Search Results (12)

Calculation of second-order derivatives of energy using the DFT method is a valuable approach for the estimation of both the thermodynamical and mechanical properties of organic crystals from the first principles. This type of calculation requires specification of several computational parameters, including the functional, supercell, and method of phonon calculations. Nevertheless, the importance of these parameters is presented in the literature very modestly. In this work, we demonstrate the influence of these computational parameters on the accuracy of calculated second-order derivatives using the practical example of pyrazinamide polymorphs, including the plastically bending α form and the β, γ, and brittle δ form. The effects of the settings used on the resulting enthalpies of the polymorphic modifications of pyrazinamide are compared: supercell setting (primitive cell vs. appropriate supercell) has a much stronger impact than functional (PBE-D3BJ vs. Hamada rev-vdW-DF2) which in turn affects results significantly more than the method for second-order derivative computation (FD vs. DFPT approach). Finally, we propose some suggestions for choosing the right settings for calculating second-order derivatives for molecular crystals. Full article

This paper is concerned with the existence of the solution to mixed-type non-linear fractional functional integral equations involving generalized proportional ($\kappa ,\varphi$)-Riemann–Liouville along with Erdélyi–Kober fractional operators on a Banach space $C\left(\right[1,\mathtt{T}\left]\right)$ arising in biological population dynamics. The key findings of the article are based on theoretical concepts pertaining to the fractional calculus and the Hausdorff measure of non-compactness (MNC). To obtain this goal, we employ Darbo’s fixed-point theorem (DFPT) in the Banach space. In addition, we provide two numerical examples to demonstrate the applicability of our findings to the theory of fractional integral equations. Full article

In this paper, we present some results of coupled fixed points for the system of non-linear integral equations in Banach space. Our results enlarge the results of newer papers. Additionally, we prove the applicability of those results to the solvability of the system of non-linear integral equations. Finally, we give an example to validate the applicability of our results. Full article

The layer-structured monoclinic Li₂MnO₃ is a key material, mainly due to its role in Li-ion batteries and as a precursor for adsorbent used in lithium recovery from aqueous solutions. In the present work, we used first-principles calculations based on density functional theory (DFT) to study the crystal structure, optical phonon frequencies, infra-red (IR), and Raman active modes and compared the results with experimental data. First, Li₂MnO₃ powder was synthesized by the hydrothermal method and successively characterized by XRD, TEM, FTIR, and Raman spectroscopy. Secondly, by using Local Density Approximation (LDA), we carried out a DFT study of the crystal structure and electronic properties of Li₂MnO₃. Finally, we calculated the vibrational properties using Density Functional Perturbation Theory (DFPT). Our results show that simulated IR and Raman spectra agree well with the observed phonon structure. Additionally, the IR and Raman theoretical spectra show similar features compared to the experimental ones. This research is useful in investigations involving the physicochemical characterization of Li₂MnO₃ material. Full article

We perform first-principles calculations to explore the electronic, thermodynamic and dielectric properties of two-dimensional (2D) layered, alkaline-earth hydroxides Ca(OH)${}_2$ and Mg(OH)${}_2$. We calculate the lattice parameters, exfoliation energies and phonon spectra of monolayers and also investigate the thermal properties of these monolayers, such as the Helmholtz free energy, heat capacity at constant volume and entropy as a function of temperature. We employ Density Functional Perturbation Theory (DFPT) to calculate the in-plane and out-of-plane static dielectric constant of the bulk and monolayer samples. We compute the bandgap and electron affinity values using the HSE06 functional and estimate the leakage current density of transistors with monolayer Ca(OH)${}_2$ and Mg(OH)${}_2$ as dielectrics when combined with HfS${}_2$ and WS${}_2$, respectively. Our results show that bilayer Mg(OH)${}_2$ (EOT∼0.60 nm) with a lower solubility in water offers higher out-of-plane dielectric constants and lower leakage currents than does bilayer Ca(OH)${}_2$ (EOT∼0.56 nm). Additionally, the out-of-plane dielectric constant, leakage current and EOT of Mg(OH)${}_2$ outperform bilayer h-BN. We verify the applicability of Anderson’s rule and conclude that bilayers of Ca(OH)${}_2$ and Mg(OH)${}_2$, respectively, paired with lattice-matched monolayer HfS${}_2$ and WS${}_2$, are effective structural combinations that could lead to the development of innovative multi-functional Field Effect Transistors (FETs). Full article

The ortho-hydroxy aryl Schiff base 2-[(E)-(phenylimino)methyl]phenol and its deutero-derivative have been studied by the inelastic incoherent neutron scattering (IINS), infrared (IR) and Raman experimental methods, as well as by Density Functional Theory (DFT) and Density-Functional Perturbation Theory (DFPT) simulations. The assignments of vibrational modes within the 3500–50 cm⁻¹ spectral region made it possible to state that the strong hydrogen bond in the studied compound can be classified as the so-called quasi-aromatic bond. The isotopic substitution supplemented by the results of DFT calculations allowed us to identify vibrational bands associated with all five major hydrogen bond vibrations. Quasi-isostructural polymorphism of 2-[(E)-(phenylimino)methyl]phenol (SA) and 2-[(E)-(phenyl-D₅-imino)methyl]phenol (SA-C₆D₅) has been studied by powder X-ray diffraction in the 20–320 K temperature range. Full article

In this manuscript, we examine both the existence and the stability of solutions of the boundary value problems of Hadamard-type fractional differential equations of variable order. New outcomes are obtained in this paper based on the Darbo’s fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of the observed results. Full article

In an attempt to push the boundary of miniaturization, there has been a rising interest in two-dimensional (2D) semiconductors with superior electronic, mechanical, and thermal properties as alternatives for silicon-based devices. Due to their fascinating properties resulting from lowering dimensionality, hexagonal boron nitride (h-BN) and graphene are considered promising candidates to be used in the next generation of high-performance devices. However, neither h-BN nor graphene is a semiconductor due to a zero bandgap in the one case and a too large bandgap in the other case. Here, we demonstrate from first-principles calculations that a hybrid 2D material formed by cross-linking alternating chains of carbon and boron nitride (HCBN) shows promising characteristics combining the thermal merits of graphene and h-BN while possessing the electronic structure characteristic of a semiconductor. Our calculations demonstrate that the thermal properties of HCBN are comparable to those of h-BN and graphene (parent systems). HCBN is dynamically stable and has a bandgap of 2.43 eV. At low temperatures, it exhibits smaller thermal contraction than the parent systems. However, beyond room temperature, in contrast to the parent systems, it has a positive but finitely small linear-thermal expansion coefficient. The calculated isothermal bulk modulus indicates that at high temperatures, HCBN is less compressible, whereas at low temperatures it is more compressible relative to the parent systems. The results of our study are important for the rational design of a 2D semiconductor with good thermal properties. Full article

Chloroform (CHCl₃) and dichloromethane (CH₂Cl₂) are model systems for the study of intermolecular interactions, such as hydrogen bonds and halogen–halogen interactions. Here we report a joint computational (density-functional perturbation theory (DFPT) modelling) and experimental (Raman scattering) study on the behaviour of the crystals of these compounds up to a pressure of 32 GPa. Comparing the experimental information on the Raman band positions and intensities with the results of calculations enabled us to characterize the pressure-induced evolution of the crystal structure of both compounds. We find that the previously proposed P6₃ phase of CHCl₃ is in fact a metastable structure, and that up to 32 GPa the ambient-pressure Pnma structure is the ground state polymorph of this compound. For CH₂Cl₂ we confirm the stability of the ambient-pressure Pbcn structure up to 32 GPa. We show that the high-pressure evolution of the crystal geometry of CHCl₃ in the Pnma structure is a result of the subtle balance between dipole–dipole interactions, hydrogen bonds and Cl···Cl contacts. For CH₂Cl₂ (Pbcn structure) the dipole–dipole interactions and hydrogen bonds are the main factors influencing the pressure-induced changes in the geometry. Full article

Silicane, a hydrogenated monolayer of hexagonal silicon, is a candidate material for future complementary metal-oxide-semiconductor technology. We determined the phonon-limited mobility and the velocity-field characteristics for electrons and holes in silicane from first principles, relying on density functional theory. Transport calculations were performed using a full-band Monte Carlo scheme. Scattering rates were determined from interpolated electron–phonon matrix elements determined from density functional perturbation theory. We found that the main source of scattering for electrons and holes was the ZA phonons. Different cut-off wavelengths ranging from 0.58 nm to 16 nm were used to study the possible suppression of the out-of-plane acoustic (ZA) phonons. The low-field mobility of electrons (holes) was obtained as 5 (10) cm²/(Vs) with a long wavelength ZA phonon cut-off of 16 nm. We showed that higher electron (hole) mobilities of 24 (101) cm²/(Vs) can be achieved with a cut-off wavelength of 4 nm, while completely suppressing ZA phonons results in an even higher electron (hole) mobility of 53 (109) cm²/(Vs). Velocity-field characteristics showed velocity saturation at 3 × 10⁵ V/cm, and negative differential mobility was observed at larger fields. The silicane mobility was competitive with other two-dimensional materials, such as transition-metal dichalcogenides or phosphorene, predicted using similar full-band Monte Carlo calculations. Therefore, silicon in its most extremely scaled form remains a competitive material for future nanoscale transistor technology, provided scattering with out-of-plane acoustic phonons could be suppressed. Full article

We exploited novel two-dimensional (2D) carbon selenide (CSe) with a structure analogous to phosphorene, and probed its electronics and optoelectronics. Calculating phonon spectra using the density functional perturbation theory (DFPT) method indicated that 2D CSe possesses dynamic stability, which made it possible to tune and equip CSe with outstanding properties by way of X-doping (X = O, S, Te), i.e., X substituting Se atoms. Then systematic investigation on the structural, electronic, and optical properties of pristine and X-doped monolayer CSe was carried out using the density functional theory (DFT) method. It was found that the bonding feature of C-X is intimately associated with the electronegativity and radius of the doping atoms, which leads to diverse electronic and optical properties for doping different group VI elements. All the systems possess direct gaps, except for O-doping. Substituting O for Se atoms in monolayer CSe brings about a transition from a direct Γ-Γ band gap to an indirect Γ-Y band gap. Moreover, the value of the band gap decreases with increased doping concentration and radius of doping atoms. A red shift in absorption spectra occurs toward the visible range of radiation after doping, and the red-shift phenomenon becomes more obvious with increased radius and concentration of doping atoms. The results can be useful for filtering doping atoms according to their radius or electronegativity in order to tailor optical spectra efficiently. Full article

The vibrational dispersion relations of porous germanium (pGe) and germanium nanowires (GeNWs) were calculated using the ab initio density functional perturbation theory with a generalized gradient approximation with norm-conserving pseudopotentials. Both pores and nanowires were modeled using the supercell technique. All of the surface dangling bonds were saturated with hydrogen atoms. To address the difference in the confinement between the pores and the nanowires, we calculated the vibrational density of states of the two materials. The results indicate that there is a slight shift in the highest optical mode of the Ge-Ge vibration interval in all of the nanostructures due to the phonon confinement effects. The GeNWs exhibit a reduced phonon confinement compared with the porous Ge due to the mixed Ge-dihydride vibrational modes around the maximum bulk Ge optical mode of approximately 300 cm⁻¹; however, the general effects of such confinements could still be noticed, such as the shift to lower frequencies of the highest optical mode belonging to the Ge vibrations. Full article