In the quasi-2D electron systems of the layered transition metal dichalcogenides (TMD) there is still a controversy about the nature of the transitions to charge-density wave (CDW) phases, i.e. whether they are described by a Peierls-type mechanism or by a lattice-driven model. By performing scanning tunneling microscopy (STM) experiments on the canonical TMD-CDW systems, we have imaged the electronic modulation and the lattice distortion separately in 2H-TaS$_2$, TaSe$_2$, and NbSe$_2$. Across the three materials, we found dominant lattice contributions instead of the electronic modulation expected from Peierls transitions, in contrast to the CDW states that show the hallmark of contrast inversion between filled and empty states. Our results imply that the periodic lattice distortion (PLD) plays a vital role in the formation of CDW phases in the TMDs and illustrate the importance of taking into account the more complicated lattice degree of freedom when studying correlated electron systems.
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