Structure determination from powder diffraction data

David, W.I.F.; Shankland, K.

doi:10.1107/S0108767307064252

Notes

¹Consider a peak at position d^*. If there are [Delta] N peaks per unit d^*, then the probability of finding a peak at $[d^*+\delta d^*]$ may be determined by dividing the separation $[\delta d^*]$ into m equal segments [epsilon] ( $[\delta d^* = m\varepsilon]$ ). The probability, $[p(\delta d^*)\varepsilon]$ , of the peak being at $[d^*+\delta d^*]$ is the product of the probabilities of it not being at any of the intermediate segments and then being at $[d^*+\delta d^*]$ . This is given by $[p(\delta d^*)\varepsilon = (1-\varepsilon \Delta N)m(\varepsilon \Delta N)]$ . Since $[(1-x/m)m \rightarrow \exp(-x)]$ as $[m\rightarrow \infty]$ , then $[p(\delta d^*) = (\Delta N) (1-\varepsilon \Delta N)m = (\Delta N) [1-(\delta d^*\Delta N)/m]{}^m]$ may be written as $[p(\delta d^*) = (\Delta N)\exp(-\Delta N\delta d^*)]$ .