On Variance as a Measure of Line Broadening in Diffractometry General Theory and Small Particle Size

The mean-square breadth of a deliberately truncated portion of a diffraction line has been suggested as a measure of particle size by Tournarie. Tournarie's theory is generalized to include other causes of line broadening. For small particle size it is shown that the mean-square breadth in 2θ can be expressed in the form W 26 = ( K λδ(2θ)/2π 2 p cosθ) - ( L λ 2 /4π 2 p 2 cos 2 θ) where p is the cube root of the particle volume, Δ(2θ) is the range of 2θ used in evaluating W 2θ , K is a quantity analogous to the Scherrer constant, and L is a quantity, for which the name taper parameter . is proposed, depending on the rate of decrease of the area of cross section of the crystallites in the hkl direction. For non-spherical crystals both K and L are functions of hkl ; they are evaluated in terms of hkl for certain simple crystal shapes and Tournarie's numerical values of K are confirmed.