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Keywords = Wiedemann–Franz law

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19 pages, 3199 KB  
Article
Enhancing the Mechanical and Thermal Transport Properties of AZ31/Ti2AlC MAX-Phase Surface Composites
by Essam B. Moustafa, Ahmad Bamasag, Abudellah Alqarni, Rasha A. Youness, Mohammed A. Taha and Tamer S. Mahmoud
J. Compos. Sci. 2026, 10(8), 428; https://doi.org/10.3390/jcs10080428 - 14 Aug 2026
Viewed by 332
Abstract
This study investigates the evolution of microstructural, mechanical, and transport properties in AZ31 magnesium alloy surface composites reinforced with Ti2AlC MAX-phase particles at volume fractions of 6, 9, and 12 vol.%, which were fabricated by solid-state friction stir processing (FSP). In [...] Read more.
This study investigates the evolution of microstructural, mechanical, and transport properties in AZ31 magnesium alloy surface composites reinforced with Ti2AlC MAX-phase particles at volume fractions of 6, 9, and 12 vol.%, which were fabricated by solid-state friction stir processing (FSP). In contrast to conventional brittle ceramics, Ti2AlC MAX-phase mitigates interfacial reactivity and thermal mismatch. FSP successfully fabricated a highly consolidated, macroscopically defect-free, dynamically recrystallized fine-grained stirred zone with homogeneous particle distribution and metallurgically clean interfaces. Mechanically, the addition of 12 vol.% Ti2AlC significantly improved the elastic response, increasing the Young’s modulus from 51 GPa to 67 GPa. The microhardness of the stirred zone reached 60.14 HV, a 53.4% increase over the base metal. The controlled electron and phonon scattering, enabled by the introduction of heterogeneous Mg/Ti2AlC interfaces, decreased the electrical and thermal conductivities from initial values of 1.15 × 107 S/m and 86.0 W/m·K for the unreinforced matrix down to 7.8 × 106 S/m and 76.0 W/m·K, respectively, and caused a significant reduction in the coefficient of thermal expansion. Theoretical analysis, utilizing the Wiedemann–Franz law and Maxwell–Eucken approximations, provided a supportive baseline indicating the dominance of electronic thermal transport and interfacial scattering mechanisms. These results outline a viable route for developing lightweight magnesium-based composites with tailored mechanical and thermal characteristics for advanced structural applications. Full article
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33 pages, 10229 KB  
Article
Temperature-Dependent Lorenz Number in BiSbTe Thermoelectrics
by Elkin I. Gutierrez-Velasquez, Hector Parra-Peñuela and Jesús Gutiérrez Bernal
J. Compos. Sci. 2026, 10(8), 424; https://doi.org/10.3390/jcs10080424 - 12 Aug 2026
Viewed by 285
Abstract
The Lorenz number is a critical parameter for separating the electronic and lattice contributions to thermal conductivity in thermoelectric materials through the Wiedemann–Franz law. However, the classical Sommerfeld approximation often fails to accurately represent the temperature-dependent transport behavior of BiSbTe-based thermoelectric materials. This [...] Read more.
The Lorenz number is a critical parameter for separating the electronic and lattice contributions to thermal conductivity in thermoelectric materials through the Wiedemann–Franz law. However, the classical Sommerfeld approximation often fails to accurately represent the temperature-dependent transport behavior of BiSbTe-based thermoelectric materials. This study presents a systematic analysis of the temperature dependence of the Lorenz number using experimental data compiled from eleven independent studies. A unified database was established through literature review, data extraction, normalization, and statistical analysis. Linear, exponential, and quadratic regression models were evaluated to identify the mathematical representation that best describes the reported behavior, and a Processing Complexity Index (PCI) was introduced to examine potential relationships between fabrication-route complexity and the degree of nonlinearity. The compiled datasets consistently exhibited an overall increase in the Lorenz number with temperature, although noticeable variability in magnitude and curvature was observed among studies, reflecting differences in material composition, processing routes, and experimental conditions. While the quadratic model generally achieved the best statistical performance, linear and exponential models provided comparable fits for some datasets, indicating that no single functional form is universally optimal. The proposed correlations provide a statistically representative framework for improving thermal conductivity decomposition and thermoelectric characterization within the investigated temperature range (300–500 K). Nevertheless, the correlations are constrained by the scope of the literature-derived database and should not be interpreted as universally applicable predictive models. Full article
(This article belongs to the Section Composites Modelling and Characterization)
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13 pages, 1473 KB  
Article
First-Principles Study on the Electrical and Thermal Conductivities of Cu–Zn Binary Alloys
by Lei Huang, Bo Peng, Qinchi Yue, Guojie Huang, Changhao Wang, Ruzhi Wang and Ning Tian
Materials 2025, 18(10), 2310; https://doi.org/10.3390/ma18102310 - 15 May 2025
Cited by 7 | Viewed by 2234
Abstract
Cu–Zn alloys are widely used engineering materials with well-known industrial applications. However, studies on their electrical and thermal conductivities have primarily relied on experimental measurements, while theoretical investigations remain limited. In this work, eight crystal structure models were constructed to represent three phase [...] Read more.
Cu–Zn alloys are widely used engineering materials with well-known industrial applications. However, studies on their electrical and thermal conductivities have primarily relied on experimental measurements, while theoretical investigations remain limited. In this work, eight crystal structure models were constructed to represent three phase configurations (α single phase, α + β′ dual phase, and β′ single phase) of Cu–Zn alloys with Zn concentrations ranging from 0 to 50 at.%. Based on the first-principles calculations combined with the Boltzmann transport equation, the electrical and thermal conductivities of these models were computed, and the electronic structure of the α-phase configurations was further analyzed. The results show that both electrical and thermal conductivities exhibit a non-monotonic trend with increasing Zn content, initially decreasing and then increasing. This trend is in strong agreement with available experimental data. Further analysis of the electronic structure reveals that, in the α-phase region, the density of states near the Fermi level is mainly contributed by Cu d-orbitals. As Zn content increases, the effective DOS near the Fermi level decreases, leading to reduced electron transport capability. For thermal conductivity, both the Wiedemann–Franz law and the first-principles calculations were employed, yielding results consistent with experimental trends. In summary, this study systematically investigates the variation of electrical and thermal conductivities of Cu–Zn binary alloys with Zn content and explores the underlying physical mechanisms from the perspective of electronic structure. The findings provide valuable theoretical support for understanding and optimizing the transport properties of complex alloy systems. Full article
(This article belongs to the Special Issue Advances in Modelling and Simulation of Materials in Applied Sciences)
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12 pages, 2650 KB  
Article
Improvement of Electrical and Thermal Properties of Carbon Nanotube Sheets by Adding Silver Nanowire and Mxene for an Electromagnetic-Interference-Shielding Property Study
by Matthew Kurilich, Jin Gyu Park, Joshua Degraff, Qiang Wu and Richard Liang
Nanomaterials 2024, 14(19), 1587; https://doi.org/10.3390/nano14191587 - 1 Oct 2024
Cited by 1 | Viewed by 3335
Abstract
Hybrid carbon nanotube (CNT) sheets were fabricated by mixing CNTs with silver nanowires (AgNWs) and MXene to study their electromagnetic-interference (EMI)-shielding properties. CNT/AgNW and CNT/MXene hybrid sheets were produced by ultrasonic homogenization and vacuum filtration, resulting in free-standing CNT sheets. Three different weight [...] Read more.
Hybrid carbon nanotube (CNT) sheets were fabricated by mixing CNTs with silver nanowires (AgNWs) and MXene to study their electromagnetic-interference (EMI)-shielding properties. CNT/AgNW and CNT/MXene hybrid sheets were produced by ultrasonic homogenization and vacuum filtration, resulting in free-standing CNT sheets. Three different weight ratios of AgNW and MXene were added to the CNT dispersions to produce hybrid CNT sheets. Microstructure characterization was performed using scanning electron microscopy, and the Wiedemann–Franz law was used to characterize transport properties. The resulting hybrid sheets exhibited improved electrical conductivity, thermal conductivity, and EMI-shielding effectiveness compared to pristine CNT sheets. X-band EMI-shielding effectiveness improved by over 200%, while electrical conductivity improved by more than 1500% in the hybrid sheets due to a higher charge-carrier density and synergistic effects between nanomaterials. The addition of AgNW to CNT sheets resulted in a large improvement in electrical conductivity and EMI shielding; however, this may also result in increased weight and sample thickness. Similarly, the addition of MXene to CNT sheets may result in an increase in weight due to the presence of the denser MXene flakes. Full article
(This article belongs to the Section Nanoelectronics, Nanosensors and Devices)
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14 pages, 3921 KB  
Article
The Electrical Resistivity of Liquid Fe-16wt%S-2wt%Si at High Pressures and the Effect of S and Si on the Dynamo in the Ancient Vestan Core
by Erin M. Lenhart, Wenjun Yong and Richard A. Secco
Crystals 2024, 14(6), 565; https://doi.org/10.3390/cryst14060565 - 19 Jun 2024
Cited by 4 | Viewed by 1877
Abstract
A critical component of predicting thermal convection and dynamo action in the cores of terrestrial planetary bodies is the adiabatic heat flux at the top of the core. Powders of Fe, FeS, and Fe-9wt%Si were mixed to imitate the core of Asteroid 4 [...] Read more.
A critical component of predicting thermal convection and dynamo action in the cores of terrestrial planetary bodies is the adiabatic heat flux at the top of the core. Powders of Fe, FeS, and Fe-9wt%Si were mixed to imitate the core of Asteroid 4 Vesta, which studies of HED meteorites indicate is comprised of 13–16wt%S and 1–2wt%Si. In a 1000-ton cubic anvil press, the voltage drop across an Fe-16wt%S-2wt%Si sample of 8–10 mm3 was measured at 2, 3, 4, and 5 GPa and ~300–2000 K. The resistivity of Fe-16wt%S-2wt%Si is 400 ± 50 μΩ·cm for 2–5 GPa for the complete liquid state. Using the Wiedemann–Franz Law, this gives an electronic thermal conductivity of 11 ± 1.5 W/m/K for 2–4 GPa at complete melting and an adiabatic heat flow of 55 ± 15 MW at the top of an early Fe-16wt%S-2wt%Si Vestan core. The 2 GPa boundary of the miscibility of Fe-16wt%S-2wt%Si is observed. The adiabatic heat flow through an Fe-16wt%S-2wt%Si core of variable size is discussed, as well as the resistivity of liquid Fe alloy at small planetary core conditions as a function of S and Si alloying composition. On the basis of previous studies on binary and ternary alloys of Fe with S and/or Si, we interpolate the separate effects of S and Si on the resistivity (and inversely on thermal conductivity and core adiabatic heat flow). Full article
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18 pages, 6619 KB  
Article
Effect of Starting Powder Particle Size on the Thermoelectric Properties of Hot-Pressed Bi0.3Sb1.7Te3 Alloys
by Ioanna Ioannou, Panagiotis S. Ioannou, Theodora Kyratsi and John Giapintzakis
Materials 2024, 17(2), 318; https://doi.org/10.3390/ma17020318 - 8 Jan 2024
Cited by 6 | Viewed by 2998
Abstract
P-type Bi0.3Sb1.7Te3 polycrystalline pellets were fabricated using different methods: melting and mechanical alloying, followed by hot-press sintering. The effect of starting powder particle size on the thermoelectric properties was investigated in samples prepared using powders of different particle [...] Read more.
P-type Bi0.3Sb1.7Te3 polycrystalline pellets were fabricated using different methods: melting and mechanical alloying, followed by hot-press sintering. The effect of starting powder particle size on the thermoelectric properties was investigated in samples prepared using powders of different particle sizes (with micro- and/or nano-scale dimensions). A peak ZT (350 K) of ~1.13 was recorded for hot-pressed samples prepared from mechanical alloyed powder. Moreover, hot-pressed samples prepared from ≤45 μm powder exhibited similar ZT (~1.1). These high ZT values are attributed both to the presence of high-density grain boundaries, which reduced the lattice thermal conductivity, as well as the formation of antisite defects during milling and grinding, which resulted in lower carrier concentrations and higher Seebeck coefficient values. In addition, Bi0.3Sb1.7Te3 bulk nanocomposites were fabricated in an attempt to further reduce the lattice thermal conductivity. Surprisingly, however, the lattice thermal conductivity showed an unexpected increasing trend in nanocomposite samples. This surprising observation can be attributed to a possible overestimation of the lattice thermal conductivity component by using the conventional Wiedemann–Franz law to estimate the electronic thermal conductivity component, which is known to occur in nanocomposite materials with significant grain boundary electrical resistance. Full article
(This article belongs to the Topic Thermoelectric Energy Harvesting)
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27 pages, 3455 KB  
Review
Next-Generation Quantum Materials for Thermoelectric Energy Conversion
by Shiva Kumar Singh, Julian Munevar, Letície Mendonça-Ferreira and Marcos A. Avila
Crystals 2023, 13(7), 1139; https://doi.org/10.3390/cryst13071139 - 21 Jul 2023
Cited by 6 | Viewed by 6879
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advances in Intermetallic and Metal-Like Compounds)
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12 pages, 1333 KB  
Article
Impact of Thermophysical Properties of High-Alloy Tool Steels on Their Performance in Re-Purposing Applications
by Aaron Berger, Santiago Benito, Philipp Kronenberg and Sebastian Weber
Materials 2022, 15(23), 8702; https://doi.org/10.3390/ma15238702 - 6 Dec 2022
Cited by 7 | Viewed by 2716
Abstract
Resource efficiency and circularity in the context of sustainability are rapidly gaining importance in the steel industry. One concept regarding circular economy is “repurposing”. In the context of this work, worn-out machine circular knives are used to produce new chisels for woodturning. The [...] Read more.
Resource efficiency and circularity in the context of sustainability are rapidly gaining importance in the steel industry. One concept regarding circular economy is “repurposing”. In the context of this work, worn-out machine circular knives are used to produce new chisels for woodturning. The chisels can be extracted parallel or perpendicular to the rolling direction of the primary production process, resulting in an associated carbide orientation of the repurposed tool. The rolling direction, and therefore carbide alignment, will influence the wear resistance and the thermophysical properties, whereby the thermal conductivity will determine the temperatures at the tip of the chisel. Therefore, the thermal conductivity was investigated with the dynamic measurement method, where the specific heat capacity, density and thermal diffusivity of the extracted chisels and industrial reference chisels were measured separately. Moreover, the electrical resistivity was measured in order to calculate the electronic thermal conductivity according to the Wiedemann–Franz–Lorenz law. It was shown that all of these parameters exhibited different degrees of variability with rising temperature. In a detailed analysis, the thermal diffusivity could be identified as an essential parameter of thermal conductivity. By taking two conventional chisels with different chemical compositions and heat treatments into account, it can be seen that the microstructure determines the thermophysical properties. Considering the carbide direction, the chisels that were extracted parallel to the rolling direction showed differing thermophysical properties. Therefore, the carbide orientation is shown to play a significant role regarding the heat dissipation at the cutting edge, because differences, especially in the electronic thermal conductivity in the parallel and perpendicular extracted chisels, can be measured. In addition to the wear resistance factor, the thermal conductivity factor now also supports the removal of the repurposed chisels parallel to the rolling direction. Full article
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9 pages, 4408 KB  
Article
Thermal Convection in Vesta’s Core from Experimentally-Based Conductive Heat Flow Estimates
by Oluwasanmi A. Orole, Wenjun Yong and Richard A. Secco
Crystals 2022, 12(12), 1752; https://doi.org/10.3390/cryst12121752 - 3 Dec 2022
Cited by 4 | Viewed by 2569
Abstract
Electrical resistivity measurements of Fe-5 wt% Ni were made in situ under pressures of 2–5 GPa and temperatures up to 2000 K in a cubic-anvil press. The thermal conductivity was calculated from the measured electrical resistivity data using the Wiedemann–Franz law. Comparison of [...] Read more.
Electrical resistivity measurements of Fe-5 wt% Ni were made in situ under pressures of 2–5 GPa and temperatures up to 2000 K in a cubic-anvil press. The thermal conductivity was calculated from the measured electrical resistivity data using the Wiedemann–Franz law. Comparison of these data with previous studies on pure Fe and Fe-10 wt% Ni shows that a change in the Ni content within the range 0–10 wt% Ni has no significant effect on electrical resistivity of Fe alloys. Comparing the estimated adiabatic core heat flux of ~331 MW at the top of Vesta’s core to the range of estimated heat flux through the CMB of 1.5–78 GW, we infer that the mechanism stirring Vesta’s liquid outer core to generate its surface magnetic field tens of millions of years ago in its early history was thermal convection. Full article
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11 pages, 2287 KB  
Article
Enhanced Electron Heat Conduction in TaS3 1D Metal Wire
by Hojoon Yi, Jaeuk Bahng, Sehwan Park, Dang Xuan Dang, Wonkil Sakong, Seungsu Kang, Byung-wook Ahn, Jungwon Kim, Ki Kang Kim, Jong Tae Lim and Seong Chu Lim
Materials 2021, 14(16), 4477; https://doi.org/10.3390/ma14164477 - 10 Aug 2021
Cited by 3 | Viewed by 4849
Abstract
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 κ of TaS3 as a [...] Read more.
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 κ of TaS3 as a function of temperature. Electrons dominate the heat conduction of a metal. The Wiedemann–Franz law states that the thermal conductivity κ of a metal is proportional to the electrical conductivity σ with a proportional coefficient of L0, known as the Lorenz number—that is, κ=σLoT. 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 L=12L0. This result implies the possibility of an existing heat conduction path that the Sommerfeld theory cannot account for. Full article
(This article belongs to the Topic Multiple Application for Novel and Advanced Materials)
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11 pages, 18098 KB  
Article
Thermal Convection in the Core of Ganymede Inferred from Liquid Eutectic Fe-FeS Electrical Resistivity at High Pressures
by Joshua A. H. Littleton, Richard A. Secco and Wenjun Yong
Crystals 2021, 11(8), 875; https://doi.org/10.3390/cryst11080875 - 28 Jul 2021
Cited by 12 | Viewed by 3106
Abstract
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 [...] Read more.
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. Full article
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20 pages, 1757 KB  
Article
Wiedemann–Franz Law for Massless Dirac Fermions with Implications for Graphene
by Adam Rycerz
Materials 2021, 14(11), 2704; https://doi.org/10.3390/ma14112704 - 21 May 2021
Cited by 21 | Viewed by 5391
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Multilayer and Hybrid Two-Dimensional Materials)
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