The Synthesis of X-Ray Spectrometer Line Profiles with Application to Crystallite Size Measurements

Abstract

An improved convolutional method is used to synthesize theoretical line profiles generated by the joint action of seven instrumental weight functions characteristic of the x-ray spectrometer. These include in addition to the five geometrical factors described in a previous publication: (VI) a so-called misalignment function and (VII) a spectral impurity function. The method is applied to the new spectrometer design incorporating a narrow x-ray source, Soller slits, and an angular range 2θ=0 to 165° or higher. Good agreement between theoretical and experimental line profiles is achieved for quartz reflections at 2θ=24.0 and 90.7°. The improved treatment is used to define new curves for correcting experimental spectrometer line breadths for instrumental broadening effects. It is demonstrated that spectrometers of the new design are capable of measuring crystallite dimensions as large as 3000A.