Other factors affecting peak positions

For the most commonly used Bragg-Brentano focusing geometry (see Chapter 3), the overall correction is generally a sum of six factors  

The first two parameters, p and p2, account for the axial divergence of the incident beam and they can be expressed as 

The fifth parameter characterizes specimen displacement, s, from the goniometer axis and it is expressed as 

In routine experiments most or even all peak displacement corrections (Eq. 2.40) may be ignored when their effect falls into the range of 

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In conventional polymer composites, the interlayer spacing will remain the same, similar to clay, and there will therefore be no shift of the diffraction peak. But if there is intercalation, the peak position will shift to a lower angle than in the original nanomaterial. The absence of a characteristic diffraction peak is usually the first indication of exfoliation of the nanomaterial, although it is not conclusive. However, several other factors such as a decrease in the degree of coherent layer stacking, very low concentration of nanomaterial and strong absorption by heavy atoms/ions (e.g. bromide) may also affect the accuracy of this analysis. 

Section 2.2.3 described factors that can affect relative intensities of peaks. These include the preferential orientation of crystal grains, residual stress and other crystal defects. Eventually, we must rely on human judgment to make the final identification. In this case, the matches of relative intensities are very good in general and no other calcium phosphate PDFs can provide matches as good as hydroxyapatite. Thus, hydroxyapatite can be positively identified. 

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