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NASA NTRS1976

Diatomic molecule variations

The rotational energy is separated from vibrational energy in the two-particle, steady-state wave equation and to first order the solutions are harmonic oscillator functions. The classical phase integral gives a partition function valid only at high temperature, but the quantum summation is easily performed to give analytic expressions for all the thermodynamic properties of the harmonic oscillator at all temperatures. Anharmonic effects are treated by small perturbation solutions to the wave equation and the relation between energy levels and a series expansion of the perturbation potential is derived. Next, the quantum solutions for an oscillator with a Morse-function potential are derived in terms of Laguerre polynomials.

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NASA NTRS1976

Polyatomic molecule vibrations

Polyatomic molecule vibrations are analyzed as harmonic vibrations along normal coordinates. The energy eigenvalues are found for linear and nonlinear symmetric triatomic molecules for valence bond models of the potential function with arbitrary coupling coefficients; such models can usually be fitted to observed energy levels with reasonably good accuracy. Approximate normal coordinates for the H2O molecule are discussed. Degenerate vibrational modes such as occur in CO2 are analyzed and expressions for Fermi resonance between close-lying states of the same symmetry are developed. The bending modes of linear triatomic molecules are expressed in terms of Laguerre polynomials in cylindrical coordinates as well as in terms of Hermite polynomials in Cartesian coordinates. The effects of large-amplitude bending such as occur in the C3 molecule are analyzed, along with anharmonic effects, which split the usually degenerate bending mode energy levels. Finally, the vibrational frequencies, degeneracies, and symmetry properties of XY3, X2Y2, and XY4 type molecules are discussed.

Source record↗

NASA NTRS1976

Argon hydrochloride, Ar.HCl, bond energy by infrared spectroscopy

The infrared absorption of argon (200 to 760 torr) and hydrogen chloride (2 to 6 torr) mixtures is reexamined in the missing Q branch region (spectral region between 2860 and 3010 wavelength/cm) at temperatures ranging from 195 to 298 K. The temperature dependence of two absorption features of the argon hydrogen chloride complex, at 2887 and 2879 wavelength/cm, leads to a bond energy estimate that depends on the assumptions made about the internal degrees of freedom of the complex. It is shown that agreement with experiment can be reached for well depths near 1.2 kcal/mole. This result is relatively insensitive to the choice of the vibrational frequencies and anharmonicities, but does depend on the extent to which the energy level manifolds are truncated to avoid molecular excitation in excess of the bond energy. The bond energy is found to deviate from the commonly accepted value of 0.4 kcal/mole. Possible causes for the discrepancy are considered.

Miziolek, A. W.↗

NASA NTRS1977

The influence of molecular rotation on vibration-translation energy transfer

A three-dimensional vibration-rotation collision model is formulated within a semiclassical framework to study the effect of coupled rotational motion on the rate of vibrational energy transfer for collisions between anharmonic diatomic molecules and structureless atoms. Emphasis is on the net rates of vibrational energy transfer summed over all final rotational states rather than those for individual vibration-rotation transitions. The corresponding three-dimensional rate parameters are cast into forms that may be identified with equivalent parameters associated with the collinear approximation. Their comparisons allow the validity of a collinear model to be evaluated and some constraints on its application to be implied. The mechanisms of vibrational energy transfer including rotational transitions are shown to be separable into three classes which are identified and discussed

Mckenzie, R. L.↗

NASA NTRS1978

Modified lattice-statics approach to dislocation calculations. I - Formalism

A modified lattice-statics method to calculate the atomic displacements associated with a screw dislocation is outlined. The model incorporates an anharmonic region wherein the forces are derived from a pair potential. Appropriate energy and force expressions are derived. The modifications necessary for the implementation of the conjugate-gradient function minimization method are also derived.

Esterling, D. M.↗

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 NTRS1979

Convergent perturbation analysis of intense coherent multiphoton interactions

Use has been made of flow graphs to deduce Feenberg perturbation expansions for radiative interactions. It is demonstrated that these expansions can in certain cases be summed to provide closed form expressions for the molecular response. In particular, it is shown that the coherent state response can be obtained by the summation of a continued fraction perturbation expansion for the harmonic oscillator. Anharmonicity in the lower levels is treated and its shown to introduce Rabi flopping identifiable with multiphoton transitions among isolated tightly coupled subsystems of levels. Relevance to laser induced multiphoton excitation and energy level shift calculations in the presence of a strong field are also discussed.

Gower, M. C.↗

NASA NTRS1980

Generalized Grueneisen tensor from solid nonlinearity parameters

Anharmonic effects in solids are often described in terms of generalized Grueneisen parameters which measure the strain dependence of the lattice vibrational frequencies. The relationship between these parameters and the solid nonlinearity parameters measured directly in ultrasonic harmonic generation experiments is derived using an approach valid for normal-mode elastic wave propagation in any crystalline direction. The resulting generalized Grueneisen parameters are purely isentropic in contrast to the Brugger-Grueneisen parameters which are of a mixed thermodynamic state. Experimental data comparing the isentropic generalized Grueneisen parameters and the Brugger-Grueneisen parameters are presented.

Cantrell, J. H., Jr.↗

NASA NTRS1980

Anorthite - Thermal equation of state to high pressures

New shock-wave data are presented for anorthite from which a full high-temperature, high-pressure equation of state is derived. Whereas anorthite has relatively low values of thermal expansion and Grueneisen parameter at zero pressure, it is found that these attain relatively high values in the high density state corresponding to the high-pressure phase Hugoniot but decrease upon compression as expected. It is noted that higher order anharmonic contributions decrease more rapidly with pressure and that the thermal expansion therefore saturates to a high temperature value at pressures above about 100 GPa. Reduction of the Hugoniot data permits shock temperatures to be calculated; it also yields a principal adiabat for the high pressure branch of the Hugoniot. The initial bulk modulus of this adiabat is essentially identical to that of anorthite, whereas the initial density is about 3.40 Mg/cu m.

Jeanloz, R.↗

NASA NTRS1982

Synoptic studies of chromospheric variability in F - K dwarfs with the IUE

Time-sequential series of IUE spectra for ten F, G and K dwarfs were obtained in 1980 and 1981 to study the rotational dependence of chromospheric flux in the ultraviolet. An interactive computational method using unbiased estimators was developed to measure emission line fluxes free of arbitrary judgement concerning the behavior of the underlying spectrum and shapes of the line profiles. Due to the limited number of observational samples per star, we have used special techniques to analyze the sparsely and anharmonically sampled emission line flux data. Two different autocorrelation measures were computed for each emission line as a function of temporal frequency. Examples and results of this analysis now in progress are given for several stars.

Hallam, K. L.↗

NASA NTRS1984

Experimental Determination of the 1 Sigma(+) State Electric-Dipole-Moment Function of Carbon Monoxide up to a Large Internuclear Separation

Experimental intensity information is combined with numerically obtained vibrational wave functions in a nonlinear least squares fitting procedure to obtain the ground electronic state electric-dipole-moment function of carbon monoxide valid in the range of nuclear oscillation (0.87 to 1.01 A) of about the V = 38th vibrational level. Mechanical anharmonicity intensity factors, H, are computed from this function for delta V + = 1, 2, 3, with or = to 38.

Chackerian, C., Jr.↗

NASA NTRS1985

Conducting a thermal conductivity survey

A physically transparent approximate theory of phonon decay rates is presented starting from a pair potential model of the interatomic forces in an insulator or semiconductor. The theory applies in the classical regime and relates the 3-phonon decay rate to the third derivative of the pair potential. Phonon dispersion relations do not need to be calculated, as sum rules relate all the needed quantities directly to the pair potential. The Brillouin zone averaged phonon lifetime turns out to involve a dimensionless measure of the anharmonicity multiplied by an effective density of states for 3-phonon decay. Results are given for rare gas and alkali halide crystals. For rare gases, the results are in good agreement with more elaborate perturbation calculations. Comparison to experimental data on phonon linewidths and thermal conductivity are made.

Allen, P. B.↗

NASA NTRS1985

Nondestructive ultrasonic characterization of engineering materials

The development of an ultrasonic method for the nondestructive characterization of mechanical properties of engineering material is described. The method utilizes the nonlinearity parameter measurement which describes the anharmonic behavior of the solid through measurements of amplitudes of the fundamental and of the generated second harmonic ultrasonic waves. The nonlinearity parameter is also directly related to the acoustoelastic constant of the solid which can be determined by measuring the linear dependence of ultrasonic velocity on stress. A major advantage of measurements of the nonlinearity parameter over that of the acoustoelastic constant is that it may be determined without the application of stress on the material, which makes it more applicable for in-service nondestructive characterization. The relationships between the nonlinearity parameter of second-harmonic generation and the percentage of solid solution phase in engineering materials such as heat treatable aluminum alloys was established. The acoustoelastic constants are measured on these alloys for comparison and confirmation. A linear relationship between the nonlinearity parameter and the volume fraction of second phase precipitates in the alloys is indicated.

Salama, K.↗

NASA NTRS1986

Infrared absorption and emission characteristics of interstellar PAHs

The mid-infrared interstellar emission spectrum with features at 3.28, 6.2, 7.7, 8.7 and 11.3 microns is discussed in terms of the Polycyclic Aromatic Hydrocarbon (PAH) hypothesis, which is based on the suggestive, but inconclusive comparison between the interstellar emission spectrum with the infrared absorption and Raman spectra of a few PAHs. The fundamental vibrations of PAHs and PAH-like species which determine the IR and Raman properties are discussed. Interstellar IR band emission is due to relaxation from highly vibrationally excited PAHs excited by ultraviolet photons. The excitation/emission process is described and the IR fluorescence from one PAH, chrysene, is traced. Generally, there is sufficient energy to populate several vibrational levels in each mode. Molecular vibrational potentials are anharmonic and emission from these higher levels will fall at lower frequencies and produce weak features to the red of the stronger fundamentals. This process is also described and can account for some spectroscopic details of the interstellar emission spectra previously unexplained. Analysis of the interstellar spectrum shows that PAHs contain between 20 and 30 carbon atoms are responsible for the emission.

Barker, J. R.↗

NASA NTRS1987

The effect of the isotopic composition of oxygen on the non-mass-dependent isotopic fractionation in the formation of ozone by discharge of O2

Isotopic fractionation processes in the formation of O3 by 20-kV 60-kHz discharge of O2 in a fused silica container at 77 K are investigated experimentally, with a focus on the effects of changes in the isotopic composition of O2, the O2 pressure, the degree of O3 formation, and the discharge geometry on the isotope abundances in the postdischarge O2 and O3. The results are presented in tables and graphs and compared with the predictions of theoretical models involving vibrational anharmonicity and symmetry effects on O3 predissociation. In experiments using O2 enriched with O-17 and O-18, the heavy isotope is enriched in the residual O2 and not in the O3, whereas the opposite is true when atmospheric isotope abundances are used. It is inferred that the predissociation rate depends on the symmetry and mass of the O3 molecules and not on self-shielding or symmetry effects in the reactant O2. The potential value of the present findings for studies of anomalous isotope abundances in meteorites is indicated.

Yang, Jongmann↗

NASA NTRS1987

The effect of pressure and excitation energy on the isotopic fractionation in the formation of ozone by discharge of O2

Isotopic fractionation processes in the formation of O3 by discharge (at 20 kV and 3 MHz) of O2 in a fused silica container at 77 K are investigated experimentally, with a focus on the effects of changes in the isotopic abundances in the predischarge O2, the O2 pressure, and the excitation energy on the isotope abundances in the postdischarge O2 and O3. The results are presented in extensive tables and graphs and characterized in detail, and good general agreement is found with data obtained using 60-kHz excitation (Yang and Epstein, 1987). It is shown that O-17 and O-18 enrichment of the residual O2 (when the predischarge gas is enriched) or of the O3 (when atmospheric isotope abundances are used) can occur independently of one another. It is inferred that the rate of anharmonic predissociation of vibrationally hot O3 depends on the symmetry and mass of the O3 molecules. The significance of the present findings for studies of anomalous oxygen isotope abundances in meteorites is indicated.

Yang, Jongmann↗

NASA NTRS1987

Infrared absorption and emission characteristics of interstellar PAHs

Allamandola, L. J.↗

NASA NTRS1987

Infrared emission from interstellar PAHs

The mid-IR absorption and Raman spectra of polycyclic aromatic hydrocarbons (PAHs) and the mechanisms determining them are reviewed, and the implications for observations of similar emission spectra in interstellar clouds are considered. Topics addressed include the relationship between PAHs and amorphous C, the vibrational spectroscopy of PAHs, the molecular emission process, molecular anharmonicity, and the vibrational quasi-continuum. Extensive graphs, diagrams, and sample spectra are provided, and the interstellar emission bands are attributed to PAHs with 20-30 C atoms on the basis of the observed 3.3/3.4-micron intensity ratios.

Allamandola, L. J.↗