Conduction Process Research Articles

Modeling Thermal Impedance of IGBT Devices Based on Fractional Calculus Techniques

The thermal impedance characteristics of insulated gate bipolar transistor (IGBT) modules are critical for the thermal management and design of electronic devices. This paper proposes a fractional-order equivalent thermal impedance model, which is inspired by the correlation between multi-time-scale dissipation characteristics of heat conduction processes and fractional calculus. The fractional-order equivalent thermal impedance model is derived based on the connection between fractional-order calculus and the Foster thermal network model in mathematical operations, with only two parameters to be identified: heat capacity C and fractional order α. Moreover, this paper provides a parameter identification method for the proposed fractional-order equivalent thermal impedance model based on the multi-objective particle swarm optimization (MOPSO) algorithm. In order to validate the effectiveness and superiority of this work, experiments and comparative works are provided in this paper. The results indicate that the fractional-order equivalent thermal impedance model can accurately describe the frequency domain characteristic curves of the thermal impedance of the Foster thermal network model for IGBT modules, with the difference between the amplitude frequency characteristics not exceeding 1 dB and the difference between the phase frequency characteristics not exceeding 1° within the operating frequency range of (1 kHz, 1 MHz).

A {Ru(C6H6)}-Containing Isopolymolybdate with Good Photocatalytic Activity for Oxidative Coupling of Amines, and Proton Conduction Properties.

We present a nonclassical {Ru(C6H6)}-containing isopolymolybdate Cs8K2Na2H4{[(C6H6)Ru]6Mo24O86}·35H2O (1) via one-pot reaction. The crystallographic characterization of compound 1 revealed that it contains an unusual {Mo24O86} cluster together with six {Ru(C6H6)} groups, having the largest number of {Ru(C6H6)} groups within the field of {Ru(C6H6)}-containing polyoxometalates. Results showed that compound 1 displayed excellent proton conductivity (9.8 × 10-3 S cm-1) at 90 °C and 95% relative humidity. Based on the calculation result of activation energy, which was more than 0.4 eV (1.47 eV), it was determined that the proton conduction process for compound 1 was in accordance with the Vehicle mechanism. More interestingly, compound 1 was exploited as a catalyst to achieve the heterogeneous oxidative coupling of amines and realized a high yield (98.9%) toward N-benzylidenebenzylamine under ambient temperature and visible light irradiation (>400 nm) and O2 atmosphere.

Electrospun Sulfonated Poly(ether ether ketone) and Chitosan/Poly(vinyl alcohol) Bifunctional Nanofibers to Accelerate Proton Conduction at Subzero Temperature.

Multilayered microstructures can accelerate the proton conduction process in proton exchange membranes (PEMs). Herein, we design and construct PEMs with microstructures based on bifunctional nanofibers and sulfonated poly(ether ether ketone) (SPEEK) nanofibers. Specifically, the bifunctional nanofibers composed of poly(vinyl alcohol) and chitosan are prepared and then combined with the electrospun SPEEK nanofibers. The stable microstructure is derived from the compatible interfacial property of nanofibers and the formed hydrogen bonds. The multilayered microstructure consisting of nanofibers accelerates the proton conduction even at subzero temperature because of regulating the proton conduction pathways. Specifically, the (SKNF/CPNF/SKNF)/PA membrane exhibits the proton conductivities of (0.951 ± 0.138) × 10-2 S/cm at -30 °C and (7.32 ± 0.37) × 10-2 S/cm at 160 °C. Additionally, the fine proton conductivity stability is demonstrated by the proton conductivity in the long-term test and the cooling/heating cycle test, such as 1.67 × 10-2 S/cm at -30 °C (after 1000 h), 4.52 × 10-2 S/cm at 30 °C (after 810 h), 1.12 × 10-2 S/cm at -30 °C, and 1.01 × 10-1 S/cm at 30 °C in the cooling/heating process (5 cycles). The single fuel cell possesses an open-circuit voltage of 0.886 V and a peak power density of 0.508 W/cm2 at 130 °C.

Initial temperature conduction process and fracture response of rock impacted by ultra-low-temperature fluid: A case study of polymethyl methacrylate

Injecting ultra-low-temperature fluids, such as liquid carbon dioxide (CO2) and liquid nitrogen (LN2), into deep, low-permeability reservoirs for fracturing is an emerging waterless fracturing technology. When these fluids enter the reservoir, they rapidly exchange heat with the fracture walls, triggering intense cold shock, which influences fracture development. Although many scholars have studied the effects of nitrogen freezing and thawing on coal seams, the initial thermal exchange and cold shock process when LN2 first enters the rock mass remains unclear. This paper uses the visualizable material polymethyl methacrylate (PMMA) as the research object, conducting low-temperature impact experiments under different preset temperatures (20 °C, 40 °C, 60 °C, and 80 °C) to investigate the impact of thermal exchange during cold shock on PMMA fracturing. The results show: (1) During LN2 impact, PMMA's temperature changes in three stages: slow cooling (micro-cracks initiation), rapid cooling (formation of long fractures), and temperature recovery (crack formation completion). (2) In prolonged impacts, PMMA temperature decreases linearly, while in short-term cyclic impacts, temperature decreases exponentially with faster recovery, increasing the likelihood of micro-cracks formation. (3) Temperature differences have a dual effect on crack formation and propagation: they significantly enhance internal thermal stress, leading to rapid micro-cracks initiation and expansion, while also causing uneven temperature gradients in the crack propagation region, shifting fracture modes from tensile to complex composite failures and promoting secondary crack formation. However, a significant temperature differential may result in the development of a singular crack propagation path, hindering the formation of complex fracture networks. These findings offer theoretical insights into fracture network formation in waterless fracturing of low-permeability reservoirs.

Chemical and structural features of spin-coated magnesium oxide (MgO) and its impact on the barrier parameters and current conduction process of Au/undoped-InP Schottky contact as an interfacial layer

This work examines the structural and chemical characteristics of spin-coated magnesium oxide (MgO) on undoped InP (un-InP) and its effects on the barrier parameters and current transport phenomena in the Au/un-InP Schottky contact (SC). Using XRD and XPS, the structural and chemical features of MgO are assessed, confirming that the MgO was deposited on un-InP. The current-voltage (log(I)-V) features were measured for the SC and Au/MgO/un-InP metal/insulator/semiconductor (MIS)-type Schottky contact. The MIS contact revealed an excellent rectification behavior as compared to the SC. The calculated barrier height (Φb) was higher for the MIS contact (0.61 eV) than the SC (0.52 eV), which implies that the MgO interlayer influences the Φb of the SC. The Φb was also estimated using the Cheung’s, Mikhelashvili and Norde procedures, the values are similar, indicating their stability and reliability. The acquired interface state density (NSS) of the MIS contact was less than the SC, proving that the MgO interlayer reduced the NSS. The ohmic behavior was observed in the lower bias region for the SC and MIS contacts, while the trap-free space-charge-limited current (SCLC) was noted in the moderate and upper bias regions of the MIS contact under forward bias. Poole-Frenkel emission (PFE) governs at a lower bias, while Schottky emission (SE) dominates at the upper bias of SC and MIS contacts under reverse bias. These findings demonstrate the potential application of MgO interlayer in advancing electronic devices.

Development of mathematical models of heat conductivity for modern electronic devices with elements containing foreign inclusions

This paper considers the heat conduction process for an isotropic medium containing a foreign half-through inclusion and heated by a locally concentrated heat flow. Linear and non-linear mathematical models for determining the temperature field have been built to establish the temperature regimes for the effective operation of electronic devices. The coefficient of thermal conductivity of a non-uniform structure is represented as a whole, using asymmetric unit functions, which automatically provides the conditions of ideal thermal contact on the surfaces of materials. This results in solving one heat conduction equation with discontinuous and singular coefficients. A linearizing function was introduced to linearize the nonlinear boundary value problem. Analytical-numerical solutions of linear and nonlinear boundary-value problems have been obtained in a closed form. A linear temperature dependence of the coefficient of thermal conductivity of structural materials was chosen for a heat-sensitive medium. As a result, an analytical-numerical solution was derived, which determines the temperature distribution in this medium. On this basis, a numerical experiment was performed, the results of which are graphically displayed and confirm the adequacy of the constructed mathematical models to a real physical process. The materials of the plate and inclusion are silicon and silver. The results for these materials based on the linear and non-linear model differ by 7 %. Their slight difference is explained by the fact that the values of the temperature coefficient of thermal conductivity are small. The models built make it possible to analyze the given environments in terms of their thermal resistance. As a result, it becomes possible to improve it, and protect structures from overheating, which could lead to the failure of individual nodes and their elements and the entire electronic device

Investigation of the melting and solidification processes of a phase change material in cylindrical annular enclosures: A parametric study for energy densification in hot water tanks

The present study focuses on the analysis of the effect of the phase change material (PCM) cavity size on the melting and solidification processes for application to thermal energy densification in a hot water tank through latent heat thermal energy storage in cylindrical annular cavities. A 2D axisymmetric composite geometrical pattern is considered, formed by a phase change material surrounded by a conductive and an insulating material. A parametric study is conducted on the phase change material cavity size, and the results are presented using non-dimensional numbers: Fourier number, Rayleigh number, and aspect ratio. Two approaches have been developed based on local and global analyses. The local one showed the predominance of the conductive or convective heat transfer process concerning the influence of the phase change material size, and thus the Rayleigh number, on the evolution of the solid/liquid interface and streamline shapes. The global one allowed correlations for melting and solidification Fourier numbers with respect to the Rayleigh number and aspect ratio to be built from simulation data. Two parameters for each process have been identified and defined from the present study: the critical Fourier number and the aspect ratio constant. The critical Fourier number corresponds to the maximum Fourier number that the phase change material needs to achieve for a melting or solidification process. The aspect ratio constant provides information on the phase change material aspect ratio value where the Rayleigh number no longer influences the process. In the case of the melting process, this parameter is an indication that convection has reached a maximum intensity and no longer influences the process. Finally, this study proposes a suitable aspect ratio for optimizing the melting process: 19.32, and another for optimizing the solidification process: 16.29.

A numerical investigation on the conductive drying process for phosphate sludge

Phosphate production generates huge quantities of waste materials that pose both economic and environmental challenges. They are characterized by a high-water content, making disposal a very difficult task. To address this issue, conductive drying emerges as a viable solution to reduce the water content in the phosphate sludge to facilitate handling and specially recycling them as construction materials. This paper presents a simplified numerical model based on Fick's law, depicting heat and mass transfer in porous media to simulate the conductive drying process within the phosphate sludge. To provide more accuracy to the numerical model solution, the experimental data are integrated into the numerical model as boundary conditions, enabling the prediction of temperature profiles, thermal conductivity, and effective moisture diffusivity throughout the conductive drying process. The water evaporation capacity is found between 1.25 and 2.1 kg water/m2.h.These findings could be a tool for designing a suitable dryer for phosphate washing sludge.

Boosting supercapacitive performance of SnS2 via trace Pb doping

High-performance electrode materials are crucial for enhancing the performance of supercapacitors. Among various candidates, pseudo-capacitive SnS2 is a promising one due to its high specific capacitance, earth-abundance, nontoxicity as well as low-cost. However, its actual electrochemical performance is restricted owing to the poor intrinsic conductivity and current fabrication processes on improving the conductivity are usually complicated. In this study, based on first-principles calculations, Pb doping is introduced to enhance the conductivity of SnS2. Pb-doped SnS2 nanosheets are synthesized via a simple one-step hydrothermal method. With trace Pb doping (Pbo.o1SnS2), an impressive 4-order-of-magnitude increase in conductivity was achieved compared to pristine SnS2. Furthermore, Pb-doped SnS2 nanosheets exhibit a superior mass-specific capacitance of 533.7 F g−1 at 50 mV s−1 and excellent long-term capacitance retention of 90.2 % over 100,000 cycles at 5 A g−1. This study presents a simple and effective approach to enhancing the supercapacitor performance of SnS2 and advances the practical applications of electrochemical energy storage devices based on 2D materials.

Corrosion and conductivity damage of AgNW transparent conductive thin films under a simulated sulfur-containing atmosphere and mechanical force

Silver nanowire (AgNW) transparent conductive thin films possess high flexibility, high conductivity, high light transmittance and etc., demonstrating significant advantages in flexible electronics applications. However, in the service occasions, the coupled effect of corrosion and mechanical force easily makes the electrical conductivity of AgNW films deteriorate or even fail, which seriously affects the service reliability of AgNW films. In this work, scanning vibrating electrode technique was firstly used to confirm the existence of electrochemical corrosion on AgNW films. Furthermore, electrochemical measurements (including OCP, PDP and EIS) were carried out for researching the electrochemical corrosion process on AgNW films under different environmental factors and mechanical forces. Their surface morphologies and electrical conductivity were characterized and evaluated by the Scanning Electron Microscopy and square resistance tester respectively. Experimental results indicate that the corrosion-mechanics interaction effect aggravates the damage process of electrical conductivity of AgNW films.

Conduction mechanisms and dielectric relaxations in ternary ZnO/Zn2SiO4/SiO2 composites for energy storage systems

In this paper, ZnO-based composite (ZnO/Zn2SiO4/SiO2) powders were prepared and investigated as a function of SiO2 added amount. Indeed, the X-ray diffraction patterns (XRD) confirm the formation of ternary ZnO/Zn2SiO4/SiO2 composites. The structural defects are shown to increase with the SiO2 amount. In addition, the SEM observations reveal agglomerated and heterogenic grain shape distribution. Furthermore, dielectric properties were investigated as a function of SiO2 added amount. The Nyquist plots are simulated by an electric circuit formed by a parallel distribution of resistance (R), capacitance (C), and a constant phase element (CPE), in all composites. Moreover, using the Jonscher's law, we demonstrate a change in conduction mechanism as a function of SiO2 content. Indeed, for the 10% SiO2 doping, the conduction process is ensured by defects such as Zn interstitial and the oxygen vacancies, consistent with the Correlated Barrier Hopping (CBH) model. Whereas, for the 20% SiO2 doping, the conduction is dominated by grain boundaries contribution, according to the Non-Overlapping Small Polaron Tunneling (NSPT) model. Besides, the 10% SiO2-doped composite exhibits localized relaxation process, while the 20% SiO2-doped sample reveals simultaneously long-range and localized relaxations. These variations, caused by the increase of SiO2 percent, can be explained by the influence of the growth of Zn2SiO4 phase, and subsequently the development of further interfacial defects. Accordingly, the composites display capacitive behavior, high permittivity, and low dielectric losses, which make them good candidates for energy storage systems.

Impact of chromium substitution on structural, spectroscopic, and dielectric properties of Ba4Ni2Fe36O60 ceramics

Cr-substituted Ni2U hexaferrite series (Ba4Ni2Fe36-xCrxO60for x = 0.0 to x = 2.0 with a step size of 0.5) was prepared via sol-gel auto-combustion route and annealed at 1200 °C for 6 h. The samples were investigated using XRD, FTIR, SEM, XPS, and high frequency (1 MHz–6 GHz) dielectric and microwave absorption measurements (VNA). XRD studies revealed that Cr3+ ions successfully substituted in BaNi2U-type hexaferrite and have a single-phase structure. The average crystallite size decreased while the percentage of porosity increased with the substitution. FTIR spectra confirmed the formation of the hexaferrite phase in all compositions. SEM micrographs revealed that the prepared samples are hexagonal. XPS spectra show the presence of all constituent elements in the samples. The dielectric constant, dielectric loss, and A.C. conductivity of samples was analyzed. Cole-Cole plots with single semicircles of different radii show the grain and grain boundaries affecting the conduction process. Moreover, Cr-substitution enhanced the microwave absorption capability. The hexaferrite sample Ba4Ni2Fe35 Cr1.0O60, with a pellet thickness of 1.81 mm, showed the highest M.W. absorption at 1.09 GHz frequency with a reflection loss (R.L.) value of −55 dB. The hexagonal-shaped morphology, high porosity, and enhanced reflection loss value suggest their use in high-frequency microwave applications.

Investigation into the mechanism of ignition of magnesium alloy plates by high-temperature molten droplet

The ignition and spread of magnesium alloy fires are mainly attributed to the ignition of high-temperature molten metal droplets, but the underlying ignition mechanism remains unclear. This study addresses this knowledge gap by employing metallic aluminum and copper particles heated to temperatures over 1200 °C. Systematically, these heated particles were released at a fixed rate onto a magnesium alloy plate located inside a controlled heating furnace that maintained a constant temperature of 500 °C. Experimental results show that whether there are irregular pores and cracks in the resulting molten product can be used as a criterion for judging whether the magnesium alloy sample ignites. Furthermore, it is worth noting that molten copper droplets of the same size exhibit a higher heat-carrying capacity than their aluminum counterparts when both are heated to the same temperature. In addition, this study expanded the research scope through numerical simulation and analysis, using the PATO (Porous-Material Analysis Toolbox) solver to clarify the transient heat conduction process between the high-temperature droplet and the magnesium alloy plate. Simulations show that heat transfer upon droplet impact is primarily longitudinal, directed toward the base of the material. This results in a significantly higher temperature in the center of the affected magnesium alloy plate than at its periphery. In summary, this study helps to improve the understanding of the dangers of high-temperature molten droplets, and it is of great significance to investigate fire accidents caused by high-temperature molten droplets.

Large Deflection of a Single-Phase-Lag Non-Simple Hygrothermoelastic Elliptic Plate Under Heat-Moisture Load

A novel mathematical model in hygrothermoelastic theory has developed to describe heat and moisture distribution in a nonsimple medium. The model incorporates non-Fourier and non-Fick laws using a single phase-lag model to establish a relation between hygrothermoelasticity and unstable conduction processes. The model is applied to an ellipse-shaped composite material subjected to humid-heat loading. The Laplace and Mathieu integral transform was employed to obtain an exact solution of linearly coupled partial differential equations in an elliptical coordinate system. The Gaver–Stehfest algorithm is utilized for the inversion of Laplace functions. Berger’s approximation equation was employed to simplify the calculation of significant deformations for elliptic plates. The model also provides quantitative results for the composition of T300/5208, which consists of epoxy resin reinforced with graphite fibers. The hygrothermal behaviors due to the single-phase-lag time, geometry dimensions, material type, and the two temperatures are explored. The results reveal that nonclassical theories with single-phase-lag time and two-temperature have significant influences on the hygrothermoelastic behaviors in elliptic-shaped objects. The investigation can be effectually led using micro- and nano-elliptic shape resonators in future research.

An inverse ferroelastic type phase transition and electric properties in bis(ethylenediammonium)tetrachlorozincate chloride crystal

Here we present TGA, DSC, dielectric studies and polarized microscopy observations of bis-ethylenediammonium tetrachlorozinc dichloride. In our studies, we found a high-temperature first-order phase transition at about 478/470 K for the heating/cooling cycle, respectively. The reversibility of the phase transition was detected by DSC and dielectric measurements and also by polarized microscopy observations. The appearance of a ferroelastic-type domain structure phase above the phase transition temperature indicates a reduction in symmetry during the heating cycle. The domain walls observed in the (100) plane are characteristic of a ferroelastic-type phase transition and can be classified as mmmF2/m Aizu species. The reduction in symmetry above the phase transition temperature allows us to classify the phase transition at 476 K as a "reverse" type. Dielectric studies in the frequency range of 40 Hz - 8 MHz allowed to estimate the activation energy for conduction and relaxation processes both with increasing and decreasing temperature. Activation energies obtained both from conductivity (σdc) measured in the temperature range from 445 to 485 K and relaxation process are practically the same both for low- and high-temperature phases as well. Taking into account the results for all directions (a, b, c) and all temperatures, conductivity is 10−7 – 10−4 S/m and is within the range characteristic for semiconductors (10−8 – 106) S/m. The conductivity and relaxation activation energies determined for the directions (a, b, c) have values in the range from 0.58 to 3.7 eV, which are also within the range characteristic for semiconductors. Electrical properties show clearly anisotropic character of the studied material.

Pulsed X‐Ray Detector Based on Vertical p‐NiO/β‐Ga2O3 Heterojunction Diode

Gallium Oxide (Ga2O3) devices have shown great potential for radiation detection. However, developing Ga2O3 detectors for pulsed radiation monitoring is still challenging, which requires high response sensitivity (R), low noise, high time resolution, and linear outputs. Herein, a vertical p‐NiO/β‐Ga2O3 heterojunction diode (HJD) is fabricated and its performance in X‐ray detection is analyzed. Benefiting from the high quality of the p‐n heterojunction, the HJD exhibits a low‐leakage current density of less than 1.73 × 10−7 A cm−2 at 100 V and features a high R of 7.92 μC Gy−1 cm−2, a low noise equivalent dose rate of 9.14 × 10−12 Gy−1 Hz−0.5 at an X‐ray dose rate of 0.383 Gy s−1, and good linear outputs to X‐ray dose rates from 0.0383 to 1.149 Gy s−1. The conductive process of the HJD detector is dominated by the tunneling mechanism, which leads to a longer response time associated with the trapping and releasing process of the deep‐level traps under the continuous X‐ray illumination. However, the pulsed X‐ray response property shows no significant influence from the slow trapping/releasing process of the traps. As a result, pulsed X‐ray radiation detection with a 50 ns full width is achieved, and the time resolution of the detector is characterized to be 3.31 ns by a 20 ps laser source.

Two birds with one stone: A ferrocene-based zirconium(IV)-organic framework nanosheet denoting intrinsic high proton conductivity and acting as a fine dopant to chitosan-based composite membranes

Recently, it was demonstrated that employing metal-organic frameworks (MOFs) with prominent proton conductivity (σ) as fillers with organic substrates such as chitosan (CS) or Nafion is an effective approach for preparing composite membranes (CMs) with outstanding functionalities. Inspired by this, one extremely stable Zr(IV)-MOF (namely Zr-FDC) with a nanosheet structure produced by 1,1′-ferrocene dicarboxylic acid (H2FDA) was successfully manufactured in this research and subsequently used as a filler to synthesize a series of CS-based CMs via casting method. The alternating current (AC) impedance determinations manifested that both Zr-FDC and the related CS-based CMs (CS/MOF-x; x = 2, 4, 6, 8 being the mass percentage of Zr-MOF in the CM) showed ultrahigh σ values, indicating the structural advantages of the Zr-MOF. Further research verified that when the MOF doping quantity is 4 %, the CM's (CS/MOF-4) σ is the greatest, being 2.22 × 10−2 S/cm, which is boosted by nearly tenfold at 100 °C and 98 % relative humidity (RH) compared to the original MOF (3.2 × 10−3 S/cm). Furthermore, the CM exhibits superior thermal stability and tensile resistance. Finally, considering the structural features of the MOF and CS, activation energy data, and other determinations, we thoroughly theorized the proton conduction process within the MOF framework and CMs, referencing the subsequent proton exchange membrane design.

Uncovering the Possibilities of Ceramic Ba(1−x)CoxTiO3 Nanocrystals: Heightened Electrical and Dielectric Attributes

The hydrothermal synthesis of Ba1−xCoxTiO3 (BCT) ceramic nanocrystals across varied substitution fractions (x = 0, …, 1) is the subject of this study. Hydrothermal synthesis is well known for producing high-purity and well-crystallized nanocrystals. A thorough examination is conducted to examine the effects on the structural and electrical properties of the resultant BCT nanocrystals by altering the cobalt substitution fraction. X-ray diffraction (XRD) is used to analyze the structure, while complex impedance spectroscopy (CIS) is used to analyze the electrical properties. As the cobalt content rises, XRD examination reveals a smooth transition from the ferroelectric BaTiO3 phase to the ferromagnetic CoTiO3 phase, offering extensive insights into the phase composition and crystallographic alterations. This phase shift is important because it creates new opportunities to adjust the properties of the material for particular uses. The electrical activity of BCT nanocrystals is clarified further by CIS measurements. A distribution of relaxation times, frequently linked to complex microstructures or heterogeneous materials, is suggested by the detected non-Debye relaxation. A thermally activated conduction process, in which higher temperatures promote the passage of charge carriers, is suggested by the temperature-dependent increase in conductivity. This behavior is strongly dependent on the cobalt content, suggesting that cobalt enhances electrical conductivity and crystallinity through a catalytic effect. A frequency-dependent dielectric constant that rises with temperature and cobalt content is shown by investigating the dielectric characteristics of BCT nanocrystals. Improved polarization mechanisms inside the material are suggested by this increase in dielectric constant, which may be the result of cobalt ion presence. With a thorough grasp of the dielectric behavior, the examination of the loss angle further validates the non-Debye relaxation process.

T-phPINN: Physics-informed neural networks for solving 2D non-Fourier heat conduction equations

Non-Fourier heat conduction plays a dominant role in many extreme transient heat conduction processes, such as laser pulses and heat transfer in biological systems, but the heat wave effect makes it difficult to solve the temperature field accurately and quickly. In order to solve this problem, the first order time derivative enhanced parallel hard constraints physics-informed neural networks (T-phPINN) is proposed. T-phPINN comprises two subnetworks and incorporates a first order time derivative to capture sharp temperature changes. Two numerical cases show that the minimum relative error of T-phPINN is 0.001 % and 0.015 %, which is 1.04 % and 12.30 % of the error of conventional PINN respectively, proving the accuracy of our architecture. A transfer learning framework is established for scenarios of different parameters, the training only requires 1/6 iterations of the basic model, and close accuracy is obtained. The computational cost of T-phPINN is evaluated using the finite element method as the baseline. For the two cases, the single calculation time is 33.43 % and 51.50 % of the baseline, while the multiple calculation time under the acceleration of transfer learning is 11.59 % and 17.75 % of the baseline. This study will be helpful for solving large-scale non-Fourier heat conduction equations precisely and expeditiously.

Polaron-assisted dielectric relaxation processes in donor-doped BaTiO3-based ceramics

Ceramic samples based on the Ba1-xGdxTiO3 system, where x = 0.001, 0.002, 0.003, 0.004 and 0.005, were prepared via the Pechini’s chemical synthesis route. Structural properties, analyzed from X-ray diffraction and Rietveld refinement, revealed the formation of the pure ABO3 perovskite structure with tetragonal symmetry (P4mm) for all the studied compositions. Doping with Gd3+ promoted a reduction in the unit-cell volume, confirming the preferential substitution of the rare-earth cation at the A-site. The dielectric properties have been analyzed over a wide temperature and frequency range, revealing a significant contribution of the conduction mechanisms in the dielectric response of the studied ceramics. In fact, by using the Davidson-Cole formalism, the observed electrical behavior was found to be associated with relaxation processes related to intrinsic defects mobility promoted by a thermally-activated polaronic mechanism. The obtained values of the activation energy for the relaxation processes, estimated from the Arrhenius’ law for the mean relaxation time, revealed a decrease from 0.29 up to 0.21 eV as the Gd-doping concentration increases, which suggests the conduction process to be associated with the polaronic effects due to the coexistence of Ti4+ and Ti3+ ions in the structure. Analysis from the conductivity formalism, by using the Jonscher’s universal power-law, confirmed the polaron-type conduction mechanism for the dielectric dispersion, as suggested by the dielectric analysis, being the nature of the hopping mechanism governed by small polaron hopping (SPH) charge transport in the studied Ba1–xGdxTiO3 ceramics.