Lorentz-Lorenz Law Research Articles

Physical and electrical characteristics of metal-organic decomposed CeO2 gate spin-coated on 4H-SiC

The effects of post-deposition annealing temperatures (600–1150°C) in 95%N2–5%H2 ambient on the electrical and physical properties of metal-organic decomposed CeO2 spin-coated on n-type 4H-SiC were investigated. As the annealing temperature increased, oxides changed from polycrystalline to preferred oriented structures and, eventually, to silicate structures. The oxides also showed an incremental increase in surface roughness as annealing temperature increased. The Lorentz-Lorenz law was utilized to determine the density of the oxides. The highest density was obtained by a sample annealed at the highest temperature. Electrical results showed that this sample obtained the lowest leakage current density. Parameters affecting this observation were also investigated.

Physical characterization of post-deposition annealed metal-organic decomposed cerium oxide film spin-coated on 4H-silicon carbide

Cerium oxide (CeO 2) precursor, prepared by metal-organic decomposition method, was spin-coated on n-type 4H-SiC substrate. Effect of post-deposition annealing (600, 800, and 1000 °C) in argon ambient on physical properties of the deposited film (∼110 nm) was investigated. Refractive index ( n f ) of the film was measured by ellipsometer. Lorentz–Lorenz law was applied to estimate the film density ( ρ f ). n f and ρ f were increased with increasing annealing temperature. Film with defect-free surface had been revealed under field-emission scanning electron microscope. In order to study topography and surface roughness of the annealed oxides and SiC surfaces, atomic force microscope was used. The film showed an increment in surface roughness when the annealing temperature was increased. X-ray diffraction (XRD) was employed to detect the presence of crystalline phases and orientations in the films. Williamson–Hall plots were constructed from XRD line broadening, in which grain size ( D) and microstrains were determined. Opposite relationship between D and microstrains was observed with the increase of annealing temperature. Coefficient of texture was calculated and used to measure preferred orientation of the film. All of the films annealed at different temperatures demonstrated (2 0 0)-preferred orientation.

Quantitative estimation of film forming polymer–plasticizer interactions by the Lorentz–Lorenz Law

Molar refraction as well as refractive index has many uses. Beyond confirming the identity and purity of a compound, determination of molecular structure and molecular weight, molar refraction is also used in other estimation schemes, such as in critical properties, surface tension, solubility parameter, molecular polarizability, dipole moment, etc. In the present study molar refraction values of polymer dispersions were determined for the quantitative estimation of film forming polymer–plasticizer interactions. Information can be obtained concerning the extent of interaction between the polymer and the plasticizer from the calculation of molar refraction values of film forming polymer dispersions containing plasticizer.

An high sensitivity optical sensor for chloroform vapours detection based on nanometric film of δ-form syndiotactic polystyrene

A film of syndiotactic polystyrene (sPS) in the nanoporous crystalline δ form has been used for the detection of chloroform in the vapor phase at very low concentration The variation of the refractive index due to the chloroform sorption within the polymer has been used as transduction property. Reflectivity measurements by a fiber optic refractometer, coated with a nanometric (73 nm) film has been performed at very low pressure of chloroform (between 0.2 and 5 Torr) at three different temperatures (35, 49 and 56 °C). Mass sorption experiments have been concurrently performed with an electronic microbalance operating in the same conditions of the optical sensor. Major result from the gravimetric tests is that the analyte is mainly adsorbed into the nanoporous phase where the penetrant molecules can be hosted with a certain selectivity based on both size exclusion and host guest interactions. The quantitative correlation between the mass of analyte sorbed within the polymer layer and the refractive index variation has been observed to be temperature independent. A phenomenological equation based on the Lorentz–Lorenz law has been proposed to describe the effect of the chloroform uptake including both concentration and polarizability changes on the refractive index of the sensible layer.

Measurement of the refractive-index variations with temperature of hybrid sol–gel glasses

We report the measurement of variation in refractive index vs. temperature for organic–inorganic slab waveguides. The following parameters have been obtained: refractive index n; thermo-optic constant d n/d T; and linear thermal expansion coefficient. The refractive index has been measured between approximately 10 and 80 °C. For both polarization TE (Transverse Electric) and TM (Transverse Magnetic), the slopes (d n/d T) are linear over the temperature range with a correlation coefficient r≥0.997 at a wavelength of 632.8 nm. Using the prism coupling method we verified that the refractive index variations follow the Lorentz–Lorenz law. A zero-birefringence is obtained. The thermo-optic coefficient for different slab waveguides was found to be almost constant and not exceeding 10 −4/°C.

A fiber optic thermoset cure monitoring sensor

AbstractCuring determines the chemical and physical properties of a reacting resin. Among these, the optical properties strongly correlate with the structural features of the developing polymeric network. By monitoring changes of the refractive index, it is possible to analyze the polymerization of thermoset resin. In this work, a fiber optic sensor system has been designed and developed (based on the optical time domain reflectometry principle) to measure the reflection coefficient at the interface between the fiber optic and the resin during a curing process. Correlation between the sensor output and conversion has been proposed, following the Lorentz‐Lorenz law. Isothermal data from the sensor have been compared with calorimetric analysis of an epoxy‐based resin.

Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow

Dense media radiative transfer (DMRT) equations based on quasicrystalline approximation (QCA) for densely distributed moderate size particles are developed. We first compute the effective propagation constant and coherent transmission into a dense medium on the basis of the generalized Lorentz‐Lorenz law and the generalized Ewald‐Oseen extinction theorem. The absorption coefficient of the dense media is then calculated. The distorted Born approximation is next applied to a thin layer to determine the bistatic scattering coefficients and the scattering coefficient. The phase matrix in DMRT is then obtained as bistatic scattering coefficient per unit volume. The model is applied to multiple sizes and for sticky particles. Numerical results are illustrated for extinction and brightness temperatures in passive remote sensing using typical parameters in snow terrain. The QCA‐based DMRT is also used to compare with satellite Special Sensor Microwave Imager (SSM/I) brightness temperatures for four channels at 19 and 37 GHz with vertical and horizontal polarizations and for two snow seasons. It shows reasonable agreement to snow depth of 1 m.

Measurement of absolute stopping cross sections by backscattering in thin dielectric films

The present work deals with a different approach to the existing method of backscattering in determining absolute stopping cross sections of light ions in thin dielectric films. In this method, the uncertain molecular density (molecules/cm 3) of the film is replaced (using the Lorentz-Lorenz law) by refractive index of the film, refractive index and the molecular density of the corresponding bulk material, which may be known with better reliability. The method has been applied successfully to a study of the stopping cross sections of He 2+ in thin films of MoO 3, TiO 2, Ge, ZnSe and ZnS.

Density of vapor deposited amorphous Ge films

The density of vapor-deposited amorphous Ge films (a-Ge) was determined by spectrophotometry combined with Rutherford backscattering spectroscopy. It was found to be 0.99±3% of the bulk value for crystalline Ge (c-Ge). This density is in agreement with the Lorentz-Lorenz law which, based upon the existing infrared data on the index of refraction of a-Ge, suggests that the density of a-Ge should be close (within 4%) to that of c-Ge.

Study of the Lorentz-Lorenz law and the energy loss of 4He ions in titanium oxide films

The optical constants, thicknesses and densities of thin titanium oxide films, deposited by electron beam evaporation, were measured. The variation of the refractive index with the density, of titanium oxide samples in the form of thin films (present work) and bulk crystalline form (data from the literature), was observed to follow the Lorentz-Lorenz law. The molecular electronic polarizability deduced from the law was close (within the uncertainty in the measurement) to the value reported in the literature. Rutherford backscattering spectroscopy and X-ray photoelectron spectroscopy studies were carried out on the thin films.

Determination of the interaction second virial coefficients for the carbon dioxide-ethane system from refractive index measurements

The compressibility behavior of the CO/sub 2/-C/sub 2/H/sub 6/ system was investigated experimentally. In this work, the refractive indexes of the pure gases and the mixtures were measured using an optical apparatus. On the basis of these data, density and compressibility factors were computed using the Lorentz-Lorenz law. For the pure components, carbon dioxide and ethane, the data from the optical system were slightly adjusted by a fit to Burnett apparatus data measured separately. The experiments produced very accurate virial coefficients and refraction virial coefficients. This paper reports on the effect of temperature on the second and third virial coefficients. For the first refraction virial coefficient, no influence of temperature was found with the equipment used. The interaction second virial coefficient B /sub 12/ (as a function of temperature) was computed from experimental data for the CO/sub 2/-C/sub 2/H/sub 6/ binary system. The data, for which an accuracy of +/- 1.5 cm/sup 3/ mol/sup -1/ was estimated, are in agreement with the data published by Holste et al.

Thermal variations of refractive index of PMMA, polystyrene, and poly (4-methyl-1 -pentene)

Abstract The refractive indexes of PMMA, polystyrene, and poly-(methyl pentene), three transparent polymers having various morphologies, have been measured between about -100°C and +150°C. The prism method was used in order to make the sample quite free of any contact and mechanical interaction. Thermally stimulated current experiments were concurrently performed to observe and to confirm the existence of the transitions occurring in the various samples. It is verified that the refractive index variations, on the one hand, perfectly follow the Lorentz-Lorenz law and, on the other hand, systematically exhibit anomalies every time a morphological change temperature is overstepped by the material. So, it is shown that measurement of the thermal variations of the refractive index of polymers is another means to follow the behavior of their specific volume while avoiding the application of any stress from the experimental device.

Ultraviolet Irradiation Induced Compaction and Photoetching in Amorphous, Thermal SiO2

ABSTRACTLaser irradiation (λ = 248 nm, E = 5 eV) of thermal, amorphous SiO2 is found to produce thermally reversible, linear compaction reaching a maximum of 16 % (accumulated, incident dose of ∼ 2000 J/cm2 followed by irreversible compaction and photoetching. Assuming the volume fluctuation to be ΔV/V = 3(Δ1/1)/(1+2σ) this corresponds to a maximum volume fluctuation of −36 %. An approximately linear refractive index versus ΔV/V relationship found in the linear compaction regime agrees with the predictions of the Lorentz-Lorenz law. Laser compaction results are found to be consistent with those obtained using hydrostatic pressure. That is argued by comparison with crystalline SiO2 polymporph, that compaction occurs via collapse of a high order ring structure into one having predominately 2 or 3 membered rings. Irreversible compaction/etching occurs when the lattice can no longer support a reduction in ring dimension and dangling bond defects are created. The presence of a large number of defects is sufficient for mechanism of superficial desorption and photoetching to become important.

Quantitative ATR spectroscopy: some basic considerations

A comprehensive treatment of ATR spectra on the basis of the Lorentz-Lorenz law and Fresnel equations is given. The standard equation for the effective thickness is redefined showing how the lossy case deviates from the lossless case. A matrix effect due to the influence of the real part of the refractive index within an absorption band is demonstrated theoretically as well as experimentally. The concentration of a nonab-sorbing solute sample, i.e., glucose, is determined by ATR spectroscopy near the critical angle.

Density and refractive index hysteresis in compressed silicate glasses

The increased refractive index of diopside and albite glass, quenched from liquidus temperatures at pressures to 50 kb, can be accurately calculated from compressibility data on the crystals at 25°C and the Lorentz-Lorenz refraction law. The results indicate that the pressure effect is locked in by ‘configurational trapping’ on cooling through the glass point, but thermal relaxation takes place with the thermal expansion coefficient characteristic of the applied pressure. The resulting permanent compression is therefore that predicted at 25°C and load pressure. Permanent compression of glasses at temperatures below the glass point should be that predicted at load pressure and (1) 25°C, if temperature is released before pressure, or (2) run temperature, if pressure is released before temperature, because thermal relaxation then takes place with the low-pressure thermal expansion coefficient. For SiO2 the glass compressibility is known as a function of temperature, and the overlap field parameter (β = 1.37) can be established from other data. Refractive indices of SiO2 glass compressed at various P and T with varying quenching cycles are consistent with the values calculated for permanent compression when T > ∼500°C. At lower temperatures the compression is partly elastic and the resultant indices are thus lower than expected. In all these glasses, configurational trapping of pressure deformation is adequate to explain the permanent compression. The direct relationship of permanent compression with compressibility shows that the model of H. M. Cohen and R. Roy (1961, 1965), based on second-order structural changes at high P followed by elastic decompression, is not necessary to explain any of the existing data.

Resonance Broadening of Absorption Lines

A general theory of line broadening is used to study the effects of collisions on absorption line shapes when self-broadening is important. Special attention is focused on the role of processes in which an excited atom transfers its electronic excitation to an unexcited atom; it is this process which distinguishes self-broadening from foreign-gas broadening. Several forms for the absorption rate are presented corresponding to particular assumptions about the amplitudes associated with this phenomenon. For example, one approximation leads to a generalized Lorentz-Lorenz law in which the one-atom polarizability is replaced by one that accounts for line broadening. Finally, the importance of many-body effects in the calculation of the linewidth is briefly discussed to determine when simple impact theories are applicable.

Wave propagation through an assembly of spheres: IV. Relations between different multiple scattering theories

The exact determinantal equation satisfied by the coherent wave vector in a statistically defined medium of spherical scatterers, which was obtained by Lloyd in III of this series of papers, is used to show two things. First, the determinant can be written as an infinite series similar to that obtained by ordinary resummation methods, except that it does not involve elements of the T matrix off the energy shell. Secondly, the first two terms of the series are specialized to the case of point scatterers which are uncorrelated except for an infinitesimal sphere of exclusion about each of them, and the results found to disagree with those of other calculations; this discrepancy is clarified. The formalism is generalized to deal with vector waves, and it is shown that, for electric dipole scattering, the simplest approximations to the functions appearing in the determinant lead to the Lorentz-Lorenz law.

Influence of mechanical stress on the polarizability of atoms in a solid medium

Mueller has developed an atomistic theory of photoelasticity for transparent, isotropic solids like glasses wherein the validity of Lorentz-Lorenz law is varifled. An extension of this theory and an empirical assumption that the fractional change in polarizability of an ion within the glass is proportional to the applied stress has allowed the present author to make a theoretical expression for the photo-elastic constants. This expression contains some atomic parameters which relate the change in polarizability to the applied stress. It is shown how these parameters can be calculated from an accurate experimental determination of the photo-elastic constants.