Internal diffraction efficiency

Fig. 10.7 Field dependence of (a) the optical gain and linear absorption of a DMNPAA, PVK, ECZ, TNF composite (reprinted with permission from Nature, Meerholz et al., 1994 copyright 1994 Macmillan Magazines Limited), and (b) internal diffraction efficiency and ellipsometric transmission of a DMNPAA, PVK, ECZ composite (reproduced with permission of Wiley-VCH from Bittner et al., 1999).

Inorganic organic hybrid polymer dispersed liquid crystalline nanocomposites are reported as suitable candidate for fahricatirHi of photorefractive medium. Winiarz et al. reported one such photorefractive medium which consists of hole transporting polymer composite matrix, electro-opticaUy active nanodroplets of liquid crystal and Cadmium sulphide quantum dots as photosentizers (Winiarz and Prasad 2002). They employed poly(methylmethacrylate) (PMMA) as polymer matrix, N-ethylcarbazole (ECZ) as hole transporting medium and commercial nematic liquid crystal mixture TL 202 for fabrication of the photorefractive medium with Cadmium sulphide as photosentizer. The reported medium exhibits more than 90 % internal diffraction efficiency which is relatively high compared with other PDLC photorefractive medium. 

Recent developments and prospects of these methods have been discussed in a chapter by Schneider et al. (2001). It was underlined that these methods are widely applied for the characterization of crystalline materials (phase identification, quantitative analysis, determination of structure imperfections, crystal structure determination and analysis of 3D microstructural properties). Phase identification was traditionally based on a comparison of observed data with interplanar spacings and relative intensities (d and T) listed for crystalline materials. More recent search-match procedures, based on digitized patterns, and Powder Diffraction File (International Centre for Diffraction Data, USA.) containing powder data for hundreds of thousands substances may result in a fast efficient qualitative analysis. The determination of the amounts of different phases present in a multi-component sample (quantitative analysis) is based on the so-called Rietveld method. Procedures for pattern indexing, structure solution and refinement of structure model are based on the same method. 

One can conceive various experimental arrangements to demonstrate the wave-nature of material particles and many interferometers have already been built for molecules as mentioned in Sec. 1. However, all these arrangements needed well collimated beams or experimentally distinguishable internal states in order to separate the various diffraction orders. This requirement makes them less suitable for large clusters and molecules for which brilliant sources and highly efficient detection schemes still have to be developed. 

Every crystalline phase in a sample has a unique powder diffraction pattern determined from the unit cell dimensions and the atomic arrangement within the unit cell. It can be considered a fingerprint of the material. Thus, powder diffraction can be used for phase identification by comparing measured data with diffraction diagrams from known phases. The most efficient computer searchable crystallographic database is the PDF-4 from the International Centre for Diffraction Data (ICDD) [3]. It is used by very efficient computer-based search-processes. In 2007 the PDF-4-i- database contains information about Bragg-positions and X-ray intensities for more than 450000 compounds, out of which there are about 107 500 data sets with atomic coordinates. New entries are added every year. The positions of the peaks in the measured pattern have to be determined. This can be done manually, but effective, fast and reliable automatic peak search methods have been developed. The method can obviously be successful only if the phases in the sample are included in the database. However, the database can also help to determine unknown phases if X-ray data exist for another isostructural compound albeit with a different composition. 

The numerical aperture (more exactly the square of the numerical aperture) describes the light collection efficiency of an objective and thus determines resolution and sensitivity. The values of numerical apertures above unity can be reached only if one takes advantage of total internal reflection. For that purpose, the objective and object holder are connected by a medium with high index of refraction (e.g., an immersion oil or water). In this way light is refracted via the immersion medium towards the normal of the objective (Fig. 8.4). Hence a larger number of Airy diffraction orders reach the imaging system and thus the contrast increases. 

The absorption effect has already been referred to in Section II. Clearly, in a multiphase mixture, different phases will absorb the diffracted photons by different amounts. As an example, the mass absorption coefficient for CuKa, radiation is 308 cm/g for iron, but only 61 cm/g for silicon. Thus iron atoms are five times more efficient than silicon atoms in absorbing CuKo, photons. There is a variety of standard procedures for correcting for the absorption problem, of which by far the most common is the use of the internal standard. In this method a standard phase is chosen that has about the same mass absorption coefficient as the analyte phase, and a weighed amount of this material is added to the unknown sample. The relative intensities of lines from the analyte phase and the internal standard phase are then used to estimate the relative concentrations of internal standard and analyte phases. The relative sensitivity of the diffractometer for these two phases is determined by a separate experiment. Other procedures are available for the analysis of complex mixtures, but these are beyond the scope of this particular work. For further information the reader is referred to specific fexts dealing with the X-ray powder method. 

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