  Charge density waves (CDW) and their concomitant periodic lattice distortions
(PLD) govern the electronic properties in many layered transition-metal
dichalcogenides. In particular, 1T-TaS2 undergoes a metal-to-insulator phase
transition as the PLD becomes commensurate with the crystal lattice. Here we
directly image PLDs of the nearly-commensurate (NC) and commensurate (C) phases
in thin exfoliated 1T-TaS2 using atomic resolution scanning transmission
electron microscopy at room and cryogenic temperature. At low temperatures, we
observe commensurate PLD superstructures, suggesting ordering of the CDWs both
in- and out-of-plane. In addition, we discover stacking transitions in the
atomic lattice that occur via one bond length shifts. Interestingly, the NC
PLDs exist inside both the stacking domains and their boundaries. Transitions
in stacking order are expected to create fractional shifts in the CDW between
layers and may be another route to manipulate electronic phases in layered
dichalcogenides.
