THE BACKGROUND - FROM OBSERVATION TO A NON-EVENT IN SINGLE-CRYSTAL DIFFRACTOMETRY

The background-peak-background procedure is applied to calculate I and sigma(2)(I) from diffractometer data. A standard measurement produces a raw intensity R and a local background B. This standard operating p rocedure results in I = R - gamma B and sigma(2)(I) = sigma(2)(R) + ga mma(2)sigma(2)(B), in which gamma is the ratio of the times spent in m easuring R and B. This approach has led to the conviction that the ran dom error on I is determined by the signal and by the local background . Unfortunately, this concept is based on tradition. The strategic err or in the background-peak-background routine is its complete neglect o f the physical reality. Background intensities are produced by a singl e source, viz incoherent scattering. The relevant scattering processes are elastic (Rayleigh), inelastic (Compton) and pseudoelastic (TDS) s cattering. Their intensities are proportional to f(2), (Z - f(2)/Z) an d f(2)[1 - exp(-2Bs(2))], which results in a background intensity full y defined by theta only. With observed backgrounds available, a backgr ound model has been constructed with its proper mix of the three scatt ering processes mentioned. This model is practically error free becaus e it is based on a signal with size Sigma B(H). The model-inferred bac kground 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 t he mean and the variance are available through the background model. S o P(I) = P(R)/P(B). This leads to I = R - b and sigma(2)(I) approximat e to I. If serious attention is paid to the observed background intens ities, the latter-ironically enough - ceases to be an important elemen t in the random error sigma(I).