Fig. 2.

Illustration and benchmarking of X-TEC. (A) A flowchart describing the execution of X-TEC. The steps are described in the Implementation of X-TEC section and further detailed in SI Appendix, section 1. (B) Raw XRD image showing a slice of the reciprocal space in the $(h,k,l=0)$ plane, at T = 30 K (Left) and T = 220 K (Right). The CDW superlattice peaks are visible at T = 30 K and are absent at T = 220 K. (C and D) X-TECs results of the Sr₃Rh₄Sn₁₃ XRD data with ${\overrightarrow{q}}_i$ spanning the reciprocal space $(h,k,l=0)$ where $h,k\in [-15,15]$ reciprocal lattice units (r.l.u.). The clustering assignments are color-coded as blue, brown, and gray. In C, the lines represent cluster means, and the shaded region shows 1 SD, interpolated between 24 temperature points of measurement. D shows the pixels at ${\overrightarrow{q}}_i$ in the $(h,k,0)$ plane that passed the thresholding (SI Appendix, section 1B), colored according to their cluster assignments. X-TEC correctly identifies the blue clusters with the CDW super lattice peaks, brown clusters with Bragg peaks, and gray clusters with diffuse scattering. The blue cluster mean (solid line) in C represents the rescaled intensity trajectories of all CDW peaks in the data. (E) An order parameter like quantity $\mathrm{\Delta }(T)$ is estimated from the CDW (blue) cluster and is shown for four samples at different values of Ca doping x. The $\mathrm{\Delta }(T)$ is estimated from the cluster means by subtracting the minimum from each cluster mean and appropriate normalization. (F) $\mathrm{\Delta }(T)$ extracted from a manually selected CDW peak at $(h,k,l)=(13.5,4.5,0)$ for the four Ca doping x shows a qualitatively similar trajectory to that of X-TEC in E. (G) The critical temperatures estimated from the X-TEC extracted $\mathrm{\Delta }(T)$ (yellow filled circles) overlaid onto the known phase diagram from ref. 26 based on phase boundaries from thermodynamic measurements and transport.