Question

GeO2 exists in a number of structures, most commonly a hexagonal form that is built on corner sharing GeO4 tetrahedra and a tetragonal structure in the mineral argutite built from edge sharing GeO6 octahedra.
Giving your reasoning predict if a direct transformation between the hexagonal and tetragonal structures is likely to be first order or continuous.

Answer 1

The two polymorphs of $GeO_2$ are hexagonal and tetragonal.

Hexagonal $GeO_2$ has the same structure quartz , with germanium having coordination number $4$ . Tetragonal $GeO_2$ (The mineral argutite) has the notile-like structure seen in stishovite. Germanium in this motif has coordination number 6.

$GeO_2$ is a chemical analogue of $SiO_2$ . It is, to some extent a structural analogue, as the low and high-pressure short-range order (tetrahedral and octahedral) is the same. However, a number of differences exist. The $GeO_2$ phase diagram, and all three $GeO_2$ phases (crystalline, glass, liquid) have an increased sensitivity to pressure, undergoing pressure induced changes at much lower pressures than their equivalent $SiO_2$ analogues.