Showing papers by "David Vanderbilt published in 1994"

Giant LO-TO splittings in perovskite ferroelectrics

Abstract: We perform a first-principles investigation of the role of Coulomb interactions in eight AB${\mathrm{O}}_{3}$ cubic perovskite compounds. The predicted spontaneous polarization and the LO and TO phonon frequencies are found to be in good agreement with experiment. Anomalously large dynamical effective charges give rise to very strong mixing of the mode eigenvectors on going from the TO to the LO case, resulting in a ``giant LO-TO splitting'' in the sense that the soft TO mode is most closely related to the hardest LO modes. The results help explain the extreme sensitivity of these compounds to electrostatic boundary conditions.

First-principles calculations of the energetics of stoichiometric TiO2 surfaces.

Abstract: We present self-consistent ab initio total-energy calculations of the equilibrium relaxed structures and surface energies of the stoichiometric (1\ifmmode\times\else\texttimes\fi{}1) (110), (100), (001), and (011) surfaces of ${\mathrm{TiO}}_{2}$. The relaxations of atoms on these surfaces are found to be substantial, and are responsible for a large reduction of the calculated surface energies. A Wulff construction is used to display the relative energetics of these surfaces. The (100) surface is found to be stable with respect to forming macroscpic (110) facets, while the (001) surface is nearly unstable with respect to forming macroscopic (1\ifmmode\times\else\texttimes\fi{}1) (011) facets. These results shed light on published experimental results on the structures of these surfaces.

First-principles investigation of ferroelectricity in perovskite compounds

Abstract: We have used a first-principles ultra-soft-pseudopotential method in conjunction with an efficient preconditioned conjugate-gradient scheme to investigate the properties of a series of eight cubic perovskite compounds. The materials considered in this study are ${\mathrm{BaTiO}}_{3}$, ${\mathrm{SrTiO}}_{3}$, ${\mathrm{CaTiO}}_{3}$, ${\mathrm{KNbO}}_{3}$, ${\mathrm{NaNbO}}_{3}$ ${\mathrm{PbTiO}}_{3}$ , ${\mathrm{PbZrO}}_{3}$, and ${\mathrm{BaZrO}}_{3}$. We computed the total-energy surface for zone-center distortions correct to fourth order in the soft-mode displacement, including renormalizations due to strain coupling. Quantities calculated for each material include lattice constants, elastic constants, zone-center phonon frequencies, Gr\"uneisen parameters, and band structures. Our calculations correctly predict the symmetry of the ground-state structures of all compounds whose observed low-temperature structure retains a primitive five-atom unit cell. The database of results we have generated shows a number of trends which can be understood using simple chemical ideas based on the sizes of ions, and the frustration inherent in the cubic perovskite structure.

Phase transitions in BaTiO3 from first principles.

Abstract: We develop a first-principles scheme to study ferroelectric phase transitions for perovskite compounds. We obtain an effective Hamiltonian which is fully specified by first-principles ultrasoft pseudopotential calculations. This approach is applied to BaTi${\mathrm{O}}_{3}$, and the resulting Hamiltonian is studied using Monte Carlo simulations. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. The order-disorder versus displacive character of the transitions and the roles played by different interactions are discussed.

Generalization of the density-matrix method to a nonorthogonal basis.

Abstract: We present a generalization of the Li, Nunes, and Vanderbilt density-matrix method to the case of a nonorthogonal set of basis functions. A representation of the real-space density matrix is chosen in such a way that only the overlap matrix, and not its inverse, appears in the energy functional. The generalized energy functional is shown to be variational with respect to the elements of the density matrix, which typically remains well localized.

Defects on TiO2 (110) surfaces.

Abstract: We present self-consistent ab initio total-energy calculations on ${\mathrm{TiO}}_{2}$ (110) surfaces for which the atomic geometry has been relaxed to equilibrium. For stoichiometric supercells we find no surface states in the bulk band gap, in accord with experiment. Oxygen vacancies on the surface give rise to Ti 3d-like surface states at the edge of the bulk conduction band. The relaxations of the atoms at the surface were found to be substantial, and those induced by a vacancy were localized in its vicinity. Bulk vacancies introduce states about 0.3 eV below the edge of the bulk conduction band.

Real-space approach to calculation of electric polarization and dielectric constants.

Abstract: We describe a real-space approach to the calculation of the properties of an insulating crystal in an applied electric field, based on the iterative determination of the Wannier functions (WF's) of the occupied bands. It has been recently shown that a knowledge of the occupied WF's allows the calculation of the spontaneous (zero-field) electronic polarization. Building on these ideas, we describe a method for calculating the electronic polarization and dielectric constants of a material in non-zero field. The method is demonstrated for a one-dimensional tight-binding Hamiltonian.

First-principles study of crystalline silica

Abstract: We have investigated the structural properties of five different crystalline forms of ${\mathrm{SiO}}_{2}$ using a first-principles approach. An ultrasoft Vanderbilt pseudopotential is generated for oxygen which enables us to use a small plane-wave cutoff of 25 Ry. The relative stability, the equation of state, and pressure-dependent structural parameters of all five polymorphs have been calculated and found to be in very good agreement with available experimental results.

Competing structural instabilities in cubic perovskites

Abstract: We study the antiferrodistortive instability and its interaction with ferroelectricity in cubic perovskite compounds. Our first-principles calculations show that coexistence of both instabilities is very common. We develop a first-principles scheme to study the thermodynamics of these compounds when both instabilities are present, and apply it to SrTiO$_3$. We find that increased pressure enhances the antiferrodistortive instability while suppressing the ferroelectric one. Moreover, the presence of one instability tends to suppress the other. A very rich $P$--$T$ phase diagram results.

Unoccupied electronic structure of Al(111).

Abstract: The unoccupied electronic states of the Al(111) surface have been studied using k-resolved inverse-photoemission spectroscopy (KRIPES). In addition, a first-principles calculation of the bulk Al electronic structure has been performed to facilitate interpretation of the experimental data. The KRIPES spectra obtained along the [1\ifmmode\bar\else\textasciimacron\fi{}10], [112\ifmmode\bar\else\textasciimacron\fi{}], and [1\ifmmode\bar\else\textasciimacron\fi{} 1\ifmmode\bar\else\textasciimacron\fi{}2] azimuths of the surface Brillouin zone are characterized by well-defined features within 5 eV of the Fermi level, and broad, weak features at higher energies. In general, surface states and resonances appeared as strong spectral features while bulk transitions were weak for this surface. First-principles electronic-structure calculations were necessary to obtain a qualitative account of the bulk features, and semiquantitative agreement was obtained when excitation effects were considered. Dispersion of an unoccupied surface resonance along the [112\ifmmode\bar\else\textasciimacron\fi{}] azimuth is consistent both with an occupied surface resonance found by an earlier photoemission study and with the predictions of surface electronic-structure calculations in the literature. A strong feature observed in the [1\ifmmode\bar\else\textasciimacron\fi{}12] direction is identified as an odd surface state occurring in a symmetry gap and may account for earlier electron-energy-loss data.