Supercell Size Research Articles

First-principles investigation on metal tantalum under conditions of electronic excitation

Intense laser irradiated on metals can excite the electrons to high energy levels, and lead to a high electronic temperature established in a period of 10–100fs. The properties of metals would be affected by the high electronic temperature. In this paper, finite-temperature density functional theory with hot electron is used to investigate the free energy F and DFT energy E of metal tantalum varying with the supercell volume at different electronic temperatures. In addition, the formation enthalpies of a monovacancy are calculated at different electronic temperatures. The convergence tests for the k-points grid, the bands and the supercell size we selected are carefully carried out to improve accuracy of calculation. The calculated value of monovacancy formation enthalpy at ambient pressure and temperature is good agreement with previous experimental and theoretical values. What is more, the tendency of the monovacancy formation enthalpy increasing as the increment of the electronic temperature can explain the fact that the increase of the melting temperature under high electronic temperature.

Ab initio investigation on the magnetic ordering in Gd doped ZnO

The current study investigates the magnetic properties of the GdxZn1-xO, with x=0.0625 and 0.0185, doped semiconductor using the full potential (linearized) augmented plane wave plus local orbital method. We show that in contrast to the findings of Shi et al. [J. Appl. Phys. 106, 023910 (2009)], the implementation of the Hubbard U parameter to the Gd f states favors an antiferromagnetic phase in both wurtzite GdO and GdxZn1-xO. Spin polarized calculations on GdxZn1-xO indicate that, even if a ferromagnetic ground state were favored, the magnetic influence of Gd in a perfect ZnO wurtzite lattice is highly localized and limited to the first three nearest neighboring O atoms. Increasing the supercell size and thus diluting the concentration of Gd within the ZnO matrix does not show any changes in the net magnetic moment between these three O atoms nor in the remaining lattice sites, indicating that sizing effects do not influence the range of matrix polarization. We conclude that the localized Gd induced polarization can not account for long range magnetic ordering in a defect-free ZnO wurtzite lattice.

Adaptive dynamical cell-clustering in coordinated multipoint network-MIMO transmission systems

As one of the most promising techniques for next generation wireless communication, coordinating transmission by multiple points (i.e., radio access points or base stations) have recently attracted a lot of attention because of its potential for intercell co-channel interference mitigation and significant spectral efficiency improvement. This paper firstly presents the system structure and mathematical signal model for multipoint coordinating downlink transmission, and then gives a detailed discussion on dynamical cell-clustering strategies, scheduling utility-metric and resources allocation scheme in adaptively forming cooperation cluster of cells based on detected system parameters, where the user is serviced by a cluster selected from a set of clusters that has been adapted to its particular network circumstance and location. Some numerical analysis shows that with dynamical cell-clustering, a clustered supercell size of 7 is a reasonable choice for improving spectral efficiency. Also, some simulation results are also given to show that the proposed adaptive dynamical cell-clustering methods are beneficial to user performance improvement.

Magnetic perturbation and associated energies of the antiphase boundaries in ordered Ni3Al

The anisotropy of antiphase boundary (APB) energies in ordered L12–Ni3Al is studied, owing to its importance in understanding the anomalous flow behavior of this intermetallic compound. We report first-principle calculations for two types of APBs in the ordered compound: (001) and (111). The magnetic perturbations associated with these APBs are calculated as a function of supercell size to ensure that their periodic images are isolated both magnetically and elastically. The magnetic perturbation associated with the (111) APB is wider than that of the (001) APB. The fully relaxed, spin-polarized APB energies for (001) and (111) APBs are calculated to be 82 mJ/m2 and 177 mJ/m2, respectively. The resulting anisotropy ratio of σ(111)/σ(001)=2.16, which is significantly higher than previously reported values, suggests that cross-slip between (001) and (111) is highly favorable.

Band gap bowing of binary alloys: Experimental results compared to theoretical tight-binding supercell calculations forCdxZn1−xSe

Compound semiconductor alloys of the type ${\text{A}}_{x}{\text{B}}_{1\ensuremath{-}x}\text{C}$ find widespread applications as their electronic bulk band gap varies continuously with $x$, and therefore a tailoring of the energy gap is possible by variation in the concentration. We model the electronic properties of such semiconductor alloys by a multiband $s{p}^{3}$ tight-binding model on a finite ensemble of supercells and determine the band gap of the alloy. This treatment allows for an intrinsic reproduction of band bowing effects as a function of the concentration $x$ and is exact in the alloy-induced disorder. In the present paper, we concentrate on bulk ${\text{Cd}}_{x}{\text{Zn}}_{1\ensuremath{-}x}\text{Se}$ as a well-defined model system and give a careful analysis on the proper choice of the basis set and supercell size, as well as on the necessary number of realizations. The results are compared to experimental results obtained from ellipsometric measurements of ${\text{Cd}}_{x}{\text{Zn}}_{1\ensuremath{-}x}\text{Se}$ layers prepared by molecular beam epitaxy and photoluminescence measurements on catalytically grown ${\text{Cd}}_{x}{\text{Zn}}_{1\ensuremath{-}x}\text{Se}$ nanowires reported in the literature.

Role of structural disorder in optical absorption in silicon

Using density-functional theory calculations, we explore the effects of structural disorder on optical absorption in crystalline Si. We incorporate neutral, ground-state vacancy clusters (${V}_{n}$, $n\ensuremath{\le}6$, $n=12$ and 32) to incrementally introduce disorder and compare results to the limiting cases exemplified by amorphous and crystalline Si. In particular, we compute optical spectra for the dielectric function, $\ensuremath{\epsilon}(\ensuremath{\omega})$, and absorption coefficient, $\ensuremath{\alpha}(\ensuremath{\omega})$, and observe substantial absorption enhancement for all fourfold-coordinated vacancy clusters, similar to the expanded $\ensuremath{\alpha}(\ensuremath{\omega})$ envelope of amorphous Si over crystalline Si. We isolate structural contributions to absorption using constant-density vacancy cluster distributions to show that increased structural disorder predictably enhances absorption. In addition, we observe diminished absorption of ${V}_{1}$ as a function of supercell size, suggesting dilute ${V}_{n}$ concentrations may be difficult to physically verify. Furthermore, we found the density effect on absorption insignificant in amorphous Si at the subnanometer scale, so we discuss the expected contribution of density from a multiscale perspective.

Order–disorder phase boundary between ice VII and VIII obtained by first principles

We report fundamental progress in the description of an archetypical hydrogen-bonded system: H 2 O –ice. We calculated by first principles the ice VII–VIII phase boundary, an order–disorder phase boundary, by performing a complete sampling of configurations in a 16-molecule supercell. Vibrational effects are included within quasiharmonic theory. Several important features were successfully described: negative Clapeyron slope, isotope effect, and nearly-constant T c at low pressures. The equation of state was very well described below 40 GPa. Inclusion of tunneling effects and increase of supercell size should decrease the remaining discrepancies, i.e., the overestimation of volume above ∼40 GPa and the underestimation of T c .

Convergence study of neutral and charged defect formation energies in Si nanowires

We present a systematic study of the convergence with the supercell size of the defect formation energy of a substitutional Al impurity in a Si nanowire within density-functional theory. We discuss the case of neutral and charged impurities, highlighting the importance, in the presence of ionized defects and periodic boundary conditions, of including a Madelung-like correction to the total energy in order to get correct results, which cannot be obtained by the simple use of a large vacuum buffer layer or an extrapolation thereof.

First-principles study on the formation of a vacancy in Ge under biaxial compressive strain

The effects of the biaxial compressive strain on the atomic relaxation and the formation energy of a neutral vacancy in Ge were investigated using first-principles calculations. Prior to this, the effects of the supercell size and Brillouin zone sampling were tested. The vacancy formation energy and atomic configuration around a vacancy are strongly affected by the inter-vacancy distance determined by the supercell size, due to the periodic boundary condition. The biaxial compressive strain reduced the formation energy of the vacancy nearly linearly by up to 1.34 eV as the magnitude of the biaxial compressive strain increased to the “Ge on Si ( GoS)” condition. This was explained in terms of the bond strength characterized by the spatial electron density. The behavior of the vacancy in Ge was also compared with that in Si.

First-principles calculations of twin-boundary and stacking-fault energies in magnesium

The interfacial energies of twin boundaries and stacking faults in metal magnesium have been calculated using first-principles supercell approach. Four types of twin boundaries and two types of stacking faults are investigated, namely, those due to the ( 1 0 1 ¯ 1 ) mirror reflection, the ( 1 0 1 ¯ 1 ) mirror glide, the ( 1 0 1 ¯ 2 ) mirror reflection, the ( 1 0 1 ¯ 2 ) mirror glide, the I1 stacking fault and the I2 stacking fault. The effects of supercell size on the calculated interfacial energies are examined.

Modeling of hydrogen and hydroxyl group migration on graphene

Density functional calculations of optimized geometries for the migration of single hydrogen and hydroxyl groups on graphene are performed. It is shown that the migration energy barrier for the hydroxyl group is three times larger than for hydrogen. The crucial role of supercell size for the values of the migration barriers is discussed. The paired migration of hydrogen and hydroxyl groups has also been examined. It could be concluded that hydroxyl group based magnetism is rather stable in contrast with unstable hydrogen based magnetism of functionalized graphene. The role of water in the migration of hydroxyl groups is also discussed, with the results of the calculations predicting that the presence of water weakens the covalent bonds and makes these groups more fluid. Increasing the number of water molecules associated with hydroxyl groups provides an increase of the migration energy.

Free energies of ferroelectric crystals from a microscopic approach

The free energy of barium titanate is computed around the Curie temperature as a function of polarization P → from the first-principles derived Effective Hamiltonian of Zhong, Vanderbilt and Rabe [Phys. Rev. Lett. 73 (1994) 1861], through Molecular Dynamics simulations coupled to the method of the Thermodynamic Integration. The algorithms used to fix the temperature (Nosé–Hoover) and/or the pressure/stress (Parrinello–Rahman), combined with fixed-polarization molecular dynamics, allow to compute a Helmholtz free energy (fixed volume/strain) or a Gibbs free energy (fixed pressure/stress). The main feature of this approach is to calculate the gradient of the free energy in the 3-D space ( P x , P y , P z ) from the thermal averages of the forces acting on the local modes, that are obtained by Molecular Dynamics under the constraint of fixed P → . This work extends the method presented in [Phys. Rev. B 79 (2009) 064101] to the calculation of the Gibbs free energy and presents new features about the computation of the free energy of ferroelectric crystals from a microscopic approach. A careful analysis of the states of constrained polarization is performed at T = 280 K (≈15–17 K below T c ) especially at low order parameter. These states are found reasonably homogeneous for small supercell size ( L = 12 and L = 16 ), until inhomogeneous states are observed at low order parameter for large supercells ( L = 20 ). The effect of this evolution towards multidomain configurations on the mean force and free energy curves is shown. However, for reasonable supercell sizes ( L = 12 ), the free energy curves obtained are in very good agreement with phenomenological Landau potentials of the literature and the states of constrained polarization are homogeneous. Moreover, the free energy obtained is quite insensitive to the supercell size from L = 12 to L = 16 at T = 280 K , suggesting that interfacial contributions, if any, are negligible at these sizes around T c . The method allows a numerical estimation of the free energy barrier separating the paraelectric from the ferroelectric phase at T c ( Δ G ≈ 0.012 – 0.015 meV / 5 -atom cell ). However, our tests evidence phase separation at low temperature and low order parameter, in agreement with the results of Tröster et al. [Phys. Rev. B 72 (2005) 094103]. Finally, the natural decomposition of the forces into onsite, short-range, dipole–dipole and elastic–local mode interaction allows to make the same decomposition of the free energy. Some parts of this decomposition can be directly calculated from the coefficients of the Effective Hamiltonian.

Single and multiple scattering XAFS Debye-Waller factors for crystalline materials using periodic Density Functional Theory

We present an accurate and efficient technique for calculating thermal X-ray absorption fine structure (XAFS) Debye-Waller factors (DWFs) applicable to crystalline materials. Using Density Functional Theory on a 3×3×3 supercell pattern of MnO structure, under the nonlocal hybrid B3LYP functional paired with Gaussian local basis sets, we obtain the normal mode eigenfrequencies and eigenvectors; these parameters are in turn used to calculate single and multiple scattering XAFS DWFs. The DWFs obtained via this technique are temperature dependent expressions and can be used to substantially reduce the number of fitting parameters, when experimental spectra are fitted with a hypothetical structure. The size of the supercell size limits the R-space range that these parameters could be used. Therefore corresponding DWFs for paths outside of this range are calculated using the correlated Debye model. Our method is compared with prior cluster calculations and with corresponding values obtained from fitting experimental XAFS spectra on manganosite with simulated spectra.

First-principles calculations of the electronic structure and Mössbauer parameters of Sb-doped [formula omitted

The electronic structure and the 119Sn and 121Sb Mössbauer parameters of Sb-doped SnO 2 were calculated using a first-principles method. We show that substitution of Sn by Sb leads to a small decrease of the distances between the dopant and the six oxygen first-nearest neighbours. The most important modifications in the electronic structure are related to the bottom of the conduction band, which has Sb 5s, Sn 5s and O 2p characters. By considering two supercell sizes and charged supercells we show that antimony oxidation state is Sb 5+ and we explain the origin of the Mössbauer parameters from the local electronic structure of the cations.

First-principles study of neutral silicon interstitials in 3C- and 4H-SiC

The structures and stability of single silicon interstitials in their neutral state are investigated via first principles calculations in 3C- and 4H-SiC. By carefully checking the convergence with Brillouin zone (BZ) sampling and supercell size, we explain the disagreement between previous published results and show that the split interstitial along ⟨110⟩ direction and tetrahedrally carbon coordinated structure have competing formation energies in the cubic polytype. A new migration mechanism for the silicon interstitial in the neutral state is presented here, which could be important for the evolution of defect populations in SiC. For 4H-SiC, the most energetically favourable silicon interstitial is found to be the split interstitial configuration ISisp⟨110⟩ but situated in the hexagonal layer. The defect formation energies in 4H-SiC are, in general, larger than those in 3C-SiC, implying that the insertion of silicon interstitial introduces a large lattice distortion to the local coordination environments and affects even the second- or third-nearest neighbours. We also present a comparison between well converged plane-waves calculations and calculations with three localised orbital basis sets; one of them, in spite of providing a reasonable description for bulk properties, is clearly not suitable to describe interstitial defects.

A theoretical study of intrinsic point defects and defect clusters in magnesium aluminatespinel

Point and small cluster defects in magnesium aluminate spinel have been studiedfrom a first principles viewpoint. Typical point defects that occur during collisioncascade simulations are cation anti-site defects, which have a small formationenergy and are very stable, O and Mg split interstitials and vacancies. IsolatedAl interstitials were found to be energetically unfavourable but could occur aspart of a split Mg–Al pair or as a three atom–three vacancy Al ‘ring’ defect,previously observed in collision cascades using empirical potentials. The structure andenergetics of the defects were investigated using density functional theory (DFT)and the results compared to simulations using empirical fixed charge potentials.Each point defect was studied in a variety of supercell sizes in order to ensureconvergence. It was found that empirical potential simulations significantly overestimateformation energies, but that the type and relative stability of the defects are wellpredicted by the empirical potentials both for point defects and small defect clusters.

All‐electron LCAO calculations of the LiF crystal phonon spectrum: Influence of the basis set, the exchange‐correlation functional, and the supercell size

For the first time the convergence of the phonon frequencies and dispersion curves in terms of the supercell size is studied in ab initio frozen phonon calculations on LiF crystal. Helmann-Feynman forces over atomic displacements are found in all-electron calculations with the localized atomic functions (LCAO) basis using CRYSTAL06 program. The Parlinski-Li-Kawazoe method and FROPHO program are used to calculate the dynamical matrix and phonon frequencies of the supercells. For fcc lattice, it is demonstrated that use of the full supercell space group (including the supercell inner translations) enables to reduce essentially the number of the displacements under consideration. For Hartree-Fock (HF), PBE and hybrid PBE0, B3LYP, and B3PW exchange-correlation functionals the atomic basis set optimization is performed. The supercells up to 216 atoms (3 x 3 x 3 conventional unit cells) are considered. The phonon frequencies using the supercells of different size and shape are compared. For the commensurate with supercell k-points the best agreement of the theoretical results with the experimental data is found for B3PW exchange-correlation functional calculations with the optimized basis set. The phonon frequencies at the most non-commensurate k-points converged for the supercell consisting of 4 x 4 x 4 primitive cells and ensures the accuracy 1-2% in the thermodynamic properties calculated (the Helmholtz free energy, entropy, and heat capacity at the room temperature).

PHON: A program to calculate phonons using the small displacement method

The program phon calculates force constant matrices and phonon frequencies in crystals. From the frequencies it also calculates various thermodynamic quantities, like the Helmholtz free energy, the entropy, the specific heat and the internal energy of the harmonic crystal. The procedure is based on the small displacement method, and can be used in combination with any program capable to calculate forces on the atoms of the crystal. In order to examine the usability of the method, I present here two examples: metallic Al and insulating MgO. The phonons of these two materials are calculated using density functional theory. The small displacement method results are compared with those obtained using the linear response method. In the case of Al the method provides accurate phonon frequencies everywhere in the Brillouin Zone (BZ). In the case of MgO the longitudinal branch of the optical phonons near the centre of the BZ is incorrectly described as degenerate with the two transverse branches, because the non-analytical part of the dynamical matrix is ignored here; however, thermodynamic properties like the Helmholtz free are essentially unaffected. Program summary Program title: PHON Catalogue identifier: AEDP_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 19 580 No. of bytes in distributed program, including test data, etc.: 612 193 Distribution format: tar.gz Programming language: Fortran 90 Computer: Any Unix, Linux Operating system: Unix RAM: Depends on super-cell size, but usually negligible Classification: 7.8 External routines: Subprograms ZHEEV and DSYEV (Lapack); needs BLAS. A tutorial is provided with the distribution which requires the installation of the quantum-espresso package ( http://www.quantum-espresso.org) Nature of problem: Stable crystals at low temperature can be well described by expanding the potential energy around the atomic equilibrium positions. The movements of the atoms around their equilibrium positions can then be described using harmonic theory, and is characterised by global vibrations called phonons, which can be identified by vectors in the Brillouin zone of the crystal, and there are 3 phonon branches for each atom in the primitive cell. The problem is to calculate the frequencies of these phonons for any arbitrary choice of q-vector in the Brillouin zone. Solution method: The small displacement method: each atom in the primitive cell is displaced by a small amount, and the forces induced on all the other atoms in the crystal are calculated and used to construct the force constant matrix. Supercells of ∼100 atoms are usually large enough to describe the force constant matrix up to the range where its elements have fallen to negligibly small values. The force constant matrix is then used to compute the dynamical matrix at any chosen q-vector in the Brillouin zone, and the diagonalisation of the dynamical matrix provides the squares of the phonon frequencies. The PHON code needs external programs to calculate these forces, and it can be used with any program capable of calculating forces in crystals. The most useful applications are obtained with codes based on density functional theory, but there is no restriction on what can be used. Running time: Negligible, typically a few seconds (or at most a few minutes) on a PC. It can take longer if very dense meshes of q-points are needed, for example, to compute very accurate phonon density of states.

Stability of Neutral Silicon Interstitials in 3C- and 4H-SiC: A First-Principles Study

The structural stability and properties of single silicon interstitials in their neutral state are investigated via ab initio methods in 3C- and 4H-SiC. By carefully checking the convergence with Brillouin Zone (BZ) sampling and supercell size we show that the split interstitial along <110> direction and tetrahedrally coordinated structure have similar formation energies in the cubic polytype. We discuss possible artifacts coming from the well known Density Functional Theory (DFT) underestimation of the band gap, which is particularly relevant for 3C-SiC. For 4H-SiC, the most energetically favorable silicon interstitial is found to be the split interstitial configuration ISisp<110> but situated in the hexagonal layer. The defect formation energies in 4H-SiC are in general larger than those in 3C-SiC, implying that the insertion of silicon interstitial introduces a large lattice distortion to the local coordination environments and affect even the second- or third-nearest neighbors. We also present an extensive comparison between well converged plane waves calculations and SIESTA [1,2] calculations based on localised orbitals basis sets.

Adsorption of Molecular Hydrogen in a Graphene-Carbon Nanotube System

In this theoretical study, the H2 adsorption is considered in a novel system formed by a (6,6) carbon nanotube fragment and a planar graphene layer portion, when they are separated 4.72 a.u., with both subsystems inside a cubic supercell box of 25 a.u. side. There is greater H2 adsorption inside the carbon nanotube than in the interstitial space between the graphene layer and the carbon nanotube. The results are compared with the way the H2 molecule is adsorbed upon a lonely graphene layer and inside or outside the (6,6) carbon nanotube. It is studied if in the interstitial space close to the middle point between the wall and the graphene layer the hydrogen molecule could be adsorbed with a greater binding energy that in any other case. This was not possible for the selected supercell, but there are given some suggestions to be explored (using a nanotube with smaller radii or increasing the size of the supercell), that perhaps can optimize the binding energy for H2 adsorption. A general result is that the size of the cubic supercell can be selected to confine not only hydrogen inside the carbon nanotube but also in the interstitial space between the carbon nanotube wall and the graphene layer. It is believed that the studied system or a modification of this could sooner or later be used in a competitive way in comparison with other H2 storage materials respect to the hydrogen adsorption and desorption process.