Supercell Approach Research Articles

Exploring stacking fault energy with the axial Ising model: A renewed approach

In this work we revisit the axial Ising model for computing intrinsic stacking fault energies (γISF), which are important in alloy design. We find that the supercell approach, which directly compares the energies of fcc stacking with and without a fault, is a specific solution of the Ising model and is the most elegant and efficient among the solutions of the same order of accuracy. Contrary to the traditional belief that only the supercell approach can capture the effect of local chemistry, we demonstrate that local chemistry also influences γISF in the axial Ising model. We also propose a new formula γISF=5EABABC−5EABC, which is similarly efficient, simpler, and more accurate compared to the widely used γISF=EAB+2EABAC−3EABC. We tested the new formula on pure Ni, Ni-Co alloys, and Cr-Mn-Fe-Co-Ni high entropy alloys and found satisfactory results.

Changing magnetic ground state by an electric field in a single-layer FeCl2

Abstract Employing the electric field has been performed to investigate the magnetic ground state in a single-layer iron dichloride (FeCl2). We provided some lattice parameters to see the ground state dependency on the electric field. To minimize the computational time, we applied the generalized Bloch theorem via density functional theory to avoid the supercell approach. As we varied the electric field, we saw the magnetic transition for some lattice parameters. In addition, the magnetic moments were nearly stable for all those states, indicating the high spin state. As a concluding remark, employing the electric field is very useful to manipulate the ground state that can be applied to magnetism-based nanotechnology.

2d van der Waal SiC/borophene heterostructure as a promising anode for high-capacity Li ion battery: First principles study

We constructed SiC/borophene heterostructure based on the method of commensurate lattice with supercell approach and studied the structural, electronic and electrochemical properties using density functional theory (DFT). The interfacial binding energy of SiC/borophene is as high as −26.07 meV/Å2. Significant amounts of charge were found to drift from SiC to borophene, resulting in interfacial charge redistribution and increased Li binding affinity on the surfaces. The electronic properties of SiC/borophene showed pronounced metallic conductivity, a trait conducive to anodic applications in electrochemical cells. The calculated Li adsorption energy at the interface of SiC/borophene is −2.23 eV. Multiple layer adsorption is also observed, with the heterostructure retaining much of its structural integrity after adatom adsorption, indicating possible good cycling stability. At the maximum concentration, the Li storage capacity for SiC/borophene is 1980.63 mAh/g, surpassing a large variety of other reported 2D complexes. Also, an overall average operating voltage of 1.06 V is maintained in the structure, which is in proximity of the optimal 1.5 V threshold requisite for anodic operations. The diffusion energy barriers associated with lithium ion migration across the three distinct adsorption sites of the heterostructure all reveal a nominal magnitude with the lowest barrier energy of 0.54 eV at the top of borophene adsorption layer and site. These findings show that SiC/borophene could be used as an anode in very high-capacity lithium-ion batteries.

First-Principles Calculations on Electronic, Optical, and Phonon Properties of γ-Bi2MoO6.

The wide band gap γ-Bi2MoO6 (BMO) has tremendous potential in emergent solar harvesting applications. Here we present a combined experimental-first-principles density functional theory (DFT) approach to probe physical properties relevant to the light sensitivity of BMO like dynamic and structural stability, Raman and infrared absorption modes, value and nature of band gap (i.e., direct or indirect), dielectric constant, and optical absorption, etc. We solvothermally synthesized wide band gap Pca21 phase pure BMO (≳3 eV) for two different pH values of 7 and 9. The structural parameters were correlated with the stability of BMO derived from elastic tensor simulations. The desired dynamical stability at T = 0 K was established from the phonon vibrational band structure using a finite difference-based supercell approach. The DFT-based Raman modes and phonon density of states (DOS) reliably reproduced the experimental Raman and infrared absorption. The electronic DOS calculated from Heyd-Scuseria-Ernzerhof HSE06 with van der Waals (vdW) and relativistic spin-orbit coupling (SOC) corrections produced a good agreement with the band gap obtained from diffuse reflectance spectroscopy (DRS). The optical absorption obtained from the complex dielectric constant for the HSE06+SOC+vdW potential closely resembled the DRS-derived absorption of BMO. The BMO shows ∼43% photocatalytic efficiency in degrading methylene blue dye under 75 min optical illumination. This combined DFT-experimental approach may provide a better understanding of the properties of BMO relevant to solar harvesting applications.

The effect of vanadium on the magnetic and mechanical properties of B2 FeCo alloy: a DFT approach

FeCo alloys play an important role in soft magnetic materials with a wide range of technological applications due to their high saturation magnetization and Curie temperature. However, these alloys have low ductility at room temperature. The ductility can be improved by the ternary addition of elements such as V. A density functional theory supercell approach was used to generate B2 Fe50Co50-xVx (0 < x < 50) structures and the properties were evaluated at different atomic percentage compositions to determine the ductility at room temperature. The structures were fully optimized to obtain better equilibrium ground-state properties such as lattice parameters and thermodynamic properties for both binary and ternary systems. The stability of Fe50Co50-xVx was evaluated from the heats of formation, elastic properties, and phonon dispersion curves. Furthermore, magnetic strength was evaluated from magnetic moments. It was found that all structures are thermodynamically stable due to the negative heats of formation. The calculated Pugh's ratio and Poisson's ratio confirm that alloying with V effectively improved the ductility. It was also found that Fe50Co50-xVx showed a positive shear modulus for the entire concentration range investigated, in agreement with phonon dispersion curves. The ternary addition of V to the FeCo system resulted in reduced magnetic strength due to a decrease in magnetic moments. These findings reveal that B2 FeCo-V alloys can be used as components and actuators for the automotive industry.

Disorder induced band gap lowering in kesterite type Cu2ZnSnSe4 and Ag2ZnSnSe4: a first-principles and special quasirandom structures investigation

Quaternary chalcogenides, i.e. Cu2ZnSnS4, crystallising in the kesterite crystal structure have already been demonstrated as potential building blocks of thin film solar cells, containing only abundant elements and exhibiting power conversion efficiencies of about 14.9% so far. However, due to the potential presence of several structurally similar polymorphs, the unequivocal identification of their ground state crystal structures required the application of more elaborate neutron diffraction experiments. One particular complication arose from the later identified Cu–Zn disorder, present in virtually all thin film samples. Subsequently, it has been shown experimentally that this unavoidable Cu–Zn disorder leads to a band gap lowering in the respective samples. Additional theoretical investigations, mostly based on Monte-Carlo methods, tried to understand the atomistic origin of this disorder induced band gap lowering. Here, we present theoretical results from first-principles calculations based on density functional theory for the disorder induced band gap lowering in kesterite Cu2ZnSnSe4 and Ag2ZnSnSe4, where the Cu–Zn and Ag–Zn disorder is modelled via a supercell approach and special quasirandom structures. Results of subsequent analyses of structural, electronic, and optical properties are discussed with respect to available experimental results, and will provide additional insight and knowledge towards the atomistic origin of the observed disorder induced band gap lowering in kesterite type materials.

Unveiling ductile, rare-earth-free structural materials: A DFT exploration of MnTi and MnZr

This paper presents a theoretical exploration of the electronic, structural, and mechanical attributes inherent in three rare-earth-free intermetallic compounds, namely, MnTi, MnZr, and MnHf. Employing density functional theory (DFT) calculations with the Implementation of projector augmented wave (PAW); our investigation adopts the supercell approach to meticulously determine the structural and mechanical properties of these materials. The findings reveal that MnTi and MnZr exhibit intrinsic ductility, positioning them as viable contenders for applications demanding high-strength structures. In contrast, MnHf demonstrates mechanical instability. This study provides promising insights into the mechanical characteristics of MnTi and MnZr, underscoring their potential as sustainable structural materials, given the abundance and non-toxic nature of their constituents. The research findings presented herein contribute to the understanding of rare-earth-free intermetallics, offering valuable information for applications in materials science and engineering.

Effects of oxygen vacancies on the structural, electronic, and optical properties of the photocatalytic InTaO4 compound

We conducted first-principles calculations based on density functional theory to investigate the impact of the oxygen vacancies on the structural, electronic, and optical properties of the InTaO4 compound. The latter is a famous photocatalytic semiconductor with its optical absorption in the visible range being an object of controversial interpretations. The presence of two types of isolated oxygen vacancies, O1 and O2, occupying 4g(1) and 4g(2) Wyckoff positions respectively, has been simulated within the frame of the supercell approach. Electronic structure and optical absorption (OA) have been calculated using the Becke-Johnson exchange-correlation potential. It is found that the presence of both types of vacancies generates defect states (DS) inside the band gap, primarily involving In-6s and O-2p states. The calculated valence-to-conduction-band band gap (4.25 eV) and DS-to-conduction-band band gap (2.5 eV) closely align with the experimentally determined OA edges for two onsets of InTaO4 absorption. The analysis of the calculated OA spectra leads to the conclusion that only O1 vacancy-induced absorption is consistent with the experimental OA, while O2 vacancy-induced absorption appears absent. This discrepancy probably arises from a higher concentration of O1 vacancies formed during crystal growth, attributed to the fact that the calculated defect formation energy of O1 vacancy is 0.258 eV lower compared to O2 vacancy. Consequently, the photocatalytic activity of InTaO4 is ascribed to intrinsic defects, primarily O1-type vacancies, though the influence of other defects cannot be entirely ruled out.

Crucial Role of Ni Point Defects and Sb Doping for Tailoring the Thermoelectric Properties of ZrNiSn Half-Heusler Alloy: An Ab Initio Study.

In the wide group of thermoelectric compounds, the half-Heusler ZrNiSn alloy is one of the most promising materials thanks to its thermal stability and narrow band gap, which open it to the possibility of mid-temperature applications. A large variety of defects and doping can be introduced in the ZrNiSn crystalline structure, thus allowing researchers to tune the electronic band structure and enhance the thermoelectric performance. Within this picture, theoretical studies of the electronic properties of perfect and defective ZrNiSn structures can help with the comprehension of the relation between the topology of defects and the thermoelectric features. In this work, a half-Heusler ZrNiSn alloy is studied using different defective models by means of an accurate Density Functional Theory supercell approach. In particular, we decided to model the most common defects related to Ni, which are certainly present in the experimental samples, i.e., interstitial and antisite Ni and a substitutional defect consisting of the replacement of Sn with Sb atoms using concentrations of 3% and 6%. First of all, a comprehensive characterization of the one-electron properties is performed in order to gain deeper insight into the relationship between structural, topological and electronic properties. Then, the effects of the modeled defects on the band structure are analyzed, with particular attention paid to the region between the valence and the conduction bands, where the defective models introduce in-gap states with respect to the perfect ZrNiSn crystal. Finally, the electronic transport properties of perfect and defective structures are computed using semi-classical approximation in the framework of the Boltzmann transport theory as implemented in the Crystal code. The dependence obtained of the Seebeck coefficient and the power factor on the temperature and the carrier concentration shows reasonable agreement with respect to the experimental counterpart, allowing possible rationalization of the effect of the modeled defects on the thermoelectric performance of the synthesized samples. As a general conclusion, defect-free ZrNiSn crystal appears to be the best candidate for thermoelectric applications when compared to interstitial and antisite Ni defective models, and substitutional defects of Sn with Sb atoms (using concentrations of 3% and 6%) do not appreciably improve electronic transport properties.

Ab Initio Study on the Vibrational and Electronic Properties of Radiation-Induced Defects in Potassium Bromide

The vibrational and electronic properties of several basic radiation defects in potassium bromide are computed at the quantum mechanical level using a periodic supercell approach based on hybrid functionals, an all-electron Gaussian-type basis set, and the Crystalcomputer code. The exciton energy in alkali halides is sufficient to create lattice defects, such as F–H Frenkel defect pairs, resulting in a relatively high concentration of single defects and their complexes. Here, we consider eight defects: the electronic F+- and F-centers (bromine vacancy without and with trapped electrons) and their dimers; hole H-center (neutral bromine atom forming the dumbbell ion with a regular Br− ion.); VK-center (Br2− molecular ion consisting of a hole and two regular ions); and two complex Br3− defects, combinations of several simple defects. The local geometry and the charge- and spin-density distributions of all defects are analyzed. Every defect shows its characteristic features in Raman spectra, and their comparison with available experimental data is discussed.

Numerical simulation of the electromagnetic wave reflection from 2D random semi-infinite strongly scattering media

Light scattering in disordered media plays an important role in several areas of applied science from biophysics to astronomy. In this paper using a two-dimensional system as an example we study approaches to calculate the scattering properties of semi-infinite densely packed media with high contrast and wavelength scale inhomogeneities. We develop two methods by combining the Fourier Modal Method and the super-cell approach. Our work demonstrates the ability to obtain ensemble averaged solutions to the Maxwell's equations in complex media, while the demonstrated numerical convergence on the size parameters of the system supports the consistency of the approaches considered.

Ab initioinvestigation of the lattice dynamics and thermophysical properties of BCC vanadium and niobium.

In the present work, we have performed the phonon dispersion calculations of body-centered cubic vanadium (V) and niobium (Nb) with the supercell approach using different supercell size. Using DFT method, the calculated phonon spectra of V and Nb are found to be in a good agreement with the available experimental data. Our calculated results show a 'dip'-like feature in the longitudinal acoustic phonon mode along the Γ-H high symmetric path for both transition metals in the case of supercell size4×4×4. However, in supercell size2×2×2and3×3×3, the 'dip'-like feature is not clearly visible. In addition to this, thermodynamical properties are also computed, which compare well with the experimental data. Apart from this, the phonon lifetime due to electron-phonon interactions (τephph) and phonon-phonon interactions (PPIs) (τphph) are calculated. The effect of PPIs is studied by computing the average phonon lifetime for all acoustic branches. The value ofτephphof V (Nb) is found to be 23.16 (24.70)×10-15s at 100 K, which gets decreased to 1.51 (1.85)×10-15s at 1000 K. Theτphphof V (Nb) is found to be 8.59 (18.09)×10-12and 0.83 (1.76)×10-12s at 100 and 1000 K, respectively. Nextly, the lattice thermal conductivity is computed using linearized phonon Boltzmann equation. The present work suggests that studying the variation of phonon dispersion with supercell size is crucial for understanding the phonon properties of solids accurately.

Weighted average effective band structure of disordered solids

In this paper, a straightforward first-principles based method is proposed to determine the average effective electron band structure of disordered solids using supercell approach and plane-wave basis. Calculations have been done by determining the expectation values of the supercell Hamiltonian in a primitive-cell-periodic basis. The formulation and implementation details are presented and discussed. Also, it is shown that, in the cases with small differences in bonding characteristics at atomic-scale resolution, the weighted average bands are almost continuous. Therefore, it is possible to calculate the average effective band gap and average effective mass of electron/hole in different valleys. Analysis of the results for a number of disordered compounds shows that the proposed technique has the potential to explain and predict the experimental observations. This method is a promising tool for the study of the role of order/disorder in the electronic properties of random alloys and 2D and 3D imperfect materials.

Dynamical Stability and Physical Properties of Fe Dihalide Nanowires

AbstractAn extensive first‐principles and atomistic Monte Carlo study on isolated Fe ( = F, Cl, Br, I) nanowires is presented. The structural properties of the Fe chains are determined and compared with their bulk structures. The results indicate that in the lowest energy configuration, the wires crystalize in a system that belongs to the space group (No. 131, Z = 2, point group ), with antiferromagnetic arrangement. The stability is determined by calculating the phonon frequencies in the whole Brillouin zone within the supercell approach. The relative stability of the periodic chains is also determined by calculating the elastic properties and comparing them with bulk cases. The band structure, the density of states, the magnetic properties, the anisotropy energy, and topological analysis, performed with the Quantum Theory of Atoms in Molecules approach, are also reported and discussed. The results support the idea that these Fe nanowire systems are promising materials for practical applications, like lithium‐ion batteries.

Tuning the magnetic interactions in van der Waals Fe3GeTe2 heterostructures: A comparative study of ab initio methods

We investigate the impact of mechanical strain, stacking order, and external electric fields on the magnetic interactions of a two-dimensional (2D) van der Waals (vdW) heterostructure in which a 2D ferromagnetic metallic Fe$_3$GeTe$_2$ monolayer is deposited on germanene. Three distinct computational approaches based on \textit{ab initio} methods are used, and a careful comparison is given: (i) The Green's function method, (ii) the generalized Bloch theorem, and (iii) the supercell approach. First, the shell-resolved exchange constants are calculated for the three Fe atoms within the unit cell of the freestanding Fe$_3$GeTe$_2$ monolayer. We find that the results between methods (i) and (ii) are in good qualitative agreement and also with previously reported values. An electric field of ${\cal E}= \pm 0.5$~V/{\AA} applied perpendicular to the Fe$_3$GeTe$_2$/germanene heterostructure leads to significant changes of the exchange constants. We show that the Dzyaloshinskii-Moriya interaction (DMI) in Fe$_3$GeTe$_2$/germanene is mainly dominated by the nearest neighbors, resulting in a good quantitative agreement between methods (i) and (ii). Furthermore, we demonstrate that the DMI is highly tunable by strain, stacking, and electric field, leading to a large DMI comparable to that of ferromagnetic/heavy metal (FM/HM) interfaces. The geometrical change and hybridization effect explain the origin of the high tunability of the DMI at the interface. The electric-field driven DMI obtained by method (iii) is in qualitative agreement with the more accurate \textit{ab initio} method used in approach (ii). However, the field-effect on the DMI is overestimated by method (iii) by about 50\%. The magnetocrystalline anisotropy energy can also be drastically changed by the application of compressive or tensile strain in the Fe$_3$GeTe$_2$/germanene heterostructure.

Effect of Confinement and Coulomb Interactions on the Electronic Structure of the (111) LaAlO3/SrTiO3 Interface.

A tight binding supercell approach is used for the calculation of the electronic structure of the (111) LaAlO3/SrTiO3 interface. The confinement potential at the interface is evaluated solving a discrete Poisson equation by means of an iterative method. In addition to the effect of the confinement, local Hubbard electron-electron terms are included at the mean-field level within a fully self-consistent procedure. The calculation carefully describes how the two-dimensional electron gas arises from the quantum confinement of electrons near the interface due to the band bending potential. The resulting electronic sub-bands and Fermi surfaces show full agreement with the electronic structure determined by angle-resolved photoelectron spectroscopy experiments. In particular, we analyse how the effect of local Hubbard interactions change the density distribution over the layers from the interface to the bulk. Interestingly, the two-dimensional electron gas at the interface is not depleted by local Hubbard interactions which indeed induce an enhancement of the electron density between the first layers and the bulk.

First-principles study of the strain effect with half-metallic ferromagnetism in Cd 1−x V x Te alloys: supercell approaches

In this work, we study the effect of vanadium (V) dopantson the structural, electronic, and magnetic properties of the CdTe alloys using density functional theory (DFT). The calculations are performed as a function of the concentration of V in the host CdTe semiconductor using a 2 × 2 × 1 tetragonal supercell and a 2 × 2 × 2 cubic supercell. The lattice constants and bulk modulus of Cd 1−x V x Te alloys are determined. The analysis of the density of states shows that the Cd0.75 V0.25Te alloys in both supercells present a total polarization of 100% at the Fermi level, which confirms a stable half-metallic ferromagnetism phase in these materials, in contrast to the Cd 0.9375 V 0.0625 Te and Cd 0.875 V 0.125 Te alloys, which have a polarizability that does not reach 100%. In addition, the electronic band structures are used to estimate the s(p) − d exchange constants mainly resulting from the p − d hybridization between V- 3d and Te-p. Furthermore, the local magnetic moment of V of its free space charge value decreases, leading to the appearance of a small magnetic moment on the Cd and Te sites. Besides, the magnetic stability at different doping concentrations in the ferromagnetic (FM) and anti-ferromagnetic (AFM) states is examined, where the total energy of the systems is considered as a stability criterion. The robustness of the half-metallicity and the curie temperatures under the strain effect are also investigated. Finally, we rely on the binding energy to evaluate the energetic stability of the vanadium in the intrinsic compound CdTe under external deformations.

VTAnDeM: A python toolkit for simultaneously visualizing phase stability, defect energetics, and carrier concentrations of materials

Phase stability, defect formation energies, and carrier concentrations are closely interrelated features of semiconductors. Due to their joint dependence on the multidimensional chemical potential space, it is challenging to quantitatively establish patterns between these quantities in a given semiconductor, especially when the semiconductor is comprised of multiple elements. To enable synchronous visualization and analysis of these complementary material properties and their interdependence, we developed the Visualization Toolkit for Analyzing Defects in Materials (VTAnDeM). This python-based toolkit allows users to interactively explore how defect formation energies and carrier concentrations vary across the composition and chemical potential spaces of multicomponent semiconductors. Here, we illustrate the computational workflow that employs VTAnDeM as a post-processing tool for first-principles calculations and describe the data organization and theory underlying the visualization scheme. We believe that this software will serve as a useful tool for simultaneously visualizing the often complex and non-intuitive chemical potential – defect – carrier concentration phase space of semiconductors. Program summaryProgram Title: VTAnDeM – Visualization Toolkit for Analyzing Defects in MaterialsCPC Library link to program files:https://doi.org/10.17632/hz7dyc489v.1Developer's repository link:https://github.com/ertekin-research-group/VTAnDeMLicensing provisions: MIT LicenseProgramming language: PythonNature of problem: Defect thermodynamics are often studied from the perspective of phase stability and defect formation energetics using first-principles calculations. The results are comparable to experimentally-measurable carrier concentrations. However, visualizing all properties simultaneously by exploring the multidimensional chemical phase space is not trivial.Solution method: VTAnDeM offers a graphical interface that allows the user to interact directly with the chemical phase space of a given material and to visualize the defect formation energetics and ensuing carrier concentrations. The computational methods derive from standard defect theory within the supercell approach. The synchronous visualization scheme provides a streamlined approach to analyzing defect-related properties in semiconductors and insulators, all in real time.Additional comments including restrictions and unusual features: Required packages, installation, and tutorials can be found on the Github page.

Ductility reduction upon cobalt substitution in B2 NiTi

This paper reports the effect of ternary addition of cobalt to B2 NiTi by varying concentrations × = 0.125, 0.25 and 0.375 in Ni0.5−xCoxTi0.5 and the impact on their crystal structure, electronic and mechanical properties using first-principles calculations. The third element Co was substituted on both Ni and Ti sub-lattices using the supercell approach, site preference energy and formation energy suggest the preference of Co substitution on Ni sub-lattice agreeing with literature. The evolution of the electronic and mechanical properties from undoped NiTi to TiCo by substitution of Ni by Co is hereby discussed. Young’s (E) and shear (G) modulus is found to gradually increase as concentration (x) is increased. Importantly, ductility decreases with increasing cobalt concentration. From DOS, it is observed that the delocalized d states are reduced upon increasing Co addition due to strong d-d hybridization which reduces the metallicity and in turn ductility. This increase in Young’s modulus and decrease in ductility upon cobalt addition is indicative of the overall stiffness and resistance to deformation.

Monitoring Amine Intercalation in H3Sb3P2O14 Thin Films Based on Real-Time X-ray Diffraction Data Analysis

Thin films comprised of 2D materials have attracted significant attention, as they can be assembled into novel functional materials. However, to further enhance their application scope, it is necessary to harvest the large property space of 2D materials by fine-tuning them on a molecular level, e.g., by intercalation. In order to fully exploit the potential of intercalated 2D materials and design their properties, it is vital to gain a fundamental understanding of the underlying intercalation mechanism. In this work, we present a method for the quantitative analysis of changes in the peak profile and position observed by in situ synchrotron measurements upon the intercalation of the guest molecule into the layered host. We do this by monitoring the intercalation of n-butylamine (3 M in ethanol) into a H3Sb3P2O14 thin film in real time. Our approach includes a state-of-the-art recursive supercell approach that accounts for peak broadening and shifting caused by randomly occurring intercalation, which enabled quantitative Rietveld refinements of the XRD patterns obtained during the interstratification process. This allowed us to reveal the transient formation of intermediates and the critical role of ethanol, which acts as a vehicle for amine intercalation into the layered host.