Materials Theory

We apply results derived in other contexts for the spectrum of the Laplace operator in curved geometries to the study of an ideal polymer chain confined to a spherical annulus in arbitrary space dimension D and conclude that the free energy compared to its value for an uncurved box of the same thickness and volume, is lower when D<3 , stays the same when D=3 , and is higher when \mbox{ D>3 }. Thus confining an ideal polymer chain to a cylindrical shell, lowers the effective bending elasticity of the walls, and might induce spontaneous symmetry breaking, i.e. bending. (Actually, the above mentioned results show that {\em {any}} shell in D=3 induces this effect, except for a spherical shell). We compute the contribution of this effect to the bending rigidities in the Helfrich free energy expression.

We use ab initio pseudopotential total energy calculations with a plane wave basis set to investigate the structural energetics of various phases of polymorphic NbN. Particular attention is given to its recently discovered superconducting phase with a T c of 16.4 K, reported to have the NbO structure type. Results of total energy calculations show that it is in fact energetically unfavorable for NbN to form in this cubic structure, and its predicted theoretical lattice constant is significantly smaller than the experimental value. Various approaches to the identification of an alternative structure are discussed. In preliminary investigations, we have found two new structures that are energetically more favorable than the NbO structure.

The potential energy surface (PES) of dissociative adsorption of H_2 on Pd(100) is investigated using density functional theory and the full-potential linear augmented plane wave (FP-LAPW) method. Several dissociation pathways are identified which have a vanishing energy barrier. A pronounced dependence of the potential energy on ``cartwheel'' rotations of the molecular axis is found. The calculated PES shows no indication of the presence of a precursor state in front of the surface. Both results indicate that steering effects determine the observed decrease of the sticking coefficient at low energies of the H_2 molecules. We show that the topology of the PES is related to the dependence of the covalent H(s)-Pd(d) interactions on the orientation of the H_2 molecule.

We have extended the validity of the correlation between the surface 3d-core-level shift (SCLS) and the surface d band shift (SDBS) to the entire 4d transition metal series and to the neighboring elements Sr and Ag via accurate first-principles calculations. We find that the correlation is quasilinear and robust with respect to the differencies both between initial and final-state calculations of the SCLS's and two distinct measures of the SDBS's. We show that despite the complex spatial dependence of the surface potential shift (SPS) and the location of the 3d and 4d orbitals in different regions of space, the correlation exists because the sampling of the SPS by the 3d and 4d orbitals remains similar. We show further that the sign change of the SCLS's across the transition series does indeed arise from the d band-narrowing mechanism previously proposed. However, while in the heavier transition metals the predicted increase of d electrons in the surface layer relative to the bulk arises primarily from transfers from s and p states to d states within the surface layer, in the lighter transition metals the predicted decrease of surface d electrons arises primarily from flow out into the vacuum.

The pressure dependence of the Born effective charge, dielectric constant and zone-center LO and TO phonons have been determined for 3C -SiC by a linear response method based on the linearized augmented plane wave calculations within the local density approximation. The Born effective charges are found to increase nearly linearly with decreasing volume down to the smallest volume studied, V/ V 0 =0.78 , corresponding to a pressure of about 0.8 Mbar. This seems to be in contradiction with the conclusion of the turnover behavior recently reported by Liu and Vohra [Phys.\ Rev.\ Lett.\ {\bf 72}, 4105 (1994)] for 6H -SiC. Reanalyzing their procedure to extract the pressure dependence of the Born effective charges, we suggest that the turnover behavior they obtained is due to approximations in the assumed pressure dependence of the dielectric constant ε ∞ , the use of a singular set of experimental data for the equation of state, and the uncertainty in measured phonon frequencies, especially at high pressure.

We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform mesh is made possible, thus enabling us to deal with localized systems with ease. To illustrate the utility of this method, we perform an all-electron calculation of hydrogen molecule in a supercell with LDA approximation. Our method is also applicable to mesoscopic systems.

We present a real-space adaptive-coordinate method, which combines the advantages of the finite-difference approach with the accuracy and flexibility of the adaptive coordinate method. The discretized Kohn-Sham equations are written in generalized curvilinear coordinates and solved self-consistently by means of an iterative approach. The Poisson equation is solved in real space using the Multigrid algorithm. We implemented the method on a massively parallel computer, and applied it to the calculation of the equilibrium geometry and harmonic vibrational frequencies of the CO_2, CO, N_2 and F_2 molecules, yielding excellent agreement with the results of accurate quantum chemistry and Local Density Functional calculations.

A reciprocal space formulation of the Cluster Variation is used in order to extract effective pair interactions in alloys from experimental short-range order diffuse intensities. The method is applied to the analysis of the short range order contribution to the neutron diffuse scattering of a Fe−19.5%Al single crystal. A detailed comparison with real space methods is carried out for three different levels of approximations. For the highest level of approximation used in this study, effective pair interactions up to fifth neighbors are obtained.

We present a method for calculating ab initio interatomic forces which scales quadratically with the size of the system and provides a physically transparent representation of the force in terms of the spatial variation of the electronic charge density. The method is based on a reciprocity theorem for evaluating an effective potential acting on a charged ion in the core of each atom. We illustrate the method with calculations for diatomic molecules.

The (001) surfaces of cubic SiC were investigated with ab-initio molecular dynamics simulations. We show that C-terminated surfaces can have different c(2x2) and p(2x1) reconstructions, depending on preparation conditions and thermal treatment, and we suggest experimental probes to identify the various reconstructed geometries. Furthermore we show that Si-terminated surfaces exhibit a p(2x1) reconstruction at T=0, whereas above room temperature they oscillate between a dimer row and an ideal geometry below 500 K, and sample several patterns including a c(4x2) above 500 K.