# How High Energy X Rays Are Used On A Crystal Essay

1714 WordsDec 11, 20167 Pages

Figure 1: Top: Shows how high energy X-rays are used on a crystal to create an XRD pattern (Law 2009). Bottom: An example XRD pattern for a sample point (Xue et al. 2016). Then the collected XRD patterns are organized and the underlying structures are found. Meaning that for each library there should be a small number of underlying XRD patterns, usually less than ten, such that every pattern in the library can be reconstructed as a linear combination of these underlying patterns. These underlying patterns can then be used to interpret the crystal structure of each sample point, as well as give insights into the material properties of each sample point. These underlying XRD patterns are often called a phase. This signal de-mixing of material systems is referred to as the phase mapping problem. Using traditional methods material scientists can process approximately ten XRD patterns per day, whereas sample points are generated on the order of thousands per day (Gregoire et al. 2009; 2014). Clearly there is a need for a scalable algorithmic approach to address this problem. To address this problem the novel solver AgileFD was created that is based on convolutive non-negative matrix factorization (cNMF), which has been previously used for source separation problems (Smaragdis 2004; Mørup and Schmidt 2006). AgileFD uses lightweight iterative update rules that allows for fast solutions, on the order of minutes (Xue et al. 2016). However the many constraints that a solution must