Wiedemann-Franz Law Research Articles

Enhanced Electron Heat Conduction in TaS3 1D Metal Wire.

The 1D wire TaS3 exhibits metallic behavior at room temperature but changes into a semiconductor below the Peierls transition temperature (Tp), near 210 K. Using the 3ω method, we measured the thermal conductivity of TaS3 as a function of temperature. Electrons dominate the heat conduction of a metal. The Wiedemann–Franz law states that the thermal conductivity of a metal is proportional to the electrical conductivity σ with a proportional coefficient of L0, known as the Lorenz number—that is, . Our characterization of the thermal conductivity of metallic TaS3 reveals that, at a given temperature T, the thermal conductivity κ is much higher than the value estimated in the Wiedemann–Franz (W-F) law. The thermal conductivity of metallic TaS3 was approximately 12 times larger than predicted by W-F law, implying . This result implies the possibility of an existing heat conduction path that the Sommerfeld theory cannot account for.

Thermal Convection in the Core of Ganymede Inferred from Liquid Eutectic Fe-FeS Electrical Resistivity at High Pressures

The core of Ganymede is suggested to be mainly Fe but with a significant proportion of S. Effects of S as a core constituent are freezing-point depression, allowing for a molten core at relatively low core temperatures, and modification of transport properties that can influence the dynamo and thermal evolution. The electrical resistivity of solid and liquid Fe-FeS (~24–30 wt.% S) was measured up to 5 GPa and thermal conductivity was calculated using the Wiedemann–Franz law. These first well-constrained experimental data on near eutectic Fe-FeS compositions showed intermediate values of electrical and thermal conductivities compared to the end-members. Eutectic temperatures were delineated from the solid to liquid transition, inferred from sharp changes in electrical resistivity, at each pressure. Combined with thermal models, our calculated estimates of the adiabatic heat flow of a molten Fe-FeS eutectic composition core model of Ganymede showed that thermal convection is permissible.

Transport signatures of the pseudogap critical point in the cuprate superconductor Bi2Sr2−xLaxCuO6+δ

Five transport coefficients of the cuprate superconductor ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ were measured in the normal state down to low temperature, reached by applying a magnetic field (up to 66 T) large enough to suppress superconductivity. The electrical resistivity, Hall coefficient, thermal conductivity, Seebeck coefficient, and thermal Hall conductivity were measured in two overdoped single crystals, with La concentration $x=0.2$ (${T}_{\mathrm{c}} =18$ K) and $x=0.0$ (${T}_{\mathrm{c}} =10$ K). The samples have dopings $p$ very close to the critical doping ${p}^{★}$ where the pseudogap phase ends. The resistivity displays a linear dependence on temperature whose slope is consistent with Planckian dissipation. The Hall number ${n}_{\mathrm{H}}$ decreases with reduced $p$, consistent with a drop in carrier density from $n=1+p$ above ${p}^{★}$ to $n=p$ below ${p}^{★}$. This drop in ${n}_{\mathrm{H}}$ is concomitant with a sharp drop in the density of states inferred from prior NMR Knight shift measurements. The thermal conductivity satisfies the Wiedemann-Franz law, showing that the pseudogap phase at $T=0$ is a metal whose fermionic excitations carry heat and charge as do conventional electrons. The Seebeck coefficient diverges logarithmically at low temperature, a signature of quantum criticality. The thermal Hall conductivity becomes negative at low temperature, showing that phonons are chiral in the pseudogap phase. Given the observation of these same properties in other, very different cuprates, our study provides strong evidence for the universality of these five signatures of the pseudogap phase and its critical point.

Structural and thermal properties of Sn–Ag alloys

Microstructure and thermal properties of slowly cooled Sn–10% Ag and Sn–20% Ag alloys were experimentally investigated in this study. It was found that microstructure of the studied alloys is composed of large, plate-like grains of Ag3Sn intermetallic phase in the Sn-rich eutectic matrix. Phase transition temperatures and corresponding heat effects were experimentally determined and compared with the results of thermodynamic and phase equilibria calculations using the CALPHAD (CALculation of PHAse Diagrams) method and optimized thermodynamic parameters from literature. The xenon flash method was employed for the measurements of thermal diffusivity and determination of thermal conductivity in the temperature range from 25 to 150 °C. The results show that the thermal diffusivity and thermal conductivity gradually decrease with increasing temperature. The determined values of thermal conductivities of the investigated alloys are very close to each other and only slightly higher than that of pure tin. The contributions of electrons and phonons to the thermal conductivity of the studied alloys at room temperature were determined using the Wiedemann-Franz law and the obtained values of the thermal and electrical conductivities. The percentage contributions of the phonon component to the thermal conductivity for Sn–10% Ag and Sn–20% Ag alloys at 25 °C were found to be 20.5% and 28.9%, respectively.

Microstructure, melting behavior and thermal conductivity of the Sn–Zn alloys

Four hypereutectic Sn-Zn alloys with 69.5, 48.3, 28.1 and 14.1 at% of Zn were produced by mixing and melting of pure metals Sn and Zn followed by cooling in air to room temperature. Microstructure and chemical compositions of prepared samples were analyzed by using scanning electron microscopy (SEM) with energy dispersive X-ray spectrometry (EDS). It was found that morphology of primary (Zn) phase changes from rounded and equiaxed dendritic structure to plate-like grains and finally to needle-like shape of grains with decreasing Zn content. Formation of characteristic broken-lamellar type of eutectic microstructure was observed in all investigated alloys. Melting behavior of the alloys was studied using differential scanning calorimetry (DSC). Phase transition temperatures and corresponding heat effects were experimentally determined and compared with the results of thermodynamic and phase equilibria calculations using the CALPHAD (CALculation of PHAse Diagrams) method and optimized thermodynamic parameters from literature. Thermal diffusivity of the studied alloys was measured using xenon flash method in the temperature range from 25 to 150 °C. Based on the measured values of thermal diffusivity and calculated specific heat capacity data, thermal conductivities of the solid alloys were obtained. It was found that thermal conductivity decreases monotonously with increasing temperature and Sn content. The results of thermal conductivity measurements were compared with literature data and with the data obtained from the Wiedemann-Franz law and measured electrical conductivities.

Thermal chiral anomaly in the magnetic-field-induced ideal Weyl phase of Bi1-xSbx.

The chiral anomaly is the predicted breakdown of chiral symmetry in a Weyl semimetal with monopoles of opposite chirality when an electric field is applied parallel to a magnetic field. It occurs because of charge pumping between monopoles of opposite chirality. Experimental observation of this fundamental effect is plagued by concerns about the current pathways. Here we demonstrate the thermal chiral anomaly, energy pumping between monopoles, in topological insulator bismuth-antimony alloys driven into an ideal Weyl semimetal state by a Zeeman field, with the chemical potential pinned at the Weyl points and in the absence of any trivial Fermi surface pockets. The experimental signature is a large enhancement of the thermal conductivity in an applied magnetic field parallel to the thermal gradient. This work demonstrates both pumping of energy and charge between the two Weyl points of opposite chirality and that they are related by the Wiedemann-Franz law.

Effects of Ge Doping on the Charge Transport and Thermoelectric Properties of Permingeatites Cu3Sb1−yGeySe4

Permingeatites Cu3Sb1−yGeySe4 (0 ≤ y ≤ 0.14) were synthesized by mechanical alloying and hot pressing. The charge-transport parameters (Hall coefficient, carrier concentration, mobility, and Lorenz number) and thermoelectric properties (electrical conductivity, Seebeck coefficient, power factor, thermal conductivity, and figure of merit) were examined with respect to the Ge doping level. A single permingeatite phase with a tetragonal structure was obtained without subsequent heat treatment, but a small amount of the secondary phase Cu2GeSe3 was found for the specimens with y ≥ 0.08. All hot-pressed compacts exhibited a relative density of 97.5%–98.3%. The lattice constants of the a-axis and c-axis were decreased by the substitution of Ge at the Sb sites. As the Ge content increased, the carrier concentration increased from 5.2 × 10<sup>18</sup> to 1.1 × 10<sup>20</sup> cm<sup>−3</sup>, but the mobility decreased from 92 to 25 cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>. The Lorenz number of the undoped Cu3SbSe4 implied a non-degenerate semiconductor behavior, ranging from (1.57–1.56) × 10<sup>−8</sup> V<sup>2</sup>·K<sup>−2</sup> at 323–623 K. The thermoelectric figure of merit was 0.39 at 623 K, resulting from a power factor of 0.49 mW·m<sup>−1</sup>·K<sup>−2</sup> and a thermal conductivity of 0.76 W·m<sup>−1</sup>·K<sup>−1</sup>. However, the Lorenz numbers of the Gedoped specimens indicated degenerate semiconductor characteristics, increasing to (1.63–1.94) × 10<sup>−8</sup> V<sup>2</sup>·K<sup>−2</sup> at 323–623 K. The highest thermoelectric figure of merit of 0.65 was at 623 K for Cu3Sb0.86Ge0.14Se4, resulting from the significantly improved power factor of 0.93 mW·m<sup>−1</sup>·K<sup>−2</sup> and the thermal conductivity of 0.89W·m<sup>−1</sup>·K<sup>−1</sup>. As a result, the thermoelectric properties were remarkably enhanced by doping Ge into the Sb sites of the permingeatite.

Ionization and transport in partially ionized multicomponent plasmas: Application to atmospheres of hot Jupiters.

We study ionization and transport processes in partially ionized multicomponent plasmas. The plasma composition is calculated via a system of coupled mass-action laws. The electronic transport properties are determined by the electron-ion and electron-neutral transport cross sections. The influence of electron-electron scattering is considered via a correction factor to the electron-ion contribution. Based on these data, the electrical and thermal conductivities as well as the Lorenz number are calculated. For the thermal conductivity, we consider also the contributions of the translational motion of neutral particles and of the dissociation, ionization, and recombination reactions. We apply our approach to a partially ionized plasma composed of hydrogen, helium, and a small fraction of metals (Li, Na, Ca, Fe, K, Rb, and Cs) as typical for atmospheres of hot Jupiters. We present results for the plasma composition and the transport properties as a function of density and temperature and then along typical P-T profiles for the outer part of the hot Jupiter HD 209458b. The electrical conductivity profile allows revising the Ohmic heating power related to the fierce winds in the planet's atmosphere. We show that the higher temperatures suggested by recent interior models could boost the conductivity and thus the Ohmic heating power to values large enough to explain the observed inflation of HD 209458b.

Modulation of the Conductive Filament Growth During the Electroforming Process in Metal Oxide-Based RRAM

Metal oxide-based Resistive Random-Access Memories (RRAM) exhibit multiple intermediate resistive states, due to the formation/rupture of a conductive filament (CF) inside a switching layer. While there have been extensive studies on the resistive switching behavior caused by a pre-existing CF, the initial stage of the formation and growth of a CF, i.e., the electroforming process has been less understood. In this work, we developed a physical model to fundamentally understand the formation and growth behavior of a CF in a metal oxide layer constrained by the top/bottom electrodes. It is revealed that the CF formation is assisted by the supply of oxygen vacancies at the anode and the oxygen vacancies transport in the oxide layer. The effects of the external conditions (the oxygen exchange rate j 0 and the applied voltage) and the physical properties of the oxides (the electrical σ and thermal conductivity k th ) on the CF morphology evolution, current density evolution, and local temperature and electrical potential distribution have been systematically explored. It is found that larger oxygen vacancy exchange rate and relatively small voltage sweep rate result in a more uniform CF. Furthermore, by choosing oxides with lower Lorenz number (ratio of k th and σ ), CF with more homogeneous morphology can be realized. This work provides a fundamental understanding of the kinetic behaviors of the CF formation and growth during the electroforming process, and could potentially guide the oxide and electrode materials selection, synthesis and working conditions for switching to achieve improved RRAM stability and functionality.

Wiedemann-Franz Law for Massless Dirac Fermions with Implications for Graphene.

In the 2016 experiment by Crossno et al. the electronic contribution to the thermal conductivity of graphene was found to violate the well-known Wiedemann–Franz (WF) law for metals. At liquid nitrogen temperatures, the thermal to electrical conductivity ratio of charge-neutral samples was more than 10 times higher than predicted by the WF law, which was attributed to interactions between particles leading to collective behavior described by hydrodynamics. Here, we show, by adapting the handbook derivation of the WF law to the case of massless Dirac fermions, that significantly enhanced thermal conductivity should appear also in few- or even sub-kelvin temperatures, where the role of interactions can be neglected. The comparison with numerical results obtained within the Landauer–Büttiker formalism for rectangular and disk-shaped (Corbino) devices in ballistic graphene is also provided.

Wiedemann-Franz laws and Sl(2, \u2124) duality in AdS/CMT holographic duals and one-dimensional effective actions for them

In this paper we study the Wiedemann-Franz laws for transport in 2+1 dimensions, and the action of Sl(2, ℤ) on this transport, for theories with an AdS/CMT dual. We find that Sl(2, ℤ) restricts the RG-like flow of conductivities and that the Wiedemann-Franz law is overline{L}=overline{kappa}/left( Tsigma right)={cg}_4^2uppi /3 , from the weakly coupled gravity dual. In a self-dual theory this value is also the value of L = κ/(Tσ) in the weakly coupled field theory description. Using the formalism of a 0+1 dimensional effective action for both generalized SY Kq models and the AdS4 gravity dual, we calculate the transport coefficients and show how they can be matched at large q. We construct a generalization of this effective action that is invariant under Sl(2, ℤ) and can describe vortex conduction and integer quantum Hall effect.

Electrical Resistivity of FeS at High Pressures and Temperatures: Implications of Thermal Transport in the Core of Ganymede

AbstractTerrestrial‐type planetary cores are thought to be predominantly composed of Fe with varying amounts of lighter chemical species or impurities chosen from a narrow range of possible elements, which includes S. These impurity elements may contribute significant effects to the transport properties of these cores, which have direct influence over dynamo and thermal evolution of the planetary body. Recent experimental methods have partially eased the substantial challenges that arise in direct measurements of electrical transport properties at high pressures and temperatures. In this study we show how this methodology can be used to measure the electrical resistivity of a sample in powder form. The electrical resistivity of FeS was measured in both solid and molten states at pressures up to 5 GPa and the thermal conductivity was calculated using the Wiedemann–Franz Law from the electrical measurements. The results showed FeS is notably more electrically and thermally conductive when compared to previous studies in both the solid and molten states. The results were used to estimate the adiabatic conductive heat flow of a molten FeS core model of Ganymede, which showed that thermal convection is permissible as a dynamo power source.

Know the enemy: 2D Fermi liquids

We describe an analytical theory investigating the regime of validity of the Fermi liquid theory in interacting, via the long-range Coulomb coupling, two-dimensional Fermi systems comparing it with the corresponding 3D systems. We find that the 2D Fermi liquid theory and 2D quasiparticles are robust up to high energies and temperatures of the order of Fermi energy above the Fermi surface, very similar to the corresponding three-dimensional situation. We calculate the phase diagram in the frequency–temperature space separating the collisionless ballistic regime and the collision-dominated hydrodynamic regime for 2D and 3D interacting electron systems. We also provide the temperature corrections up to third order for the renormalized effective mass, and comment on the validity of 2D Wiedemann–Franz law and 2D Kadawoki–Woods relation.

Inelastic Tunnel Transport and Nanoscale Junction Thermoelectricity with Varying Electrode Topology

AbstractIntricacies in the charge transport behavior of single‐molecule junctions often revolve around the complex nature of orbital hybridization stemming from diversified metal‐molecule coupling at interfaces. It will hence be pertinent to fathom the myriad aspect of inelastic charge transport and nanoscale thermoelectricity in single‐molecule junctions. It is examined from first‐principles, achiral and chiral quasi‐1D electrodes to understand the role of junction heterogeneity in overall thermoelectric behavior during charge transport. This calculated inelastic electron tunneling spectra exhibit intense peaks in the low‐frequency regime (< 25 meV) with characteristic bending and rocking modes, which auger well with the available measured data. It is subsequently found that the thermopower can be as high as 212 µV K−1 for σ‐saturated molecular moieties, depending strongly on the configuration of electrodes. Besides, a majority of such single‐molecule junctions turn out to deviate from the Wiedemann–Franz law, leading to anomalies in the electronic thermal conductance. The authors' analysis suggests that as nanoscale electrodes, Au(111) nanowires are likely to render a relatively high thermoelectric figure of merit (ZT > 1) for a small molecular junction at room temperature. Discerning the diversity as driven exigently by the electrode topology may thus augment the device performance in terms of thermal stability at molecular scale.

Low thermal conductivity of SrTiO3−LaTiO3 and SrTiO3−SrNbO3 thermoelectric oxide solid solutions

AbstractElectron‐doped SrTiO3 has been attracting attention as oxide thermoelectric materials, which can convert wasted heat into electricity. The power factor of the electron‐doped SrTiO3, including SrTiO3‐LaTiO3 and SrTiO3‐SrNbO3 solid solutions, has been clarified. However, their thermal conductivity (κ) has not been clearly identified thus far. Only a high κ (>12 W m−1 K−1) has been assumed from the electron contribution based on Wiedemann–Franz law. Here, we show that the κ of the electron‐doped SrTiO3 is lower than the assumed κ, and its highest ZT exceeded 0.1 at room temperature. The κ slightly decreased with the carrier concentration (n) when n is below 4 × 1021 cm−3. In the case of SrTiO3‐SrNbO3 solid solutions, an upturn in κ was observed when n exceeds 4 × 1021 cm−3 due to the contribution of conduction electron to the κ. On the other hand, κ decreased in the case of SrTiO3‐LaTiO3 solid solutions probably due to the lattice distortion, which scatters both electrons and phonons. The highest ZT was 0.11 around n = 1 × 1021 cm−3. These findings would be useful for the future design of electron‐doped SrTiO3‐based thermoelectric materials.

Investigation of electron and phonon transport in Bi-doped CaMnO3 for thermoelectric applications

The electron and phonon transports in CaMnO3 and in one of its Bi-doped counterparts, namely, Bi0.03Ca0.97MnO3, are investigated using the thermoelectric transport measurements and first-principles calculations. We find that antiferromagnetic insulator CaMnO3 breaks the Wiedemann–Franz law with the Lorenz number reaching four times that of ordinary metals at room temperature. Bismuth doping reduces both the electrical resistivity and Seebeck coefficient of CaMnO3; thus, it recovers the Wiedemann–Franz law behavior. In addition, Bi0.03Ca0.97MnO3 possesses a shorter phonon lifetime according to the transport measurements. As a result, Bi0.03Ca0.97MnO3 exhibits superior thermoelectric properties over pristine CaMnO3 owing to the lower thermal conductivity and electrical resistivity.

Semiconductor to metal transition in the solids/melts of Te and pseudo-binary of Hg1−xCdxTe for x = 0, 0.1, and 0.2

This paper reports the experimentally measured thermal and electrical conductivities from which the Lorenz numbers as functions of temperature were derived for the solids and melts of elemental Te and samples of Hg1−xCdxTe of x = 0, 0.1, and 0.2. The structural changes in the vicinity of the solid–liquid phase transition of elemental Te and various Hg1−xCdxTe solid solutions were assessed by closely examining these experimental properties and the derived Lorenz numbers. The values of Lorenz numbers for the solids of these samples were higher than the value of L0, i.e., the Lorenz number for the free-electron gas derived by Sommerfeld [Naturwissenschaften 15, 825 (1927)], implying the characteristics of a non-degenerate semiconductor. With the increasing value of x, or the larger bandgap, the materials become more non-degenerate with larger deviation from L0. As the solids started to melt, the measured values of the Lorenz number for all samples started to decrease and eventually reached and maintained at values close to L0 at higher temperatures. The trend of the Lorenz number indicates the transition from a non-degenerate semiconductor of the solid samples to a metal or degenerate semiconductor when the temperatures of the samples reached above their liquidus temperatures.

Thermoelectric power properties of Ge doped PbTe alloys

In this work, stoichiometric Pb1−xGexTe (x = 0.0, 0.03, 0.06, 0.09, 0.12) crystalline alloys were synthesized using the monotonical temperature melting technique. The synthesized alloys were examined using x-ray diffraction and scanning electron microscope. It was revealed that the crystal structure in all samples is a cubic phase of PbTe. In terms of Seebeck coefficient and electrical conductivity, thermoelectric measurements were carried out in the temperature range of 83–373 K. The Seebeck coefficient of the compounds showed a positive sign, which refers to p-type conduction. The thermoelectric power factor (PF) was studied as a function of temperature, with different amounts of Ge content (x). The highest PF was recorded for the highly Ge-doped samples at higher temperatures (373 K). The maximum PF was observed at 3.2 × 102 µW/m K2 for the sample with x = 0.09, which is quite high for the studied compounds. The electronic part of thermal conductivity was calculated using the Wiedemann-Franz law. A noticeable reduction of this thermal conductivity was detected due to stronger point defect scattering introduced by Ge doping. The reduction in the electronic thermal conductivity can led to a considerable enhancement in the thermoelectric figure of merit.

First-principles based analysis of thermal transport in metallic nanostructures: Size effect and Wiedemann-Franz law

Metallic nanostructures (the nanofilms and nanowires) are widely used in electronic devices, and their thermal transport properties are crucial for heat dissipation. However, there are still gaps in understanding thermal transport in metallic nanostructures, especially regarding the size effect and validity of the Wiedemann-Franz law. In this work, we perform mode-by-mode first-principles calculations combining the Boltzmann transport equation to understand thermal transport in metallic nanostructures. We take the gold (Au) and tungsten (W) nanostructures as prototypes. It is found that when the size of nanostructures is on the order of several tens of nanometers, the electronic/phonon thermal conductivity is smaller than the bulk value and decreases with size. The phonon contribution increases in nanostructures for those metals with small bulk phonon thermal conductivity (like Au), while the phonon contribution may increase or be suppressed in nanostructures for those metals with large bulk phonon thermal conductivity (like W). By assuming that the grain boundary does not induce inelastic electron-phonon scattering, the Wiedemann-Franz law works well in both Au and W nanostructures if the Lorentz ratio is estimated using electronic thermal conductivity. The Wiedemann-Franz law also works well in Au nanostructures when the Lorentz ratio is estimated by total thermal conductivity.

High performance thermal link with small spring constant for cryogenic applications

We developed a soft and high thermal conductive thermal link for cryogenic applications. The measured maximum thermal conductivity was approximately 18500 W/m/K at 10 K. This spring constant was 1/43 of that of a single thick wire with the same cross-sectional area at room temperature. We reached these performances by utilizing high purity aluminum (99.9999%, 6 N) and by stranding many thin wires that are 0.15 mm in diameter. The electrical Residual Resistivity Ratio was also measured and used to estimate the thermal conductivity by the Wiedemann–Franz law. We observed the size effect on the electrical conductivity, and evaluated the effect of mechanical deformation to the RRR. These evaluations allow us to design a pragmatic thermal link for cryogenic application.