A variance approach to the X-ray diffractometric estimation of microfibril angle in wood

TLDR: In this paper, a new method was presented for estimating microfibril angle in wood by X-ray diffractometry, where the variance, S 2, of the azimuthal 002 (cellulose I) diffraction profile was shown to be related to micro-fibrils angle, μ, by a very simple approximate relationship: S 2 =μ 2 /2+σ 2, where σ is the standard deviation of micro-bibril orientation about μ.

Abstract: A new method is presented for estimating microfibril angle in wood by X-ray diffractometry. The variance, S 2 , of the azimuthal 002 (cellulose I) diffraction profile is shown to be related to microfibril angle, μ, by a very simple approximate relationship: S 2 =μ 2 /2+σ 2 , where σ is the standard deviation of microfibril orientation about μ. Advantages in interpretation flow from the principle of variance additivity, making possible the analysis of composite diffraction patterns accumulated over regions of wood with strongly varying microfibril orientation. Experimental advantages include insensitivity to fibre cross-section shape, the orientation of the fibre about its axis, and noise in the diffraction pattern.