C. Rebmann et al., STANDARD UNCERTAINTY OF ANGULAR POSITIONS AND STATISTICAL QUALITY OF STEP-SCAN INTENSITY DATA, Acta crystallographica. Section A, Foundations of crystallography, 54, 1998, pp. 225-231
In step-scan diffraction measurements, the diffraction angle 2 theta i
s an observation with standard uncertainty u(2 theta). By the law of u
ncertainty propagation, u(2 theta), typically 0.001 < u(2 theta) < 0.0
04 degrees, affects the standard uncertainty u(total)(y) of the intens
ity y at each step 2 theta(i), depending on the local slope y'(i) = dy
/d(2 theta)\(2 theta i) by u(total)(2)(y(i)) = u(Poisson)(2) + [y'(i)u
(2 theta)](2), where u(Poisson) = (y(i))(1/2) is the conventional Pois
son statistics. For the intensity y at 2 theta of steepest slope, u(to
tal)(y) is given by u(total)(2)(y) = u(Poisson)(2)(1 + v(2)), where v
= 2u(2 theta)y(0)(1/2)/h is the ratio of y'(i)u(2 theta) and u(Poisson
) y(0) 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: u(total)(2
)(Int) = u(Poisson)(2) (Int)(1 + v(2)/2). As v depends on y(0)(1/2)/h,
it is evident that the importance of the correction increases with in
creasing count rates and decreasing line width. In most practical case
s, y'(i)u(2 theta) contributes a multiple of Poisson statistics to the
standard uncertainty of intensity. It will be shown that with a reali
stic weighting scheme the chi(2) as well as the Durbin-Watson test bec
ome more meaningful.