My random doodle

Bragg's law, discovered a century ago, is a fundamental principle widely used to investigate the microscopic structure of crystals. However, there is a large gap between the classroom X-ray diffraction (XRD) concept and a practical XRD experiment in real-life. This software is written to simulate a modern XRD experiment, with multiple degrees of motion and a 2-dimensional detector.  This program is designed to give students a head start on their first experiment, and also to help to plan more complex experiments often conducted at synchrotron facilities. 

A schematic drawing of the six-circle diffractometer. 

From H. You, J. Appl. Cryst. 32, 614-623 (1999).

X-ray diffraction experiments are conducted on so called "diffractometer", which equipped with multiple degrees of rotational freedom. This allows for the precise control of the sample's and detector's orientation relative to the incident X-ray beam.Typically, diffractometers use up to six circles of rotation: four for the sample (ϕ, χ, η, μ, from inner to outer motor) and two for the detector (δ, ν, from inner to outer). By combining rotations from these different axes, specific Bragg peaks or regions in reciprocal space can be accessed. While the lab diffractometer often use point or line detector due to lower X-ray intensity and limited budget, two-dimensional detector are more common (with exceptions!) at synchrotron light sources because they can survey the reciprocal space more efficiently.

This program simulates a real XRD experiment on a given crystal by visualizing the portion of reciprocal space that can be reached with a certain combination of motor values. Interactive sliders allow for a quick and intuitive understanding of how effective a particular motor scan is at covering reciprocal space and what volume is explored by the scan. This visualization helps users understand how changes in these angles affect the position and orientation of the detector in reciprocal space, which is crucial for targeted measurements of Bragg reflections and diffuse scattering.

Example geometry 1: Forward scattering geometry

In the forward scattering geometry, the detector is positioned near the direct beam (at δ, ν ~ 0°) to capture X-rays scattered at very small angles. This setup is primarily used for two types of experiments: 

• 1. Small Angle X-ray (Neutron) Scattering (SAXS/SANS), which probe structural correlation at large length scales about 1~100 nm; 

• 2. Crystallography, typically combined with high-energy photons (>tens and hundreds of keV) that can penetrate the sample and have large reciprocal space coverage. By a 360° rotation scan (e.g. ϕ in the animation), it collects a large number of Bragg peaks (e.g. with indices -5 < h,k,l < 5 or even more). The measured intensity of these 1000+ Bragg peaks are used to refine the crystal structure. Pre-orient the sample is not required for this type of measurements. I conducted experiment at QM2 at CHESS with this geometry.

Example 2: Backward scattering geometry