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NASA NTRS1975

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.↗

NASA NTRS1976

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.↗

NASA NTRS1975

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.↗

NASA NTRS1976

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.↗

NASA NTRS1976

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.↗

NASA NTRS1978

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.↗

NASA NTRS1982

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.↗

NASA NTRS1982

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.↗

NASA NTRS1982

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.↗

NASA NTRS1982

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.↗

NASA NTRS1985

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.↗

NASA NTRS1985

Theoretical Studies of the Surface Tension of Liquid Metal System

A major goal of this project is to understand the surface tension and other thermophysical properties of liquid metals and alloys from a fundamental viewpoint. The approach is to calculate these quantities by a first principles technique which combines the statistical-mechanical theory of the liquid state with an electronic pseudopotential theory of electrons in metals. The inhomogeneity of the surface is treated using an ionic-density-functional formalism developed with the support of NASA. Of particular interest are the variation of surface tension with temperature and impurity concentration: such variations strongly influence the types of convection which make take place in a low-gravity environment. Some progress has already been achieved in computing the reduction of surface tension due to the presence of low-surface-tension impurities, and the corresponding surface segregation of such impurities. In the coming year, it is planned to concentrate on the surface properties of materials of particular interest to the MSA program: Si, Ga and GaSn alloys. An additional goal is to gain some theoretical understanding of the high temperature thermophysical properties of liquid metals, particularly high melting point materials which have not been studied extensively from a theoretical viewpoint.

Stroud, D. G.↗

NASA NTRS1986

Optical constants of GaAs-AlGaAs superlattices and multiple quantum wells

The optical properties of GaAs-Al sub x Ga sub 1-xAs superlattices are calculated as a function of the frequency and superlattice structure. The comutations are performed using a partition method which combines the vectors k.p method with the pseudopotential technique. The influence of the super-structure on the electronic properties of the systems is accounted for by appropriate quantization conditions. The anisotropy and structure dependence of the dielectric constant result mainly from the contribution of the gamma region while the contributions of the other regions of the Brillouin zone are rather insensitive to the superlattice structure. The superlattice index of refraction values are shown to attain maxima at the various quantized transition energies, where for certain structures, the difference between the refractive indices of the superlattices and its corresponding Al sub x Ga sub 1-xAs alloy can be as large as 2%. In general results are in good agreement with the experimental data.

Kahen, K. B.↗

NASA NTRS1986

Theoretical Study of the Transverse Dielectric Constant of Superlattices and Their Alloys

The optical properties of III to V binary and ternary compounds and GaAs-Al(x)Ga(1-x)As superlattices are determined by calculating the real and imaginary parts of the transverse dielectric constant. Emphasis is given to determining the influence of different material and superlattice parameters on the values of the index of refraction and absorption coefficient. In order to calculate the optical properties of a material, it is necessary to compute its electronic band structure. This was accomplished by introducing a partition band structure approach based on a combination of the vector k x vector p and nonlocal pseudopotential techniques. The advantages of this approach are that it is accurate, computationally fast, analytical, and flexible. These last two properties enable incorporation of additional effects into the model, such as disorder scattering, which occurs for alloy materials and excitons. Furthermore, the model is easily extended to more complex structures, for example multiple quantum wells and superlattices. The results for the transverse dielectric constant and absorption coefficient of bulk III to V compounds compare well with other one-electron band structure models and the calculations show that for small frequencies, the index of refraction is determined mainly by the contibution of the outer regions of the Brillouin zone.

Kahen, K. B.↗

NASA NTRS1985

General theory of the transverse dielectric constant of III-V semiconducting compounds

A general model of the transverse dielectric constant of III-V compounds is developed using a hybrid method which combines the kp method with a nonlocal pseudopotential calculation. In this method the Brillouin zone is partitioned into three regions by expanding the energy bands and matrix elements about the F, X, and L symmetry points. The real and imaginary parts of the dielectric constant are calculated as a sum of the individual contributions of each region. By using this partition method, it is possible to get good insight into the dependence of the dielectric constant on the shape of the band structure.

Kahen, K. B.↗

NASA NTRS1989

Stationary nonlinear Alfven waves and solitons

Stationary solutions of the derivative nonlinear Schroedinger equation are discussed and classified by using a pseudopotential formulation. The solutions consist of a rich family of nonlinear Alfven waves and solitons with parallel and oblique propagation directions. Expressions for the envelope and the phase of nonlinear waves with periodic envelope modulation, and 'hyperbolic' and 'algebraic' solitons are given. The propagation angle for the slightly modulated elliptic, periodic waves and for oblique solitons is evaluated.

Hada, T.↗

NASA NTRS1989

3-D composite velocity solutions for subsonic/transonic flows

A composite velocity procedure for the three-dimensional reduced Navier-Stokes equations is developed. In the spirit of matched asymptotic expansions, the velocity components are written as a combination multiplicative and additive composite of viscouslike velocities and pseudopotential or inviscid velocities. The solution procedure is then consistent with both asymptotic inviscid flow and boundary layer theory. For transonic flow cases, the Enquist-Osher flux biasing scheme developed for the full potential equation is used. A quasi-conservation form of the governing equations is used in the shock region to capture the correct rotational shock with the standard nonconservation form of the equations used in nonshock regions. The consistent coupled strongly implicit procedure coupled with a plane relaxation procedure is used to solve the discretized equations.

Gordnier, R. E.↗

NASA NTRS1991

Solution of three-dimensional afterbody flow using reduced Navier-Stokes equations

The flow over afterbody geometries was investigated using the reduced Navier-Stokes (RNS) approximation. Both pressure velocity flux-split and composites velocity primitive variable formulations were considered. Pressure or pseudopotential relaxation procedures are combined with sparse matrix or coupled strongly implicit algorithms to form a three-dimensional solver for general non-orthogonal coordinates. Three-dimensional subsonic and transonic viscous/inviscid interacting flows were evaluated. Solutions with and without regions of recirculation were obtained.

Almahroos, H. M. H.↗