Determination of the full deformation tensor by multi-Bragg fast scanning nano X-ray diffraction

Abstract

This work showcases a method to map the full deformation tensor in a single micro-sized crystal. It is shown that measuring the position of two Bragg reflections in reciprocal space is sufficient to obtain the full deformation tensor, if the condition of incompressibility of the material is imposed. This method is used to reveal the surface tension induced deformation at the edges of an asgrown single-crystal VO 2 microwire. All components of the deformation tensor of the microwire were measured down to an absolute value of 10 À4 in an 8 Â 14 mm projected area of the wire. With a beam-defined spatial resolution of 150 Â 150 nm, the measurement time was merely 2.5 h.

Local Strain Distribution in ZnO Microstructures Visualized with Scanning Nano X‐Ray Diffraction and Impact on Electrical Properties

“…To this end, advanced techniques to investigate the crystalline structure are extremely helpful. A combined approach using highly resolved TEM measurements, [47] multi Bragg diffraction, [48] and visualizations of the 3D strain distributions by coherent X-ray diffraction imaging [49,50] or ptychography [51,52] can provide deeper insights in the future studies. For textured or polycrystalline samples, texture investigations, [53] or extending investigations to amorphous systems, pair distribution function analysis from total scattering would be beneficial.…”

X-ray Diffraction Imaging of Deformations in Thin Films and Nano-Objects

“…Recently, it has been shown that the set of components ε ij of the strain tensor can be determined from two Bragg reflections [111], if the material incompressibility condition is imposed. This method was used to reveal the surface stress-induced strain on the edges of a monocrystalline micrometer-long VO 2 wire [112] (see Figure 11). All microwire strain tensor components were measured up to an absolute minimum value of 10 −4 , over a microwire projected area of 8 × 14 µm 2 .…”

“…-c, and -b directions are colored black, green, red, and blue, respectively. This orientation is superimposed on the maps to guide the reader [112]. Reproduced from [112] with the permission of the International Union of Crystallography.…”

“…Facets perpendicular to the c, b,-c, and -b directions are colored black, green, red, and blue, respectively. This orientation is superimposed on the maps to guide the reader[112]. Reproduced from[112] with the permission of the International Union of Crystallography.…”