Fig. 2: Temperature progression of atomic structure in 1T-TaS₂.

a Stack of diffraction patterns revealing a polymporphic transformation on warming at ~630 K. Inset: intensity collapse of the (012) \({{{{{\rm{P}}}}}}\bar{3}{{{{{\rm{m}}}}}}\) Bragg reflection during the restructuring from pure 1T to a hybrid 1T & 1H coordination. Further restructuring above 880 K results in additional Bragg reflections, marked by asterisk. b Corresponding PDFs over a narrow r-range. Data feature isosbestic points (circled) - nodes of temperature-invariant PDF intensity. Label 1 T* indicates presence of local distortions in the 1T-type layers. Vertical blue arrow (1T*) marks polaronic distortion intensity. Inset: Change of fraction of distorted 1T* environments, relative to 600 K, estimated over the shaded region on the abscissa. c Polaron signature, seen in the M phase (top), persists in the restacked polymorph structure (bottom), and is associated with the 1T-type layers. Adding distortions, described in g, as nanoscale inclusions results in improved fit (cyan trace). In d, e a stack of PDF data on different length scales is shown over the 15–500 K range, color-coded according to the electronic phase they belong to. At high temperature longer length-scale peaks sharpen (indicated by vertical arrows) due to apparent average symmetry increase, despite expected broadening due to ADP increase at elevated temperature and in contrast to the shorter length-scale behavior. Features exhibiting negative thermal expansion (NTE) are indicated by block arrows. f At 15 K clear distortions associated with the star of David (SoD) are seen in the local structure, incompatible with the \({{{{{\rm{P}}}}}}\bar{3}{{{{{\rm{m}}}}}}\) symmetry (top) but explained well (bottom) by a simple \({{{{{\rm{P}}}}}}\bar{3}\) broken symmetry model, depicted in g with focus on Ta atoms. Colored arrows show the Ta displacements. Out-of-plane degrees of freedom (exaggerated in the illustration for clarity) provide for puckering distortions.