  Hybrid semiconductor/superconductor nanowires constitute a pervasive platform
for studying gate-tunable superconductivity and the emergence of topological
behavior. Their low-dimensionality and crystal structure flexibility facilitate
novel heterostructure growth and efficient material optimization; crucial
prerequisites for accurately constructing complex multi-component quantum
materials. Here, we present an extensive optimization of Sn growth on InSb,
InAsSb and InAs nanowires. We demonstrate how the growth conditions and the
crystal structure/symmetry of the semiconductor drive the formation of either
semi-metallic $\mathrm{\alpha-Sn}$ or superconducting $\mathrm{\beta-Sn}$. For
InAs nanowires, we obtain phase-pure, superconducting $\mathrm{\beta-Sn}$
shells. However, for InSb and InAsSb nanowires, an initial epitaxial
$\mathrm{\alpha-Sn}$ phase evolves into a polycrystalline shell of coexisting
$\mathrm{\alpha}$ and $\mathrm{\beta}$ phases, where the $\beta/\alpha$ volume
ratio increases with Sn shell thickness. Whether these nanowires exhibit
superconductivity or not critically relies on the $\mathrm{\beta-Sn}$ content.
Therefore, this work provides key insights into Sn phase control on a variety
of semiconductors, with consequences for the yield of superconducting hybrids
suitable for generating topological systems.
