Lattice constant measurement from electron backscatter diffraction patterns

Kikuchi bands in election backscattered diffraction patterns (EBSP) contain information about lattice constants of crystallographic samples that can be extracted via the Bragg equation. An advantage of lattice constant measurement from EBSPs over diffraction (XRD) is the ability to perform local analysis. In this study, lattice constants of cubic STN and cubic YSZ in the pure materials and in co-sintered composites were measured from their EBSPs acquired at 10 kV using a silicon single crystal as a calibration reference. The EBSP distortion was corrected by spherical back projection and Kikuchi band analysis was made using in-house software. The error of the lattice constant measurement was determined to be in the range of 0.09-1.12% compared to values determined by XRD and from literature. The confidence level of the method is indicated by the standard deviation of the measurement, which is approximately 0.04 angstrom. Studying Kikuchi band size dependence of the measurement precision shows that the measurement error decays with increasing band size (i.e. decreasing lattice constant). However, in practice, the sharpness of wide bands tends to be low due to their low intensity, thus limiting the measurement precision. Possible methods to improve measurement precision are suggested. Lay description When a beam of electrons in a scanning electron microscope (SEM) interacts with a highly tilted and well-polished flat sample surface electrons enter the sample and can either be absorbed in the sample generating x-rays and secondary electrons or exit the sample. The exiting electrons are scattered in a cone shaped range of directions from the sample. For crystalline materials, some of these electrons will be reflected' from the crystal planes forming a pattern of Kikuchi bands. The technique of analysing Kikuchi patterns in the SEM, electron backscatter diffraction (EBSD) captures the reflected electrons to form an image. In EBSD patterns, angles between crystal planes are typically used to determine the type and orientation of crystals within a sample. The width of the bands is not normally used in EBSD analysis but can be used in combination with Bragg's law to determine crystal plane spacing and thereby the lattice constants of the crystal. As EBSD collects patterns from the specific location of the electron beam on the sample surface, it is possible to analyse lattice constants of crystals present in small volume fractions of the sample. This is usually not possible by other techniques such as x-ray diffraction. Here we investigate the possibility of using Kikuchi band widths to determine distortions in lattice constants induced by mixing different ratios of the oxides niobium doped strontium titanate and yttria-stabilised zirconia exposed to different heat treatment atmospheres. In this work we present an EBSD methodology to measure lattice constants, investigate the limitations of the method and discuss potential improvements. It was found for samples investigated, due primarily to the EBSD camera resolution, the changes in lattice constant between samples was approximately the same degree as the resolution of the technique based on comparison to reference x-ray diffraction measurements.