Data transformations, particle sizing

The effects of particle size on the EXAFS region of the XAS spectra are reflected in the coordination numbers obtained in the fits to the EXAFS data. Figure 15 shows the EXAFS or xi ) data and corresponding Fourier transforms for a Pt foil, a Pt02... 

Data Transformation. The raw size distribution obtained in PCS is intensity weighted. Most particle sizing results are either mass, area, or number weighted. Therefore, to compare results, the PCS measurements would have to be transformed. If the ratio of the concentrations in each peak is desired, then a transformation is also necessary. The intensity of light scattered by a sphere is given by... 

Data Transformations. The deconvolution of correlation functions yields the intensity-weighted diffusion coefficient distribution. Transformation to a size distribution requires division by the diameter raised to a high power and by an angular dependent function which oscillates over several orders of magnitude for particles larger than a half a micron. Given the artifacts from the primary deconvolution, extreme caution is advised when transforming data. 

The results discussed show that crystal structure transformations are considerably dependent on the thermal history of the samples to be more specific, the crystallite size, particle size and surface area have measurable effects on the transformation. It would, therefore, probably be difficult to reproduce strictly transformation data with different samples. The magnitudes of these effects are, however, not too great to result in the wide variability of temperatures of polymorphic transformations. The wide variations in transformation temperature can only be due to other factors... 

AIO.5.2.3.1 For a standard set-up of three replicate test vessels and two replicate samples per test vessel at each sampling time, it is reasonable to anticipate that for a constant loading of a substance, tested in a narrow particle size (e.g. 37 - 44 pm) and total surface area range, the within-vessel variation in transformation data should be less than 10% and the between-vessel variation should be less than 20 % (reference 5, this annex). 

With the advancement of online measurement techniques such as focused beam reflectance measurement (FBRM) and Fourier transform infrared (FTIR), it is now possible to obtain particle size distribution and solution concentration information rapidly through these in-situ probes. In one experiment, hundreds of data points can be generated. With proper experiment design, the model-based experimental design for crystallization is capable of obtaining high-quality crystallization kinetic data with a small number of experiments. This approach can thus save significant experimental effort and time in the development of crystallization processes. 

It follovys from the data in Tab.2, that reduction of the V2O5 particles size results in VPO-D precursor in increased intensity of the 0.570 nm peak attributed to the exposure of (001) plane containing the vanadyl groups. Also some decrease of the temperatures, at which the amorphous (Tendo) and the crystal (Texo) phases are formed in the course of vanadyl pyrophosphate preparation, was observed (see [10,15] for details on phase transformations). 

The statistical fluctuation or noise level of a toner image is also by these postulates dependent on the particle size distribution. The function which relates the statistical fluctuations to spatial frequency is the Wiener spectrum, which is the Fourier transform of the optical density autocorrelation function. In terms of toner images, it is a measure of the dimensional extent over which the presence or absence of a particular toner particle will contribute to density. The density fluctuations can be measured as a function of position, normally with a slit aperture. This is schematically represented in Figure 6 where the left-hand sketch is related to large particles and the right-hand one to small particles. The density data can be used to calculate noise power or Wiener spectrum (8). Formally, the Wiener spectrum is ... 

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