X-ray scattering from graphite crystals containing interstitial basal-plane loops

Abstract

The diffraction effects arising from the presence of interstitial basal-plane loops in a graphite crystal are analyzed using a high-speed computer. The atomic displacements were computed using expressions for the displacement field of a prismatic dislocation loop in an anisotropic hexagonal crystal given by Ohr. The loops are assumed to be circular clusters of atoms in the $C$ position of the normal $\mathrm{ABAB}\ensuremath{\cdots}$ sequence of graphite planes. The resulting defect is a finite extrinsic fault and its associated strain field. The effects of loop size and concentration on the lattice parameters, Bragg intensities, and diffuse scattering are given. Graphs are presented which allow loop size and concentration to be determined from measurements of lattice parameters and Bragg intensities. Isodiffusion contour maps of the diffuse scattering in the ($HH\ifmmode\cdot\else\textperiodcentered\fi{}L$) and ($HO\ifmmode\cdot\else\textperiodcentered\fi{}L$) planes of reciprocal space are presented. The diffuse scattering around reciprocal-lattice points for which $H\ensuremath{-}K=\mathrm{mod}(3)$ is different from those for which $H\ensuremath{-}K\ensuremath{\ne}\mathrm{mod}(3)$. The former depends on the symmetry of the loop strain field and is concentrated around the reciprocal-lattice point, while the latter reflects the disruption of the stacking sequence and is characterized by streaks connecting reciprocal-lattice points. The size of the loops can be determined approximately by the full width at half-maximum of the streak connecting the (10 \ifmmode\cdot\else\textperiodcentered\fi{} 0) and (10 \ifmmode\cdot\else\textperiodcentered\fi{} 1) reflections. These predicted effects are compared with diffraction effects seen in neutron-irradiated graphite.