Equilibrium Bulk Research Articles

Theoretical investigation of pressure-induced structural transitions in americium usingGGA+Uand hybrid density functional theory methods

First-principles calculations have been performed for americium (Am) metal using the generalized gradient approximation $+$ orbital-dependent onsite Coulomb repulsion via Hubbard interaction (GGA+$U$) and hybrid density functional theory (HYB-DFT) methods to investigate various ground state properties and pressure-induced structural transitions. Both methods yield equilibrium volume and bulk modulus in good agreement with the experimental results. The GGA+spin orbit coupling+$U$ method reproduced all structural transitions under pressure correctly, but the HYB-DFT method failed to reproduce the observed Am-I to Am-II transition. Good agreement was found between calculated and experimental equations of states for all phases, but the first three phases need larger $U$ (\ensuremath{\alpha}) parameters (where \ensuremath{\alpha} represents the fraction of Hartree-Fock exchange energy replacing the DFT exchange energy) than the fourth phase in order to match the experimental data. Thus, neither the GGA+$U$ nor the HYB-DFT methods are able to describe the energetics of Am metal properly in the entire pressure range from 0 GPa to 50 GPa with a single choice of their respective $U$ and \ensuremath{\alpha} parameters. Low binding-energy peaks in the experimental photoemission spectrum at ambient pressure relate, for some parameter choices, well to peak positions in the calculated density of states function of Am-I.

Computational Approaches for the Dynamics of Structure Formation in Self-Assembling Polymeric Materials

Polymeric materials can assemble into a multitude of intricate nanoscale morphologies whose free energy differs by only a fraction of the thermal energy per molecule. Such small free-energy differences pose a challenge for modeling and simulation but also offer exciting opportunities to direct the assembly of such materials into morphologies that do not correspond to those of equilibrium bulk structures. Over the past decade, significant progress has been achieved in our ability to guide their self-assembly through the use of confinement, topographical or chemical patterns, and electric fields. In contrast, approaches to guide self-assembly by tailoring the dynamics of structure formation have received less attention. This review discusses opportunities and challenges of recently developed computational strategies to predict the dynamics of self-assembly of polymeric materials on the basis of the underlying free-energy landscape.

Diffusion-induced fractionation of niobium and tantalum during continental crust formation

Differentiation of the Earth into its major spheres – crust, mantle and core – has proceeded dominantly through magmatic processes involving melting and melt separation. Models that describe these differentiation processes are guided by elemental abundances in the different reservoirs. Elements are fractionated between coexisting phases during partial melting, and geochemical models are generally based on the fundamental assumption that trace-element equilibrium is established between the partial melts and the restitic minerals. The element pair niobium and tantalum is key to the distinction of different melting regimes involved in crustal differentiation, but equilibrium partition models have largely failed to reproduce the Nb/Ta patterns observed in nature, posing a long-standing geochemical conundrum. Here we demonstrate that kinetic fractionation of Nb and Ta by diffusion may have produced the low Nb/Ta observed in the continental crust. On the basis of the diffusivities of Nb and Ta in rutile (TiO2) determined experimentally in this study, we conclude that equilibrium cannot be expected for the natural range of grain sizes, temperatures and time scales involved in partial melting of crustal rocks. Instead, the observed fractionation of the geochemical twins, Nb and Ta, in the silicate Earth most likely proceeds by partial – as opposed to complete – equilibration of rutile and melt. Hence, the assumption of bulk equilibrium during partial melting for the processes of crustal differentiation may not be justified, as is demonstrated here for Nb/Ta. The concept presented here is based on kinetic fractionation melting and explains the observed low Nb/Ta ratio of the continental crust.

Study of MgxCd1−xO applying density functional theory: Stability, structural phase transition and electronic properties

Stability of B1 and B2 phases of MgxCd1−xO is studied by calculating the formation energy within the framework of density functional theory applying the crystalline-orbital program package. Structural and electronic properties of the two polymorphs are reported for x=0.25, 0.50 and 0.75. The equilibrium lattice constants and bulk moduli are computed. Enthalpy calculations show pressure induced B1→B2 phase transitions at 92 GPa, 138 GPa and 212 GPa, respectively, for Mg0.25Cd0.75O, Mg0.50Cd0.50O and Mg0.75Cd0.25O compositions. Formation energy of ternary oxides in the B1 phase is negative with respect to mixing of B2-MgO with B1-CdO. Mixing B1-MgO with B2-CdO also leads to negative formation energy in Cd rich B1 phase ternary oxides (0≤x≤0.5). Band structure calculations predict direct band gaps in the B1 phase and indirect band gaps in the B2 phase ternary oxides. Mulliken population analysis is performed for the two polymorphs to study the charge transfer.

Accurate determination of band gaps within density functional formalism

In this paper, we report an adaptation of the Harbola-Sahni (HS) exchange potential to the tight-binding linear muffin-tin orbital (TB-LMTO) method to determine band gaps (BGs) of solids accurately. We show that the electrostatic basis of derivation of the Harbola-Sahni potential allows this nonvariational approach to improve substantially over local-density approximation derived BGs, bringing them very close to experimental values. That the accuracy of the HS potential is directly responsible for the determination of correct BGs is demonstrated by performing similar calculations with an accurate model potential that too leads to BGs close to their experimental values. Moreover, ground-state properties like equilibrium lattice parameters and bulk moduli (BM) for various semiconductors like C, Si, AlN, AlP, BP, and 3C-SiC calculated with the HS approach are in close agreement with the experiments. The clear physical interpretation of HS potential leads us to suggest exploring its use for calculating various properties of solids.

Electronic structure of francium

This article presents the first calculations of the electronic structure of francium for the bcc, fcc, and hcp structures, using the linearized augmented plane wave (LAPW) method. Both the local density approximation (LDA) and generalized gradient approximation (GGA) were used to calculate the electronic structure and total energy of francium (Fr). The GGA and LDA both found the total energy of the hcp structure to be slightly below that of the fcc and bcc structures, respectively. This is in agreement with similar results for the other alkali metals where the bcc structure is found not to be the ground state in contradiction to experiment. The equilibrium lattice constant, bulk modulus, and superconductivity parameters were calculated. Calculations of the enthalpy of the system suggest a structural transition from hcp to bcc under a pressure of 0.57 GPa. Using the McMillan-Gaspari-Gyorffy theories, we found that under further pressures, in the range of 3–14 GPa, Fr could be a superconductor with critical temperature up to 7 K. This is consistent with the other alkali metals and originates from an increase of the d-like density of states at the Fermi level, which makes the alkali metals behave like transition metals. © 2013 Wiley Periodicals, Inc.

First-principles prediction of the structural and electronic properties of zinc blende GaNxAs1−x alloys

To investigate the structural and electronic properties of zinc blende GaNxAs1−x alloys, we performed full-potential linearized augmented plane wave (FP-LAPW) calculations based on density functional theory. We assessed GaNxAs1−x alloys for 0≤x≤1 using 16-atom special quasi-random structures. The generalized gradient approximation (GGA) of Wu and Cohen was used as the exchange correlation potential to calculate the structural and electronic properties of GaNxAs1−x. In addition, the alternative GGA proposed by Engel and Vosko and the modified Becke–Johnson potential were used for better reproduction of the band structure and electronic properties. The equilibrium lattice parameters and bulk modulus were calculated and analyzed for binary and ternary alloys. The lattice constants for GaNxAs1−x positively deviate from Vegard's law with an upward bowing parameter of −0.4708Å. All our materials are direct-bandgap semiconductors for which the valence band maximum is located at Γv and the conduction band minimum at Γc. We observed that the direct bandgap of GaNxAs1−x increases nonlinearly with x. To shed light on the bandgap trend for increasing nitrogen concentrations in GaNxAs1−x, we used the atoms-in-molecule formalism. Special attention was paid to the increase in charge transfer for the nitrogen atom and to ionicity as a function of increasing x concentration.

FP-LMTO method to calculate the structural, thermodynamic and optoelectronic properties of SixGe1−xC alloys

The structural and electronic properties of the ternary SixGe1−xC alloys have been calculated using the full-potential linear muffin-tin-orbital (FP-LMTO) method based on density functional theory within both local density approximation (LDA) and generalised gradient approximation (GGA). The calculated equilibrium lattice constants and bulk moduli are compared with previous results. The concentration dependence of the electronic band structure and the direct and indirect band gaps are investigated. Using the approach of Zunger and co-workers, the microscopic origins of the band gap bowing are investigated also. Moreover, the refractive index and the optical dielectric constant for SixGe1−xC are studied. The thermodynamic stability of the alloys of interest is investigated by means of the miscibility. This is the first quantitative theoretical prediction to investigate the effective masses, optical and thermodynamic properties for SixGe1−xC alloy, and still awaits experimental confirmations.

Antiferromagnetic half-metallicity of transition metal nitrides under volume expansion

The transition metal pnictides ABX2 have been recently proposed as half-metallic fully compensated ferrimagnets, also briefly referred to as half-metallic “antiferromagnets” [N. Long, M.Ogura, H. Akai, J. Phys.: Condens. Matter 21, 064241 (2009)]. In this work we carry out a systematic study of the more promising cases of the transition metal nitrides MnCoN2 and NiCrN2 on the basis of density functional theory in the framework of full-potential linearized augmented plane wave method. The electronic structures and the magnetic properties of the above hypothetical compounds in Zinc-blende-type, NaCl-type, and Wurtzite-type structure are calculated within generalized gradient approximation. The results reveal that, although these compounds are metallic in their bulk equilibrium in all three structures, they exhibit antiferromagnetic half-metallicity under negative stress or volume expansion in a limited range of lattice parameters, which is significantly larger than the equilibrium values. This suggests that a situation in which half-metallicity may arise, is when these compounds are coated on semiconducting layers of larger lattice constant.

Electronic, mechanical and optical properties of Y2O3 with hybrid density functional (HSE06)

In this paper, we have investigated the electronic, optical and mechanical properties of the Y2O3 crystal by first-principle calculations based on the density–functional theory. The generalized gradient approximation (GGA-PBE) and hybrid exchange–correlation functional (HSE06) are both used for comparative study. It is found that, the band gap of Y2O3 calculated by HSE06 method (6.0eV) is in good agreement with the experimental band gap data (5.5eV), and HSE06 gives better electronic structure description close to experiments. Then we calculate the elastic constants, and derive the corresponding properties i.e.; bulk, shear and Young’s moduli, and Poisson’s ratio. Our calculated elastic and mechanical properties correspond well with experimental data. Besides, we also obtain the equilibrium lattice and bulk modulus of yttria by fitting the Birch–Murnaghan equation of state. It is found that, the HSE06 well reproduce the experimental lattice parameters, equilibrium volume and bulk modulus of Y2O3. Based on the accurate described crystal and electronic structure and mechanical properties by HSE06 method, the optical properties of this material are also analyzed.

Electronic Structure and Ground State Properties of A<sub>4</sub>[Ag<sub>4</sub>O<sub>4</sub>] (A=Na, K and Rb): A First-Principles Study

The first-principles calculation within density functional theory is used to study in detail the electronic structure and ground state properties of alkali-metal oxoargenates A4[Ag4O4] (A= Na, K and Rb). The total energies calculated within the atomic sphere approximation (ASA) were used to determine the ground state properties such as equilibrium lattice parameter, c/a ratio, bulk modulus and cohesive energy. The theoretically calculated equilibrium lattice constants values are in well agreement with the available experimental values. The electronic band structures, total and partial density of states are calculated. The result of electronic band structure shows that the KAgO and RbAgO are direct band gap semiconductors with their gap lying between the Γ-Γ points, whereas NaAgO is found to be an indirect band gap semiconductor with its gap lying between Z-Γ points.

Half-Metallic Ferromagnetism in MgS by Doping with <i>Sp</i>-Element: A First-Principles Calculations

The first-principles calculations using full potential linearized augmented plane wave method (FP-LAPW) was performed to determine the influence of dopants (N, P, As and Sb) on the electronic structure of MgS in the rock salt structure. In the present work both local spin density approximation (LSDA) and generalized gradient approximation (GGA) were used for exchange correlation potential functional. Among the group V elements N-doping alone induce half-metallic ferromagnetism in MgS host with a magnetic moment of 1.00 μB/f.u. Total energy calculations show that ferromagnetic state is more stable than non-magnetic state in all the compounds. The ground state properties such as equilibrium lattice constant, bulk modulus and bond length were calculated. The spin polarized electronic band structure, total and partial density of states calculations were carried out to study the origin of half-metallic ferromagnetism in these compounds. The difference between two exchange-correlation functions is also analyzed.

Structure and thermodynamic properties of BeO: Empirical corrections in the quasiharmonic approximation

The equilibrium lattice parameters, bulk modulus, and phase transition of BeO are investigated by using the density functional theory with the Perdew-Burke-Ernzerhof (PBE) and Perdew and Zunger (PZ) functionals. With two different exchange-correlation functionals, we predict the similar results that BeO is stable in hexagonal wurtzite (B4) phase up to pressure of 100 GPa and then transforms directly into the rocksalt (B1) phase. The calculated phonon dispersion curves of the B4 phase BeO are in excellent agreement with the experimental data. Under compression, the phonon dispersion curves of BeO in the B4 phase do not show any anomaly or instability. Within the quasiharmonic approximation (QHA) plus empirical energy corrections (EEC) calculations, the thermal equation of state and thermodynamic properties of BeO are obtained. The EECs improve the systematic deviations of PBE and PZ functionals and reproduce the experimental results in the range of the validity of the QHA. Moreover, the effect of EECs on the phase stability has been investigated.

Size‐Dependent Structural Distortions in One‐Dimensional Nanostructures

Nanoscale materials have been intensely studied since the discovery that the optical properties of semiconductor nanoparticles are size dependent. This and subsequent research has demonstrated that a given physical property of a particle exhibits a size dependence when the size becomes comparable to its characteristic length scale. Examples of relevant length scales include the de Broglie wavelength and/or the mean free path of electrons, phonons, and elementary excitations, all of which typically range from one to a few hundred nanometers. The ability to tune a wide variety of properties by controlling the particle size has spurred the development of novel chemistries for preparing nanostructured elements and compounds with goals of precisely controlling size, shape, and ligand shell. As the size of a nanocrystal decreases, the ratio of bulk to surface atoms decreases. This progression increases the relative contribution of the surface free-energy relative to the volume free-energy of the bulk structure, such that distortions from bulk equilibrium structures might be expected as the nanoparticle size decreases. Unfortunately, while researchers have demonstrated the ability to prepare ordered lattices of nanoparticles, the isolation of lattices of nanoparticles with long-range atomic periodicity is rare. Hence detailed atomic structures and, in turn, the size-structure-property relationships of most nanoparticle systems cannot readily be determined. Recently we reported that the intergrown compounds [(MSe)1+y]m(TSe2)n, with M= {Pb, Bi, Ce} and T= {W, Nb, Ta} self-assemble from designed precursors. The values of m and n represent, respectively, the number of MSe and TSe2 structural units of the unit cell of the superstructure and y describes the misfit between these structural units. As reported herein, the long-range structural order along the modulation direction permits us to determine the atomic structure of these precisely defined one-dimensional (1D) nanolaminate structures as a function of m and n using a combination of scanning transmission electron microscopy (STEM) high-angle annular dark-field (HAADF) imaging and X-ray diffraction (XRD) with Rietveld refinement. STEM-HAADF images of the first five [(PbSe)1.00]m(MoSe2)n compounds in the family where m= n are shown in Figure 1 along with aggregate intensity plots used to quantify the PbSe intraand inter-pair distances. All have a regular periodic structure along the modulated axis with well-defined layers of PbSe and MoSe2. The STEM images show ordered domains of PbSe with characteristic dimensions of a single structural unit along the layering direction and tens of nanometers perpendicular to the layering direction, with random in-plane rotational variants both within a layer and between layers. The orientations of the MoSe2 domains are more difficult to discern from the STEM images, but rotational variants have been observed between individual MoSe2 structural units. The STEM-HAADF images reveal a distortion of the PbSe layers, with the atomic planes grouped into pairs rather than being evenly spaced as expected for the equilibrium (bulk) rock salt structure. The distortion is most evident in the structural variant (m, n)= (2, 2) and decreases in magnitude until it can no longer be observed for (5, 5).

P-TEstimates and Timing of the Sapphirine-Bearing Metamorphic Overprint in Kyanite Eclogites from Central Rhodope, Northern Greece

Sapphirine bearing symplectites that replace kyanite in eclogites from the Greek Rhodope Massif have previously been attributed to a high pressure granulite facies metamorphic event that overprinted the eclogitic peak metamorphic assemblage. The eclogitic mineralogy consisted of garnet, omphacitic pyroxene, rutile and kyanite and is largely replaced by low pressure minerals. Omphacite was initially replaced by sym plectites of diopside and plagioclase that were subsequently replaced by symplectites of amphibole and pla gioclase. Garnet reacted during decompression to form a corona of plagioclase, amphibole and magnetite. Rutile was partly transformed to ilmenite and kyanite decomposed to produce a high variance mineral assemblage of symplectitic spinel, sapphirine, plagioclase and corundum. The presence of quartz and corun dum in the kyanite eclogites is evidence for the absence of bulk equilibrium and obviates a conventional anal ysis of phase equilibria based on the bulk rock composition. To circumvent this difficulty we systematically explored the pressure temperature composition (P–T–X) space of a thermodynamic model for the symplec tites in order to establish the pressure temperature (P T) conditions at which the symplectites were formed after kyanite. This analysis combined with conventional thermometry indicates that the symplectites were formed at amphibolite facies conditions. The resulting upper pressure limit (~0.7 GPa) of the sapphirine producing metamorphic overprint is roughly half the former estimate for the lower pressure limit of the sym plectite forming metamorphic event. Temperature was constrained (T ~ 720°C) using garnet amphibole mineral thermometry. The P T conditions inferred here are consistent with thermobarometry from other lithologies in the Rhodope Massif, which show no evidence of granulite facies metamorphism. Regional geo logical arguments and ion probe (SHRIMP) zircon dating place the post eclogite facies metamorphic evo lution in Eocene times. DOI: 10.1134/S0869591113050032

Anisotropic quantum quench in the presence of frustration or background gauge fields: A probe of bulk currents and topological chiral edge modes

Bosons and fermions, in the presence of frustration or background gauge fields, can form manybody ground states that support equilibrium 'charge' or 'spin' currents. Motivated by the experimental creation of frustration or artificial gauge fields in ultracold atomic systems, we propose a general scheme by which making a sudden anisotropic quench of the atom tunneling across the lattice and tracking the ensuing density modulations provides a powerful and gauge invariant route to visualizing diverse equilibrium current patterns. Using illustrative examples of trapped superfluid Bose and normal Fermi systems in the presence of artificial magnetic fluxes on square lattices, and frustrated bosons in a triangular lattice, we show that this scheme to probe equilibrium bulk current order works independent of particle statistics. We also show that such quenches can detect chiral edge currents in gapped topological states, such as quantum Hall or quantum spin Hall insulators.

Density-decomposed orbital-free density functional theory for covalently bonded molecules and materials

We propose a density decomposition scheme using a Wang-Govind-Carter- (WGC-) based kinetic energy density functional (KEDF) to accurately and efficiently simulate various covalently bonded molecules and materials within orbital-free (OF) density functional theory (DFT). By using a local, density-dependent scale function, the total density is decomposed into a highly localized density within covalent bond regions and a flattened delocalized density, with the former described by semilocal KEDFs and the latter treated by the WGC KEDF. The new model predicts reasonable equilibrium volumes, bulk moduli, and phase-ordering energies for various semiconductors compared to Kohn-Sham (KS) DFT benchmarks. The decomposition formalism greatly improves numerical stability and accuracy, while retaining computational speed compared to simply applying the original WGC KEDF to covalent materials. The surface energy of Si(100) and various diatomic molecule properties can be stably calculated and also agree well with KSDFT benchmarks. This linear-scaled, computationally efficient, density-partitioned, multi-KEDF scheme opens the door to large-scale simulations of molecules, semiconductors, and insulators with OFDFT.

Parity of the weak Fréedericksz transition

Motivated by the recent experimental findings by Kumar et al. (Phys. Rev. E., 82, 011701 (2010)) in which the inverse Fréedericksz transition is observed, we have theoretically investigated the parity and the stability of the equilibrium configurations of a Fréedericksz cell with weak planar boundary conditions. Within the one-constant approximation of the Frank theory, the bulk equilibrium equation reduces to the nonlinear pendulum equation. Its solutions, when combined with boundary conditions deriving by the energy anchoring, lose uniqueness, exhibiting various symmetries. Thus, at a given anchoring strength and applied field, the cell becomes a system with metastable discrete energy levels. Our analysis proposes an explanation of the experimental results.

Hybrid Functional Study of the Structural and Electronic Properties of Co and Ni

Density functional theory calculations for the ground-state properties of Co and Ni have been performed using conventional generalized gradient approximation (GGA) and screened hybrid functionals for an exchange–correlation functional. Here, we have calculated structural (equilibrium lattice constants, bulk moduli, and cohesive energies) and electronic (magnetic moments and densities of states) properties. The GGA functional calculations gave the correct ferromagnetic (FM) ground states [FM hcp (Co) and FM fcc (Ni) ground states], while the hybrid functional calculations gave incorrect ground states. In the experimental ground-state configurations [FM hcp (Co) and FM fcc (Ni)], except for the equilibrium lattice constant c0 and bulk modulus of Co, the structural parameters obtained using the hybrid functional calculations were in good agreement with experimental values. Further inspection showed that the description of cohesive energies and magnetic moments in the ground state exhibited different behaviors. An unusually small cohesive energy and a large magnetic moment were observed in the hybrid functional calculations, which are in contrast to the GGA calculation results. The reason for this difference is discussed in connection with the calculated electronic structures.

Assessing modern GGA functionals for solids

We present periodic calculations carried out with Gaussian-type basis sets on a test set of 21 solids with nine exchange-correlation functionals, extending previous works performed with two parameter-free correlation functionals (TCA and revTCA) which showed promising results for molecules in terms of key structural and energetic properties. Two LDAs and seven GGAs were considered for the prediction of equilibrium lattice constants, bulk moduli, and cohesive energies, using the same test set for all properties when possible. The effect of combining the TCA correlation with exchange potentials other than the PBE form originally used is also addressed. We find that the previously noted good accuracy of the parameter-free TCA functional for molecules also holds for solids, as long as a modified form of the exchange potential that is more biased towards solids than PBE is taken into account. In particular, the PBEsolTCA functional performs well overall for the three key structural and energetic properties considered here.