Electronic Thermal Conductivity Research Articles

Excellent optical and thermoelectric features of two-dimensional half-metallic ferromagnet Zn1-x(TM)xO: A first principle investigation

The electronic, magneto-optical, and thermoelectric properties of graphene-like ZnO nanosheets doped with transition-metal TM (= Fe, Co, Ni, or Cu) were analyzed using spin-polarized first-principles computations. When a TM atom substitution with the Zn atom, the resultant material exhibits significant spin-polarization around the Fermi level and displays a half-metallic ferromagnet within the PBEsol-GGA. Doped ZnO nanosheets by Fe-, Co-, Ni-, and Cu-dopants generate the total magnetic moment of 4μB, 3μB, 2μB, and 1μB, respectively, which is produced primarily by the TM-3d atoms. The p-d hybridization explains the ferromagnetic interactions caused by the robust coupling among Co-, Ni-, or Cu-3d and anion O-2p orbitals. We have investigated the optical characteristics of TM-doped ZnO nanosheets in parallel (EǁX) and perpendicular (EǁZ) polarization directions. Our analysis demonstrates that the Zn1-x(TM)xO two-dimensional nanosheets can absorb visible sunlight in the (EǁX) polarization direction comparatively to pristine ZnONS. Along the x-axis, we studied the Seebeck coefficient, electrical, electronic thermal conductivities, and power factor for various temperatures. All the TM-doped ZnO (2D) nanosheets demonstrate superior electrical conductivity and high power factor in n-type doping than in p-type doping. According to these findings, TM-doped ZnO nanosheets could represent the next evolution in Spintronic, photovoltaic cells, and thermoelectric technologies.

Vacancy Suppression Induced Synergetic Optimization of Thermoelectric Performance in Sb-Doped GeTe Evidenced by Positron Annihilation Spectroscopy.

Synergetic optimization of the electrical and thermal transport performance of GeTe has been achieved through Sb doping in this work, resulting in a high thermoelectric figure of merit ZT of 2.2 at 723 K. Positron annihilation measurements provided clear evidence that Sb doping in GeTe can effectively suppress the Ge vacancies, and the decrease of vacancy concentration coincides well with the change of hole carrier concentration after Sb doping. The decreased scattering by hole carriers and vacancies causes notable increase in carrier mobility. Despite this, the density of states effective mass is not enhanced by Sb doping, a maximum power factor of 4562 μW m-1 K-2 at 723 K is obtained for Ge0.94Sb0.06Te with an optimized carrier concentration of ∼3.65 × 1020 cm-3. Meanwhile, the electronic thermal conductivity κe is reduced because of the decreased electrical conductivity σ with the increase of the Sb doping amount. In addition, the lattice thermal conductivity κL is also suppressed due to multiple phonon scattering mechanism, such as the large mass and strain fluctuations by the substitution of Sb for Ge atoms, and also the unique microstructure including grain boundary, nano-pore, and dislocation in the samples. In conclusion, a maximum ZT of 2.2 is gained at 723 K, which contributes to preferable TE property for GeTe-based materials.

The Transport and Optical Characteristics of a Metal Exposed to High-Density Energy Fluxes in Compressed and Expanded States of Matter

This article presents a theoretical study of the optical and transport properties of metals. Iron, as an example, was used to discuss, through a theoretical description, the peculiarities of these properties in the compressed and expanded states under the influence of high-density energy fluxes. By solving the semi-classical Boltzmann equation for conduction electrons for a broad range of densities and temperatures, the expressions of electrical conductivity, electronic thermal conductivity, and thermoelectric coefficient calculations were derived. The real and imaginary parts of the iron permittivity and the energy absorption coefficient for the first and second harmonics of Nd:YAG laser radiation were obtained. The calculation peculiarities of the metal’s optical characteristics of matter in an expanded state in a broad range of densities and temperatures were considered. The analysis of the obtained results shows their agreement with the theoretical description for cases of ideal non-degenerate and dense degenerate electron plasmas. It is shown that the behavior of the electrical conductivity and optical characteristics in the critical and supercritical regions of density and temperature are in agreement with the known experimental results.

Quantifying the lattice and electronic thermal conductivity of arsenic from first principles

Quantifying the lattice and electronic thermal conductivity of arsenic from first principles

Electronic, optical, and thermoelectric properties of multifunctional zintl compound BaAg2Te2 for energy conversion

Using the FP-APW + lo method, the structural, electronic, and optical properties of the Zintl BaAg2Te2 compound were investigated. The calculated unit cell parameters are well matching with the experimental results. In addition, the study of electronic properties reveals that BaAg2Te2 is a semiconductor with a direct bandgap of about 1.445 eV. The optical constants such as loss energy, refractive index, reflectivity, and absorption coefficient have been calculated and analyzed. These constants show a clear anisotropy caused by the different electron polarizability in the x-, y-, and z-directions. Moreover, the direct bandgap and good optical absorption make BaAg2Te2 promising candidates for photovoltaic applications. The thermoelectric properties of the BaAg2Te2 compound in the x, y, and z directions have been studied to obtain the Seebeck coefficient, electrical conductivity, electronic thermal conductivity, power factor, and figure of merit (ZT) against temperature and carrier concentrations. Our investigations showed an improvement in the ZT values of BaAg2Te2 with increase in temperature. Moreover, the BaAg2Te2 demonstrated optimal ZT values along the y-axis.

Isotope dependence of transport in ST40 hot ion mode plasmas

The ST40 compact, high-field spherical tokamak, operating at 2.1 T and with 1.8 MW of neutral beam heating, achieved central carbon impurity ion temperatures in excess of 10 keV, surpassing their business milestone of 100 M ∘C (8.6 keV). The high temperature discharges were in the hot ion mode, with , and they were achieved in both hydrogen and deuterium plasmas with deuterium neutral beam injection. In order to achieve the high temperature scenarios, careful wall conditioning and scenario optimization was carried out in , , and finally in plasmas. The TRANSP transport code was employed to study the dependence of confinement and transport on isotopic mass, and the conditions that led to the high measured central ion temperatures in the and plasmas. The kinetic profiles input into TRANSP were inferred from line-of-sight and limited radial measurements as well as consistency with a number of other experimental constraints. The TRANSP results first showed that the main species central ion temperature was only 0.5–1 keV lower than the measured carbon impurity temperature, and thus in the high performance plasmas also surpassed the 100 M ∘C level. TRANSP also showed that while the electron thermal conduction loss was dominant, reductions in central ion transport, and an effective decoupling of the ions from the electrons, led to an increase in central ion temperatures with increasing plasma mass. In fact, the associated confinement times exhibited a strong dependence on the isotopic mass of the thermal plasma. These preliminary results are foundations for dedicated experiments with full kinetic profile measurements on ST40 in the next run campaign.

Structural, electronic, optical, and thermoelectric properties of 2D honeycomb-like 1T-Rb2S monolayer: A DFT study

The unique and alluring properties of 2D materials in contrast to the bulk counterparts have fascinated many researchers worldwide. They show excellent tunable properties due to the quantum confinement effect. In this study, ab initio simulations for the 1T-Rb2S monolayer have been performed based on the Density Functional Theory (DFT). DFT calculations are carried out by the PBE-GGA exchange-correlation functional via Wien2K software. On performing electronic and structural studies, the Rb2S monolayer shows an indirect band gap and is a semiconductor that has a bandgap value of about 1.64 eV. The dynamical and structural stability of the Rb2S monolayer is validated via phonon calculations. The optical properties were studied to determine the photovoltaic applications of the material in the nano regime. The optical properties of the Rb2S were carried out using the OPTIC package in Wien2k. The optical properties such as dielectric function (ε), absorption coefficient (α), Energy Loss (L), Reflectivity (R), and the refractive index (n), as a function of energy, have been computed. Rb2S monolayers display more prominent results in the ultra-violet region than the visible region ensuring that Rb2S monolayers are exceptional candidates for photovoltaic applications. The thermal properties of the 2D 1T-Rb2S have been computed by employing BoltzTraP interface, the thermoelectric analysis such as electrical conductivity, electronic thermal conductivity, Seebeck coefficient (S), the figure of merit (ZT) and the power factor (PF) has been computed and it rigidly ensures that the Rb2S monolayer is a potential candidate for thermoelectric device applications. The charge transfer mechanism is analysed by computing the mobility of charge carriers (ϑ), effective mass (meff) and relative ratio of the effective mass (D).

A first-principles study of stabilities, magnetic, electronic, elastic and transport properties of the metal borides TM2B (TM = Mn, Fe, Co and Ni)

This work addresses the physical properties of the highly correlated electron systems; transition metal borides TM2B (TM = Mn, Fe, Co and Ni) and provides a solid foundation for resolving the longstanding debate concerning the stable magnetic phase of Mn2B. The generalized gradient approximation along with Hubbard U (GGA + U) approach handling the high correlated electron systems; a valuable insight into this article has been utilized in the domain of Density Functional Theory. The calculated lattice parameters are found consistent with the experiments. The optimization energies in different magnetic phases and magnetic susceptibilities reveal that Mn2B is antiferromagnetic (AFM) in nature. The replacement of the TM in these intermetallics; transform the AFM behavior of Mn2B in to ferromagnetic (Fe2B and Co2B) and then paramagnetic (Ni2B), respectively. Electronic properties, electrical resistivities and thermal electronic conductivities of these compounds confirm their metallic nature. The investigated elastic properties demonstrate the stability and show that Fe2B is harder and brittle among this series while the rest compounds are ductile. All these intermetallics are incompressible and possess high melting temperatures. Based on the above properties, it is expected that these compounds could be used in high temperature technology like furnaces, reactors, aerospace and other high temperature processing equipments.

Attaining High Figure of Merit in the N-Type Bi2Te2.7Se0.3-Ag2Te Composite System via Comprehensive Regulation of Its Thermoelectric Properties.

n-Type Bi2Te2.7Se0.3 (BTS) is the state-of-the-art thermoelectric material near room temperature. However, the figure of merit ZT of commercial BTS ingots is still limited and further improvement is imperative for their wide applications. Here, the results show that through dispersion of the Ag2Te nanophase in BTS, one can not only elevate its power factor (PF) by as high as 14% (at 300 K) but also reduce its thermal conductivity κtot to as small as ∼29% (at 300 K). Experimental evidences show that the improved PF comes from both increased electron mobility via inhibited Te vacancies and enhanced thermopower due to energy filtering effect, while the reduction of κtot originates from the drop of both electronic thermal conductivity largely owing to the reduced number of vacancy VTe·· and intensified phonon scattering chiefly from the dispersed Ag2Te nanophase. Consequently, the largest ZTmax = 1.31 (at 350 K) and average ZTave = 1.16 (300-500 K) are achieved for the Bi2Te2.7Se0.3-0.3 wt % Ag2Te composite sample, leading to a projected conversion efficiency η = 8.3% (300-500 K). The present results demonstrate that incorporation of nanophase Ag2Te is an effective approach to boosting the thermoelectric performance of BTS.

A Comparative Study of Electronic, Optical, and Thermoelectric Properties of Zn-Doped Bulk and Monolayer SnSe Using Ab Initio Calculations.

In this study, we explore the effects of Zn doping on the electronic, optical, and thermoelectric properties of α-SnSe in bulk and monolayer forms, employing density functional theory calculations. By varying the doping concentrations, we aim to understand the characteristics of Zn-doped SnSe in both systems. Our analysis of the electronic band structure using (PBE), (SCAN), and (HSE06) functionals reveals that all doped systems exhibit semiconductor-like behavior, making them suitable for applications in optoelectronics and photovoltaics. Notably, the conduction bands in SnSe monolayers undergo changes depending on the Zn concentration. Furthermore, the optical analysis indicates a decrease in the dielectric constant when transitioning from bulk to monolayer forms, which is advantageous for capacitor production. Moreover, heavily doped SnSe monolayers hold promise for deep ultraviolet applications. Examining the thermoelectric transport properties, we observe that Zn doping enhances the electrical conductivity in bulk SnSe at temperatures below 500 K. However, the electronic thermal conductivity of monolayer samples is lower compared to bulk samples, and it decreases consistently with increasing Zn concentrations. Additionally, the Zn-doped 2D samples exhibit high Seebeck coefficients across most of the temperature ranges investigated.

Effects of Double Doping Germanium and Indium on the Thermoelectric Properties of Permingeatite

Cu3Sb1–x–yGexInySe4 (0.02 ≤ x ≤ 0.12; 0.04 ≤ y ≤ 0.08) permingeatite compounds doped with Ge and In were prepared using solid-state synthesis. The phases and microstructures were analyzed, and the charge transport and thermoelectric properties were evaluated according to the Ge and In doping content. Most of the samples contained a single phase of permingeatite with a tetragonal structure; however, secondary phases (Cu0.875InSe2, In2Se3, and InSb) were detected in the samples with x = 0.12 and y = 0.08. Both the a-axis and c-axis lattice constants of permingeatite were increased by Ge and In doping, with a = 0.5651–0.5655 nm and c = 1.1249–1.1255 nm, but the change in lattice constant due to the change in doping amount was insignificant. The melting point of the sample double-doped with Ge and In was determined to be 736 K, which was lower than the melting point (741 K) of pure Cu3SbSe4. This lowering of the melting point was attributed to the formation of a solid solution. The electrical conductivity exhibited degenerate semiconductor behavior, decreasing with increasing temperature. As the Ge and In doping content increased, the carrier concentration and electrical conductivity increased; however, when x ≥ 0.12, the electrical conductivity did not increase further. The Seebeck coefficient exhibited positive values and p-type conduction characteristics. In addition, intrinsic transitions did not occur in the measurement temperature range, and the Seebeck coefficient increased as the doping level increased. The power factor exhibited a positive temperature dependence, and Cu3Sb0.86Ge0.08In0.06Se4 exhibited the highest value of 0.89 mWm–1K–2 at 623 K. As the temperature increased, the thermal conductivity tended to decrease because of the decreased lattice thermal conductivity and slightly increased electronic thermal conductivity. All the samples exhibited minimum thermal conductivities of 0.94–1.11 Wm–1K–1 at 523 K. At high temperatures, the double doping of Ge and In improved the thermoelectric performance; thus, the dimensionless figure of merit obtained at 623 K for Cu3Sb0.86Ge0.08In0.06Se4, was 0.47.

Flexible Ag-S-Te System with Promising Room-Temperature Thermoelectric Performance.

Silver chalcogenides demonstrate great potential as flexible thermoelectric materials due to their excellent ductility and tunable electrical and thermal transport properties. In this work, we report that the amorphous/crystalline phase ratio and thermoelectric properties of the Ag2SxTe1-x (x = 0.55-0.75) samples can be modified by altering the S content. The room-temperature power factor of the Ag2S0.55Te0.45 sample is 4.9 μW cm-1 K-2, and a higher power factor can be achieved by decreasing the carrier concentration as predicted by the single parabolic band model. The addition of a small amount of excessive Te into Ag2S0.55Te0.45 (Ag2S0.55Te0.45+y) not only enhances the power factor by decreasing the carrier concentration but also reduces the total thermal conductivity due to decreased electronic thermal conductivity. Owing to the effectively optimized carrier concentration, the thermoelectric power factor and dimensionless figure of merit zT of the sample with y = 0.007 reaches, respectively, 6.2 μW cm-1 K-2 and 0.39, while the excellent plastic deformability is well maintained, demonstrating its promising potential as a flexible thermoelectric material at room temperature.

Tracking X-Ray Source Movement in a Retracting Flux Tube

Solar flares produce sources of localized, enhanced X-ray emission, thought to be due to the acceleration of nonthermal electrons and the transport of energy away from the reconnection site. The 2002 November 28 C1.6 limb flare showed clear X-ray source motion in the Reuven Ramaty High Energy Solar Spectroscopic Imager observations at 3–10 keV propagating from the apex of the flaring arcade, down toward the footpoints, and then rising back into the corona. Previous work attempted to model this motion using simulations driven by heating with an electron beam or thermal conduction front, finding reasonable agreement only if there were large initial densities. This work extends the previous model by considering a flux tube that retracts through a current sheet away from a magnetic reconnection site. The retraction model includes drag to slow motion in the current sheet, which allows us to vary the energy released by the retraction. This retraction causes a dense and superhot plug of material to form at the loop apex, naturally causing a thermal X-ray source to form in the corona. We find that the observed X-ray source motion, however, is most likely thermal and a signature of the evaporation fronts after initially filling the flux tube.

Investigation of thermoelectric response, mechanical stability and thermodynamic behavior of Sr2MgPdO6 and Sr2MgPtO6 double perovskites: A DFT insights

The Density Functional Theory (DFT) study of Sr2MgPdO6 and Sr2MgPtO6 double perovskite compounds has been carried out to explore the properties of these materials and their nature. It was observed that these compounds are formed into crystals of cubic perovskite structural arrangement which resides with the Fm-3m (No.225) space group. Electronic band structure confirmed that these double perovskite oxides are semiconductors in nature. The estimated elastic constants and other mechanical parameters confirmed the ductile nature of Sr2MgPdO6 and Sr2MgPtO6. The thermodynamic properties include entropy, internal energy, specific heat, and vibrational free energy are observed for these double perovskites. Using BoltzTrap software, the thermoelectric behavior of these materials has been investigated by calculating electrical conductivity and electronic thermal conductivity concerning scattering time, and Seebeck-coefficient. Power factor and figure of merit are also calculated with the help of these parameters to check the applicability of the materials for waste heat recovery systems and advanced technologies.

Polyaspartic polyurea/graphene nanocomposites for multifunctionality: Self-healing, mechanical resilience, electrical and thermal conductivities, and resistance to corrosion and impact

Polyurea elastomers have attracted increasingly more attention due to excellent mechanical performance, and their wide industrial applications are in need of multifunctionality such as thermal conductivity. We herein prepared polyaspartic polyurea elastomers with optimal tensile strength and fracture strain by adjusting the isocyanate index and free isocyanate content. As a class of nanofiller, isocyanate-modified graphene nanoplatelets (IP-GNPs) were developed and they formed a stable, robust interface with the polyurea matrix, resulting in mechanical reinforcement and multifunctionality. The nanocomposite at 0.05 vol% of IP-GNPs revealed a tensile strength of 15.72 ± 0.67 MPa, representing an increment of 108.21% over pure polyurea, with excellent resistance to acidic and alkali corrosion. After 9 h of post-maintenance at 60 °C, the nanocomposite reached a healing efficiency up to 80.10% as driven by hydrogen bonds. An electrical percolation threshold was observed at 3.61 vol% of IP-GNP for the nanocomposites. The thermal conductivity reached 38.49 W/m K at 7.00 vol% due to the formation of the IP-GNP network in polyurea, where the electron thermal conductivity plays a dominant role. In comparison with those high thermal conductivity values obtained by back-filling polymers into a network established beforehand, this facile approach would be highly favored in industry for the development of elastomer nanocomposites with multifunctionality for many applications, e.g. smart sensors, protective coatings, energy harvesting, etc.

Spin Seebeck effect and thermal properties of zigzag graphene nanoribbons with edge magnetism

Zigzag graphene nanoribbons (GNRs), demonstrating edge magnetism, are fascinating materials for electronic and spintronic applications. In this paper, we investigate with explicit consideration of electron-phonon scattering the Seebeck effect and thermal conductivity at various carrier densities in zigzag GNRs, which undergo antiferromagnetic, ferromagnetic, and paramagnetic transitions. Seebeck coefficients are spin dependent in ferromagnetic zigzag GNRs and can have opposite signs for the majority and the minority spin carriers, which enables the separation of spin carriers spatially under a thermal gradient. The electronic thermal conductivity is small compared to the lattice thermal conductivity, except for GNRs in the ferromagnetic state. A 100% increase in thermal conductivity is expected at antiferromagnetic to ferromagnetic transition. These results demonstrate that zigzag GNRs are also materials of high interest for spin caloritronics.

Thermoelectric Properties Investigation of Ni/Co Doped ZrCoBi Half-Heusler Alloy

Half-Heusler (HH) thermoelectric (TE) composites have been extensively inspected due to their excellent TE properties in the medium- to high-temperature range. First-principle calculations make it easier to discover or improve more HH compounds. This article presents an ab initio theoretical evaluation of TE properties of Half-Heusler alloy, when doped with Nickel (Ni), using FP-LAPW and the semi classic Boltzmann theory. Thermoelectric parameters were calculated using BoltzTraP code, like Seebeck coefficient ( ), electrical conductivity to relaxation time ratio ( ), electronic thermal conductivity to relaxation time ratio ( ), thermoelectric power factor to relaxation time ratio ( ), and the dimensionless figure-of-merit ( ) in a temperature range of . Calculated Seebeck coefficient reveals that the studied alloys show a tendency to conduct as p-type with balanced TE performance between both charge carriers (holes and electrons). A high electronic thermal conductivity value is found, which predicts a potential use in heat sink applications for the investigated alloys. Obtained results, such as a high thermoelectric power factor and , postulate that alloys could have potential thermoelectric applications.

Effects of Coulomb Blockade on the Charge Transport through the Topological States of Finite Armchair Graphene Nanoribbons and Heterostructures.

In this study, we investigate the charge transport properties of semiconducting armchair graphene nanoribbons (AGNRs) and heterostructures through their topological states (TSs), with a specific focus on the Coulomb blockade region. Our approach employs a two-site Hubbard model that takes into account both intra- and inter-site Coulomb interactions. Using this model, we calculate the electron thermoelectric coefficients and tunneling currents of serially coupled TSs (SCTSs). In the linear response regime, we analyze the electrical conductance (Ge), Seebeck coefficient (S), and electron thermal conductance (κe) of finite AGNRs. Our results reveal that at low temperatures, the Seebeck coefficient is more sensitive to many-body spectra than electrical conductance. Furthermore, we observe that the optimized S at high temperatures is less sensitive to electron Coulomb interactions than Ge and κe. In the nonlinear response regime, we observe a tunneling current with negative differential conductance through the SCTSs of finite AGNRs. This current is generated by electron inter-site Coulomb interactions rather than intra-site Coulomb interactions. Additionally, we observe current rectification behavior in asymmetrical junction systems of SCTSs of AGNRs. Notably, we also uncover the remarkable current rectification behavior of SCTSs of 9-7-9 AGNR heterostructure in the Pauli spin blockade configuration. Overall, our study provides valuable insights into the charge transport properties of TSs in finite AGNRs and heterostructures. We emphasize the importance of considering electron-electron interactions in understanding the behavior of these materials.

Thermal Conductivity for p–(Bi, Sb)2Te3 Films of Topological Insulators

In this study, we investigated the temperature dependencies of the total, crystal lattice, and electronic thermal conductivities in films of topological insulators p–Bi0.5Sb1.5Te3 and p–Bi2Te3 formed by discrete and thermal evaporation methods. The largest decrease in the lattice thermal conductivity because of the scattering of long-wavelength phonons on the grain interfaces was observed in the films of the solid-solution p–Bi0.5Sb1.5Te3 deposited by discrete evaporation on the amorphous substrates of polyimide without thermal treatment. It was shown that in the p–Bi0.5Sb1.5Te3 films with low thermal conductivity, the energy dependence of the relaxation time is enhanced, which is specific to the topological insulators. The electronic thermal conductivity was determined by taking into account the effective scattering parameter in the relaxation time approximation versus energy in the Lorentz number calculations. A correlation was established between the thermal conductivity and the peculiarities of the morphology of the interlayer surface (0001) in the studied films. Additionally, the total κ and the lattice κL thermal conductivities decrease, while the number of grains and the roughness of the surface (0001) increase in unannealed films compared to annealed ones. It was demonstrated that increasing the thermoelectric figure of merit ZT in the p–Bi0.5Sb1.5Te3 films formed by discrete evaporation on a polyimide substrate is determined by an increase in the effective scattering parameter in topological insulators due to enhancement in the energy dependence of the relaxation time.

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.