  We describe the local structural properties of the iron oxychalcogenides,
La$_2$O$_2$Fe$_2$O$M_2$ ($M$ = S, Se), by using pair distribution function
(PDF) analysis applied to total scattering data. Our results of neutron powder
diffraction show that $M$ = S and Se possess similar nuclear structure at low
and room temperatures. The local crystal structures were studied by
investigating deviations in atomic positions and the extent of the formation of
orthorhombicity. Analysis of the total scattering data suggests that buckling
of the Fe$_2$O plane occurs below 100 K. The buckling may occur concomitantly
with a change in octahedral height. Furthermore, within a typical range of 1-2
nm, we observed short-range orthorhombic-like structure suggestive of nematic
fluctuations in both of these materials.

Strongly Correlated Electrons;Superconductivity