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From Multipole Methods to Photonic Crystal Device Modeling
Published in Kiyotoshi Yasumoto, Electromagnetic Theory and Applications for Photonic Crystals, 2018
Lindsay C. Botten, Ross C. McPhedran, C. Martijn de Sterke, Nicolae A. Nicorovici, Ara A. Asatryan, Geoffrey H. Smith, Timothy N. Langtry, Thomas P. White, David P. Fussell, Boris T. Kuhlmey
This form is identical to that of (2.27), with the exception of the interior or exterior source terms. Before dealing with this problem further and, in particular, the characterization of the periodicity, we generalize the treatment to consider a lattice of identical unit cells, each of which comprises a common, finite set of identically placed cylinders (Figure 2.5). For such composite structures, it is common to refer to the unit cell as a supercell. The characterization of the geometry of this structure requires two vector bases: A basis of lattice vectors {a1, a2} that generates the supercells with the vector rl defining the position of the center of supercell l′ = (l′2, l′2) given by rl = l′1a1 + l′2a2. A local basis within each supercell, where the vector ρl″, determines the position of cylinder l″ relative to a reference point in each supercell (typically the center of the supercell).
κ dielectrics
Published in Michel Houssa, κ Gate Dielectrics, 2003
Gian-Marco Rignanese, Xavier Gonze, Alfredo Pasquarello
In tackling this technological problem, we face the more general issue of predicting the dielectric properties of amorphous alloys from first principles. Brute force analysis of numerous large supercells is beyond present computational capabilities. To overcome this difficulty, we establish a relationship between the dielectric properties of Zr silicates and their underlying nanoscopic structure. Using DFT, we compute optical and static dielectric constants for various model structures of Zr silicates, both ordered and disordered. We introduce a scheme which relates the dielectric constants to the local bonding of Si and Zr atoms. This scheme is based on the definition of parameters characteristic of the basic SUs formed by Si and Zr atoms and their nearest neighbours.
First Principles Calculations in Exploring the Magnetism of Oxide-Based DMS
Published in Jiabao Yi, Sean Li, Functional Materials and Electronics, 2018
In general, a periodically repeated supercell is adopted to simulate the structure of the material and its properties. However, spurious interactions may emerge due to the periodic supercell boundary, especially when defects are introduced into the systems. In addition, the ionic relaxations are artificially introduced into the supercell, to which the errors in the geometry optimization and relaxation and elastic energies can be accounted.
Systematic derivation of maximally orthogonalized supercells
Published in Science and Technology of Advanced Materials: Methods, 2022
Finding supercells with a desirable size and reasonable geometry is a non-trivial task. One application of supercells is investigation of dilute defects and alloys, where a small portion of atoms among symmetrically equivalent sites is replaced by a vacancy or another element. Supercells are used in the defect energy correction formalism by Freysoldt, Neugebauer, and Van de Walle [1] as well as its extension to anisotropic systems and/or relaxed geometries by Kumagai and Oba [2]. The defect concentration can be adjusted by using supercells of different sizes, but choosing reasonable basis vectors for a supercell of a given size is a separate and important problem. Basis vectors with almost the same length and close to orthogonality are typically favored than, for instance, a rod-shaped orthorhombic cell or a rhombohedral cell very elongated in one direction because the distance between neighboring defects can become unnecessarily close to each other. Moreover, orthogonal basis vectors allow trivial transformation between fractional and Cartesian coordinates of atoms, and the atom environments at the unit cell boundaries are easy to imagine from visualization of a single unit cell compared to crystals with basis vectors that are far from orthogonality.
Quantum-mechanical simulations of pressure effects on MgIn2S4 polymorphs
Published in Phase Transitions, 2018
S. Belarouci, T. Ouahrani, N. Benabdallah, Á. Morales-García, R. Franco
Some other works [10,11,12], have studied electronic, optical and thermodynamic properties of MgInS under pressure conditions. Nonetheless, these investigations remain insufficient because they consider only the direct (x=0) phase, whereas the recent consistent experimental observations of Refs. [1,2,3] have shown that the ambient conditions phase of MgInS has an inversion parameter close to 1. Theoretical investigations of this stable phase remain scarce. Computational studies of theorder–disorder behavior in spinel compounds are possible [13,14,15] by means of a combination of Monte Carlo [16] and cluster expansion [17,18] (special quasyrandom structure) simulations or by periodic crystalline calculations with specific x values [19,20]. The involvement of temperature in these schemes and the need of large supercell structures make them very expensive in computational terms. Fortunately, and to reasonably mimic the observed polymorphs with an affordable computational cost, it is possible to simultaneously model both the ideal inverse spinel and the high-pressure phase, using the same orthorhombic space group Imma [1].
Room-temperature ferromagnetism in boron-doped oxides: a combined first-principle and experimental study
Published in Philosophical Magazine Letters, 2020
Homnath Luitel, Sujata Roy, Mahuya Chakrabarti, P. Chettri, A. Tiwari, V. Naik, D. Sanyal
Theoretical calculations have been performed using density functional theory (DFT) with MedeA software based on the Vienna ab-initio simulation (VASP) code [44–47]. Throughout the calculations, the generalised gradient approximation (GGA) and the Perdew–Burke–Ernzerhof (PBE) method is used to calculate the exchange and correlation energies [48]. A tetragonal unit cell with lattice constants a = 4.59 Å and c = 2.96 Å has been used to study the TiO2 system. A 2 × 2 × 3 supercell has been made by multiplying unit cells along the crystallographic axes (i.e. with 72 atoms in a supercell of TiO2). Similarly, for CdO and MgO, an FCC unit cell (lattice constants a = 4.699 Å for CdO and a = 4.211 Å for MgO) has been taken to construct a supercell with 2 × 2 × 2 unit cells consisting of 64 atoms. In the case of ZnO, a wurtzite structured unit cell (a = 3.25 Å and c = 5.2 Å) has been used to construct a 3 × 3 × 3 supercell with 108 atoms. Periodic boundary conditions have been implemented along all the basis vectors while constructing the supercell. In all the cases, a pristine supercell has been taken and two oxygen atoms in the matrix were substituted by two boron atoms. Then an optimisation of each doped structure was performed with lattice parameter optimisation and the atoms allowed to relax unless the value of the residual force became less than 0.02 eV/Å. The Monkhorst–Pack (MP) method [49] was used to generate 4 × 4 × 4 k-points in the Brillouin zone (BZ). To ensure self-consistency, the difference in total energies between two consecutive loops was set to 10−5 eV and the mesh cut-off energy to expand the plane wave fixed at 400 eV. Density of states (DOS) calculations have been performed, at spin-polarized condition, for each optimised structure and the value of the magnetic moment generated in the system calculated. The DOS calculation results are compared with the local magnetic density (LMD) distribution in the spin-polarized condition. Spin–spin interaction study has been undertaken to understand the stability of the magnetically ordered system. Two identical defects are created at two different positions; in the first case, two doping positions have been chosen in the same unit cell and in another case, two dopants have been added in adjacent unit cells. The ferromagnetic and anti-ferromagnetic ordered systems are constructed by aligning the spins of all atoms in parallel and anti-parallel directions respectively. The difference of ground-state energy in the ferromagnetic (parallel spin-ordered) state and anti-ferromagnetic (anti-parallel spin-ordered) state is considered to understand the stability of spin ordering in all both cases. The spin-ordered system with the lower value of ground-state energy is found to be the stable state.