The Background: from Observation to a `Non-Event' in Single-Crystal Diffractometry

Abstract

The background-peak-background procedure is applied to calculate I and o'2(1) from diffractometer data. A standard measurement produces a raw intensity R and a local background B. This standard operating procedure results in I = R -FB and o.2(/) = o-2(R ) + y2o'Z(B), in which y is the ratio of the times spent in measuring R and B. This approach has led to the conviction that the random error on I is determined by the signal and by the local background. Unfortunately, this concept is based on tradition. The strategic error in the background-peak-background routine is its complete neglect of the physical reality. Background intensities are produced by a single source, viz incoherent scattering. The relevant scattering processes are elastic (Rayleigh), inelastic (Compton) and pseudoelastic (TDS) scattering. Their intensities are proportional to f2, (Z-f2/Z) and f2[1 -exp(-2Bs2)], which results in a background intensity fully defined by 0 only. With observed backgrounds available, a background model has been constructed with its proper mix of the three scattering processes mentioned. This model is practically error free because it is based on a signal with size y~ B(H). The model-inferred background defines a zero level upon which the coherent Bragg intensities are superimposed. The distribution P(R) of the raw intensity is given by the joint probability P(I)P(B). P(R) is known via the observation R(H). The distribution P(B) is a counting statistical one, for which the mean and the variance are available through the background model. So P(/) = P(R)/P(B). This leads to I = R --b and 0.2(/) ~ I. If serious attention is paid to the observed background intensities, the latterironically enough -ceases to be an important element in the random error o-if).