Domain size resolution

Figure 5 Effect of grid resolution (A.) on the time-averaged dimensionless slip velocity (us/uT). Geldart group A particles are used. The ordinate is scaled with the terminal velocity of single particles (uT 21.84 cm/s) and the abscissa is scaled with the particle diameter dp. The domain size is 1.5 x 6 cm2, comparable to the coarse-grid used in normal simulations.

The inverse proportionality between peak width and mean size stated by the Scherrer equation places practical limits to the range of domain sizes that produce measurable effects in a powder pattern. While the lower bound [a few ( 2)nm, depending on the specific phase] is related to the approximations used, the upper bound depends on the instrumental resolution, i.e. on the width of the instrumental profile. Traditional laboratory powder diffractometers, using standard commercial optics, typically allow the detection of domain sizes up to 200 run. Above this value, domain size effects can hardly be distinguished from the instrumental broadening. This limit, however, can considerably be extended by using suitable high resolution optics, as is the case of many diffractometers in use with synchrotron radiation. In this case the practical limit can reach several micrometres. 

High resolution NMR has been used to investigate the photo-dimerisation of 9-methylanthracene. In the solid state, only the trans dimer is formed whereas in benzene solution both the trans and cis dimers are produced. Studies show that the maximum domain size of the minor component is about 0.3 pm, and that the reaction occurs at crystal defects in the monomer. Photodimerisation of the 9-substituted anthracenes An-CHzN- MejBr- (166), AnCH2C02 Na-" (167), AnCH20H (168), AnCOMe... 

Fig. 5.16. Imaging polymer morphology by spin-diffusion contrast on a sample of electrically aged polyethylene, (a) Sample for electrical aging in needle-plate geometry and region cut out for spin diffusion imaging with one-dimensional spatial resolution, (b) Spatially resolved distribution of the domain sizes derived from fitting theoretical diffusion curves of a sandwich layer model to the experimental data. Pronounced changes in the thickness for crystalline, interfacial and amorphous layers are obtained [58].

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