Sample broadening

Contributions to the line broadening from the sample is dealt with in detail in Chapter 13. One equation can be applied to powder diffraction data of any kind (with or without three-dimensional ordering liquids, amorphous or crystalline solids, and any intermediate stage) the Debye scattering equation  

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The reason for this is that a series of strong interactions within a solid sample broaden the linewidth to such an effect that no signal appears to be present under these measurement conditions. 

In utilizing the Scherrer equation, care must be exercised to properly account for instrumental factors which contribute to the measured peak width at half maximum. This "intrinsic" width must be subtracted from the measured width to yield a value representative of the sample broadening. When the experimental conditions have been properly accounted for, reasonably accurate values for the average crystallite size can be determined. Peak shapes and widths, however, can also provide other information about the catalyst materials being studied. For example, combinations of broad and sharp peaks or asymmetric peak shapes in a pattern can be manifestations of structural disorder, morphology, compositional variations, or impurities. 

The line profile in X-ray powder diffraction for a monochromatic beam is determined by sample broadening and instrumental aberration. Figure 6.1 shows schematically contributions to the observed profile h (p) from instrumental aberration g (p) and physical profile ftp) for monochromatic X-rays. Measurements of a sample of the material without physical broadening ( ideal sample ) with the diffractometer without instrumental aberration would give the profile as a Dirac d-function. 

In segmented flow analysis, the presence of successive drops of a second immiscible phase inside the flowing sample leads to the formation of vortices that define a circulating flow pattern between two successive solution plugs (see also Fig. 5.2). These vortices improve the mixing conditions and minimise sample broadening. 

The flow pattern is also modified when reactors other than straight open tubes are used. In coiled reactors, all fluid elements cannot be displaced on parallel trajectories, as the distances travelled are dependent on their relative positions. This results in split circulation of the fluid elements (Fig. 3.5), which is a consequence of the establishment of secondary flows [48]. The effect becomes more pronounced at higher flow rates. Its beneficial influence on mixing conditions, hence, on sample broadening and sampling rate, has often been emphasised [10,49]. An analogous but more pronounced effect is observed with knitted (or 3-D) reactors [50]. 

Packed bed reactors [51] incorporate beads, and the presence of these solid materials in the analytical path also has a beneficial influence on the flow pattern, reducing sample broadening and, hence, sample dispersion. However, hydrodynamic pressure tends to be increased, especially when small particles and/or particles with heterogeneous sizes are used. Single bead string reactors [5] were proposed to circumvent this drawback. These reactors utilise large (particle diameters about 70% or the tube inner... 

Several samples are simultaneously handled in the analytical path the number should be as high as possible at any one time in order to optimise the sampling frequency for a given mean sample residence time and an acceptable degree of carryover [7], However, this number cannot be increased at will due to tailing effects, which are a consequence of sample broadening, and manifest themselves mainly at the sample edges (Fig. 5.5). 

Temperature influences both molecular diffusion and viscosity, and hence the distribution of velocities of the different fluid lines (see also Fig. 3.1). Consequently, both convective and diffusive mass transport are, in principle, affected. An increase in temperature (and the concomitant decrease in viscosity) promotes radial mixing, thus reducing sample broadening and increasing the recorded peak height. 

The length of the analytical path plays an important role in the extent of sample dispersion in flow injection analysis. Increasing this length decreases the recorded peak height and increases sample broadening, with these effects being more evident for lower path lengths (Fig. 5.13). 

This mode of flow analysis was proposed [128] as a means of easily and efficiently achieving extended sample handling times without excessive sample dispersion. The sample volume is inserted into an unsegmented carrier stream, and two air plugs are added at its ends in order to minimise sample broadening, and hence axial dispersion. The beneficial effects arising from the presence of air plugs at both ends of the sample bolus were already emphasised in 1972, in relation to a chemilumino-metric determination of low concentrations of Cr(III) [129]. 

The flow cell inner volume should be selected as a compromise between sample broadening, collimation of the radiation beam and measurement repeatability. For too large a volume, the flow cell can act as... 

Analysis. The flow reverses in the cold trap and the trap tube is rapidly heated at a rate of up to 100,000°C/s. Because the sample is trapped and injected from the same end of the trap, it is in the heated metal trap tube for a minimal period of time. This reduces the possibility of decomposition of thermally labile samples. Broadening from the dead volume of the tube itself is also reduced. 

Just as the use of more than one element strengthens the interpretation of a sample, so the collection of more than one type of sample broadens the base for interpretation of a survey. Results from well water and surface rock may be only indirectly related, yet both may be important to definition of the mineral potential. For example, groundwater samples might show evidence of a reducing environment and little or no uranium in solution, whereas analyses from the outcrop of the host formation could verify a good source of uranium in the rock. 

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