Thermal Conductivity Measurements Research Articles

A high geothermal setting in the Linyi geothermal field: Evidence from the lithospheric thermal structure

The lithospheric thermal structure has a profound indicative significance for the potential evaluation and exploration of geothermal resources. The Linyi geothermal field, located in the southern section of the Yishu fault in Shandong Province, boasts abundant geothermal resources. However, its origin is still unclear. This study analyzed the characteristics of terrestrial heat flow using the temperature logging of geothermal wells and measurements of thermal conductivity and heat production. Combined with the geophysical information of the Xiangshui (Jiangsu Province)-Mandula (Nei Mongol) geoscience transect and the lithology revealed by the geothermal wells, this study built a conceptual model of the lithospheric thermal structure using the one-dimensional steady-state heat conduction equation. Based on this model, the heat flow is 64.9 mW/m2, indicating a high geothermal setting in the study area. Furthermore, the ratio of crustal to mantle heat flow is < 1 (0.67), implying that surface heat flow originates predominantly from the mantle. The Yishu fault probably acts as a pathway for heat transfer from the mantle. The temperature of the Moho boundary in the study area was estimated to be 614.8 °C. The Curie depth was calculated to be 29.5 km (585 °C), which is consistent with the depth estimated using the aeromagnetic data. In sum, the Linyi geothermal field has a high geothermal setting, which contributes to the formation of geothermal resources.

Development and investigation of thermal composite insulation from environmentally hazardous waste fly ash

Researchers all over the world are working on developing fly ash (FL-A) utilization technologies and turning the environmentally hazardous waste into a useful product. In the present study, an attempt to develop FL-A thermal insulation was made. Three thermal composite insulation were prepared with combination of FL-A (40, 60 and 70%), Sand (40, 20 and 10%), Cement (10, 5 and 15%) and Perlite (10, 15 and 5%) with water curing. The sequence of preparation of mixture was modified to improve the samples strength, and investigated for thermal conductivity. The samples with 60% FLA showed the lowest thermal conductivity of 0.1388, 0.136, and 0.1601 W/mK for thicknesses of 30 mm, 50 mm, and 70 mm, respectively, compared to other samples. The optimal composition was obtained in the sample with a ratio of FL-A: S: C: P = 60:20:5:15. The minimum density (750 kg/m3) was obtained. An optimized composite specimen shows the best thermal resistance with the thermal conductivity (k = 0.1388 W/mK) measured by the thermal conductivity measurement apparatus. The properties of the composites will help in estimating their suitability and potential for various commercialized applications in thermal insulation, thus also utilizing waste and reducing environmental concerns.

Quantifying Interfacial Bonding Using Thermal Boundary Conductance at Cubic Boron Nitride/Copper Interfaces with a Large Mismatch of Phonon Density of States.

Interfacial bonding that directly influences the functional and mechanical properties of metal/nonmetal composites is commonly estimated by destructive pull-off measurements such as scratch tests, etc. However, these destructive methods may not be applicable under certain extreme environments; it is urgently necessary to develop a nondestructive quantification technique to determine the composite's performance. In this work, the time-domain thermoreflectance (TDTR) technique is applied to study the inter-relationship between interfacial bonding and interface characteristics through thermal boundary conductance (G) measurements. We think that interfacial phonon transmission capability plays a decisive role in influencing interfacial heat transport, especially for scenarios with a large mismatch of phonon density of states (PDOS). Moreover, we demonstrated this method at (100) and (111) cubic boron nitride/copper (c-BN/Cu) interfaces by both experimental and simulation efforts. The results show that the TDTR-measured G of the (100) c-BN/Cu interface (30 MW/m2·K) is about 20% higher than that of the (111) c-BN/Cu (25 MW/m2·K), which is ascribed to that higher interfacial bonding of the (100) c-BN/Cu endows it with better interfacial phonon transmission capability. In addition, detailed comparison of 10+ other metal/nonmetal interfaces exhibits similar positive relationship for interfaces with a large PDOS mismatch but negative relationship for interfaces with a small PDOS mismatch. The latter one is attributed to that extra inelastic phonon scattering and electron transport channels abnormally promoting interfacial heat transport. This work may provide some insights into quantitatively establishing inter-relationship between interfacial bonding and interface characteristics.

Convergence criteria analysis for thermal conductance measurements of building walls: A case study

The significance of on-site measurements for the thermal characterization of building components is widely recognized. Walls thermal performance can be identified through the widely used Heat-Flow Meter (HFM) method, which has been frequently applied in literature. However, only a few scientific works have examined the convergence criteria suggested by the ISO 9869–1. Starting from this, the aim of this work is evaluating the convergence criteria in a case study using the progressive average method. Thermal conductance (C-value) measurements were carried out in a small-scale building, placed in the external area of a building school site near Rome (Italy). The building is internally equipped with an electric heating system. Heat-flux sensor and surface temperature probes were applied to assess the C-value of the envelope. The different switching-on of the heater characterized by different power levels and the reaching of regular thermal conditions after initial transients were considered to evaluate the acquired data and their influence on the results. The known walls stratigraphy allowed to compute and compare theoretical and experimental C-values. Based on the examined data, it is possible to assert that the convergence conditions are very strict, mainly due to the third criterion.

Estimating soil water retention curves from thermal conductivity measurements: A percolation-based effective-medium approximation

A soil water retention curve (SWRC) describes the relationship between soil water content (θ) and suction (h, also the absolute value of pressure head). Earlier work indicated that correlations existed between the percolation-based effective medium approximation (P-EMA) thermal conductivity (λ) model parameters and soil hydraulic properties. In this study, the critical water content (θc) of the P-EMA model was related to the pore size distribution parameter (m) of the van Genuchten model, water content at the inflection point of a SWRC (θi) and hydraulic continuity water content (θhc). And a pedo-transfer function was established to estimate the van Genuchten model parameter α from soil properties and P-EMA parameters. Based on these relationships, three approaches were developed to estimate the van Genuchten models parameters from λ(θ) measurements, porosity, sand and clay contents. The three approaches were then validated on six independent soils, and results showed that all of the approaches estimated θ well at selected h values, with the average root mean square errors from 0.025 to 0.029 cm3 cm−3, the average mean relative absolute errors ranging from 0.111 to 0.157, and the average Akaike Information Criterion from −18.3 to −16.2. Two new approaches outperformed the original Fu et al approach but with fewer input parameters (no need for organic carbon content), thus also facilitating their broader application.

Measurement of thermal conductivity of the cortical bone: experimental studies and comparative analysis

Thermal conductivity is an ambiguous material property of bone tissue that directly impacts the surgical procedure and the patient’s convalescence (thermal necrosis). The study aimed to determine the thermal coefficient experimentally and compare the results with previous results. The comparative method was used with the reference material, PMMA, with a coefficient value of 0.167 W*(mK)−1 to measure the thermal conductivity. Thanks to the obtained results, the thermal diffusivity coefficient was also determined. The results allowed to choose the coefficient of thermal conductivity at the level: 0.26-0.34 W*(mK)−1 and thermal diffusivity: 0.103-0.135 mm2*s−1. The confrontation of the results established their compliance with the latest research. The thermal conductivity coefficient varies depending on the condition of the tissue (dry or fresh) and its porosity. Due to its anisotropic structure, bone tissue can change its thermal properties depending on its location (body or head). Further extensive experimental evaluation of these properties is required.

Changes in Thermal Conductivity of the Rocks of the West Siberian Basin Lithosphere in the Vicinity of the Tumenskaya SG-6 Well

Numerical reconstructions of the thermal regime of the lithosphere of the West Siberian basin in the Koltogor-Urengoi graben in the vicinity of the Tyumenskaya SG-6 superdeep well are used to analyze the depth distribution of thermal conductivity of basin rocks. Five depth intervals which differ in the character of changes in thermal conductivity of rocks are distinguished: the permafrost zone, the sedimentary section below this zone, the zone of anomalous rock weakening, the consolidated crust, and the mantle. The algorithms for calculating the thermal conductivity are considered and the main factors affecting its change with depth are determined for each of the five intervals. A sharp decrease in the thermal conductivity of rocks in the bottom part of the sedimentary cover and in the basement top in the vicinity of the SG-6 well is associated with rock weakening due to tectonic fracturing and hydrothermal erosion. The analysis suggests that the stationarity conditions of the process are not observed in optical scanning thermal conductivity measurements and, therefore, this method may overestimate the true thermal conductivity of rocks.

Thermal contact resistance measurement between two intersecting PAN type carbon fibers using the T-type 3ω method

The prediction of the effective thermal conductivity of composites filled with carbon fibers requires the knowledge of the microstructure, the relative amount and thermal properties of filler and matrix materials, the orientation of non-isometric filler phases and the thermal contact resistances between fibers and matrix and also between fibers. However, information at small scale are often missing especially thermal contact resistances. The present work describes the measurement of the thermal contact resistance (TCR) between two crossed carbon fibers which is performed by an adaptation of the T-type 3ω method for thermal conductivity measurement of wires. The first carbon fiber is connected to two copper blocks supplied by a modulated electrical current providing a volumetric heating. The second fiber fixed on a U-shape holder is delicately implemented over the first one. After performing a secondary vacuum, the 3ω voltage V3ω of the first fiber is recorded as function of the frequency of the modulated current. Knowing the applied force, the contact area between the two carbon fibers is calculated from bending and deformations then a 3D numerical model describing heat transfer in two crossed carbon fibers is used to estimate the TCR at their intersection. In addition, a detailed sensitivity analysis of the unknown parameter TCR is performed allowing to find optimal operating conditions especially the frequency range. Measurements are performed with PAN type carbon fibers (FT300B) picked up from the same bundle. Different TCR estimations were performed by fitting numerical and computed V3ω voltage as function of frequency. Finally, values of TCR between crossed carbon fibers were found equal (10.4 ± 10.1) 105 kW−1 which provides an order of magnitude for such phenomenon.

A microfluidic strategy for accessing the thermal conductivity of liquids at different temperatures

Biomass-based biofuels represent a promising alternative fossil energy source, for which conversion processes - mostly performed at high pressure and temperature conditions - require thermophysical property data, particularly thermal conductivity. Conventional methods to measure thermal conductivity are often time consuming and/or need important quantities of products. Microfluidics has been proven to be a viable solution to these issues thanks to its low reagent consumption, fast screening capabilities, improvement of heat and mass transfers etc. However, microfabrication materials used in previous works, do not exhibit sufficient chemical inertness, nor thermomechanical properties to apply such methods to large ranges of fluids systems and conditions. Here, we develop new microreactors including sensors integrated into microfluidic channels with an operating principle based on the transient thermal offset approach for thermal conductivity measurement, built with materials commonly used for microreactors operated in harsh conditions. The sensor calibration is performed on water/ethanol mixtures and externally validated for two fluids: n-pentadecane and ethan-1,2-diol along with the evolution of their thermal conductivity with temperature. Finally, the microfluidic device is used to generate thermal conductivity data for 2,5-dimethylfuran, a biomass-based compound with high potential as biofuel and for which experimental data has not been reported so far.

Possible evidence of Weyl fermion enhanced thermal conductivity under magnetic fields in the antiferromagnetic topological insulator Mn(Bi1−xSbx)2Te4

We report thermal conductivity and Seebeck effect measurements on $\text{Mn}{({\text{Bi}}_{1\ensuremath{-}x}{\text{Sb}}_{x})}_{2}{\text{Te}}_{4}$ (MBST) with $x=0.26$ under applied magnetic fields below $50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Our data shows clear indications of the electronic structure transition induced by the antiferromagnetic (AFM) to ferromagnetic (FM) transition driven by applied magnetic field as well as significant positive magnetothermal conductivity in the Weyl semimetal state of MBST. Further, by examining the dependence of magnetothermal conductivity on field orientation for MBST and comparison with the magnetothermal conductivity of ${\text{MnBi}}_{2}{\text{Te}}_{4}$, we see possible evidence of a contribution to thermal conductivity due to Weyl fermions in the FM phase of MBST. From the temperature dependence of the Seebeck coefficient under magnetic fields for MBST, we also observed features consistent with the Fermi surface evolution from a hole pocket in the paramagnetic state to a Fermi surface with coexistence of electron and hole pockets in the FM state. These findings provide further evidence for the field-driven topological phase transition from an AFM topological insulator to a FM Weyl semimetal.

Thermal Conductivity of Carbon/Boron Nitride Heteronanotube and Boron Nitride Nanotube Buckypapers: Implications for Thermal Management Composites.

To date, there has been limited reporting on the fabrication and properties of macroscopic sheet assemblies (specifically buckypapers) composed of carbon/boron nitride core-shell heteronanotubes (MWCNT@BNNT) or boron nitride nanotubes (BNNTs). Herein we report the synthesis of MWCNT@BNNTs via a facile method involving Atmospheric Pressure Chemical Vapor Deposition (APCVD) and the safe h-BN precursor ammonia borane. These MWCNT@BNNTs were used as sacrificial templates for BNNT synthesis by thermal oxidation of the core carbon. Buckypaper fabrication was facilitated by facile sonication and filtration steps. To test the thermal conductivity properties of these new buckypapers, in the interest of thermal management applications, we have developed a novel technique of advanced scanning thermal microscopy (SThM) that we call piercing SThM (pSThM). Our measurements show a 14% increase in thermal conductivity of the MWCNT@BNNT buckypaper relative to a control multiwalled carbon nanotube (MWCNT) buckypaper. Meanwhile, our BNNT buckypaper exhibited approximately half the thermal conductivity of the MWCNT control, which we attribute to the turbostratic quality of our BNNTs. To the best of our knowledge, this work achieves the first thermal conductivity measurement of a MWCNT@BNNT buckypaper and of a BNNT buckypaper composed of BNNTs not synthesized by high energy techniques.

Thermal Flow Meter with Integrated Thermal Conductivity Sensor.

This paper presents a novel gas-independent thermal flow sensor chip featuring three calorimetric flow sensors for measuring flow profile and direction within a tube, along with a single-wire flow independent thermal conductivity sensor capable of identifying the gas type through a simple DC voltage measurement. All wires have the same dimensions of 2000 μm in length, 5 μm in width, and 1.2 μm in thickness. The design theory and COMSOL simulation are discussed and compared with the measurement results. The sensor's efficacy is demonstrated with different gases, He, N2, Ar, and CO2, for thermal conductivity and thermal flow measurements. The sensor can accurately measure the thermal conductivity of various gases, including air, enabling correction of flow rate measurements based on the fluid type. The measured voltage from the thermal conductivity sensor for air corresponds to a calculated thermal conductivity of 0.02522 [W/m·K], with an error within 2.9%.

Thermal conductivity controlled by a segregated network prepared using carbon nanotube/polyamide 6 composite with glass bubbles

AbstractIn this study, a carbon nanotube‐glass bubble/polyamide 6 (CNT‐GB/PA6) multiscale hybrid composite was manufactured. Through a coagulation process including CNT and GB, a segregated network was formed to produce a composite structure with tunable thermal conductivity. Within the segregated network structure, a complex phenomenon of decrease and increase in thermal conductivity owing to the interaction by CNT and GB, and an equation to predict thermal conductivity through the contents of GB and CNT was formulated. A model to predict the thermal conductivity using the RSM analysis was presented, and the contents of GB and CNT were adjusted according to the required thermal conductivity. It was confirmed through the LFA thermal conductivity measurement that the thermal conductivity increased with GB and CNT contents. Moreover, when 30% of GB was added to the 5 wt% CNT composite, the thermal conductivity increased by about 17%. However, in the experiment to confirm the effect of GB alone, it was confirmed that the thermal conductivity decreased as the GB content increased. Thus, the size of the structural path, which was controlled by the GB content through which electrons pass, played an important role in this study. The results of this study can be used in astronautic fields that require insulation to save energy and in construction engineering where thermal insulation and heat emission are important.

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.

Measurement of Thermal Conductivity of Epoxy Resin Reinforced With Different Weight Ratios of Glass and Carbon Powders

The effect of thermal conductivity was studied on the composites prepared before and after reinforcement with different weight fractions (10, 20, 30, 40, 50, 60 wt %), using a Disc Lee's device, and the dispersion of the filler was studied by morphological analysis of the complexes using scanning electron microscopy (SEM). The (SEM) of glass composite powders, showed a smooth surface with a chance of forming very few voids, clusters and blisters on the surface of the sample, which increased with the increase of the weight fractions of the filled powder. While the composites filled with carbon powders show smooth and free from micro-cracks with the chance of formation of some flakes on the surface, whereby, as the weight concentrations of powders rise, transform to rough surface with micro-cracks and voids which revealing that the surface was porous. The results also showed that adding these powders to the epoxy resin has an effect on the thermal conductivity of the prepared composites, implying that there is a direct relationship between the thermal conductivity as a function of the weight ratios of the reinforcing materials, as the thermal conductivity values increase with the increase in the weight ratios for all samples, but differ from one reinforcement to another, with the highest value being at a weight ratio of (60 wt %), which raised the conductivity by (34.511%±0.031) and (26.488%±0.045) for glass and carbon composites, respectively, in comparison to pure epoxy resin. The results also revealed that the thermal conductivity of epoxy glass composites is greater than that of carbon composites at all reinforcing material weight fractions.

Measurement of Thermal Conductivity of Epoxy Resin Reinforced With Different Weight Ratios of Glass and Carbon Powders

Measurement of Thermal Conductivity of Epoxy Resin Reinforced With Different Weight Ratios of Glass and Carbon Powders

Thermal conductance and noise of Majorana modes along interfaced ν=52 fractional quantum Hall states

We study transport along interfaced edge segments of fractional quantum Hall states hosting non-Abelian Majorana modes. With an incoherent model approach, we compute, for edge segments based on Pfaffian, anti-Pfaffian, and particle-hole-Pfaffian topological orders, thermal conductances, voltage biased noise, and delta-$T$ noise. We determine how the thermal equilibration of edge modes impacts these observables and identify the temperature scalings of transitions between regimes of differently quantized thermal conductances. In combination with recent experimental data, we use our results to estimate thermal and charge equilibration lengths in real devices. We also propose an experimental setup which permits measuring several transport observables for interfaced fractional quantum Hall edges in a single device. It can, e.g., be used to rule out edge reconstruction effects. In this context, we further point out some subtleties in two-terminal thermal conductance measurements and how to remedy them. Our findings are consistent with recent experimental results pointing towards a particle-hole-Pfaffian topological order at filling $\nu=5/2$ in GaAs/AlGaAs, and provide further means to pin-point the edge structure at this filling and possibly also other exotic fractional quantum Hall states.

Picosecond magneto-optic thermometry measurements of nanoscale thermal transport in AlN thin films

The thermal conductivity Λ of wide bandgap semiconductor thin films, such as AlN, affects the performance of high-frequency devices, power devices, and optoelectronics. However, accurate measurements of Λ in thin films with sub-micrometer thicknesses and Λ > 100 W m−1 K−1 is challenging. Widely used pump/probe metrologies, such as time–domain thermoreflectance (TDTR) and frequency–domain thermoreflectance, lack the spatiotemporal resolution necessary to accurately quantify thermal properties of sub-micrometer thin films with high Λ. In this work, we use a combination of magneto-optic thermometry and TiN interfacial layers to significantly enhance the spatiotemporal resolution of pump/probe thermal transport measurements. We use our approach to measure Λ of 100, 400, and 1000 nm AlN thin films. We coat AlN thin films with a ferromagnetic thin-film transducer with the geometry of (1 nm-Pt/0.4 nm-Co)x3/(2 nm-TiN). This PtCo/TiN transducer has a fast thermal response time of <50 ps, which allows us to differentiate between the thermal response of the transducer, AlN thin film, and substrate. For the 100, 400, and 1000 nm thick AlN films, we determine Λ to be 200 ± 80, 165 ± 35, and 300 ± 70 W m−1 K−1, respectively. We conclude with an uncertainty analysis that quantifies the errors associated with pump/probe measurements of thermal conductivity, as a function of transducer type, thin-film thermal conductivity, and thin-film thickness. Time resolved magneto-optic Kerr effect experiments can measure films that are three to five times thinner than is possible with standard pump/probe metrologies, such as TDTR. This advance in metrology will enable better characterization of nanoscale heat transfer in high thermal conductivity material systems like wide bandgap semiconductor heterostructures and devices.

Ultrasonic Velocity, Viscosity and Thermal Conductivity Studies on Barium Oxide: Silicone Oil Nanofluids

In this study, we focused on the preparation and characterization of Barium oxide (BaO): Silicone oil nanofluids with the assistance of ultrasonication. The purpose was to investigate the potential impact of these nanofluids on solar radiation absorption. To achieve this, six different concentrations (ranging from 0.01 g to 0.06 g) of BaO: Silicone oil nanofluids were prepared. The nanofluids were subjected to various characterization techniques to evaluate their properties. Ultrasonic velocity measurements were conducted to assess the dispersion quality and stability of the nanofluids. Fourier transform infrared (FTIR) spectroscopy was utilized to examine any potential interactions between the nanoparticles and the fluid medium. Ultraviolet-Visible (UV-Visible) spectroscopy was employed to investigate the optical properties of the nanofluids, particularly their ability to absorb solar radiation. Additionally, electron microscopy analysis provided insights into the morphology and size distribution of the BaO nanoparticles. The results obtained from the UV-Visible analysis provided valuable information regarding the solar radiation absorption efficiency of the BaO: Silicone oil nanofluid systems. These findings contribute to our understanding of the potential application of these nanofluids in solar energy harvesting. Furthermore, the ultrasonic studies and FTIR analysis confirmed that there were no significant particle-fluid interactions, indicating the stability of the nanofluids. Thermal conductivity measurements were carried out to determine the heat transfer efficiency of the BaO: Silicone oil nanofluid system at different concentrations. The results revealed an optimal concentration that exhibited the highest heat transfer efficiency, suggesting the potential of these nanofluids for enhancing heat transfer processes. In conclusion, this study successfully prepared and characterized BaO: Silicone oil nanofluids. The analysis of their optical properties, stability, and thermal conductivity provides valuable insights into their potential application in solar radiation absorption and heat transfer systems. Further research can explore the practical implementation of these nanofluids in solar energy conversion and thermal management technologies.

Physical properties of the full Heusler-type Ru2-Fe NbAl (x = 0.00–0.50) alloys

We report the physical properties of a series of full Heusler-type Ru2-xFexNbAl (x = 0.00–0.50) alloys using magnetization, electrical resistivity (ρ), Seebeck coefficient (S), and thermal conductivity (κ) measurements. Structure and phase analysis via x-ray diffraction and scanning electron microscopy indicate that Fe replaces the Ru in Ru2NbAl, and the antisite disorders reduce. The dc magnetization shows predominantly paramagnetic behavior for all Fe-doped samples, as in the pristine Ru2NbAl sample. Interestingly, the electrical resistivity measurements reveal that the conduction behavior of Ru2NbAl alloy changes from semiconducting-like to metal-like with Fe substitution. In addition, a minimum in resistivity at low temperatures is observed in the Fe-doped samples. It is noted that the minimum shifts to low temperatures with Fe content, presumably due to the weak localization effect. The Seebeck coefficient measurements show that charge carriers of these alloys remain hole type with a maximum S value of ∼27 µV/K at 300 K for x = 0.13, a result of the modification of the electronic band structure. The Fe substitution is found to reduce thermal conductivity significantly. An analysis of the lattice thermal conductivity indicates that the reduction in κ is primarily due to more grain boundaries, Umklapp phonons, and electron scatterings. These observations lead to an increase in the thermoelectric performance, i.e., the figure of merit and power factor, to about 0.007 and 1.7 μW/cm K2 at 300 K for the optimized composition of Fe with x = 0.13.