Conductivity Tensor Research Articles

Monocarboluminate: Sorption dependence of thermal, elastic, and transport properties

AbstractMonocarboaluminate is the major phase in calcium aluminate cements and is the main AFm phase in modern cement that incorporates limestone additions, including limestone calcined clay cement. This study reports thermal, elastic, and transport properties of monocarboaluminate obtained from molecular simulations. Properties and structural features are computed as a function of the relative humidity (RH) and water content. Full elastic, thermal expansion and thermal conductivity tensors are provided. Quantum‐corrected estimates are provided for the heat capacity and thermal conductivity. Self‐diffusion of interlayer species is also quantified, accounting for the subdiffusive regime. This work contributes to completing property data for critical phases in cement systems.

A generalized differential scheme for the effective conductivity of percolating microinhomogeneous materials with the Hall effect

In this paper, we propose a self-consistent scheme for the calculation of the components of the effective electrical conductivity tensor. The calculations were fulfilled for a microinhomogeneous material, the components of which have the Hall effect. The presence of the Hall effect leads to appearance of asymmetry of the components of the conductivity tensor and to dependence of these components on the magnitude of the magnetic field applied to the material. Our approach is based on the Generalized Differential Effective Medium (GDEM) method. This method generalizes the classical differential scheme (DEM) for the case of several inclusion types instead of one. In this case, the GDEM scheme leads to a system of matrix differential equations that were solved numerically. This solution was obtained for materials containing spherical or cylindrical inclusions (3D and 2D-problems). In the case of cylindrical inclusions, the results were obtained for inclusions with the symmetry axes orthogonal to the magnetic field. The application of the GDEM method allows us to consider the percolation effect for 2D and 3D-microheterogeneous materials. The results obtained are compared to the experimental data and the calculation results obtained by other self-consistent schemes.

Reconstruction of intra- and extra-neurite conductivity tensors via conductivity at Larmor frequency and DWI data patterns

The developed magnetic resonance electrical properties tomography (MREPT) techniques visualize the internal conductivity distribution at Larmor frequency by measuring the B1 transceive phase data. In biological tissues, electrical conductivity is influenced by ion concentrations and mobility. To visualize the anisotropic conductivity tensor of biological tissues, we use the Einstein–Smoluchowski equation, which links the diffusion coefficient to particle mobility. By assuming a correlation between ion mobility and water diffusivity, we aim to decompose the internal isotropic conductivity at Larmor frequency into anisotropic conductivity tensors within the intra- and extra-neurite compartments. The multi-compartment spherical mean technique (MC-SMT), utilizing both high and low b-value diffusion-weighted imaging (DWI) data, characterizes the diffusion of water molecules within and across the intra- and extra-neurite compartments by analyzing the microstructural intricacies and the foundational architectural arrangement of the brain’s tissues. By analyzing the relationships between the measured DWI data, the microscopic diffusion signal, and the fiber orientation distribution function, we predict the DWI data for the intra- and extra-neurite compartments using spherical harmonic decomposition. Using the predicted DWI data for the intra- and extra-neurite compartments, we develop a conductivity tensor imaging method that operates specifically within the separated compartments. Human brain experiments, involving four healthy volunteers and a brain tumor patient, were performed to assess and confirm the reliability of the proposed method.

Deep learning surrogate for predicting hydraulic conductivity tensors from stochastic discrete fracture-matrix models

Deep learning surrogate for predicting hydraulic conductivity tensors from stochastic discrete fracture-matrix models

Investigation of the structural, electronic, magnetic, and optical properties of the double perovskite oxide semiconductor La2NiMnO6: Ab initio calculations by using GGA-PBE and GGA + mBJ approximations

In this paper, we examined the La2NiMnO6 double perovskite oxide semiconductor materials, our treatment included the structural, electronic, magnetic, and optical characteristics by utilizing the density functional theory, which was performed in the Wien2k software. The exchange–correlation potential was carried out in combination with the GGA-PBE (Perdew Burke Ernzerhof Generalized Gradient Approximation), and GGA + mBJ (modified Becke and Johnson) was used for the exchange–correlation potentials. The results suggest that the compound La2NiMnO6 exhibits in a ferrimagnetic state. It was also found that the stable ground state of the compound is ferrimagnetic. The results demonstrate that La2NiMnO6 has a band gap whose spin-up value is 0 eV and spin-down (dn) value is 2.86 eV (GGA-PBE), with up values is 0 eV and dn value being of 3 eV (GGA + mBJ). We also explored different optical properties, among them electron energy loss, absorption coefficient, real and imaginary dielectric tensor, and real and imaginary optical conductivity.

Theoretical investigation of the thermal conductivity of Ga2O3 polymorphs

Gallium oxide (Ga2O3) is a promising thermal preserving and heat-insulating material; understanding the thermal properties is important to improve its performance in technological applications. The thermal conductivities of Ga2O3 polymorphs labeled as α, β, δ, and ε are computed via the Boltzmann phonon transport equation (BTE) employing first-principles techniques. The lattice thermal conductivity tensor k of Ga2O3 for temperatures ranging from 50 K to 1000 K is derived using the second and third-order interatomic force constants (IFCs) for the potential based on a generalized gradient approximation (GGA), as well as the phonon dispersion relation, projected density of states (PDOS), and phonon group velocities. The results agree with the observed experimental values of rhombohedral polymorph β-Ga2O3 and with the previously calculated results of the other phases. At room temperature, the predicted thermal conductivity of the δ-Ga2O3 phase is 15.6 W/(m•K). By breaking down k into mode contributions, it is projected that the optical phonons contribute significantly to the lattice thermal conductivity because of a peculiar phonon dispersion relation.

Multiscale data-driven modeling of the thermomechanical behavior of granular media with thermal expansion effects

A multiscale data-driven (MSDD) methodology is proposed for simulating the thermomechanical behavior of granular materials subjected to thermal expansion. The macroscale is handled using a continuous model based on the Finite Volume Method (FVM), while the microscale response is captured at Representative Volume Elements (RVEs) with the Discrete Element Method (DEM). To significantly reduce the computational cost of the analyses, the microscale DEM computations are not performed online, i.e., simultaneously with the macroscale FVM ones, as generally done in standard multiscale approaches. Instead, they are performed in advance to create a comprehensive database of RVE solutions under different initial conditions and thermal strains. This dataset is then used to train an Artificial Neural Network (ANN), which serves as a surrogate model for the macroscale solver. The MSDD approach is validated against pure DEM solutions of problems with distinct thermal conditions. Remarkably, we demonstrate that with only three input parameters, namely porosity, fabric, and thermal strain, the surrogate model can predict the microstructure evolution, as well as the updated conductivity and Cauchy stress tensors of the granular assembly. This allows for a generally accurate simulation of transient thermomechanical analyses at a drastically lower computational cost than the pure DEM approach.

Adaptation of an Eddy Current Model for Characterizing Subsurface Defects in CFRP Plates Using FEM Analysis Based on Energy Functional

In this work, a known Eddy Current (EC) model is adapted to characterize subsurface defects in carbon fiber-reinforced polymer (CFRP) plates intended for the civil aerospace industry. The considered defects include delaminations, microcracks, porosity, fiber breakage, and the simultaneous presence of these defects. Each defect is modeled as an additive variation in the material’s electrical conductivity tensor, allowing for a detailed mathematical representation of the defect’s influence on the CFRP’s electromagnetic behavior. The additivity of the variations in the conductivity tensor is justified by the assumption that the defects are not visible to the naked eye, implying that the material does not require non-destructive testing. The adapted EC model admits a unique and stable solution by verifying that all analytical steps are satisfied. To reconstruct 2D maps of the magnetic flux density amplitude, a FEM formulation is adopted, based on the energy functional because it ensures a stable and consistent numerical formulation given its coercivity. Moreover, the numerical approach allows precise and reliable numerical solutions, enhancing the capability to detect and quantify defects. The numerical results show that the obtained 2D maps are entirely superimposable on those highlighting the distribution of mechanical stress states known in the literature, offering a clear advantage in terms of detection costs. This approach provides an effective and economical solution for the non-destructive inspection of CFRP, ensuring accurate and timely defect diagnosis for maintaining structural integrity.

Modeling variability of the electrical conductivity tensor for the induction welding of composites

Modeling variability of the electrical conductivity tensor for the induction welding of composites

Anomalous Nernst effect in the noncollinear antiferromagnet Mn5Si3

Investigating the off-diagonal components of the conductivity and thermoelectric tensor of materials hosting complex antiferromagnetic structures has become a viable method to reveal the effects of topology and chirality on the electronic transport in these systems. In this respect, Mn5Si3 is an interesting metallic compound that exhibits several antiferromagnetic phases below 100 K with different collinear and noncollinear arrangements of Mn magnetic moments determined from neutron scattering. Previous electronic transport measurements have shown that the transitions between the various phases give rise to large changes of the anomalous Hall effect. Here, we report measurements of the anomalous Nernst effect of Mn5Si3 single crystals that also show clear transitions between the different magnetic phases. In the noncollinear phase, we observe an unusual sign change of the zero-field Nernst signal with a concomitant decrease of the Hall signal and a gradual reduction of the remanent magnetization. Furthermore, a symmetry analysis of the proposed magnetic structures shows that both effects should actually vanish. These results indicate a symmetry-breaking modification of the magnetic state with a rearrangement of the magnetic moments at low temperatures, thus questioning the previously reported models for the noncollinear magnetic structure obtained from neutron scattering.

Spin-polarized second-order nonlinear Hall effect in 8-Pmmn monolayer borophene

The second-order nonlinear Hall effect in 8-Pmmn monolayer borophene under the influence of an out-of-plane electric field and intrinsic spin–orbit interaction is reported. This unconventional response sensitive to the breaking of discrete and crystal symmetries can be tuned by the applied electric field, which can vary the bandgap induced by spin–orbit coupling. It is described by a Hall conductivity tensor that depends quadratically on the applied electric field. We find that the nonlinear Hall effect strongly depends on the spin polarization. In particular, it exhibits out of the phase character for spin-up and spin-down states. Remarkably, it undergoes a phase flip in the spin-up state at a large out-of-plane electric field that generates a staggered sublattice potential greater than the spin–orbit interaction strength. It is shown that the nonlinear Hall effect in the system originates from the broken inversion symmetry that plays an indispensable role in developing finite Berry curvature and its relevant dipole moment. It is found that at zero temperature, the nonlinear Hall response is maximal when the Fermi energy is twice the bandgap parameter and vanishes at large Fermi energies. Notably, the peak of nonlinear Hall response shifts to lower Fermi energies at finite temperature.

Comprehensive measurement of three-dimensional thermal conductivity tensor using a beam-offset square-pulsed source (BO-SPS) approach

Accurately measuring the three-dimensional thermal conductivity tensor is essential for understanding and engineering the thermal behavior of anisotropic materials. Existing methods often struggle to isolate individual tensor elements, leading to large measurement uncertainties and time-consuming iterative fitting procedures. In this study, we introduce the Beam-Offset Square-Pulsed Source (BO-SPS) method for comprehensive measurements of three-dimensional anisotropic thermal conductivity tensors. This method uses square-pulsed heating and precise temperature rise measurements to achieve high signal-to-noise ratios, even with large beam offsets and low modulation frequencies, enabling the isolation of thermal conductivity tensor elements. We demonstrate and validate the BO-SPS method by measuring X-cut and AT-cut quartz samples. For X-cut quartz, with a known relationship between in-plane and cross-plane thermal conductivities, we can determine the full thermal conductivity tensor and heat capacity simultaneously. For AT-cut quartz, assuming a known heat capacity, we can determine the entire anisotropic thermal conductivity tensor, even with finite off-diagonal elements. Our results yield consistent principal thermal conductivity values for both quartz types, demonstrating the method's reliability and accuracy. This research highlights the BO-SPS method's potential to advance the understanding of thermal behavior in complex materials.

Efficient Numerical Implementation of the Time-Fractional Stochastic Stokes–Darcy Model

This paper presents an efficient numerical method for the fractional-order generalization of the stochastic Stokes–Darcy model, which finds application in various engineering, biomedical and environmental problems involving interaction between free fluid flow and flows in porous media. Unlike the classical model, this model allows taking into account the hereditary properties of the process under uncertainty conditions. The proposed numerical method is based on the combined use of the sparse grid stochastic collocation method, finite element/finite difference discretization, a fast numerical algorithm for computing the Caputo fractional derivative, and a cost-effective ensemble strategy. The hydraulic conductivity tensor is assumed to be uncertain in this problem, which is modeled by the reduced Karhunen–Loève expansion. The stability and convergence of the deterministic numerical method have been rigorously proved and validated by numerical tests. Utilizing the ensemble strategy allowed us to solve the deterministic problem once for all samples of the hydraulic conductivity tensor, rather than solving it separately for each sample. The use of the algorithm for computing the fractional derivatives significantly reduced both computational cost and memory usage. This study also analyzes the influence of fractional derivatives on the fluid flow process within the fractional-order Stokes–Darcy model under uncertainty conditions.

Effect of Coriolis force on electrical conductivity tensor for the rotating hadron resonance gas

We have investigated the influence of the Coriolis force on the electrical conductivity of hadronic matter formed in relativistic nuclear collisions, employing the hadron resonance gas model. A rotating matter in the peripheral heavy-ion collisions can be expected from the initial stage of quark matter to late-stage hadronic matter. Present work is focused on rotating hadronic matter, whose medium constituents—hadron resonances—can face a nonzero Coriolis force, which can influence the hadronic flow or conductivity. We estimate this conductivity tensor by using the relativistic Boltzmann transport equation. In the absence of Coriolis force, an isotropic conductivity tensor for hadronic matter is expected. However, our study finds that the presence of Coriolis force can generate an anisotropic conductivity tensor with three main conductivity components—parallel, perpendicular, and Hall—similarly to the effect of Lorentz force at a finite magnetic field. Our study has indicated that a noticeable anisotropy of conductivity tensor can be found within the phenomenological range of angular velocity Ω=0.001–0.02 GeV and hadronic scattering radius a=0.2–2 fm. Published by the American Physical Society 2024

Integration of inter-ply electrical percolation phenomena in the multiphysics modelling of laminated composite materials

PurposeThis study aims to introduce a predictive homogenization model incorporating electrical percolation considerations to forecast the electrical characteristics of unidirectional carbon-epoxy laminate composites.Design/methodology/approachThis study presents a method for calculating the electrical conductivity tensor for various ply arrangement patterns to elucidate phenomena occurring around the interfaces between plies. These interface models are then integrated into a three-dimensional (3D) magneto-thermal model using the finite element method. A comparative study is conducted between different approaches, emphasizing the advantages of the new model through experimental measurements.FindingsThis research facilitates the innovative integration of electrical percolation considerations, resulting in substantial improvement in the prediction of electrical properties of composites. The validity of this improvement is established through comprehensive validation against existing approaches and experimentation.Research limitations/implicationsThe study primarily focuses on unidirectional carbon-epoxy laminate composites. Further research is needed to extend the model's applicability to other composite materials and configurations.Originality/valueThe proposed model offers a significant improvement in predicting the electrical properties of composite materials by incorporating electrical percolation considerations at inter-ply interfaces, which have not been addressed in previous studies. This research provides valuable information to improve the accuracy of predictions of the electrical properties of composites and offers a methodology for accounting for these properties in 3D magneto-thermal simulations.

Validation of conductivity tensor imaging against diffusion tensor magnetic resonance electrical impedance tomography

Diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) and electrodeless conductivity tensor imaging (CTI) are two emerging modalities that can quantify low-frequency tissue anisotropic conductivity properties by assuming similar properties underlie ionic mobility and water diffusion. While both methods have potential applications to estimating neuro-modulation fields or formulating forward models used for electrical source imaging, a direct comparison of the two modalities has not yet been performed in-vitro or in-vivo. Therefore, the aim of this study was to test the equivalence of these two modalities. We scanned a tissue phantom and the head of human subject using DT-MREIT and CTI protocols and reconstructed conductivity tensor and effective low frequency conductivities. We found both gray and white matter conductivities recovered by each technique were equivalent within 0.05 S/m. Both DT-MREIT and CTI require multiple processing steps, and we further assess the effects of each factor on reconstructions and evaluate the extent to which different measurement mechanisms potentially cause discrepancies between the two methods. Finally, we discuss the implications for spectral models of measuring conductivity using these techniques. The study further establishes the credibility of CTI as an electrodeless non-invasive method of measuring low frequency conductivity properties.

A DFT study of the CaMg2As2 material for photovoltaic applications

The research focused on investigating the structural, elastic, electronic, optical, and thermoelectric characteristics of the CaMg2As2 compound. To inspect these properties, the density functional theory (DFT) method has been applied via the Wien2K code. The electronic analysis revealed that the CaMg2As2 compound demonstrates semiconductor behavior with an indirect band gap of 1.781 eV. Additionally, its elastic properties were examined, revealing a 1.980 % AVR, indicating a variation in elasticity depending on the direction of load or stress applied. We have also studied various optical properties of CaMg2As2, including the refractive index, extinction coefficient, electron energy loss, dielectric tensor, and optical conductivity. the absorption coefficient value is zero for energy levels below 2.60 eV, meaning there is no energy absorption by the material at lower energy levels. However, as the energy surpasses 2.60 eV, the absorption coefficient increases and shows multiple peaks. This signifies that as the incident radiation's energy increases, the material starts absorbing more energy at specific energy levels. In addition, one significant finding is that the thermal conductivity of the lattice (κL) in CaMg2As2 decreases exponentially as the temperature rises. This means that as the material gets hotter, its ability to conduct heat becomes less effective. In simple terms, the material becomes less efficient at transferring heat at higher temperatures. These findings suggest that CaMg2As2 has potential as a thermoelectric material with interesting properties that deserve further investigation.

Experimental and numerical estimation of thermal conductivity of bio-based building composite materials with an enhanced thermal capacity

The paper tackles the important problem of estimating and predicting the thermal conductivity of bio-based building materials that can help decarbonize the building sector. Knowledge and the possibility to optimize their insulating properties is the first criterion for determining the ability of their use in the building sector. The novel yet not well-studied hemp shives and magnesium binder composites with improved thermal mass by microencapsulated phase change material (PCM) were considered. The samples of composites without PCM having different densities as well as with different amounts of microencapsulated PCM and the same density were manufactured and tested experimentally in different states, i.e., dry and after conditioning at relative humidity (RH) of 50, 75, and 90 %, and in the case of samples with PCM also at different average measurement temperatures selected with respect to the phase change range of the PCM. A novel method of predicting bio-based composites' effective thermal conductivity tensor was also developed. The method is based on the numerical solution of the heat conduction equation at the micro-scale considering real composite microstructure. The method was tuned using micro-computed tomography (μCT) data with the microstructure of composites without PCM and then applied to predict the thermal conductivities of composites with PCM, utilizing computational domains with an artificially distributed PCM in the binder. The experimental testing of composites without PCM revealed an apparent effect of increasing thermal conductivity with rising sample density and RH applied during conditioning. With an increase in density from 394 to 576 kg/m3, their thermal conductivities varied from 0.105 to 0.159 W/m/K for the dry state and from 0.157 to 0.241 W/m/K for RH 90 %. A similar effect of sample state and RH was observed for composites with microencapsulated PCM, which had the highest thermal conductivity, equal to 0.265 W/m/K, for the lowest PCM amount and RH 90 %. Moreover, a decrease in composites' effective thermal conductivity with an increase in PCM fraction was observed, except for the lowest PCM fraction, for which it increased. It also rose with increasing the average measurement temperature. The developed micro-scale-based numerical method allowed for predicting the thermal conductivities of composites with accuracies below 4.1 and 7.2 % for composites without and with PCM, respectively, except for the composite with the lowest amount of PCM, which behaved differently. Thus, its suitability for designing and optimizing bio-based composites was shown.

Anomalous conductivity due to relativistic Landau quantization.

We use a recently developed a kinetic model derived from the Dirac equationto study electromagnetic wave propagation in superstrong magnetic fields, such as in magnetars, where relativistic Landau quantization is prominent. The leading contribution to the conductivity tensor in such a plasma is calculated. It is found that the electron Hall current has an anomalous contribution, in the quantum relativistic regime, where the effective particle energy has a significant contribution from the diamagnetic and Zeeman energy. As a result, a new quantum resonance frequency appears, and the dispersion relation for the left- and right-hand polarized modes are strongly modified for long and moderate wavelengths. The implications for magnetar physics are discussed.

Effective heat conductivity of composites with stochastic microstructure using asymptotic homogenization

This contribution presents a comprehensive methodology aimed at determining the effective heat conductivity of composites with stochastic microstructure by analyzing micro Computerized Tomography (μCT) images. We revisit asymptotic homogenization for multiscale analysis of transient heat problems and derive systems of partial differential equations (PDEs) governing the homogenized problem and two new cell problems, which are solved numerically using the Finite Element (FE) method to identify the effective thermal conductivity. The methodology does not require enforcing Dirichlet Boundary Conditions (BCs) on the interfaces, making it well-suited for analyzing stochastic microstructures with irregular interfaces. Following image preprocessing and segmentation to identify the pores (void) and the solid matrix, the workflow transforms the segmented image into a periodic computational domain suitable for the upscaling procedure to identify the effective thermal conductivity tensor. We employ the open-source computing platform FEniCSx, along with its Multi-Point Constraints (MPC), to solve the computational problems and enforce the periodic boundary condition (PBC), eliminating the need for one-by-one mapping of inlet and outlet computational nodes. To validate the methodology, we apply it to model a bi-laminated composite and compare the obtained results with analytical values. This is followed by statistical descriptions of μCT images of several samples, together with a comprehensive representativity analysis using multiple RVE realizations approach. We find the results of statistical descriptions useful to guide us in selecting suitable RVE sizes.