Difference schemes for numerical solutions of lagging models of heat conduction

Non-Fourier models of heat conduction are increasingly being considered in the modeling of microscale heat transfer in engineering and biomedical heat transfer problems. The dual-phase-lagging model, incorporating time lags in the heat flux and the temperature gradient, and some of its particular cases and approximations, result in heat conduction modeling equations in the form of delayed or hyperbolic partial differential equations. In this work, the application of difference schemes for the numerical solution of lagging models of heat conduction is considered. Numerical schemes for some DPL approximations are developed, characterizing their properties of convergence and stability. Examples of numerical computations are included.

Difference schemes for time-dependent heat conduction models with delay

Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.

Large spin splitting in the conduction band of transition metal dichalcogenide monolayers

We study the conduction band spin splitting that arises in transition metal dichalcogenide (TMD) semiconductor monolayers such as MoS2, MoSe2, WS2, and WSe2 due to the combination of spin-orbit coupling and lack of inversion symmetry. Two types of calculation are done. First, density functional theory (DFT) calculations based on plane waves that yield large splittings, between 3 and 30 meV. Second, we derive a tight-binding model that permits to address the atomic origin of the splitting. The basis set of the model is provided by the maximally localized Wannier orbitals, obtained from the DFT calculation, and formed by 11 atomiclike orbitals corresponding to d and p orbitals of the transition metal (W, Mo) and chalcogenide (S, Se) atoms respectively. In the resulting Hamiltonian, we can independently change the atomic spin-orbit coupling constant of the two atomic species at the unit cell, which permits to analyze their contribution to the spin splitting at the high symmetry points. We find that—in contrast to the valence band—both atoms give comparable contributions to the conduction band splittings. Given that these materials are most often n-doped, our findings are important for developments in TMD spintronics.

Ordered mesoporous titanium oxide for thin film microbatteries with enhanced lithium storage

A 3D mesoporous TiO2 material with well-developed mesostructure is prepared in the form of a binder-free thin (100 nm) film and studied as potential candidate for the negative electrode in lithium microbatteries. By appropriate thermal treatments, the selected crystal structure (anatase, rutile, or amorphous), and micro-/mesostructure of the materials was obtained. The effects of voltage window and prelithiation treatment improved first cycle reversibility up to 86% and capacity retention of 90% over 100 cycles. After a prolonged intercalation of lithium ions in ordered mesoporous TiO2 appeared small particles assigned to Li2Ti2O4 with cubic structure as observed from ex-situ TEM micrographs. This study highlights the flexibility of the potential window to which the electrode can operate. Maximum capacity values over 100 cycles of 470 μA h cm−2 μm−1 and 177 μA h cm−2 μm−1 are obtained for voltage ranges of 0.1–2.6 V and 1.0–2.6 V, respectively. The observed values are between 6 and 2 times higher than those obtained for films with 600 nm (80 μA h cm−2 μm−1) and 900 nm (92 μA h cm−2 μm−1) lengths. This indicates that 100 nm thin TiO2 films with high accessibility show finite-length type diffusion which is interesting for this particular application.