Standard Uncertainty of Angular Positions and Statistical Quality of Step-Scan Intensity Data

In step-scan diffraction measurements, the diffraction angle 2θ is an observation with standard uncertainty u(2θ). By the law of uncertainty propagation, u(2θ), typically 0.001 < u(2θ) < 0.004°, affects the standard uncertainty of the intensity y at each step , depending on the local slope , by , where is the conventional Poisson statistics. For the intensity y at 2θ of steepest slope, is given by , where is the ratio of and , is the peak intensity and h the full width at half-maximum of the profile. The error of the intensities at individual steps modifies also the standard uncertainty of the integrated intensity: . As v depends on , it is evident that the importance of the correction increases with increasing count rates and decreasing line width. In most practical cases, contributes a multiple of Poisson statistics to the standard uncertainty of intensity. It will be shown that with a realistic weighting scheme the as well as the Durbin–Watson test become more meaningful.