  The quasi-2D Pt-based rare earth intermetallic material LaPt$_2$Si$_2$ has
attracted attention as it exhibits strong interplay between charge density wave
(CDW) and and superconductivity (SC). However, the most of the results reported
on this material come from theoretical calculations, preliminary bulk
investigations and powder samples, which makes it difficult to uniquely
determine the temperature evolution of its crystal structure and, consequently,
of its CDW transition. Therefore, the published literature around
LaPt$_2$Si$_2$ is often controversial. In this paper, we clarify the complex
evolution of the crystal structure, and the temperature dependence of the
development of density wave transitions, in good quality LaPt$_2$Si$_2$ single
crystals, with high resolution synchrotron X-ray diffraction data. According to
our findings, on cooling from room temperature LaPt$_2$Si$_2$ undergoes a
series of subtle structural transitions which can be summarised as follows:
second order commensurate tetragonal ($P4/nmm$)-to-incommensurate structure
followed by a first order incommensurate-to-commensurate orthorhombic ($Pmmn$)
transition and then a first order commensurate orthorhombic
($Pmmn$)-to-commensurate tetragonal ($P4/nmm$). The structural transitions are
accompanied by both incommensurate and commensurate superstructural distortions
of the lattice. The observed behavior is compatible with discommensuration of
the CDW in this material.
