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NASA NTRS1976

Cubic spline function interpolation in atmosphere models for the software development laboratory: Formulation and data

A tabulation of selected altitude-correlated values of pressure, density, speed of sound, and coefficient of viscosity for each of six models of the atmosphere is presented in block data format. Interpolation for the desired atmospheric parameters is performed by using cubic spline functions. The recursive relations necessary to compute the cubic spline function coefficients are derived and implemented in subroutine form. Three companion subprograms, which form the preprocessor and processor, are also presented. These subprograms, together with the data element, compose the spline fit atmosphere package. Detailed FLOWGM flow charts and FORTRAN listings of the atmosphere package are presented in the appendix.

Kirkpatrick, J. C.↗

NASA NTRS1980

Application of the cubic polynomial strength criterion to the failure analysis of composite materials

A comparative failure analysis is presented based on the application of quadratic and cubic forms of the tensor polynomial lamina strength criterion to various composite structural configurations in a plane stress state. Failure loads have been predicted for off-angle laminates under simple loading conditions and for symmetric-balanced laminates subject to varying degrees of biaxial tension, including configurations subject to multimode failures. Some experimental data are also provided to support these calculations. From these results, the necessity of employing a cubic strength criterion to accurately predict the failure of composite laminae is demonstrated.

Tennyson, R. C.↗

NASA NTRS1983

Production of large-area single-crystal wafers of cubic SiC for semiconductor devices

A reproducible process is described for growing a thick single-crystal layer of cubic SiC on a single-crystal Si wafer by chemical vapor deposition. A buffer layer, grown in situ, is used between the cubic SiC and the Si substrate to minimize the effect of lattice mismatch. Layers of up to 34 microns thick and several sq cm in area have been grown. Wafers are obtained by chemically removing the Si substrates from the grown layers. Excellent electron channeling patterns produced by these wafers indicate very good crystal quality. Preliminary electrical measurements have yielded electron mobilities up to 380 sq cm/Vs.

Nishino, S.↗

NASA NTRS1985

Making Cubic Silicon Carbide Semiconductors

Thin buffer layer of SiC minimizes effects of lattice mismatch. Approach consists of growing single-crystal layer of cubic SiC on single-crystal silicon (Si) wafer by chemical-vapor deposition (CVD). Process developed for production of large-area single-crystal wafers of cubic silicon carbide (SiC) for semiconductor devices; also used to make devices themselves. Applications include electronics for high temperature (up to 900 C) and electronics for very high frequencies.

Powell, J.↗

NASA NTRS1985

Statistical theory of cubic Langmuir turbulence

The cubic direct-interaction approximation is applied to the truncated cubically nonlinear Schroedinger equation. The statistical theory does a satisfactory job in several important respects.

Sun, G.-Z.↗

NASA NTRS1985

Statistical theory of cubic Langmuir turbulence

The cubic direct interaction approximation is applied to a truncated (in Fourier space) version of the cubically nonlinear Schroedinger equation model of Langmuir physics. The results are compared (in the three-mode case) to those for an ensemble of numerical solutions of the dynamical equations with 10,000 different sets of Gaussianly distributed initial conditions. In the undriven, undamped case, the statistical theory (but not the ensemble) evolves to a state of thermal equilibrium. In the driven, damped case, the statistical theory appears to evolve to a state close to that corresponding to one of the limit cycles of the dynamical equations.

Sun, G.-Z.↗

NASA NTRS1985

Modified cubic convolution resampling for Landsat

An overview is given of Landsat Thematic Mapper resampling technique, including a modification of the well-known cubic convolution interpolator (nearest neighbor interpolation) used to provide geometric correction for TM data. Post launch study has shown that the modified cubic convolution interpolator can selectively enhance or suppress frequency bands in the output image. This selectivity is demonstrated on TM Band 3 imagery.

Prakash, A.↗

NASA NTRS1986

Statistical approach to cubic Langmuir turbulence

Previous work on the cubic direct interaction approximation applied to the truncated (in Fourier space) cubically nonlinear Schroedinger equation model of Langmuir turbulence is extended to more modes. In the undriven, undamped case, excellent agreement between the statistical theory and a numerical ensemble of solutions of the dynamic equations is obtained. In the driven, damped case, satisfactory agreement is obtained provided the dynamic ensemble is limited to initial conditions in the basin of attraction.

Sun, G.-Z.↗

NASA NTRS1986

Purely cubic action for string field theory

It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.

Horowitz, G. T.↗

NASA NTRS1986

Compensation in epitaxial cubic SiC films

Hall measurements on four n-type cubic SiC films epitaxially grown by chemical vapor deposition on (100) Si substrates are presented, and the temperature-dependent carrier concentrations are analyzed. Samples are found to be highly compensated (greater than 90 percent) contrary to the assumption made in previously published work, and the donor ionization energies, E(D), are shown to be less than one-half the values quoted previously. New E(D) and donor concentration values, however, provide evidence for identifying the donors as nitrogen in cubic SiC.

Segall, B.↗

NASA NTRS1988

Raman scattering studies of chemical-vapor-deposited cubic SiC films of (100)Si

Raman scattering studies for a series of CVD-grown cubic SiC single-crystal films with film thickness from 600 A to 17 microns are discussed. The results suggest that the crystalline orientations of the Si substrate and the 3C-SiC film are the same. It is found that the Si 522/cm phonon from a Si wafer is enhanced in intensity by a factor of 2-3 due to a CVD overlayer of cubic SiC, and that the 3C-SiC longitudinal optical phonon at the Gamma point from SiC/Si samples is enhanced by a factor of two or three following the removal of the Si substrate. The variation of the Raman spectrum with incident power is investigated, and a method for determining the Raman cross section for 3 C-SiC is proposed.

Feng, Z. C.↗

NASA NTRS1988

Raman determination of layer stresses and strains for heterostructures and its application to the cubic SiC/Si system

A set of formulas for a generalized axial stress in diamond and zinc-blende semiconductors under axial stress is derived to calculate stress-related Raman shifts. By analyzing known Raman data on cubic SiC under hydrostatic pressures, one of the Raman-stress coefficients was obtained, and the existing elastic stiffness constants of cubic SiC were optimized. A method for calculating the stress and strain in SiC films on (100) Si is proposed. It is suggested that the stress and strain expressions and the method of the stress and strain determinations in heterostructures are quite general and may be used for other systems.

Feng, Z. C.↗

NASA NTRS1990

Curvature continuity of cubic Bezier curves in the solid modeling aerospace research tools design software

Preliminary results are presented of an investigation into the development of a procedure to provide curvature continuity between biparametric cubic Bezier surface patches in the computer-aided design package known as SMART (Solid Modeling Aerospace Research Tools). This initial effort was aimed at providing the designer with the ability to locally impose curvature continuity at the intersection of two Bezier curves without disrupting either the curvature or slope continuity that may exist at the ends of these curves. Such a method was found if the original Bezier control points are all coplanar. If they are not, then it is possible to find a minimum deviation from exact curvature continuity. In cases where this is not sufficient, then an entire piecewise curve must be made curvature continuous simultaneously. A method was developed based on cubic splines which is very fast. The procedure returns new Bezier control points which have both slope and curvature continuity.

Roach, Robert L.↗

NASA NTRS1990

Ellipsometric study of cubic SiC

Variable angle spectroscopic ellipsometry (VASE) was applied to cubic SiC. This technique gives absolute values of the refractive index (n) and the extinction coefficient (k) of a substrate and/or a thin film of unknown material. The samples were grown by chemical vapor deposition (CVD) on p-type silicon. The substrate was aligned either on the (001) axis or 1 degree of (001). Several growth temperatures and growth durations were used. The samples were divided into two groups: (1) thick films of order 10 microns grown near optimal conditions of temperature, flow, and gas ratio; and (2) thin films of order 100 A grown at various temperatures. The ellipsometric results for samples in group 1 were analyzed using a two-phase model (substrate and ambient). Results show that for wavelengths in the visible, the refractive index of these CVD samples is equal to that reported for single crystal cubic SiC, within the experimental error, which is on the order of 1 percent. However, the extinction coefficient has a relatively large value, even above the band gap. The absorption is sample dependent and has a broad peak in the visible. The results for samples in group 2 were analyzed using a three-phase model (substrate, film, and ambient). The dielectric functions of the film, deducted from the measured n and k, were further analyzed using the effective medium approximation. The results show that the films contain 30 to 40 vol. percent amorphous silicon, i.e., silicon with only short-range order.

Alterovitz, Samuel A.↗

NASA NTRS1991

Accurate monotone cubic interpolation

Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.

Huynh, Hung T.↗

NASA NTRS1992

Data reduction using cubic rational B-splines

A geometric method is proposed for fitting rational cubic B-spline curves to data that represent smooth curves including intersection or silhouette lines. The algorithm is based on the convex hull and the variation diminishing properties of Bezier/B-spline curves. The algorithm has the following structure: it tries to fit one Bezier segment to the entire data set and if it is impossible it subdivides the data set and reconsiders the subset. After accepting the subset the algorithm tries to find the longest run of points within a tolerance and then approximates this set with a Bezier cubic segment. The algorithm uses this procedure repeatedly to the rest of the data points until all points are fitted. It is concluded that the algorithm delivers fitting curves which approximate the data with high accuracy even in cases with large tolerances.

Chou, Jin J.↗

NASA NTRS1995

The growth of cubic silicon carbide on a compliant substrate

Research has shown that silicon carbide grown on silicon and 6H silicon carbide has problems associated with these substrates. This is because silicon and silicon carbide has a 20% lattice mismatch and cubic silicon carbide has not been successfully achieved on 6H silicon carbide. We are investigating the growth of silicon carbide on a compliant substrate in order to grow defect free silicon carbide. This compliant substrate consists of silicon/silicon dioxide with 1200 A of single crystal silicon on the top layer. We are using this compliant substrate because there is a possibility that the silicon dioxide layer and the carbonized layer will allow the silicon lattice to shrink or expand to match the lattice of the silicon carbide. This would improve the electrical properties of the film for the use of device fabrication. When trying to grow silicon carbide, we observed amorphous film. To investigate, we examined the process step by step using RHEED. RHEED data showed that each step was amorphous. We found that just by heating the substrate in the presence of hydrogen it changed the crystal structure. When heated to 1000 C for 2 minutes, RHEED showed that there was an amorphous layer on the surface. We also heated the substrate to 900 C for 2 minutes and RHEED data showed that there was a deterioration of the single crystalline structure. We assumed that the presence of oxygen was coming from the sides of the silicon dioxide layer. Therefore, we evaporated 2500 A of silicon to all four edges of the wafer to try to enclose the oxygen. When heating the evaporated wafer to 900 C the RHEED data showed single crystalline structure however at 1000 C the RHEED data showed deterioration of the single crystalline structure. We conclude that the substrate itself is temperature dependent and that the oxygen was coming from the sides of the silicon dioxide layer. We propose to evaporate more silicon on the edges of the wafer to eliminate the escape of oxygen. this will allow us to grow single crystal cubic silicon carbide.

Mitchell, Sharanda↗

NASA NTRS1993

Planar Cubics Through a Point in a Direction

It is shown that the planar cubics through three points and the associated tangent directions can be found by solving a cubic equation and a 2 x 2 system of linear equations. The result is combined with a previous published scheme to produce a better curve-fitting method.

Chou, J. J.↗