The measurement of particle size by the X-ray method

TLDR

The broadening of X‑ray diffraction lines for crystals smaller than ~10⁻⁵ cm is a well‑known phenomenon first described by Scherrer in 1920. Scherrer, Bragg, and Seljakow derived a formula βx = C λ/(t cos θ) for the angular breadth of a diffraction line from a cubic crystal under parallel monochromatic radiation. The constant C in this formula has been reported as 0.94, 0.89, and 0.92 by the three authors.

Abstract

The broadening of the X-ray diffraction lines which occurs when the crystals composing the specimen are smaller than about 10 -5 cm. edge length is well known. Since the discovery of this phenomenon by Scherrer in 1920 a fair amount of work has been done on the determination of the particle size from the breadth of the lines. Scherrer (1920), Bragg (1933) and Seljakow (1925) have calculated the diffraction broadening for crystals of cubic form belonging to the cubic system. For parallel monochromatic radiation and a point specimen, they agree upon a formula β x = C λ/t cos 1/2 χ , where β x = angular breadth of the line defined below, t — edge length of cubic crystal, λ= wave-length of X-radiation, 1/2 χ = θ , the Bragg angle. The values given for the constant C are 0·94, 0·89 and 0·92 respectively.