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Spin-orbit coupling in transition metal compounds with 4d and 5d electrons is predicted to generate a wide variety of novel parity-breaking correlated electron phases, but evidence of a concomitant structural response is often lacking. Cd₂Re₂O₇ is a pyrochlore that has been proposed to exhibit multipolar nematic order below two structural phase transitions at 200K and 113K, but the symmetry of the order parameters are under dispute. We report high-energy x-ray scattering measurements of 3D reciprocal space volumes comprising over 10,000 Brillouin zones in a fine Q-grid performed at many temperatures from 300K to 30K. We have analyzed the data with unsupervised machine learning, using the newly-developed X-TEC algorithm [1], to classify the temperature dependence of both superlattice peaks and diffuse scattering. The order parameter below 200K results from cation displacements consistent with the condensation of a nearly-degenerate two-component E_u mode. X-TEC also identified diffuse scattering below 200K from Goldstone mode fluctuations between the two E_u modes, which could explain the lower transition at 113 K.

[1] Venderley et al, https://arxiv.org/abs/2008.03275