Statistical analysis of half-width of diffraction line profile

The half-width of diffraction line profile is widely used to evaluate the broadness of a diffraction line. To evaluate the reproducibility in measurements of the half-width B, the standard deviation of half-width, σB, arising from counting statistics is derived analytically. It can be calculated from a single measurement. An approximate value of sigmaB is given by σB=(2ym+3y4) 1/2 /3 1/2 M where y4 is the maximum count, and ym and M are the X-ray counts and the slope of the side of the diffraction line at half its height, respectively. This equation shows that σB depends only on X-ray counts and the slope at half height of the diffraction line, being independent of the half-width. Additionally, σB is inversely proportional to the square roots of X-ray counts and preset time.