Analysis of coherence, strain, thermal vibration and preferred orientation in carbons by X-Ray diffraction

Abstract

In ideal graphitic layers the inter-atomic (or inter-unit cell) distances l and the number of atoms (or unit cells) n( l) at a distance from any atom (or unit cell) chosen as origin may be represented by sets l and n( l) which define the structure. In the defective lattice theory presented here the structure of diffusely scattering (the so-called amorphous) carbons are likewise defined by the two sets, however n( l)'s are modified by a probability (coherence probability) function g( l) and l' s are modified for dispersion (strain effects). It is shown that the coherence probability function can be determined from the atomic radial distribution curves without a priori knowledge of distortion and temperature diffuse scattering. Analytical expressions have been developed that permit analysis of distortion and temperature diffuse scattering from the observed profiles of the diffuse peaks and from the atomic radial distribution functions. In analyzing the distortion, Gauss', Gauchy's and Laplace's distributions are considered. It is demonstrated that distortion could be responsible for the diffuseness of the diffraction profiles of carbons to a greater extent than the coherence probability, the so-called domain or particle size effect. It is also shown that the integrated intensities, I( φ), of the (00 l) reflections of anisotropic, e.g. pyrolytic, carbons are related to the angle φ that the diffraction vector makes with the pole of the sample by I( φ) = K exp (− p 2 sin 2 φ) in which K is the proportionality constant and p is the characteristic parameter of the sample. The equation has a reasonably sound physical basis and has been found to be applicable to samples having a wide range of preferred orientations.