Study of vibrational excitation mechanisms of CO2 at high temperatures
Calculating vibrational excitation of CO2 for anharmonic coupling and normal mode at high temperature
Rehm, R. G.↗
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Results for “anharmonicity”
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Part 1: Classical laser. Part 2: The effect of velocity changing collisions on the output of a gas laser
A classical model for laser action is discussed, in which an active medium consisting of anharmonic oscillators interacts with an electromagnetic field in a resonant cavity. Comparison with the case of a medium consisting of harmonic oscillators shows the significance of nonlinearities for producing self-sustained oscillations in the radiation field. A theoretical model is presented for the pressure dependence of the intensity of a gas laser, in which only velocity-changing collisions with foreign gas atoms are included. A collision model for hard sphere, repulsive interactions was derived. Collision theory was applied to a third-order expansion of the polarization in powers of the cavity electric field (weak signal theory).
Borenstein, M.↗
Characteristic temperatures of the Mossbauer fraction and thermal-shift measurements in iron and iron salts.
Measurement of Mossbauer spectra in metallic iron, sodium nitroprusside, sodium ferrocyanide, and potassium ferrocyanide absorbers between 78 and 293 K. The temperature dependences of the Mossbauer fraction and the resonant velocity were fitted to Einstein and Debye lattice-vibration models. The characteristic temperatures of the models fitted to the Mossbauer fraction are consistently lower than those fitted to the resonant velocity showing the sensitivity of the Mossbauer fraction to low-frequency modes of vibration. The characteristic temperatures obtained from the resonant velocity are higher for the salts than for the metal, indicating the presence of higher-frequency modes in the salts. This interpretation is verified semiquantitatively by comparing the thermal-shift Debye temperatures of the salts to their infrared absorption frequencies. The Mossbauer fraction of potassium ferrocyanide shows a weaker temperature dependence than that expected for a harmonic solid, which suggests that potassium ferrocyanide is anharmonic in the temperature range studied.
Lafleur, L. D.↗
Classical laser.
In this paper a completely classical model for laser action is discussed. An active medium consisting of classical anharmonic oscillators interacts with a classical electromagnetic field in a resonant cavity. Comparison with the case of a medium consisting of harmonic oscillators shows the significance of nonlinearities for producing self-sustained oscillations in the radiation field. The results for the classical model are found to be similar to those for a semiclassical model of the ammonia-beam maser. The conclusion is that laser action is not intrinsically a quantum-mechanical effect. The classical-laser theory as given in this paper can also be applied to the case of the electron-cyclotron maser.
Borenstein, M.↗
High pressure far infrared spectroscopy of ionic solids
A high-pressure far-infrared cell operating at up to truly hydrostatic pressures of 8 kbar is described and used to determine the anharmonic self-energies associated with the transverse optic modes of ionic solids in which q approximately equals zero. The cell allows far-infrared studies in the spectral range below 120 reciprocal cm. The transverse optic modes were investigated to determine their mode Gruneisen constants and the pressure dependence of their inverse lifetimes in RbI, CsI, and TlCl.
Lowndes, R. P.↗
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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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.
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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.↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗