Crystal refraction measurements

If a crystal belongs to the cubic system, the velocity of light through it (and therefore its refractive index) is isotropic (the same in all directions). The refractive index of such an isotropic crystal is measured by observing it when it is immersed in a colorless liquid of matching refractive index (obtained by mixing appropriate liquids of known refractive indices in which the crystal is insoluble). When the refractive index of the surrounding mixture of liquids exactly matches that of the crystal, the latter becomes invisible. The refractive index of the liquid mixture can be measured and is equal to the refractive index of the crystal. 

The numerical solutions of Eq. (1) are shown in Fig. 3 for three different twists and typical liquid crystal refractive indices (nQ=1.52, ne=1.75). Figures 4, 5 and 6 show that the tilt measurement is relatively insensitive to the liquid crystals optical constants, and to small alignment errors. The tilt measurement is most sensitive to the actual value of the ordinary refractive index and to the errors ((J)q) in alignment of the sample with plane of incidence bisecting the twist. The refractive index can be measured and the alignment error is easy to minimize. 

The application of refractions to the study of structures is based on comparing the experimental values with those calculated on various structural assumptions, of which the most important is additivity (Landolt, 1862) in the first approximation (within ca 10 %), the refraction of a compound is the sum of constant increments of different atoms, ions and bonds. Refractions of some isolated atoms can be measured by the deviation of an atomic beam in an inhomogeneous electric field or by spectroscopic methods. In other cases electronic polarizabilities of free atoms were calculated by ab initio methods. All available experimental and the best of the computed refractions of free atoms are presented in Table 11.5. These values can be used to calculate the energy of van der Waals interactions, magnetic susceptibility, or to establish correlations with atomic and molecular-physical properties. The formation of covalent bonds changes the refractions of isolated atoms and their values transform into the covalent refractions, which are different for isolated molecules and for crystals. Direct measurements of RI of A2 molecules or elemental solids give the most accurate information on the covalent refractions, in other cases the latter have to be calculated from molecular refractions by the additive method. 

Figure 1. shows the measured phase differenee derived using equation (6). A close match between the three sets of data points can be seen. Small jumps in the phase delay at 5tt, 3tt and most noticeably at tt are the result of the mathematical analysis used. As the cell is rotated such that tlie optical axis of the crystal structure runs parallel to the angle of polarisation, the cell acts as a phase-only modulator, and the voltage induced refractive index change no longer provides rotation of polarisation. This is desirable as ultimately the device is to be introduced to an interferometer, and any differing polarisations induced in the beams of such a device results in lower intensity modulation. 

The commercially important anatase and mtile both have tetragonal stmctures consequentiy, the values of physical properties such as refractive index and electrical conductivity depend on whether these are being measured parallel or perpendicular to the principal, ie, axis. However, in most appHcations, this distinction is lost because of random orientation of a large number of small crystals. It is thus the mean value that is significant. Representative physical properties are coUected in. Table 6. 

Kashiwagi et al.10) determined the second moment anisotropy for the one-way drawn polyethylene terephthalate sheets discussed above. The three lattice sums S00, S2q and S4o were calculated from the crystal structure determination of Daubeny et al., the proton positions being calculated on the basis of known bond angles and lengths. The isotropic lattice sum S00 was adjusted to a value consistent with the measured isotropic second moment of 10.3G2. The values for P200, P220 etc. were then used to predict the optical anisotropy. The predicted refractive indices for the sheets of draw ratio 2 1 and 2.5 1 are shown in Fig. 10, together with the experimental... 

ATR is one of the most useful and versatile sampling modes in IR spectroscopy. When radiation is internally reflected at the interface between a high-refractive index ATR crystal (usually Ge, ZnSe, Si, or diamond) and the sample, an evanescent wave penetrates inside the sample to a depth that depends on the wavelength, the refractive indices, and the incidence angle. Because the penetration depth is typically less than 2 pm, ATR provides surface specific information, which can be seen as an advantage or not if surface orientation differs from that of the bulk. It also allows one to study thick samples without preparation and can be used to characterize highly absorbing bands that are saturated in transmission measurements. 

The parameters K1/ K2/ and K3 are defined by the refractive indices of the crystal and sample and by the incidence angle [32]. If the sample has uniaxial symmetry, only two polarized spectra are necessary to characterize the orientation. If the optical axis is along the plane of the sample, such as for stretched polymer films, only the two s-polarized spectra are needed to determine kz and kx. These are then used to calculate a dichroic ratio or a P2) value with Equation (25) (replacing absorbance with absorption index). In contrast, a uniaxial sample with its optical axis perpendicular to the crystal surface requires the acquisition of spectra with both p- and s-polarizations, but the Z- and X-axes are now equivalent. This approach was used, through dichroic ratio measurements, to monitor the orientation of polymer chains at various depths during the drying of latex [33]. This type of symmetry is often encountered in non-polymeric samples, for instance, in ultrathin films of lipids or self-assembled monolayers. 

Recently Hopman and al.15 applied a quasi one-dimensional photonic crystal (length 76 pm) for optical sensing. They measured the transmission spectrum as a function of the cladding refractive index. The cladding was varied using a liquid flow, of which the index was slowly varied over a small range (Figure 9). 

Optical detection offers the most conventional technique to time-resolve the coherent phonons. It includes four-wave mixing [8], transient reflectivity [9,10] and transmission [7] measurements, as well as second harmonic generation (SHG) [15,32]. Coherent nuclear displacement Q induces a change in the optical properties (e.g., reflectivity R) of the crystal through the refractive index n and the susceptibility y,... 

The measurement of the width of the metastable zone is discussed in Section 15.2.4, and typical data are shown in Table 15.2. Provided the actual solution concentration and the corresponding equilibrium saturation concentration at a given temperature are known, the supersaturation may be calculated from equations 15.1-15.3. Data on the solubility for two- and three-component systems have been presented by Seidell and Linkiv22 , Stephen et alS23, > and Broul et a/. 24. Supersaturation concentrations may be determined by measuring a concentration-dependent property of the system such as density or refractive index, preferably in situ on the plant. On industrial plant, both temperature and feedstock concentration can fluctuate, making the assessment of supersaturation difficult. Under these conditions, the use of a mass balance based on feedstock and exit-liquor concentrations and crystal production rates, averaged over a period of time, is usually an adequate approach. 

Ni + ions show a broad absorption blue band that peaks at 405 nm in Mgp2 crystal, a tunable laser system. For a concentration of 2 x 10 ° cm Ni + ions, the absorption coefficient measured at 405 nm is 7.2 cm and the full width at half maximum is 8.2 x 10 Hz. Taking into account a refractive index of 1.39 for the Mgp2 crystal, estimate the oscillator strength, /, of the transition responsible for the mentioned absorption band. 

Because of the relatively large dispersion from the electrons compared with the almost constant refractivity of the neutrals and the negligible contribution of the ions, it is possible, with simultaneous measurements at two different wavelength, to determine independent values of the density of electrons and of the nonelectronic components in the plasma 274). Alcock and Ramsden 275) used the light from a giant-pulse ruby laser and its second harmonic generated in an ADP-crystal (ammonium dihydrogen phosphate) to probe a pulsed plasma and its time-dependent density in a Mach-Zehnder interferometer. 

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