}-cerium (double hcp) and \ensuremath{\gamma}-cerium (fcc) near the phase-transition temperature. Phonon densities of states (DOS) and crystal-field levels were extracted from the TOF spectra. A softening of the phonon DOS occurs in the transition from \ensuremath{\beta}- to \ensuremath{\gamma}-cerium, accounting for an increase in vibrational entropy of $\ensuremath{\Delta}{S}_{\mathrm{vib}}^{\ensuremath{\gamma}\ensuremath{-}\ensuremath{\beta}}=(0.09\ifmmode\pm\else\textpm\fi{}{0.05)k}_{B}/\mathrm{atom}.$ The entropy calculated from the crystal-field levels and a fit to calorimetry data from the literature were significantly larger in \ensuremath{\beta}-cerium than in \ensuremath{\gamma}-cerium below room temperature, but the difference was found to be negligible at the experimental phase-transition temperature. A contribution to the specific heat from Kondo spin fluctuations was consistent with the quasielastic magnetic scattering, but the difference between phases was negligible. To be consistent with the latent heat of the \ensuremath{\beta}-\ensuremath{\gamma} transition, the increase in vibrational entropy at the phase transition may be accompanied by a decrease in electronic entropy not associated with the crystal-field splitting or spin fluctuations. At least three sources of entropy need to be considered for the \ensuremath{\beta}-\ensuremath{\gamma} transition in cerium.

Temperature dependence of the phonon entropy of vanadium

The phonon density-of-states (DOS) of elemental vanadium was measured at elevated temperatures by inelastic neutron scattering. The phonon softening predicted by thermal expansion against the bulk modulus is much larger than the measured shifts in phonon energies. We conclude that the phonon anharmonicities associated with thermal expansion are largely canceled by effects from phonon-phonon scattering. Prior measurements of the heat capacity and calculations of the electronic entropy of vanadium are assessed, and consistency requires an explicit temperature dependence of the phonon DOS. Using data from the literature, similar results are found for chromium, niobium, titanium, and zirconium.