  The evolution of the nuclear and magnetic structures of TlFe$_{1.6}$Se$_2$
was determined in the temperature range of 5-450\,K using single crystal
neutron diffraction. The Fe layers in these materials develop a corrugation in
the magnetically ordered state. A canting away from the block checkerboard
magnetic structure is observed in the narrow temperature range between
approximately 100 and 150\,K. In this same temperature range, an increase in
the corrugation of the Fe layers is observed. At lower temperatures, the block
checkerboard magnetic structure is recovered with a suppressed magnetic moment
and abrupt changes in the lattice parameters. Microstructure analysis at 300\,K
using atomic-resolution Z-contrast scanning transmission electron microscopy
reveals regions with ordered and disordered Fe vacancies, and the iron content
is found to be uniform across the crystal. These findings highlight the
differences between the alkali-metal and thallium materials, and indicate
competition between magnetic ground states and a strong coupling of magnetism
to the lattice in TlFe$_{1.6}$Se$_2$.

Superconductivity;Strongly Correlated Electrons