Imaginary Part Of Permittivity Research Articles

Conductive carbon black/magnetite hybrid fillers in microwave absorbing composites based on natural rubber

Abstract The study presents the microwave properties of natural rubber based composites in the 1–12 GHz frequency range as determined by the conductive carbon black/magnetite hybrid fillers obtained by impregnation at different ratios between carbon and magnetite phase. It has been established that, the changes in the investigated properties exhibit a resonance character in the 3–9 GHz range and are caused by alternations both of frequency and the ratio between the hybrid phases. The real and imaginary parts of permittivity and permeability, dielectric and magnetic loss angle tangent and conductivity have been also determined. The composite comprising a hybrid filler whose carbon:magnetite phase ratio is 90:10 has turned to be the most successful. The good microwave characteristics of the composite are related to the dielectric and magnetic losses, as well as to the achieved optimal permittivity of the composite at the given ratio of the carbon and magnetite phase. The percent content of the conductive filler has a significant impact upon EMI SE of the composites. The introduction of Fe3O4 into the hybrid filler has a crucial role for decreasing the reflection by the composites surface.

Effect of Zn2+ Substituted on Structural and Magnetic Properties of Manganese Ferrite Synthesized via Combustion Route

Solution combustion method was successfully used for the synthesis of nanocrystalline Mn1-xZnxFe2O4 with stoichiometry (x = 0, 0.1, 0.3, 0.5, 0.7, 0.9 and 1.0). The room temperature dielectric studies real and imaginary part of permittivity (epsilon' and epsilon `') were undertaken in the vide frequency range 1 MHz to 1 GHz. It was found that the real part of permittivity (epsilon') is increases with increasing in frequency and it shows a resonance behavior above 1 GHz and at much higher frequencies there is a significant decrease in the loss factor (epsilon `'). The magnetic domain relaxation was investigated by inductance spectroscopy (IS) and the observed magnetic domine relaxation frequency (f(r)) was increased with increase of grain size. It was observed that the real and imaginary part of permeability (mu' and mu `'), saturation magnetization (M-s), remnant magnetization (M-r) and magneton number decreases gradually with increasing Zn2+ concentration. The decrease in the saturation magnetization may be explained as the Zn2+ concentration increases, the relative number of ferric ions on the A sites diminishes and this reduces the A-B interaction.

Theoretical and experimental studies on EMI shielding mechanisms of multi-walled carbon nanotubes reinforced high performance composite nanofibers

Electrically conductive composite nanofibers of polyvinylpyrrolidone (PVP) filled with multi-walled carbon nanotubes (MWCNTs) were prepared by electrospinning process. The complex permittivity and electromagnetic interference shielding effectiveness (EMI SE) of all composite nanofibers were measured in the X band frequency range 8.2–12.4 GHz. The electrical conductivity, real and imaginary part of permittivity, and EMI shielding behaviors of the composite nanofibers were reported as function of MWCNTs concentration. Electrical conductivity of MWCNTs/PVP composite nanofiber followed power law model of percolation theory having a percolation threshold ϕc = 0.72 vol% (~1 wt.%) and exponent t = 1.71. The total EMI SE of MWCNTs/PVP composite nanofibers increased up to 42 dB mainly base on the absorption mechanism. The EMI SE measured from experiments was also compared with the approximate value calculated from theoretical model. The obtained theory results confirmed that the selected model presented acceptable performance for evaluating the involved parameters and prediction of the EMI SE of composite nanofibers. The ability of the theoretical model to predict the EMI shielding by reflection and absorption was found to be a function of the frequency, thickness, permittivity, and conductivity.

Effect of Neutron Flux on the Frequency Dependence of Permittivity of Nano Silicon Particles

In the present work, nano silicon is irradiated with a neutron flux (2x10 13 n ⋅cm −2 s −1) up to 20 hours at different times. In the first stage frequency dependencies of real and imaginary parts of the permittivity of nanomaterials affected by neutron flux was analysed comparatively. As a result of this analysis it is known that the permittivity of nano silicon increases under the influence of neutron flux. The dependence of real and imaginary parts of permittivity of nano silicon particles is also reviewed. Moreover, the mechanism of the observed peaks and other effects is given in the work.

Effect of Sm3+-Gd3+ co-doping on dielectric properties of Mn-Zn ferrites synthesized via combustion route

Nanocrystalline Mn0.4 Zn0.6SmxGdyFe2-(x+y)O4where x and y = 0.01,0.02,0.03,0.04 and 0.05 were synthesized by Solution combustion method. The as prepared samples were characterized by X-ray diffractometer (XRD), Transmission electron microscopy (TEM) and Vibrating sample Magnetometer (VSM) at room temperature. From the XRD the crystallite size were found increases with the increase of Sm3+-Gd3+ ions concentration while lattice parameter found to decreases. The real and imaginary part of permittivity (ε′ and ε′′) were undertaken in the wide frequency range 1GHz to 5GHz at room temperature. It is found that the real and imaginary part of permittivity’s are increasing with increasing Sm3+ and Gd3+ concentration. The magnetic behaviour of as synthesized nano ferrites reveals that, the saturation magnetization (MS), remanence magnetization (MR) is increasing with increasing Sm and Gd concentration. The g-value, peak-to-peak linewidth and spin concentration evaluated from EPR spectra correlated with cations occupancy. These electromagnetic properties clearly indicates that the synthesized materials are the good candidates for L and C band frequency.

Large Electromagnetic Wave Absorbing Bandwidth of Composites Containing Fe<sub>3</sub>O<sub>4</sub> Nanoribbons

Fe3O4 nanoribbons with the average size of $\sim 17.2$ nm $\times 64.3$ nm $\times 939.1$ nm have been synthesized by a hydrothermal method. The crystal structures have been investigated by means of the X-ray diffraction pattern refinement. The frequency dependence of permittivity and permeability for a composite containing the nanoribbons has been studied within 0.5–10 GHz. Interestingly, four resonance peaks of permeability spectra have been observed within the whole measurement frequency range. To investigate the physical origins of multiresonances, the modified exchange resonance model is used. The calculated nature resonance frequency and exchange resonance frequencies are in accordance with the experimental resonance peaks. However, four low-order resonance modes have not been found. The absence of these modes can be attributed to the dispersion of nanoribbons sizes. In addition, the imaginary part of permittivity is too small compared with the real part, indicating the insignificant contribution of dielectric loss to the electromagnetic wave absorption. What is more, large magnetic losses caused by the multiresonance phenomenon are beneficial to broadband absorption within the operating frequencies. For instance, the maximum bandwidth is larger than 4 GHz with the reflection loss less than −10 dB.

Colossal permittivity and low losses in Ba1–xSrxTiO3–δ reduced nanoceramics

The oxalate route offers a controlled approach to synthesize pure Ba1–xSrxTiO3 (BST) (0≤x≤1) nanoparticles (ϕ≈150nm in diameter). Reduced BST dense nanoceramics were obtained by spark plasma sintering (SPS) and then annealed for a short time to reach colossal permittivity (ϵ′r=105) with low dielectric losses (tan δ=0.03) at 1kHz and 300K. The effects of Ba–Sr substitution on structural, microstructural and electrical properties were analyzed. Comprehensive analysis of the electrical properties indicates that polaron hopping, mediated by Ti3+ ions and oxygen vacancies is the main contributing mechanism to colossal permittivity in Ba-rich BST compounds. Substitution of Ba by Sr reduced the contribution of polaron hopping and led to a decrease of real and imaginary parts of permittivity, while preserving interfacial polarization and yielding better temperature stability. The lowest temperature coefficient of capacitance, or TCC (variation of capacitance between 310K and 450K) value, i.e., 44ppmK−1, is obtained for SrTiO3.

Preparation, characterization and microwave absorption properties of NiFe2O4 and its composites with conductive polymer

Spinel ferrite NiFe2O4 was synthesized by polyacrylamide sol–gel method, and its composites with polyaniline (PANI) and polypyrrole (PPY) were prepared via in situ emulsion polymerization. The morphology of NiFe2O4 had a flake structure, while that of NiFe2O4/PANI and NiFe2O4/PPY composites existed a flake-grain structure. The magnetic properties (Ms, Mr and Hc) of NiFe2O4/PPY were lower than those of NiFe2O4/PANI, and they were all lower than those of NiFe2O4. NiFe2O4/PPY composite exhibited a higher conductivity value of 3.76 S/cm than that of NiFe2O4 and NiFe2O4/PANI. Moreover, the imaginary part of permittivity also enhanced with the increase of conductivity, contributing to the increase of dielectric loss. The electromagnetic characteristics of NiFe2O4, NiFe2O4/PANI and NiFe2O4/PPY were also investigated with a vector network analyzer in 1–18 GHz. The absorbing peak position moved to lower frequency with the increasing thickness of NiFe2O4/PANI or NiFe2O4/PPY composites. Under the same condition, the minimum reflection loss of NiFe2O4/PPY was much lower than that of NiFe2O4 and NiFe2O4/PANI, indicating the incorporation between NiFe2O4 and PPY could reach a better matching in terms of electromagnetic parameters. The value of the minimum reflection loss was −42 dB at 8 GHz for NiFe2O4/PPY with a thickness of 3.5 mm, and a broad peak with a bandwidth lower than −10 dB was about 4.5 GHz.

Composites prepared from the waterborne polyurethane cationomers-modified graphene. Part II. Electrical properties of the polyurethane films

The research was planned to test electrical properties of polymer films made from polyurethane cationomers with 0–2 wt.% graphene admixture. The cationomers were synthetized in the reaction of 4,4′-methylenebis(phenyl isocyanate), polycaprolactone diol (M = 2000), N-methyldiethanolamine, and formic acid. It was found that addition of approx. 2 wt.% of graphene causes the loss of volume resistivity by three orders of magnitude and percolation threshold is already set at approx. 1 wt.%. The frequency characteristic of a real part of permittivity ε′ and imaginary part of permittivity ε″ were measured for the tested films. On the base of Havriliak–Negami equation, parameters of relaxation functions in frequency domain were estimated for samples containing various contents of graphene. The influence of the cationomer phase structure on observed changes of dielectric losses coefficient tgδ in the full-measuring frequency spectrum was discussed.

Absorption properties of twinned SiC nanowires reinforced Si3N4 composites fabricated by 3d-prining

Near net- and complex shaped porous silicon nitride (Si3N4) composites reinforced with in-situ formed twinned silicon carbide (SiC) nanowires (NWs) were successfully fabricated by 3d-printing (3DP) followed by polymer precursor infiltration and pyrolysis (PIP) up to 1400°C. An increase of the PIP cycle number of the printed bodies resulted in a homogeneous distribution of SiC NWs in the fabricated composites. An increase of SiC NW content in the fabricated composites led to the growth of both the real and the imaginary parts of permittivity. The formation of twinned SiC NWs with high electrical conductivity led to a minimal electromagnetic wave RC of −57dB, demonstrating that Si3N4–SiC ceramics with the in-situ formed SiC NWs have a superior microwave absorbing ability.

Dielectric spectroscopy as a condition monitoring technique for cable insulation based on crosslinked polyethylene

Dielectric spectroscopy was evaluated as a condition monitoring technique for aged polyethylene electrical insulation in nuclear power plants. Bare core insulations of crosslinked polyethylene were aged at 55 and 85 °C under exposure to 60Co γ-radiation at different dose rates (0.42, 0.76 and 1.06 kGy h−1) to different total doses. The samples were studied by dielectric spectroscopy and tensile testing, and the crystallinity, mass fraction of soluble component and density were determined. The oxidation profiles along the depth of the insulations were assessed by infrared microscopy. The aged samples showed an increase in both the real and imaginary parts of the dielectric permittivity over the whole frequency range studied, an increase in the mass fraction of soluble component and in the material density, and a decrease in the strain-at-break. The imaginary part of the dielectric permittivity at 100 kHz increased in a linear fashion with increasing material density, the latter being strictly related to the extent of oxidation of the material according to infrared spectroscopy and differential scanning calorimetry. The generic relationship between the imaginary part of the permittivity and the density included all the data obtained under different ageing conditions. The results suggest that dielectric spectroscopy can be used for in-situ measurements of the degree of oxidation of polyethylene cables, in order to obtain information about the condition of the cable insulation to enable the remaining lifetime to be predicted.

Dielectric Properties of Composite Films Made from Tin(IV) Oxide and Magnesium Oxide

Impedance spectroscopy (IS) subsumes the small signal measurement of the linear electrical response of a material of interest including electrode effects and the subsequent analysis of the response to yield useful information about physicochemical properties of the systems. In the majority of cases, the nanostructured films are better represented by a more complicated network of resistances and capacitances, so-called equivalent circuit. IS analysis generally makes a considerable use of these equivalent circuits. Films made from SnO2 and MgO have been taken into consideration and analyzed using IS to find the dielectric properties. Analyzing the Nyquist plots, the sheet resistance of the CTO glass was found to be around 610 Ω. But the parallel resistance of the film varied dramatically while altering the composition. 10% of MgO in the SnO2/MgO composite showed a high impedance which is in two orders of magnitude higher than pure MgO. This is due to the confinement of electrons in quantum well structure formed by layer of MgO around SnO2 particles. The dielectric loss is also found to be minimal at this composition. The variation of real and imaginary parts of permittivity of the composite films of SnO2 and MgO are being discussed for different compositions in this study. SnO2 and MgO composite films of 10% MgO could find applications in devices such as capacitors and thin film transistors to be used as a novel dielectric. DOI: http://dx.doi.org/10.4038/ouslj.v7i0.7308 OUSL Journal Vol.7 2014: 67-75

Electrical properties of FeII -terpyridine-Modified cellulose nanocrystals and polycaprolactone/FeII -CTP nanocomposites

Supramolecular crosslinked FeII-terpyridine cellulose nanocrystals (Fe-CTP) were prepared by surface modification of cellulose nanocrystals with 4′-chloro-2,2′:6′,2″-terpyridine and subsequent reaction with Fe(II)SO4. The prepared complex was characterized using transmission electron microscopy (TEM), ultraviolet spectroscopy (UV), thermogravimetric analysis (TGA), and measuring its electrical properties at temperatures from 25 to 70°C. Use of Fe-CTP at loadings from 1% to 10% (wt. ratio) in nanocomposites with polycaprolactone polymer was investigated; the nanocomposites were characterized regarding their electrical properties, which studied using broadband AC-relaxation spectroscopy in the frequency range between 0.1 Hz and 1 MHz. The results were compared to that of PCL nanocomposites containing multiwalled carbon nanotubes (CNT). Variation in real and imaginary parts of permittivity has been explained on the basis of interfacial polarization of fillers in the polymer medium. The percolation limit of the conductive CNT and Fe-CTP as studied by ac conductivity measurements has also been reported. Fe-CTP showed conductivity values in the range of semiconductors. PCL/Fe-CTP nanocomposites showed conductivity values from 1.98 × 10−11 to 3.76 × 10−6 while PCL/CNT nanocomposites showed conductivity values from 1.4 × 10−10 to 3.67 × 10−4 S/m for 1–10 wt% CNT content. POLYM. COMPOS., 2015. © 2015 Society of Plastics Engineers

Conduction mechanism, impedance spectroscopic investigation and dielectric behavior of La0.5Ca0.5-xAgxMnO3 manganites with compositions below the concentration limit of silver solubility in perovskites (0 ≤ x ≤ 0.2).

This study presents the electrical properties, complex impedance analysis and dielectrical behavior of La0.5Ca0.5-xAgxMnO3 manganites with compositions below the concentration limit of silver solubility in perovskites (0 ≤ x ≤ 0.2). Transport measurements indicate that all the samples have a semiconductor-like behavior. The metal-semiconductor transition is not observed across the whole temperature range explored [80 K-700 K]. At a specific temperature, a saturation region was marked in the σ (T) curves. We obtained a maximum σdc value at ambient temperature with the introduction of 20% Ag content. Two hopping models were applied to study the conduction mechanism. We found that activation energy (Ea) related to ac-conductivity is lower than the Ea implicated in dc-conductivity. Complex impedance analysis confirms the contribution of grain boundary to conductivity and permits the attribution of grain boundary capacitance evolution to the temperature dependence of the barrier layer width. From the temperature dependence of the average normalized change (ANC), we deduce the temperature at which the available density of trapped charge states vanishes. Such a temperature is close to the temperature at which the saturation region appears in σ(T) curves. Moreover, complex impedance analysis (CIA) indicates the presence of electrical relaxation in materials. It is noteworthy that relaxation species such as defects may be responsible for electrical conduction. The dielectric behavior of La0.5Ca0.5-xAgxMnO3 manganites has a Debye-like relaxation with a sharp decrease in the real part of permittivity at a frequency where the imaginary part of permittivity (ε'') and tg δ plots versus frequency demonstrate a relaxation peak. The Debye-like relaxation is explained by Maxwell-Wagner (MW) polarization. Experimental results are found to be in good agreement with the Smit and Wijn theory.

Cobalt ferrite sphere-coated buckhorn-like barium titanate: Fabrication, characterization, its dielectric resonance, and microwave attenuation properties

Barium titanate (BTO) with different morphology is prepared through hydrothermal method using titania spheres as precursor, then calcined at different temperatures and ultimately coated with cobalt ferrite (BTO/CFO). The dielectric dispersion of the composite containing BTO (75 wt. % ratio in paraffin wax) shows evidence of resonance behaviour in the microwave spectrum, rather than the usually observed relaxation mode. The imaginary part of permittivity (ε″) displays a strong peak in the 10–13 GHz frequency region, especially for buckhorn-like BTO (hydrothermally synthesized at 110 °C and calcined at 1100 °C). The dielectric response anomaly of BTO in special morphology is due to the emission of plane acoustic waves caused by electrostrictive and converse piezoelectric effects. An accepted model is adopted to simulate the resonance frequency. The minimum reflection loss of cauliflower-like BTO (hydrothermally synthesized at 110 °C, then calcined at 600 °C for 2 h, 75 wt. % ratio) in paraffin wax reaches −30.831 dB at 10.56 GHz with a matching thickness of 2 mm, lower than all the reported values. When the sintering temperature is changed to 1100 °C (buckhorn-like BTO), the minimum reflection loss value is −24.37 dB at 12.56 GHz under the thickness of 3 mm. After combination with CFO, the value reaches −42.677 dB when the thickness is 5.6 mm. The ginger-like BTO (hydrothermally synthesized at 200 °C and calcined at different temperatures) is inferior in microwave reflection reduction. The electromagnetic interference shielding effectiveness of buckhorn-like BTO composite is calculated to be −12.7 dB (94.6% shielding) at resonance frequency (2 mm, 11.52 GHz). This work clearly shows the potential to tune the dielectric property of ferroelectrics through control of morphology, facilitating new comprehension of the ferroelectrics in microwave regime.

The Electromagnetic Parameters' Impact of λ/4 Type Dielectric Absorber on Absorbing Properties

This paper studies electromagnetic parameters' impact of λ/4 type dielectric absorber on absorbing properties. Calculation shows that the maximum absorption amount is corresponding to specific values of K and R when absorber's permittivity is stable, when the thickness of material is determined and the real part permittivity is increased, the absorption peaks move to lower frequency and reduce the distance between adjacent peaks, while the imaginary part of permittivity and resistance of membrane resistance only affect absorption peaks' amount but have no effect on the peaks' position. Accordingly, it is reasonable to adjust the material's electromagnetic parameters according to the above rule when the high-performance λ/4 dielectric-type absorber is prepared.

Physico-chemical properties of the thin films of the SbxSe100 − x system (x = 90, 85, 80)

The bulk samples of SbxSe100−x system (x=90, 85, 80) and their amorphous thin films were prepared by flash evaporation method. The films possess good thermal stability and high values of the activation energy of crystallization. The activation energy of crystallization (Ea) of the thin films Sb85Se15 and Sb80Se20 was found to be 2.97 and 2.55eV, respectively. The Ea of Sb90Se10 was found to be 1.79eV for first step and 2.95eV for second step. The homogeneous thin amorphous films were crystallized by nanosecond laser pulses, by annealing at 235 and 360°C and during the measurement of temperature dependence of electrical resistivity. The crystalline phase possesses much lower electrical resistivity than the amorphous one (ΔRs≈103); the temperature of crystallization Tc is from the region of 150–161°C. The structure of prepared films as determined by X-ray diffraction analysis revealed that the films crystallized by laser pulses and by annealing at 235°C contain only one phase of Sb-like structure. The films of composition Sb80Se20 and Sb85Se15 annealed at 360°C contain two phases of Sb and Sb2Se3. The film of composition Sb90Se10 annealed at 360°C contains one phase of Sb-like structure. The optical reflectivity change due to crystallization is also large (ΔRopt.≈20–30%). The refractive index n of crystalline samples is higher than that of amorphous films (Δn≈1.5–3.1 for transparent part of spectrum); it is higher for films with higher Sb content. The real and imaginary parts of permittivity, evaluated from ellipsometric measurement, are also much higher for crystalline state (up to 55) than for the amorphous one (<33). The amorphous films are semiconductive, and their Egopt. (0.28–0.35eV) is decreasing with an increasing content of Sb. In spectral region of λ=360–830nm, the real part of permittivity of crystalline phase is negative and the imaginary part of permittivity is not high, especially for the Sb90Se10 samples. Such films are perspective not only as the phase change materials, but also as the plasmonic materials.

Gate-opening gas adsorption and host-guest interacting gas trapping behavior of porous coordination polymers under applied AC electric fields.

The gate-opening adsorption behavior of the one-dimensional chain compound [Ru2(4-Cl-2-OMePhCO2)4(phz)] (1; 4-Cl-2-OMePhCO2(-) = 4-chloro-o-anisate; phz = phenazine) for various gases (O2, NO, and CO2) was electronically monitored in situ by applying ac electric fields to pelletized samples attached to a cryostat, which was used to accurately control the temperature and gas pressure. The gate-opening and -closing transitions induced by gas adsorption/desorption, respectively, were accurately monitored by a sudden change in the real part of permittivity (ε'). The transition temperature (TGO) was also found to be dependent on the applied temperature and gas pressure according to the Clausius-Clapeyron equation. This behavior was also observed in the isostructural compound [Rh2(4-Cl-2-OMePhCO2)4(phz)] (2), which exhibited similar gate-opening adsorption properties, but was not detected in the nonporous gate-inactive compound [Ru2(o-OMePhCO2)4(phz)] (3). Furthermore, the imaginary part of permittivity (ε″) effectively captured the electronic perturbations of the samples induced by the introduced guest molecules. Only the introduction of NO resulted in the increase of the sample's electronic conductivity for 1 and 3, but not for 2. This behavior indicates that electronic host-guest interactions were present, albeit very weak, at the surface of sample 1 and 3, i.e., through grain boundaries of the sample, which resulted in perturbation of the conduction band of this material's framework. This technique involving the in situ application of ac electric fields is useful not only for rapidly monitoring gas sorption responses accompanied by gate-opening/-closing structural transitions but also potentially for the development of molecular framework materials as chemically driven electronic devices.

Thermodynamic calculations and kinetic verifications on the chemical vapor deposition process of Si–C–N ceramic from the SiCl3CH3–NH3–H2–Ar precursors

Based on the Gibbs principle of minimum free energy and Factsage software, the thermodynamic phase diagram and three-dimensional yield map were firstly calculated from the SiCl3CH3–NH3–H2–Ar system. The effects of temperature, total pressure, reactant ratios of 3[NH3]/[SiCl3CH3] and [H2]/[SiCl3CH3] on the formation and yield of condensed phases were discussed. Predominant condensed phases at equilibrium were SiC, Si3N4 and graphite phases. The concentration of condensed phase products was used to confirm the composition of Si–C–N. Through the kinetic verification at 1173.15K, it could be demonstrated that Si–C–N ceramics are obtained by chemical vapor deposition from the SiCl3CH3–NH3–H2–Ar system. The deposits were amorphous and mainly constituted by C–C, Si–N and Si–C bonds from XPS analysis, which were well consistent with the results of thermodynamic calculation. The real part and the imaginary part of permittivity were approximately 4 and 0, respectively, which indicated the amorphous deposits possess the low dielectric constant and loss.

Simulation and uncertainty quantification in high temperature microwave heating

Microwave heating processes are highly sensitive to variability in the operating frequency and usually there are high uncertainties associated with measurements of the material's imaginary permittivity. Therefore, the harmonic Maxwell's equations and time dependent heat equation are considered for the simulation of high temperature ceramic microwave heating with uncertain operating frequency and dielectric constants. To analyze the uncertainty of the system, the Non-Intrusive Spectral Projection Method (NISP) is used based on the Polynomial Chaos expansion. The conclusions of this work indicate that 13 Gauss collocation points and a polynomial degree of 11 must be used with the NISP in order to obtain accurate results. Furthermore it also adds that uncertainty in frequency leads to high values of variability in the stochastic solution. The uncertainty in the material's imaginary part of permittivity has only a significant impact for high temperatures of the material. Temperature probability density functions, error bars and standard deviations characterize the material heating up to high temperatures.