  The intermetallic $\tau_{11}$ Al$_4$Fe$_{1.7}$Si phase is of interest for
high-temperature structural application due to its combination of low density
and high strength. We determine the crystal structure of the $\tau_{11}$ phase
through a combination of powder neutron diffraction and density functional
theory calculations. Using Pawley and Rietveld refinements of the neutron
diffraction data provides an initial crystal structure model. Since Al and Si
have nearly identical neutron scattering lengths, we use density-functional
calculations to determine their preferred site occupations. The $\tau_{11}$
phase exhibits a hexagonal crystal structure with space group $P6_3/mmc$ and
lattice parameters of $a=7.478$~\AA\ and $c=7.472$~\AA. The structure comprises
five Wyckoff positions; Al occupies the $6h$ and $12k$ sites, Fe the $2a$ and
$6h$ sites, and Si the $2a$ sites. We observe site disorder and partial
occupancies on all sites with a large fraction of 80\% Fe vacancies on the $2d$
sites, indicating an entropic stabilization of the $\tau_{11}$ phase at high
temperature.
