Optical constant, determination

With an appropriate extrapolation of the data beyond the highest and lowest measured energies, we also calculated ft by Kramers Kronig (KK) analysis [32]. The agreement between the optical constants determined by the 7Z and T inversion procedures and those obtained from KK analysis is very good (see Fig. 2.3). 

One needs to know optical constants to calculate IRRAS spectra of molecules either adsorbed at the electrode surface or resident inside the thin-layer cavity. The isotropic optical constants of a given compound are usually determined from transmittance spectra. A pressed peUet, prepared by grinding the dispersion of the compound with a KBr or KCl powder, is typically used as a sample. Recently, Arnold et al. [41] have demonstrated that this method can yield non-reproducible results due to different histories of the sample preparation. In addition, the optical constants determined using the powder method can be quite different from those of the film at the metal/electrolyte interface because of the difference in the environment. 

Optical techniques have provided valuable information on many important properties of surface sihcides. The most common optical experiments include reflectance (R), transmittance (T), and elipsometric spectroscopy (SE). Although the physical process is the same, the method used to extract the optical functions from the experimental R, T, or SE measurements is different in the case of thin films, where the properties of the film itself and its purity and crystalline quality play a relevant role in the reliability of the optical constants determined. In particular, the results obtained from optical measurements on thin films can be affected by several contributions originating from the presence of the substrate. For qualitative analysis, it is sufficient to identify the spectral features of the substrate and normalize the measured spectra to this contribution. However, interference effects may also play... 

Early work in ellipsometry focused on improving the technique, whereas attention now emphasizes applications to materials analysis. New uses continue to be found however, ellipsometry traditionally has been used to determine film thicknesses (in the rang 1-1000 nm), as well as optical constants. " Common systems are oxide and nitride films on silicon v ers, dielectric films deposited on optical sur ces, and multilayer semiconductor strucmres. 

Ellipsometry is a very powerfiil, simple, and totally nondestructive technique for determining optical constants, film thicknesses in multilayered systems, sur ce and... 

D. E. Aspnes. In Handbook of Optical Constants of Solids. (E. Palik, ed.) Academic Press, Orlando, 1985. Description of use of ellipsometry to determine optical constants of solids. 

Determination of the optical constants and the thickness is affected by the problem of calculating three results from two ellipsometric values. This problem can be solved by use of the oscillator fit in a suitable wavenumber range or by using the fact that ranges free from absorption always occur in the infrared. In these circumstances the thickness and the refractive index outside the resonances can be determined - by the algorithm of Reinberg [4.317], for example. With this result only two data have to be calculated. 

The MOLWT-II program calculates the molecular weight of species in retention volume v(M(v)), where v is one of 256 equivalent volumes defined by a convenient data acquisition time which spans elution of the sample. I oment of the molecular weight distribution (e.g., Mz. Mw. Mn ) are calculated from summation across the chromatogram. Along with injected mass and chromatographic data, such as the flow rate and LALLS instruments constants, one needs to supply a value for the optical constant K (Equation la), and second virial coefficient Ag (Equation 1). The value of K was calculated for each of the samples after determination of the specific refractive index increment (dn/dc) for the sample in the appropriate solvent. Values of Ag were derived from off-line (static) determinations of Mw. 

Selected entries from Methods in Enzymology [vol, page(s)] Association constant determination, 259, 444-445 buoyant mass determination, 259, 432-433, 438, 441, 443, 444 cell handling, 259, 436-437 centerpiece selection, 259, 433-434, 436 centrifuge operation, 259, 437-438 concentration distribution, 259, 431 equilibration time, estimation, 259, 438-439 molecular weight calculation, 259, 431-432, 444 nonlinear least-squares analysis of primary data, 259, 449-451 oligomerization state of proteins [determination, 259, 439-441, 443 heterogeneous association, 259, 447-448 reversibility of association, 259, 445-447] optical systems, 259, 434-435 protein denaturants, 259, 439-440 retroviral protease, analysis, 241, 123-124 sample preparation, 259, 435-436 second virial coefficient [determination, 259, 443, 448-449 nonideality contribution, 259, 448-449] sensitivity, 259, 427 stoichiometry of reaction, determination, 259, 444-445 terms and symbols, 259, 429-431 thermodynamic parameter determination, 259, 427, 443-444, 449-451. 

Manifacier JC, Gasiot J, Fillard JP (1976) A simple method for the determination of the optical constants n, k and the thickness of a weakly ahsorhine thin film. J Phys E 9 1002-1004... 

A very common and useful approach to studying the plasma polymerization process is the careful characterization of the polymer films produced. A specific property of the films is then measured as a function of one or more of the plasma parameters and mechanistic explanations are then derived from such a study. Some of the properties of plasma-polymerized thin films which have been measured include electrical conductivity, tunneling phenomena and photoconductivity, capacitance, optical constants, structure (IR absorption and ESCA), surface tension, free radical density (ESR), surface topography and reverse osmosis characteristics. So far relatively few of these measurements were made with the objective of determining mechanisms of plasma polymerization. The motivation in most instances was a specific application of the thin films. Considerable emphasis on correlations between mass spectroscopy in polymerizing plasmas and ESCA on polymer films with plasma polymerization mechanisms will be given later in this chapter based on recent work done in this laboratory. 

It is well known that the SPR may be registered as the sharp minimum of the reflection coefficient for the plane-parallel light which depends on the incidence angle. The position of the resonance angle and the minimum depth of the incidence are determined by the parameters of the metal layer, and the optical constants of the external medium. As molecules adsorb and interact at the gold surface, the dielectric properties of the formed layer change, which leads to the transformation of the resonance curve and to the displacement of the resonance angle [7, 9, 15]. 

Equation (2.62) is not merely a mathematical curiosity from (2.61) it follows that at a given frequency w the optical constants are determined by the reflectance and phase however, if the reflectance is measured over a sufficiently large range of frequencies about w, the phase can be obtained from... 

A good review article on optical constants and their measurement is that by Bell (1967). Determination of optical constants from reflectance measurements is treated by Wendlandt and Hecht (1966) and from internal reflection spectroscopy by Harrick (1967). Ellipsometric techniques are discussed at length by Azzam and Bashara (1977). 

The 1/to4 high frequency limit for R can be useful in determining optical constants from Kramers-Kronig analysis of reflectance data (see Section 2.7). Reflectances at frequencies higher than the greatest far-ultraviolet frequency for which measurements are made can be calculated from (9.15) and used to complete the Kramers-Kronig integral to infinite frequency. 

In Fig. 12.166 sphere and CDE calculations are compared with measurements on MgO cubes well dispersed in KBr neither is very satisfactory. The calculated position of peak absorption by spheres is fairly close to that measured but not coincident with it the CDE calculations show appreciable absorption over approximately the same frequency range as the measurements but no structure. If the optical constants we have used accurately place the Frohlich frequency, Fig. 12.166 suggests that neither spheres nor a broad distribution of shapes are good approximations for MgO particles. This is hardly surprising because electron micrographs reveal that MgO smoke is composed of cubes. These cubes are so nearly perfect that they have been used to quickly determine the resolution of electron microscopes degraded resolution results in apparently rounded corners. 

To determine optical constants of powder samples requires one or more measurements of transmission, or diffuse reflection, or scattering, and an... 

To conclude, we venture to state that the problem of how to determine accurate optical constants from measurements on particulate samples, in contrast with homogeneous solids and liquids, has not been solved in general, even for single-component powders. This does not mean that there have not... 

Because the single-scattering albedo depends sensitively on the imaginary part of the refractive index there has been keen interest in determining optical constants of atmospheric particles. These are used to calculate the important parameters in the heat balance problem for present and predicted aerosol... 

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