Landau-Placzek Ratio Research Articles

Landau-Placzek ratio of KBr single crystals—I

The Mandel'shtam-Brillouin and Gross scattering was measured for a series of purified KBr crystals. The ratio I G 2I MB , which for a pure, perfect crystal would be the Landau-Placzek ratio, was found to vary with the type of reactive gas treatment used in the final purification. With these crystals both the longitudinal and mixed mode bands were observed with θ and φ equal to 90°. The ratio I L I M was in agreement with calculated intensity ratios and the Δμ for these bands gave C 11 + C 12 = 41.6 GPa and C 44 = 5.18 GPa.

Brillouin scattering in molten NaNO3: The Landau–Placzek ratio

An experimental study of the ratio of intensities of the central line, in the molecular scattering of light, to the Brillouin components has been made in molten NaNO3 over a temperature range from 310° to 450°C. The measurements were performed at frequencies just below any relaxation frequency. The relative intensities of the fine structure components are compared to the Landau–Placzek ratio and also to the generalized Landau–Placzek ratio, applicable to relaxing liquids.

Light Scattering and Pair-Correlation Functions in Fluids with Nonuniform Velocity Fields

We study fluctuations in a fluid with a stationary, linear shear. We find that the pair-correlation function gains a long-ranged part. The Brillouin components of scattered light are enhanced or reduced compared to equilibrium depending on the scattering angle. The Landau-Placzek ratio no longer holds and the total scattering intensity is $k$ dependent. We suggest a simple light-scattering experiment to test our predictions. The new features are explained by the differential attenuation of sound modes.

Rayleigh–Brillouin scattering and structural relaxation of a viscoelastic liquid

The linear response theory using a complete set of dynamic variables involving density, velocity, and energy fluctuations is used to analyze the Rayleigh–Brillouin spectrum of a viscoelastic liquid. The result is discussed in the fast and slow relaxation limits. In the former case, the Rayleigh–Brillouin spectrum is identical to that predicted by the classical hydrodynamic equations; whereas in the latter case a new structural central peak is found, in addition to the anomalous dispersion and relaxation effects present in the frequency and linewidth data associated with the Brillouin peak. The evolution of structural relaxation and its effect on the entire Rayleigh–Brillouin spectrum is described. The structural central peak is most pronounced when the frequency dispersion and the linewidth maximum are present. The theoretical result has been used to calculate the Rayleigh–Brillouin spectra of polypropylene glycol at various temperatures. The results of the frequency shift, the spectral linewidth, and the Landau–Placzek ratio are in good agreement with the experiment.

A note on the polarization of light scattered from entropy and la fluctuations in solids

Analysis of the theory of entropy and LA fluctuations in solids shows that the coupling to the dielectric constant is anisotropic. Scattered radiation therefore in general will change its state of polarization. Thus the observation of thermal Rayleigh and LA Brillouin scattering in solids is facilitated by detection of the depolarized component. The Landau-Placzek ratio strongly depends on polarization and scattering geometry.

Temperature dynamics of polarized and depolarized light scattering in a critical mixture

The results of Rayleigh line wing width, Landau-Placzek ratio and hypersound velocity temperature dependence at approaching the critical temperature of the exfoliating mixture of n-hexadecane-β, β'-dichlordiethyl ether are given.

Brillouin scattering studies of normal and supercooled water

High frequency sound propagation in water has been studied by Brillouin scattering in the entire temperature range of −9°C⩽t⩽100°C. Sound speeds deduced from the data show a peak at t≃70°C in agreement with previous ultrasonic results. Damping constants measured in a temperature range −9°C⩽t⩽20°C are also consistent with the ultrasonic values whenever available. A small negative dispersion of sound velocity is found however in the range 0°C⩽t⩽15°C. We explain this by a simple relaxation model similar to that used by Boon and Fleury in the case of rare gas liquids. We also use a theory of Brillouin scattering which takes into account the temperature fluctuation, and find a small correction term to the expression of the Landau–Placzek ratio. The correction term is calculated and is shown to be nonnegligible for water near 4°C. We believe the data taken in the supercooled regime are reported for the first time and their steep temperature dependence is as yet to be understood theoretically.

Brillouin–Rayleigh scattering studies of polypropylene glycol. III

A comprehensive Brillouin scattering experimental study of polypropylene glycol (PPG), average molecular weight of 1025, 2025, and 4000, has been carried out. The hypersonic velocity, attenuation coefficient, the modulus of elasticity, and the Landau–Placzek ratio have been obtained as a function of temperature for each polymer. The PPG 425 data reported earlier are also included for comparison. For all the quantities measured, only the Laudau–Placzek ratio (below ambient temperature) is molecular weight dependent; the hypersonic velocity, attenuation coefficient, and elastic modulus are found to be independent of molecular weight in the present 425–4000 weight range. The differences in the Landau–Placzek ratio between the different polymers are attributed to different degree of frozen-in density fluctuations due to the difference in the medium’s viscosity; the mechanism of structural relaxation is not sufficient to explain the increase of the Landau–Placzek ratio of each polymer below ambient temperature. All polymers display the velocity dispersion and sound attenuation maximum. However, contrary to that observed in the ultrasonic frequency region, the maximum of the hypersonic attenuation coefficient appears to lie close to the beginning of the velocity dispersion curve and not its middle. The present results on the sound velocity and attenuation can be satisfactorily fit to a theory developed by Isakovich and Chaban, who have modeled the highly viscous liquid as a microinhomogeneous medium.

Experimental determination of the Landau-Placzek ratio for liquid helium to the λ line

The measurements relate to high pressures and to the scattering of light of wavelength 0.488 mu m through 90 degrees . The observed Landau Placzek ratio is shown to be in good agreement with the best available values of gamma -1 ( gamma =Cp/Cv), both above and below the lambda point, provided that mod T-Tlambda mod >0.3 mK. For smaller temperatures differences the ratio is observed to fall below gamma -1 and to remain finite and probably continuous through the lambda line. The results are not in good quantitative agreement with those of other authors, and the reason for the discrepancy is discussed.

High-temperature Brillouin scattering in fused quartz

Thermal Brillouin scattering has been studied in fused silica from room temperature, through the glass transition temperature (1200°C), and up to near the melting temperature of quartz (∼1700°C). The shear and longitudinal Brillouin shifts, the longitudinal linewidth, Pockel's coefficient, and the Landau-Placzek ratio are measured. From these the behavior of the elastic moduli and absorption coefficient with temperature are obtained. A significant change in the temperature dependence of the moduli and Pockel's coefficient is found to occur above 500°C. In addition, by using the Landau-Placzek ratio the first measurement in fused quartz of the equilibrium static compressibility above the glass transition has been obtained. Surprisingly little temperature dependence is observed.

Light scattering: landau-placzek ratio and total intensity

Abstract The total light scattering intensity and the Landau-Placzek ratio are calculated, via thermodynamic arguments, from a model system representative of a single component relaxing fluid or a reactive binary mixture. Comparison is made with both previous thermodynamic calculations of the Landau-Placzek ratio and the results obtained from integration of the intensity distribution. In addition, the fluctuations of the dielectric constant are calculated, under varying conditions placed upon the dielectric constant, and the resulting expressions are discussed within the context of earlier works.

Mandel'shtam-Brillouin spectra in the critical mixture of nitroethane-isooctane

Results of measurements of the Madel'shtam-Brillouin scattering spectrum and the Landau-Placzek ratio in the liquid mixture of nitrocthane-isooctane over the broad temperature range near the critical stratification point are presented here.

Scattering of light by entropy fluctuations in dielectric crystals

The lattice dynamical theory of light scattering by entropy fluctuations has been developed using explicitly phonon-transport theory. Special emphasis has been put on the mechanisms of coupling of light to the entropy fluctuations. The usually considered indirect coupling via density fluctuations, which leads to the Landau-Placzek ratio for the intensities of first and second sound, is shown to be insufficient in many cases. From an analysis of experimental elasto-optic and thermo-optic constants we conclude that for a number of materials the direct coupling will be decisive for describing light scattering in the hydrodynamic regime. The direct coupling is shown to renormalize the elasto-optic constants, so that in the quasistatic limits the isothermal and adiabatic elasto-optic coefficients follow from microscopic theory in agreement with thermodynamics.

The landau-placzek ratio for multicomponent fluids

Under the assumption that the coupling between the sound modes and modes associated with heat and mass diffusion can be neglected, an expression for the Landau-Placzek ratio for multicomponent fluids is derived using thermodynamic fluctuation theory. Applications of the general formula to ternary systems arc discussed briefly.

Evidence for Structure in Plastics from Light Scattering

Measurements of the indices of refraction at 6328 Å of polymerized methyl, ethyl, and butyl methacrylate (PMMA, PEMA, PBMA) as a function of temperature show a discontinuity in the slopes at the glass–rubber transition temperature. A similar discontinuity appears in the hypersonic speeds, obtained as a function of temperature from Brillouin shift measurements and the indices of refraction. From considerations involving the annealing process as seen in the index of refraction, the enhancement of the Rayleigh scattering, the large Landau–Placzek ratio, and the pronounced Krishnan effect (unequal depolarization of the horizontal and vertical components of 90° scattered light for horizontally polarized incident light), one concludes that the polymerization process freezes into the plastic shear and compressional strains that are only partially relieved by annealing.

Brillouin Scattering Near the Glass Transition of Polymethyl Methacrylate

Brillouin scattering of laser light has been used to measure the frequency of hypersonic sound waves in the range of 1010 Hz in PMMA as a function of temperature through the glass-transition region. A discontinuity in the temperature coefficient of sound velocity is observed at the glass-transition temperature; this is explained as a consequence of a corresponding discontinuity in the temperature coefficient of the specific volume (thermal expansion coefficient). The ratio of the light scattered by isothermal density fluctuations to that scattered by adiabatic density fluctuations was also measured. This ratio was large and did not change appreciably near the glass-transition temperature. The value of the Landau-Placzek ratio is approximately what one would expect from previously observed ultrasonic-velocity-dispersion data as a function of temperature well above the glass-transition temperature. Both the velocity and intensity ratio data indicate that no velocity-dispersion effects are present for the hypersonic sound waves up to temperatures 35° above the glass-transition temperature. These results also indicate that the glass transition is not a classical second-order phase transition.

Nonlocal Hydrodynamic Equations and the Spectrum of Critical Opalescence

Both the thermodynamic theory of fluctuations and the linearized hydrodynamics equations are modified in order to take into account nonlocal effects. The description is based on the assumption that the entropy of the system is a functional of the energy and number density which can be expanded in a functional Taylor series about the homogeneous equilibrium state. In this way the well-known difficulties which arise with the “local functional expansion” of the semithermodynamic method are avoided. The modifications to be expected in the Landau–Placzek theory for the spectrum of critical opalescence are investigated. In particular, the angle or k dependence of the sound velocity, the Landau–Placzek ratio, and the width of the central component are discussed.

Light Scattering by Dilute Monatomic Gases Using the Burnett Equations

The hydrodynamic theory of light scattering is generalized by using the linearized Burnett equations instead of the linearized Navier-Stokes equations. It is emphasized that this is necessary if one is interested in phenomena which are of second order in lK, with l the mean free path and K the magnitude of the change in optical wave vector. The principal results are expressions for the initial dispersion (K dependence) of the Brillouin shift and Landau-Placzek ratio.

Thermal light scattering by ionic crystals

Abstract : The temperature and crystal orientation dependence of the thermal scattering by ionic crystals is studied in the temperature range 78 to 300 degrees Kelvin, with the following results. The absolute magnitude of the intensity, the temperature dependence in first approximation, and the shift in wavelength from the incident wavelength of the components of the ideal crystal Brillouin scattering all agree with theory. The defect scattering increases linearly with temperature in first approximation. The depolarization ratios rho sub V are approximately zero. The defect scattering as a function of the crystal orientation angle theta has 2-fold symmetry. These defect scattering results are explained in terms of clouds of point-like scattering units (vacancies) around charged edge dislocations with the dislocations aligned approximately parallel to a single (100) direction in the crystal. The core of the dislocation, a region of great disorder, acts as a source and sink of vacancies and the change in the number density of the vacancies with temperature leads to the observed temperature dependence. The measurement of the scattered light as a function of the angle theta allows the intensity of the true, ideal crystal, Rayleigh scattering and the Landau-Placzek ratio for sodium chloride to be determined for the first time. The results are obtained with the essential help of a new detection technique which eliminates the stray background light without using the immersion technique or special crystal geometries. (Author)

Brillouin Scattering in Water: The Landau—Placzek Ratio

An experimental study of the ratio of intensities of the central line, in the molecular scattering of light, to the Brillouin components has been made in water over a temperature range from 0° to 50°C. A 75-mW He–Ne gas laser was used as a light source and the scattered radiation was analyzed by a pressure-scanned Fabry—Perot interferometer in conjunction with a dry-ice-cooled phototube detector with recorder output. The ultrahigh-frequency sound velocity is compared with values obtained by using ultrasonic techniques. There is no evidence of relaxation effects in the frequency range studied. An analysis of the Landau—Placzek ratio is made for water considered as an ideal fluid. It is shown that the usual approximations used in deriving the ratio (κT—κS)/κS are not valid for water. The actual behavior of the Landau—Placzek ratio for water as a function of temperature can be explained in part when an exact solution is used.