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In the superconducting doped topological insulator Sr_xBi₂Se₃ (T_c ~ 3.1 K), a pronounced two-fold in-plane symmetry is observed in electronic properties below T_c, despite the three-fold symmetry of the R-3m space group. The axis of symmetry is always pinned to one of three rotational equivalent directions; crystallographic strain has been proposed to be the origin of this pinning. Here, we present multimodal synchrotron diffraction measurements down to ~0.7 K on a single crystal of Sr_0.1Bi₂Se₃ combining in-situ resistivity measurements and XRD. Magnetic fields up to 4.5 T were also applied. We find no crystallographic distortions from the normal-state structure to 1 part in 10⁴ indicating that the two-fold anisotropy is not caused by structural distortions but is electronic in origin.