The structure of di-valent and tri-valent metals
Pseudopotential and second order perturbation theory applied to divalent and trivalent metal structures
METAL↗
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Electronic spectrum of crystalline antimony.
Energy levels and interband oscillator strengths of antimony calculated in Brillouin zone by pseudopotential method, predicting polarization effects and spin-orbit splittings
BRILLOUIN ZONE↗
Exciton and impurity states in rare-gas solids.
Exciton and impurity states in Kr and Xe crystals and in rare-gas solids containing Xe impurity calculated by pseudopotential theory
RARE GAS↗
Structure of di- and trivalent metals.
Structures of divalent and trivalent metals in terms of pseudopotentials and second order perturbation theory
ELECTRONIC STRUCTURE↗
Prolongation structures of nonlinear evolution equations
A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.
Wahlquist, H. D.↗
Superconductivity in the palladium-hydrogen system
Band theory and phonon measurements are used to calculate the electron-phonon coupling constant wavelength for Pd and PdD. The results indicate that superconductivity is absent in Pd metal because of the large value of the Coulomb pseudopotential, and that superconductivity occurs in PdD primarily because of coupling with the optic phonons. These results are consistent with superconducting transition-temperature measurements for these systems.
Papaconstantopoulos, D. A.↗
Binding of an adatom to a simple metal surface
The density functional formalism of Hohenberg and Kohn is used to investigate the energies, charge densities and forces which hold an adatom on the surface of a simple metal. The valence wavefunction of the adatom is fitted to the Herman-Skillman solutions at large distance and is simplified somewhat in the core region. The field of the ion is represented by the Ashcroft pseudopotential. For the metal the jellium model is used. Detailed calculations are carried out for a sodium adatom on a sodium surface. Simply juxtaposing adatom and surface gives a binding energy of about 1/3 eV. This value is approximately twice the surface energy per atom in the close-packed plane. Charge redistributions as determined variationally increase the binding energy by about 10%. The equilibrium distance for the adatom turns out to be 1.66 A from the surface, as compared with 1.52 A, the observed value for one-half the distance between the close-packed planes.
Huntington, H. B.↗
Low-energy electron scattering from CO
The scattering of electrons from carbon monoxide has been studied in the framework of a previously proposed pseudopotential method. It is found that the single-center expansion of the continuum electron orbital about the center of mass of the molecule is very well converged when the two noncoincident nuclear singularities and the nonlocal exchange interactions are properly taken into account in the scattering equations. An analytical proof has been given to show that unlike the total cross section, the momentum-transfer cross section in the fixed-nuclei approximation is finite even for polar molecules. The calculated results of the momentum-transfer cross section for e(-)-CO scattering in the energy range between 0.1 and 10.0 eV are in good accord with the experimental measurements.
Chandra, N.↗
Thermodynamics
The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.
Zeleznik, F. J.↗
Aluminum under high pressure. I - Equation of state
A curve of applied pressure versus lattice constant is calculated for single-crystal aluminum. It results from an application of the method of structural expansions for deriving the energies of simple metals, a method known to give reasonable results for the elastic constants even at second order in the effective electron-ion interaction. The latter is taken from Fermi-surface analysis, and it is verified that the extant face-centered cubic structure remains the preferred crystalline phase up to the highest pressures considered. Arguments are given to suggest that the curve should have reasonable a priori accuracy and can admit possible improvement if experimental data in the intermediate-pressure region can be provided to refine the (in principle) energy-dependent pseudopotential. At three megabars, the lattice constant is reduced by only 22 per cent; the ion cores at this pressure are still very well separated.
Friedli, C.↗
Computer simulation of screw dislocation in aluminum
The atomic structure in a 110 screw dislocation core for aluminum is obtained by computer simulation. The lattice statics technique is employed since it entails no artificially imposed elastic boundary around the defect. The interatomic potential has no adjustable parameters and was derived from pseudopotential theory. The resulting atomic displacements were allowed to relax in all three dimensions.
Esterling, D. M.↗
Prolongation structures of nonlinear evolution equations. II
The prolongation structure of a closed ideal of exterior differential forms is further discussed, and its use illustrated by application to an ideal (in six dimensions) representing the cubically nonlinear Schroedinger equation. The prolongation structure in this case is explicitly given, and recurrence relations derived which support the conjecture that the structure is open - i.e., does not terminate as a set of structure relations of a finite-dimensional Lie group. We introduce the use of multiple pseudopotentials to generate multiple Baecklund transformation, and derive the double Baecklund transformation. This symmetric transformation concisely expresses the (usually conjectured) theorem of permutability, which must consequently apply to all solutions irrespective of asymptotic constraints.
Estabrook, F. B.↗
Modified lattice-statics approach to dislocation calculations. II - Application
The atomic structure of a screw dislocation core of the 110 line type in aluminum is calculated by the modified lattice-statics method developed in the preceding paper. The method includes anharmonic as well as harmonic forces and permits relaxation of the atoms in all three dimensions. All forces used in the present calculations were derived from a first-principles interatomic pair potential obtained via pseudopotential theory. Several significant differences from the ordinary lattice statics results are noted, including the displacement field, Peierl's energy barrier, and the equilibrium core-center location.
Esterling, D. M.↗
Nonlinear evolution of the ion-ion beam instability
The criterion for the existence of vortex-like ion phase-space configurations, as obtained by a standard pseudopotential method, is found to coincide with the criterion for the linear instability for two (cold) counterstreaming ion beams. A nonlinear equation is derived, which demonstrates that this instability actually evolves into such phase-space configurations. A small, but nonzero, ion temperature turns out to be essential for the saturation into stationary structures
Pecseli, H. L.↗
A note on the limits of Rossby wave amplitudes
Quasi-geostrophic dynamics, as usually formulated, centers on the conservation of pseudopotential vorticity (PV) on isobaric surfaces. The present study has the objective to investigate some simple constraints which conservation of PV imposes on internal Rossby waves. Attention is given to some of the limitations that conservation of potential vorticity imposes on the dynamics of the stratosphere. Another possible constraint imposed by hydrodynamic stability is also discussed. The quantitative limitations these constraints put on the amplitudes of internal Rossby waves are assessed and compared with observations of the lower stratosphere.
Lindzen, R. S.↗
X-ray diffraction from high pressure Ge using synchrotron radiation
The high pressure structural phase transition in Ge has been studied using the energy dispersive X-ray diffraction technique and a synchrotron radiation source. Ge was observed to transform to the beta-Sn tetragonal structure in agreement with the earlier results of Jamieson, but the phase transition began at 80 + or - 5 kilobars, a somewhat lower value than generally reported. These experimental diffraction results are compared with the recent self-consistent pseudopotential calculations of Yin and Cohen (1981) and with the observed transition pressure for shock wave loaded Ge.
Baublitz, M., Jr.↗
Ab initio calculation of the X 1 Sigma + state of CsH
Stevens et al. (1981) considered CsH as a two electron problem, but simulated the Cs core electrons by an empirical pseudopotential following the work by Bardsley (1970). These potentials, since they are derived empirically, include the relativistic effects and the atomic core-valence interactions. However, molecular core-core interactions are not accounted for. Stevens et al. obtained an R(e) value which is too small. This result was attributed to uncorrected core (proton)-core interactions in the molecule. The present investigation is concerned with a resolution of the discrepancies between the results of earlier studies. The X 1 Sigma + ground state of CsH is recalculated. The calculation employs a nine valence electron relativistic effective core potential (RECP) for Cs. The bonding in CsH is found to involve a Cs(6s)-H(1s) bond but with a significant ionic (Cs+H-) component.
Laskowski, B. C.↗
Structure variation of the index of refraction of GaAs-AlAs superlattices and multiple quantum wells
A detailed calculation of the index refraction of various GaAs-AlAs superlattices is presented for the first time. The calculation is performed by using a hybrid approach which combines the k-p method with the pseudopotential technique. Appropriate quantization conditions account for the influence of the superstructures on the electronic properties of the systems. The results of the model are in very good agreement with the experimental data. In comparison with the index of refraction of the corresponding AlGaAs alloy, characterized by the same average mole fraction of Al, the results indicate that the superlattice index of refraction values attain maxima at the various quantized transition energies. For certain structures the difference can be as large as 2 percent. These results suggest that the waveguiding and dispersion relation properties of optoelectronic devices can be tailored to design for specific optical application by an appropriate choice of the superlattice structure parameters.
Kahen, K. B.↗