Particle statistics in x-ray diffractometry

Summary

Expressions are derived for the relative r.m.s. errorσ of diffractometer intensity measurements. The result for stationary specimens:

$$\sigma = 4R[\sin \theta /m w h N_{eff} ]^{\tfrac{1}{2}} $$

withh=1/2(h _F+h _S) and$N_{eff} = cA\bar v/\mu v^2$, is identical with the result of Alexander c.s.¹), except for a slight difference in the numerical constant and in the definition ofw. The value of this parameter is found to lie betweenɛR+(w _F, w_S) _min (the last term indicating the smallest of the widthsw _F andw _S) andɛR+1/2(w _F+w _F); it reaches the latter limit in the case of integrated intensities being measured by totalizing counts while scanning through a line. For rotating specimens the particle statistics error turns out to be almost independent ofw. The following approximative formula is established:σ=6.5R sinΘ/h(mN _eff)^1/2, showing that the factor of improvement resulting from specimen rotation is of the order of (h/w)^1/2.