Equatorial aberration for powder diffraction data collected by continuous-scan integration of a silicon strip X-ray detector

The application of continuous-scan integration to collect X-ray diffraction data with a Si strip X-ray detector (CSI-SSXD) introduces additional effects on the peak shift and deformation of peak shape caused by the equatorial aberration. A deconvolutional method to correct the effects of equatorial aberration in CSI-SSXD data is proposed in this study. There are four critical angles related to the effects of spillover of the incident X-ray beam from the specimen face in the CSI-SSXD data. Exact values of cumulants of the equatorial aberration function are efficiently evaluated by 4 x 4 point two-dimensional Gauss-Legendre integral. A naive two-step deconvolutional method has been applied to remove the effects of the first and third-order cumulants of the equatorial aberration function from the observed CSI-SSXD data. The performance of the algorithm has been tested by analyses of CSI-SSXD data of three LaB6 powder specimens with the widths of 20, 10, and 5 mm, collected with a diffractometer with the goniometer radius of 150 mm.