  Using ab-initio density functional theory we study the role of interstitial
hydrogen on the energetics of the phase transformation of iron from bcc to hcp
along Bain's pathway. The impurity creates an internal stress field that can be
released through a tetragonal distortion of the lattice, promoting the bcc
(ferromagnetic) $\rightarrow$ fcc (frustrated antiferromagnetic) $\rightarrow$
hcp (ferromagnetic) transition. The transformation between crystal systems is
accompanied by a drastic magnetic reorganization and sudden variations of the
unit cell volume, that can be one of the reasons for embrittlement and
mechanical failure of iron upon hydrogen adsorption.
