Flexoelectric properties of multilayer two-dimensional material MoS2

Two-dimensional (2D) materials exhibit a high strength and flexibility along with unique electrical-mechanical multiphysics properties. In this study, we experimentally demonstrated the electromechanical response of a multilayer 2D material, 2H-phase MoS2, by using a piezoresponse force microscope. In particular, the dominant physical quantity of the deformation response was determined by independently controlling the electric field and electric field gradient by changing the probe shape and material thickness (number of layers). The multilayer MoS2 exhibited an out-of-plane electrical-mechanical deformation response that followed and was inverted with respect to positive and negative voltages, respectively. Moreover, the relationships between the electric field gradient and strain were similar for all shapes of the probe tip and film thickness values. This result indicated that the electrical-mechanical response of this material was dominated by the electric field gradient, and the strain could be attributed to the converse flexoelectric effect. The findings can provide guidance for the realization of ultrathin electromechanical devices.

Fast and Accurate Electric Field Gradient Calculations in Molecular Solids With Density Functional Theory

Modern approaches for calculating electric field gradient (EFF) tensors in molecular solids rely upon plane-wave calculations employing periodic boundary conditions (PBC). In practice, models employing PBCs are limited to generalized gradient approximation (GGA) density functionals. Hybrid density functionals applied in the context of gauge-including atomic orbital (GIAO) calculations have been shown to substantially improve the accuracy of predicted NMR parameters. Here we propose an efficient method that effectively combines the benefits of both periodic calculations and single-molecule techniques for predicting electric field gradient tensors in molecular solids. Periodic calculations using plane-wave basis sets were used to model the crystalline environment. We then introduce a molecular correction to the periodic result obtained from a single-molecule calculation performed with a hybrid density functional. Single-molecule calculations performed using hybrid density functionals were found to significantly improve the agreement of predicted 17O quadrupolar coupling constants (Cq) with experiment. We demonstrate a 31% reduction in the RMS error for the predicted 17O Cq values relative to standard plane-wave methods using a carefully constructed test set comprised of 22 oxygen-containing molecular crystals. We show comparable improvements in accuracy using five different hybrid density functionals and find predicted Cq values to be relatively insensitive to the choice of basis set used in the single molecule calculation. Finally, the utility of high-accuracy 17O Cq predictions is demonstrated by examining the disordered 4-Nitrobenzaldehyde crystal structure.

On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. II. Evaluation of the properties in an infinite crystal

The previously reported exact potential and multipole moment (EP/MM) method for fast and precise evaluation of the intermolecular electrostatic interaction energies in molecular crystals using the pseudoatom representation of the electron density [Nguyen, Macchi & Volkov (2020), Acta Cryst. A76, 630–651] has been extended to the calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) in an infinite crystal. The presented approach combines an efficient Ewald-type summation (ES) of atomic multipoles up to the hexadecapolar level in direct and reciprocal spaces with corrections for (i) the net polarization of the sample (the `surface term') due to a net dipole moment of the crystallographic unit cell (if present) and (ii) the short-range electron-density penetration effects. The rederived and reported closed-form expressions for all terms in the ES algorithm have been augmented by the expressions for the surface term available in the literature [Stenhammar, Trulsson & Linse (2011), J. Chem. Phys. 134, 224104] and the exact potential expressions reported in a previous study [Volkov, King, Coppens & Farrugia (2006), Acta Cryst. A62, 400–408]. The resulting algorithm, coded using Fortran in the XDPROP module of the software package XD, was tested on several small molecular crystal systems (formamide, benzene, L-dopa, paracetamol, amino acids etc.) and compared with a series of EP/MM-based direct-space summations (DS) performed within a certain number of unit cells generated along both the positive and negative crystallographic directions. The EP/MM-based ES technique allows for a noticeably more precise determination of the EF and EFG and significantly better precision of the evaluated ESP when compared with the DS calculations, even when the latter include contributions from an array of symmetry-equivalent atoms generated within four additional unit cells along each crystallographic direction. In terms of computational performance, the ES/EP/MM method is significantly faster than the DS calculations performed within the extended unit-cell limits but trails the DS calculations within the reduced summation ranges. Nonetheless, the described EP/MM-based ES algorithm is superior to the direct-space summations as it does not require the user to monitor continuously the convergence of the evaluated properties as a function of the summation limits and offers a better precision–performance balance.

Application Of Mössbauer Spectroscopy To Determine The Parameters Of The EFG Tensor At Barium Nodes For УBA2CU3O7-X

The method of the Messbaur emission spectroscopy on the Ba-133 isotope, the parameters of the electric field gradient (EFG) tensor are determined. It is established that the discrepancy between the experimental and calculated values of eqкр is explained by the imperfection of the models used to calculate eqкр.