The X-Ray Powder Diffraction

X-ray powder diffraction method is one of the few non-destructive methods that permit the identification and the elemental analysis of materials.

As the X-Ray diffraction pattern of a crystalline substance is unique, it is possible to characterise and identify any polycrystalline substance. In order to understand the diffraction pattern, either the incident beam is monochromatic, or the X-Ray detector can resolve the energy from the Kα1, Kα2 doublet to the Kβ1 line.

Alternatively, Sollers slits / optics can be used in order to select the corresponding angular range. A resolution better than 450eV is necessary (this being the FWHM of the measured Cu Kα1, Kα2 doublet).

Diffraction patterns consist of rings and high intensity spots due to crystallised materials, which are mixed to the existing phases and averaged over continuous sample rotations. Intensity integration over those rings allow pattern indexation. Near photon counting sensitivity maybe required for standard laboratory X-ray sources whereas high brilliance sources such as microfocus / synchrotrons will require good dynamic range: One to two-megapixel detectors with spatial resolution of 60-120 microns is usually good enough for this task.

X-Ray sCMOS 4MP Detector X-Ray sCMOS 16MP Detector

Laue & Powder Diffraction

The Laue method helps in determining the orientation of single crystals using white radiation in a reflected or transmitted geometry.

The Laue back reflection mode records X-rays scattered backwards of a sample that has come from a broad-spectrum source. This is useful if the sample is too thick or bulky for X-rays to transmit through it. Each spot can be indexed, i.e. attributed to a specific plane. Crystal orientation is determined from the position of the spots that are generated.

With modern synchrotron and laboratory optics able to deliver micrometre beam size, it is possible to highlight the grain orientation and strain distribution of individual grains in a polycrystalline alloy before and after tensile loading. This solution is also ideal for replacing film-based Laue systems for industrial applications; for example, monitoring for imperfections in high performance turbine blades made from single crystal advanced alloys and this is done to avoid poor creep resistance and failure of blades when at a high operating temperature.

X-ray Laue Back-Scattered Camera Laue Crystal Orientation System

X-ray Micro Tomography

X-ray Tomography allows a 3D reconstruction from a series of 2D radiographs, each for a different angular position of the sample, and this can be done even down to sub-micron resolution.

Typically, a full tomographic data set will require in the order of few hundreds to a few 1000s radiographs using 3D reconstruction and the Feldkamp algorithm. Optical Cone beam / fan beam reconstruction is used, with the sample rotating in a fixed plane / helicoidally around an axis perpendicular to the beam.

The total acquisition time is in the range of few seconds per frame, and this can be dependent very much on the source brilliance / geometry. 100% duty cycle detectors with simultaneous read out / exposure allows to save up to 50% of the scanning time. Resolution down to a few hundred nanometres can be achieved by using a small focal spot source and reasonable geometric magnification. The recorded data is often several Gigabytes and can be processed using the massively parallel calculation capacity of GPUs.

Micro tomography can be combined with phase contrast imaging, either in a qualitative way (“edge enhancement”) or, more quantitatively, including phase retrieval (“holotomography”). Very high-resolution cameras allow the build of scanners with sub micrometre spatial resolution whilst keeping compact dimensions and good sensitivity.

X-Ray sCMOS 4MP Detector X-Ray sCMOS 16MP Detector

X-ray Phase Contrast Imaging

X-ray Phase Contrast is a technique that is used to unveil edge contrast in low Z materials that are barely detectable using conventional X-ray transmission imaging techniques.

The contrast in X-ray images is normally generated by the difference in X-ray absorption for different materials. The X-ray absorption coefficient is roughly proportional to the fourth power of the atomic number Z, making the imaging of objects consisting of low Z elements like carbon, nitrogen and oxygen difficult.

For nearly all elements the real part (d) of the complex index of refraction n (n = 1 – d + ib) in the X-ray region is larger than the imaginary part b. Consequently, a very subtle variation (phase shift) is introduced in the X-ray path, resulting in contrast changes around the edges of an object as light and dark fringes. Those are high spatial frequencies that can only be sensed by a very high-resolution detector with excellent MTF response and good dynamic range trying to image subtle intensity changes over a large background is problematic.

A highly spatially coherent X-ray source combined with a very high-resolution detector can be used to produce a phase contrast imaging set up. Phase retrieval software can be offered for recovering quantitative information of a sample with known density, thus helping to refine 3D tomographic reconstructions.

X-Ray sCMOS 16MP Detector