X-Ray Scattering from hcp Crystals Containing Interstitial Basal-Plane Loops

Abstract

The diffraction effects arising from the presence of interstitial basal-plane loops in an ideal hcp crystal are analyzed using a high-speed computer. The atomic displacements were computed assuming that the crystal responds to the loop as an isotropic elastic medium with a Poisson's ratio of 0.3 into which a "penny-shaped" inclusion is inserted. The loops are assumed to be circular clusters of atoms in the $C$ position of the normal $\mathrm{ABAB}\cdots$ sequence of hcp 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 the determination of loop size and concentration from the measurement of lattice parameters and Bragg intensities. Isodiffusion contour maps of the diffuse scattering in the ($\mathrm{HH}·L$) and ($\mathrm{HO}·L$) planes of reciprocal space are presented. The diffuse scattering around reciprocal-lattice points for which $H-K=\mathrm{modulo} 3$ is quite different from that around reciprocal-lattice points for which $H-K\ne \mathrm{modulo} 3$. The former depends strongly on the symmetry of the loop strain field and is concentrated around the reciprocal-lattice point, while the latter reflects more strongly the disruption of the stacking sequence, having characteristically S-shaped streaks connecting the reciprocal-lattice points. The size of the loops can be determined approximately from the full width at half-maximum of the streak connecting the (10 · 0) and (10 · 1) reflections. The diffraction effects produced by basal-plane loops are discussed in connection with those seen in neutron-irradiated BeO. All of the predicted effects are seen in neutron-irradiated BeO, including the duplex nature of the reflections with $L\ne 0$ and the crosses around reciprocal-lattice points for which $H-K=\mathrm{modulo} 3$ and $L=0\mathrm{}$.