Wiedemann-Franz Law Research Articles

A computational and experimental study in resistance spot welding of thin-gauge and highly conductive dissimilar sheets for battery tab interconnects

We present a combined computational and experimental study of the role of electrical and thermal contact resistances in resistance spot welding of thin-gauge, dissimilar metal sheets with high electrical conductivity, relevant for battery manufacturing for electric vehicles. In this application, the electrical and thermal contact resistances play a dominant role in heat generation and temperature evolution within the work pieces. Previously reported approaching for simulating resistance spot welding have limited capability for representing dissimilar and thin-gauge metal sheets, particularly at higher temperatures when multiple physical phenomena become increasingly interdependent. The approach presented here uses resistivity measurements, combined with thermal modeling and known bulk resistance relationships, to infer the relationship between electrical contact resistance and temperature for different material interfaces. Corresponding thermal contact resistance models are then developed using the Wiedemann-Franz law combined with a scaling factor to account for nonmetallic behavior. The model is validated by comparing experimental and predicted voltage histories and final weld diameters of three- and five-layer stack-ups consisting of alternating aluminum and copper layers. We also analyze heat generation and redistribution during welding to elucidate the dominance of contact resistance over bulk resistivity in these stack-ups as it evolves during the welding process.

Alloying and Doping Control in the Layered Metal Phosphide Thermoelectric CaCuP.

We recently identified CaCuP as a potential low cost, low density thermoelectric material, achieving zT = 0.5 at 792 K. Its performance is limited by a large lattice thermal conductivity, κL, and by intrinsically large p-type doping levels. In this paper, we address the thermal and electronic tunability of CaCuP. Isovalent alloying with As is possible over the full solid solution range in the CaCuP1-xAsx series. This leads to a reduction in κL due to mass fluctuations but also to a detrimental increase in p-type doping due to increasing Cu vacancies, which prevents zT improvement. Phase boundary mapping, exploiting small deviations from 1:1:1 stoichiometry, was used to explore doping tunability, finding increasing p-type doping to be much easier than decreasing the doping level. Calculation of the Lorenz number within the single parabolic band approximation leads to an unrealistic low κL for highly doped samples consistent with the multiband behavior in these materials. Overall, CaCuP and slightly Cu-enriched CaCu1.02P yield the best performance, with zT approaching 0.6 at 873 K.

Cyclic thermal conductivity changes of Pd-catalyzed Ni–Mg alloy films by gasochromic hydro- and dehydrogenations

To investigate the thermal-switching properties of Pd-catalyzed Ni–Mg alloy films, we conducted in situ analyses of the films’ electrical, optical, and thermal properties through hydrogen gasochromic reactions. These reactions allow the films to reversibly switch between metallic (dehydride) and semiconductor (hydride) phases. The thermal conductivities of the metallic and semiconductor states were found to be 14 and 1.0 W m−1 K−1, respectively. By applying the Wiedemann–Franz law, we attributed the significant decrease in thermal conductivity during hydrogenation to the reduction in free electrons.

Generalized Wiedemann-Franz law in a two-site charge Kondo circuit: Lorenz ratio as a manifestation of the orthogonality catastrophe

Generalized Wiedemann-Franz law in a two-site charge Kondo circuit: Lorenz ratio as a manifestation of the orthogonality catastrophe

Next-Generation Quantum Materials for Thermoelectric Energy Conversion

This review presents the recent advances in the search for thermoelectric (TE) materials, mostly among intermetallic compounds and in the enhancement of their TE performance. Herein, contemporary approaches towards improving the efficiency of heat–electricity conversion (e.g., energy harvesting and heat pumping) are discussed through the understanding of various emergent physical mechanisms. The strategies for decoupling the individual TE parameters, as well as the simultaneous enhancement of the TE power factor and the suppression of heat conduction, are described for nanoparticle-doped materials, high entropy alloys, and nanowires. The achievement of a superior TE performance due to emergent quantum phenomena is discussed for intermetallic chalcogenides and related systems (e.g., strong and weak topological insulators, Weyl and Dirac semimetals), and some of the most promising compounds within these classes are highlighted. It was concluded that high-entropy alloying provides a methodological breakthrough for employing band engineering methods along with various phonon scattering mechanisms towards significant TE efficiency improvement in conventional TE materials. Finally, topological semimetals and magnetic semimetals with several intriguing features, such as a violation of the Wiedemann–Franz law and outstanding perpendicular Nernst signals, are presented as strong candidates for becoming next-generation TE quantum materials.

T-Square Dependence of the Electronic Thermal Resistivity of Metallic Strontium Titanate.

The temperature dependence of the phase space for electron-electron (e-e) collisions leads to a T-square contribution to electrical resistivity of metals. Umklapp scattering is identified as the origin of momentum loss due to e-e scattering in dense metals. However, in dilute metals like lightly doped strontium titanate, the origin of T-square electrical resistivity in the absence of umklapp events is yet to be pinned down. Here, by separating electron and phonon contributions to heat transport, we extract the electronic thermal resistivity in niobium-doped strontium titanate and show that it also displays a T-square temperature dependence. Its amplitude correlates with the T-square electrical resistivity. The Wiedemann-Franz law strictly holds in the zero-temperature limit, but not at finite temperature, because the two T-square prefactors are different by a factor of ≈3, like in other Fermi liquids. Recalling the case of ^{3}He, we argue that T-square thermal resistivity does not require umklapp events. The approximate recovery of the Wiedemann-Franz law in the presence of disorder would account for a T-square electrical resistivity without umklapp.

ε-Fe Electrical Resistivity at High Pressures of Stepwise Shock Compression

In situ electrical resistivity measurements are performed on samples of iron with a hexagonal close–packed lattice (ε–Fe), compressed and heated by stepwise shock loading. Equations of state for ε-Fe are constructed. The obtained experimental results are mathematically simulated in the hydrocode based on the developed equations of state. The modeling results are used to reconstruct the volumetric–temperature dependence of the ε–Fe electrical resistivity at pressures of ≈20–70 GPa and temperatures of ≈750–950 K. The volume–temperature dependence of the ε-Fe thermal conductivity coefficient is calculated according to the Wiedemann–Franz law. The results obtained for the electrical and thermal conductivity of shock compressed and heated ε-Fe are compared with literature experimental and theoretical data for iron and silicon iron.

Thermopower in 3D Dirac Semimetal Na3Bi

We study the electronic contribution to the thermopower of 3D Dirac semimetal using a semiclassical Boltzmann approach. We investigate the effect of various relaxation processes including disorder and interactions on the thermoelectric properties. We find that the thermopower have an interesting dependence on the chemical potential that is characteristic of the linear electronic dispersion, and that the electron-electron interactions modify the Lorenz number. We observed the dependence of thermopower on electron temperature and conclude that thermopower has higher values for electron-electron scattering as compared to charged impurity and short range disorder scattering mechanisms.

Thermal Hall effect and the Wiedemann–Franz law in Chern insulator

Thermal Hall effect, where a transverse temperature difference is generated by implementing a longitudinal temperature gradient and an external magnetic field in the perpendicular direction to systems, is a useful tool to reveal transport properties of quantum materials. A systematic study of the thermal Hall effect in a Chern insulator is still lacking. Here, using the Landauer–Büttiker formula, we investigated the thermal Hall transport of the Harper–Hofstadter model with flux φ = 1/2 and its generalizations. We demonstrated that the Wiedemann–Franz law, which states that the thermal Hall conductivity is linearly proportional to the quantum Hall conductivity in the low temperature limit, is still valid in this Chern insulator, and that the thermal Hall conductivity can be used to characterize the topological properties of quantum materials.

Current Noise of Hydrodynamic Electrons.

A resistor at finite temperature produces white noise fluctuations of the current called Johnson-Nyquist noise. Measuring the amplitude of this noise provides a powerful primary thermometry technique to access the electron temperature. In practical situations, however, one needs to generalize the Johnson-Nyquist theorem to handle spatially inhomogeneous temperature profiles. Recent work provided such a generalization for Ohmic devices obeying the Wiedemann-Franz law, but there is a need to provide a similar generalization for hydrodynamic electron systems, since hydrodynamic electrons provide unusual sensitivity for Johnson noise thermometry but they do not admit a local conductivity nor obey the Wiedemann-Franz law. Here we address this need by considering low-frequency Johnson noise in the hydrodynamic setting for a rectangular geometry. Unlike in the Ohmic setting, we find that the Johnson noise is geometry dependent due to nonlocal viscous gradients. Nonetheless, ignoring the geometric correction only leads to an error of at most 40% as compared to naively using the Ohmic result.

A dual-domain 3 ω method for measuring the in-plane thermal conductivity of high-conductive thin films

The thermal conductivity measurement of films with submicrometer thicknesses is difficult due to their exceptionally low thermal resistance, which makes it challenging to accurately measure the temperature changes that occur as heat flows through the film. Thus, specialized and sensitive measurement techniques are required. 3ω method is a widely used and reliable tool for measuring the thermal conductivity of films. However, the high in-plane thermal conductivity in thin films results in rapid heat dissipation across the thin film, resulting in poor measurement sensitivity and making it difficult to accurately measure the temperature gradient with the traditional 3ω method. Also, the traditional 3ω method requires cross-plane thermal conductivity to derive the in-plane counterpart. Here, we introduce a dual-domain 3ω method that adopts AC-modulated heating and electrode arrays facilitating surface temperature profiling: (1) the sensitivity was significantly improved due to the employment of low-thermal-conductivity-substrate, and (2) cross-plane thermal conductivity is not required for the analysis of in-plane counterpart. This measurement platform allows us to control heat penetration in depth via varied heating frequencies as well as spatial temperature detection through laterally distributed electrodes on the thin film surface. By utilizing the described method, we have determined the in-plane thermal conductivity of a copper film, having a thickness of 300 nm, which was found to be 346 Wm−1K−1 and validated by the Wiedemann–Franz law.

Intrinsic thermal conductivity of ZrC from low to ultrahigh temperatures: A critical revisit

Current phonon transport theory based on ground-state calculations has been successful in predicting thermal conductivity at room and medium temperatures but may misrepresent behavior at high temperatures. In this work, we predict the thermal conductivity ($\ensuremath{\kappa}$) of ZrC including electronic and phonon contributions from 300 to 3500 K, by including high-order phonon scattering; lattice expansion; temperature-dependent (TD) second-, third-, and fourth-order force constants (2FC, 3FC, and 4FC); and interband phonon conduction by using first principles. For the phonon transport, we find that four-phonon scattering (4ph) significantly reduces the phonon thermal conductivity (${\ensuremath{\kappa}}_{\mathrm{ph}}$), by as much as $\ensuremath{\sim}75%$ at 3500 K. After including 4ph scattering and all other factors, ${\ensuremath{\kappa}}_{\mathrm{ph}}$ shows a $\ensuremath{\sim}{T}^{\ensuremath{-}1.5}$ rather than $\ensuremath{\sim}{T}^{\ensuremath{-}1}$ dependence. TD 2FC decreases three-phonon scattering rates but increases 4ph rates by decreasing and increasing the scattering phase spaces, respectively. For 4ph phase space, the TD 2FC flattens phonon bands, and allows more redistribution-4ph processes $(1+2\ensuremath{\rightarrow}3+4)$ to happen. The combination effect of TD 2FC and TD 4FC reduces 4ph rates of acoustic modes but increases those of optical modes. The TD 3FC and 4FC decrease the phonon scattering cross section and increase the ${\ensuremath{\kappa}}_{\mathrm{ph}}$ significantly (by 52% at 3500 K). The contribution from interband (Wigner) phonon conduction is small, even at ultrahigh temperatures. For electronic thermal transport, we find that it is sensitive to and can be changed by 20% by the TD lattice constants. The Lorenz number varies from 1.6 to $3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$ at different temperatures. The theoretical prediction in the literature overpredicts ${\ensuremath{\kappa}}_{\mathrm{ph}}$ (e.g., $\ensuremath{\sim}28%$) and underpredicts the ${\ensuremath{\kappa}}_{\mathrm{el}}$ (e.g., $\ensuremath{\sim}38%$), resulting in an overall underprediction of $\ensuremath{\kappa}$ ($\ensuremath{\sim}26%$ at 1500 K). The impacts of grain size and defects are found to be strong, leading to the lower observed thermal conductivity in experiments.

Porosity effect on the thermal and mechanical properties of U-50Zr alloy: A molecular dynamics study

The U-50Zr alloy is a promising candidate for helical cruciform fuel application, for the superior performance in neutronics and heat transfer properties. Under in-pile conditions, the formation and aggregation of fission gas products would introduce porosity effect, and further degrade the mechanical-thermal physical properties. However, no porosity model has been established for U-50Zr alloy. In this work, the Young's modulus and lattice conductivity for U-50Zr were predicted via molecular dynamics (MD) simulations with modified embedded atom method potential. The effective Young's modulus was obtained by multi-dimensional elongation tests and Voigt averaging scheme, and the phonon conductivity was computed with reverse non-equilibrium molecular dynamics method. The electron conductivity was estimated by Wiedemann-Franz Law with published resistivity data. To fulfill porosity effect modeling, void generation technique was utilized into the MD models, and effective medium theory was incorporated into the approximations of electron conductivity. Good agreements with experimental data were achieved to verify the research methodology. The semi-empirical models on porosity effects for U-50Zr were established, which could provide preliminary predictions of Young's modulus and thermal conductivity.

High-Precision Prediction of Thermal Conductivity of Metals by Molecular Dynamics Simulation in Combination with Machine Learning Approach

Molecular dynamics (MD) simulation is a powerful tool to estimate materials properties from atomistic viewpoint. However, the scope of application of MD simulations is limited to problems where the Newton's equation of motion for atoms is dominant. Therefore, it is inherently insufficient to estimate thermal conductivity of metallic materials, which consists of phononic and electronic components. In this study, machine learning (ML)-based regression model is employed to predict thermal conductivity of metals with high accuracy using deficient results from MD simulations. A regression analysis with the least absolute shrinkage and selection operator (Lasso) including electrical conductivity as predictor variables successfully predict the thermal conductivity of metals with negative temperature dependence, which indicates a significant contribution of electrons to thermal conduction in metals. It should be stressed that our prediction is better than the conventional estimation from the Wiedemann–Franz law. This study shows us new possibilities of new ML approach for improving the accuracy of physical properties obtained from MD simulations.

Heat transport in Weyl semimetals in the hydrodynamic regime

We study heat transport in a Weyl semimetal with broken time-reversal symmetry in the hydrodynamic regime. At the neutrality point, the longitudinal heat conductivity is governed by the momentum relaxation (elastic) time, while the longitudinal electric conductivity is controlled by the inelastic scattering time. In the hydrodynamic regime, this leads to a large longitudinal Lorenz ratio. As the chemical potential is tuned away from the neutrality point, the longitudinal Lorenz ratio decreases because of suppression of the heat conductivity by the Seebeck effect. The Seebeck effect (thermopower) and the open circuit heat conductivity are intertwined with the electric conductivity. The magnitude of the Seebeck tensor is parametrically enhanced, compared to the noninteracting model, in a wide parameter range. While the longitudinal component of Seebeck response decreases with increasing electric anomalous Hall conductivity ${\ensuremath{\sigma}}_{xy}$, the transverse component depends on ${\ensuremath{\sigma}}_{xy}$ in a nonmonotonous way. Via its effect on the Seebeck response, large ${\ensuremath{\sigma}}_{xy}$ enhances the longitudinal Lorenz ratio at a finite chemical potential. At the neutrality point, the transverse heat conductivity is determined by the Wiedemann-Franz law. Increasing the distance from the neutrality point, the transverse heat conductivity is enhanced by the transverse Seebeck effect and follows its nonmonotonous dependence on ${\ensuremath{\sigma}}_{xy}$.

Significant modification of the electronic structure of biased trilayer SiC and BN via magnetic field to achieve enhanced thermoelectric performance

The two-dimensional semiconducting materials with tunable electronic structure and high thermoelectric properties have a wide range of applications, especially in nanoscale devices. This study uses the Kubo-Greenwood formula in the framework of the Green function approach and the tight binding model to calculate the thermoelectric properties of trilayer SiC (3L-SiC). 3L-SiC is a semiconductor that can transform to metallic state with increasing applying the external fields with critical strength. The thermoelectric properties of the 3L-SiC and 3L-BN were analyzed under bias voltage, magnetic field and temperature up to 1500 K and compared with each other. The results show that thermal properties of the 3L-SiC are higher than that 3L-BN and both structures exhibit strong dependence on bias voltage and magnetic field with higher sensitivity to the magnetic field. The thermal properties of the selected structures increases with temperature and the external fields enhance the increasing rate. The behavior of the Lorenz Number in terms of temperature exhibits general pattern as increasing from zero to maximum value at TM and decreasing by further temperature increasing.

Thermoelectric properties of inversion symmetry broken Weyl semimetal–Weyl superconductor hybrid junctions

We theoretically investigate the thermoelectric properties (electronic contribution) of a hybrid structure comprising an inversion symmetry broken Weyl semimetal (WSM) and intrinsic Weyl superconductor (WSC) with $s$-wave pairing, employing the Blonder-Tinkham-Klapwijk formulation for noninteracting electrons. Our study unfolds interesting features for various relevant physical quantities such as thermal conductance, the thermoelectric coefficient, and the corresponding figure of merit. We also explore the effects of an interfacial insulating (I) barrier (WSM-I-WSC setup) on the thermoelectric response in the thin barrier limit. Further, we compute the ratio of the thermal to the electrical conductance in different temperature regimes and find that the Wiedemann-Franz law is violated for small temperatures (below critical temperature ${T}_{c}$) near the Weyl points while it saturates to the Lorentz number, away from the Weyl points, at all temperatures irrespective of the barrier strength. We compare and contrast this behavior with other Dirac material heterostructures and provide a detailed analysis of the thermal transport. Our study can facilitate the fabrication of mesoscopic thermoelectric devices based on WSMs.

Effects of V concentration on the physical properties of Cr1−x Al x alloy system

Electrical resistivity (ρ), magnetic susceptibility (χ) and thermoelectric power (S) studies reported previously on the (Cr1-x Al x )99V1 alloy system indicate a suppression of antiferromagnetism in the concentration range 0.015 ≤ x ≤ 0.040. The present study incorporates Sommerfeld electronic specific heat coefficient (γ), thermal conductivity (κ), Hall coefficient (R H) and analyses of the previous results in order to have a comprehensive study of the alloy system. γ(x) depicts two peaks close to the same concentrations where dS/dT|T→2K(x) have minima, i.e. at x c1 ≈ 0.015 and x c2 ≈ 0.040. Such peaks and minima, respectively, have been considered as key signatures of quantum criticality (QC) in alloys of Cr. Evidence of band structure modification in the alloy system is shown by a change of slope in the Nordheim-Gorter (N-G) relationship showing a minimum at an extrapolated concentration x = 0.035. The slope is positive for the incommensurate (I) spin-density-wave (SDW) alloys with x < 0.035 and a negative for the commensurate (C) SDW alloys with x > 0.035. A behaviour reminiscent of changes in the band structure is also observed in the Lorenz number, L(x), for the alloy with x = 0. R H(T) results in the range 0 ≤ x ≤ 0.026 have a sharp increase in the charge carrier density, n 2K = [qR H(2k)]−1, at the ISDW to paramagnetic (P) phase transition. The concentrations x = 0.015 and x = 0.040 are therefore considered ISDW to P and P to CSDW quantum critical points, respectively.

Topological and disorder corrections to the transverse Wiedemann-Franz law and Mott relation in kagome magnets and Dirac materials

Topological and disorder corrections to the transverse Wiedemann-Franz law and Mott relation in kagome magnets and Dirac materials

Dynamically screened strongly quantized electron transport in binary neutron-star merger

We examine electron-transport coefficients in magnetized hot and dense electron-ion plasma relevant in binary neutron star merger simulation. We calculate electrical and thermal conductivities in low density, high temperature, highly magnetized plasma of binary neutron star mergers where quantum oscillatory behavior of electrons emerge. For pronounced thermodynamic effects, we consider zeroth Landau level population of electrons for the calculation of conductivity. We solve Boltzmann equation in presence of magnetic field to obtain the dissipative components of electrical and thermal conductivities. The dissipative coefficients are formulated considering frequency dependent dynamical screening in the quantized electron-ion scattering rate. Numerical estimations show that the effect of dynamical screening of photon propagator on electrical and thermal conductivities is pronounced. We observe that dynamical screening reduces the maxima of both the electrical and thermal conductivities by factors of thirty one and twenty respectively leading to a reduction in the corresponding time scales of these coefficients. The common scaling factor between electrical and thermal conductivity is also observed to follow cubic relationship with temperature violating Wiedemann–Franz law.