The octahedral void exposes \(S\) in \(FeS_2\) on the surface and made it vulnerable to a free \(Li_2\). One \(Fe-S\) ionic bond is broken with the formation of one \(Li_2-S\) bond. This one broken bond out of six with a big \(Li\) jammed in the lattice causes the lattice structure to crack, and data from X-ray absorption suggests that \(Li_2FeS_2\) is amorphous. At room temperature, on recharge the lattice does not reform and a different sets of redox reactions applies which results in the precipitation of \(Fe\) and \(S\). Both are undesirable in the operation of the battery.
It's the hole's fault, we need a bigger hole.
A mix of smaller "late" transitional metal might allow \(Fe\) to open up. Cobalt \(Co\) is a suitable candidate.
And \(CoS_2\) (beta form) can serve as a backing lattice to keep \(FeS_2\) structural integrity. But \(Co\) is further down the reactivity series, it is likely that \(Co\) is reduced by \(Li\) before \(Fe\) in which case we would use \(FeS_2\) as the backing lattice and use \(CoS_2\) to receive \(Li_2\). \(CoS_2\) will insulate \(FeS_2\) from \(Li_2\) while \(FeS_2\) provides structural integrity.
Another big "late" transitional metal is \(Mn\) with crystal radius of \(0.81\times10^{-10}\)m. \(Mn\) is more reactive than \(Fe\). In place of \(Fe\) as the backing lattice and dopant for a reactive \(CoS_2\) layer might open the lattice (\(CoS_2\) doped with \(Mn\) lattice) further and make \(S\) more accessible to \(Li_2\).