  Iron telluride doped lightly with selenium is known to undergo a first order
magneto-structural transition before turning superconducting at higher doping.
We study the effects of magneto-elastic couplings on this transition using
symmetry considerations. We find that the magnetic order parameters are coupled
to the uniform monoclinic strain of the unit cell with one iron per cell, as
well as to the phonons at high symmetry points of the Brillouin zone. In the
magnetic phase the former gives rise to monoclinic distortion while the latter
induces dimerization of the ferromagnetic iron chains due to alternate
lengthening and shortening of the nearest-neighbour iron-iron bonds. We compare
this system with the iron arsenides and propose a microscopic magneto-elastic
Hamiltonian which is relevant for all the iron based superconductors. We argue
that this describes electron-lattice coupling in a system where
electron-electron interaction is crucial.
