  Co$_{2}$FeSi/GaAs(111)B hybrid structures are grown by molecular-beam epitaxy
and characterized by transmission electron microscopy (TEM) and x-ray
diffraction. The Co$_{2}$FeSi films grow in an island growth mode at substrate
temperatures $T_{S}$ between $T_{S}$~=~100$\thinspace^{\circ}$C and
425$\thinspace^{\circ}$C. The structures have a stable interface up to
$T_{S}=275~^{\circ}$C. The films contain fully ordered $L2_{1}$ and partially
ordered $B2$ phases. The spatial distribution of long-range order in
Co$_{2}$FeSi is characterized using a comparison of TEM images taken with
superlattice reflections and the corresponding fundamental reflections. The
spatial inhomogeneities of long-range order can be explained by local
non-stoichiometry due to lateral segregation or stress relaxation without
formation of extended defects.
