Quality of intensity measurements

In powder diffraction, x-ray photons or neutrons (in x-ray and neutron diffraction experiments, respectively) are registered by the detector as random events. The measured intensity is directly proportional to the number of counts and therefore, the accuracy of intensity measurements is governed by statistics. Even though below we will refer to x-ray diffraction and photons, all conclusions remain identical when neutron diffraction and neutron count is considered. 

Assume that a total of N photon counts were registered by the detector. The spread, a, in this case is defined by the Poisson s probability distribution 

The corresponding error, s, in an individual measurement (i.e. in the number of counts registered at each Bragg angle) depends on the confidence level and is given as 

For a complete list of x-ray standards available from NIST see http //srmcatalog.nist.gov/. 

Photon flux Counting Number (N) of Spread = VN Error at 90% 

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Obviously, the quality of intensity measurements in powder diffraction is inversely proportional to the statistical measurement errors and, therefore, it is directly proportional to the square root of the total number of registered photon counts. Assuming constant brightness of the x-ray source, the most certain way to improve the quality of the diffraction data is to use a lower scanning rate or longer counting time in continuous and step scan experiments, respectively. 

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