Identifying
ordering in non-crystalline solids has been a focus
of natural science since the publication of Zachariasen’s random
network theory in 1932, but it still remains as a great challenge
of the century. Literature shows that the hierarchical structures,
from the short-range order of first-shell polyhedra to the long-range
order of translational periodicity, may survive after amorphization.
Here, in a piece of AlPO4, or berlinite, we combine X-ray
diffraction and stochastic free-energy surface simulations to study
its phase transition and structural ordering under pressure. From
reversible single crystals to amorphous transitions, we now present
an unambiguous view of the topological ordering in the amorphous phase,
consisting of a swarm of Carpenter low-symmetry phases with the same
topological linkage, trapped in a metastable intermediate stage. We
propose that the remaining topological ordering is the origin of the
switchable “memory glass” effect. Such topological ordering
may hide in many amorphous materials through disordered short atomic
displacements.