Application of Energy-Resolved Measurements to Laue Diffraction: Determination of Unit-Cell Parameters, Deconvolution of Harmonics and Assignment of Systematic Absences

The use of energy-resolved area detection of Laue diffraction patterns for the determination of unit-cell parameters and systematic absences is demonstrated. Seven different crystals having previously known unit cells were re-examined using Laue diffraction methods. These crystals included four different crystal systems including cubic, orthorhombic, tetragonal and monoclinic cells. The crystals had cell sizes ranging from 179.4 to 4588.3 Å³. Comparison of known and re-determined cells showed good agreement (ratio of known to measured cells = 0.987 ± 0.18). A single procedure was suitable for all unit-cell determinations. The accuracy of the method is presently limited by the quality of the available energy measurements. Some of the crystals represent space groups containing systematic absences normally obscured by harmonic overlap when using the Laue method. These include absences due to 2₁ screw axes (h, k or 1 = 2n + 1) and cell centering (h + k = 2n + 1). All systematic absences were identified using a combination of multiple linear regression with either stepwise elimination or stepwise inclusion and an F test for assignment of systematic absence. The methods are discussed in detail and simulations are used to evaluate critical tolerances for future systems.