hklstrain: An Algorithm for Orientation-Dependent Micro-Strain Calculation Using Laue Crystallography Methodology

The precise characterization of micro-strain distribution within crystalline materials using Laue crystallography methodology is critically important. Applying the strain tensor based on the Green–Lagrange deformation matrix to represent the hkl lattice strain tensor often suffers from insufficient accuracy and drawbacks in evaluation criteria, especially for non-cubic crystal systems. To address these challenges, a novel algorithm hklstrain is designed. The unstrained interplanar spacing d0 is obtained according to the theoretically indexed spot positions, while the strained interplanar spacing dmes is obtained via the global fitting method according to the principle of Laue X-ray reflection and orientation information, and then the micro-strain of all lattice planes of interest is mapped into the sample coordinate system. hklstrain reaches a strain resolution down to 2 × 10−4, and quantitatively determines the orientation-dependent micro-strain fields, offering intuitive insights into the characterization of crystalline materials. It has been successfully applied in the BL03HB beamline at Shanghai Synchrotron Radiation Facility (SSRF) for micro-strain analysis. In contrast to Green–Lagrange strain tensor method, hklstrain produces reliable orientation-dependent micro-strain maps of interplanar spacing variation, thus providing significant advantages in strain tensor analysis for crystalline materials using Laue crystallography methodology.