On variance as a measure of line broadening in diffractometry IV. The effect of physical aberrations

Abstract

First and second approximations to the change in variance of the line profile arising from dispersion and other physical aberrations are obtained by means of series expansions. To a first approximation the increase in variance (in 2θ) due to dispersion is 4μ3 tan4θ/λ3, and the change in variance resulting from other physical aberrations is 4R1μ3 tan2θ/λ2, where μ3 is the third moment of the line profile about its centroid and R1 is the derivative with respect to λ of the logarithm of the physical factor in question. In the first approximation the effects of the angular-velocity factor, the polarization factor, the trigonometric factor specific to the instrument, and such response variations as absorption in the filter and the quantum-counting efficiency are additive. In the second approximation cross terms appear.