Structural phase transitions in ${\mathrm{VO}}_2$ and consequent changes in its physical properties have been cornerstones in the development of condensed matter physics, not only in terms of the spectacular insulator-metal transition in the archetypical monoclinic (M1)-rutile (R) phase transition but also in closely related structure types achieved by minor perturbations of the pure system by the application of pressure or doping. In this context, the most investigated phenomenon is the triclinic (T)-monoclinic (M2)-rutile (R) phase transition. The present work, using single-crystal and powder x-ray diffraction measurements on ${\mathrm{Al}}^{3+}, {\mathrm{Cr}}^{3+}$, and ${\mathrm{Fe}}^{3+}$ doped samples, reveals a common structural behavior independent of the nature of the dopant ion. The structures of the different phases can be described in terms of V chains, characterized by different extents of V-V dimerization and tilt. The systematic structural evolution of the V chains across the T-M2-R transitions allows us to define microscopic order parameters combining the extents of dimerization and tilt to describe the T-M2 and M2-R phase transitions, which in turn help us establish that the T-M2 transition remains first-order throughout the composition range, contrary to the current belief.

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• Order parameters
• Peierls transition
• Phase transitions
• Vanadates
• X-ray diffraction