  All underdoped high-temperature cuprate superconductors appear to exhibit
charge density wave (CDW) order, but both the underlying symmetry breaking and
the origin of the CDW remain unclear. We use X-ray diffraction to determine the
microscopic structure of the CDW in an archetypical cuprate
YBa$_2$Cu$_3$O$_{6.54}$ at its superconducting transition temperature Tc ~ 60
K. We find that the CDWs present in this material break the mirror symmetry of
the CuO2 bilayers. The ionic displacements in a CDW have two components: one
perpendicular to the CuO$_2$ planes, and another parallel to these planes,
which is out of phase with the first. The largest displacements are those of
the planar oxygen atoms and are perpendicular to the CuO$_2$ planes. Our
results allow many electronic properties of the underdoped cuprates to be
understood. For instance, the CDW will lead to local variations in the doping
(or electronic structure) giving an explicit explanation of the appearance of
density-wave states with broken symmetry in scanning tunnelling microscopy
(STM) and soft X-ray measurements.
