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We report the discovery of a novel form of Ruddlesden–Popper (RP) nickelate that stands as the first example of long-range, coherent polymorphism in this class of inorganic solids. Rather than the well-known, uniform stacking of perovskite blocks ubiquitously found in RP phases, this newly discovered polymorph of the bilayer RP phase La3Ni2O7 adopts a novel stacking sequence in which single-layer and trilayer blocks of NiO6 octahedra alternate in a “1313” sequence. Crystals of this new polymorph are described in space group Cmmm, although we note evidence for a competing Imam variant. Transport measurements at ambient pressure reveal metallic character with evidence of a charge density wave transition with an onset at T ≈ 134 K. The discovery of such polymorphism could reverberate to the expansive range of science and applications that rely on RP materials, particularly the recently reported signatures of superconductivity in bilayer La3Ni2O7 with Tc as high as 80 K above 14 GPa. 

The information content of crystalline materials becomes astronomical when collective electronic behavior and their fluctuations are taken into account. In the past decade, improvements in source brightness and detector technology at modern X-ray facilities have allowed a dramatically increased fraction of this information to be captured. Now, the primary challenge is to understand and discover scientific principles from big datasets when a comprehensive analysis is beyond human reach. We report the development of an unsupervised machine learning approach, X-ray diffraction (XRD) temperature clustering (X-TEC), that can automatically extract charge density wave order parameters and detect intraunit cell ordering and its fluctuations from a series of high-volume X-ray diffraction measurements taken at multiple temperatures. We benchmark X-TEC with diffraction data on a quasi-skutterudite family of materials, (Ca x Sr 1 − x ) 3 Rh 4 Sn 13 , where a quantum critical point is observed as a function of Ca concentration. We apply X-TEC to XRD data on the pyrochlore metal, Cd 2 Re 2 O 7 , to investigate its two much-debated structural phase transitions and uncover the Goldstone mode accompanying them. We demonstrate how unprecedented atomic-scale knowledge can be gained when human researchers connect the X-TEC results to physical principles. Specifically, we extract from the X-TEC–revealed selection rules that the Cd and Re displacements are approximately equal in amplitude but out of phase. This discovery reveals a previously unknown involvement of 5 d 2 Re, supporting the idea of an electronic origin to the structural order. Our approach can radically transform XRD experiments by allowing in operando data analysis and enabling researchers to refine experiments by discovering interesting regions of phase space on the fly.