  Complex crystal structures are composed of multiple local environments, and
how this type of order emerges spontaneously during crystal growth has yet to
be fully understood. We study crystal growth across various structures and
along different crystallization pathways, using self-assembly simulations of
identical particles that interact via multi-well isotropic pair potentials. We
apply an unsupervised machine learning method to features from
bond-orientational order metrics to identify different local motifs present
during a given structure's crystallization process. In this manner, we
distinguish different crystallographic sites in highly complex structures.
Tailoring this newly developed order parameter to structures of varying
complexity and coordination number, we study the emergence of local order along
a multi-step crystal growth pathway -- from a low-density fluid to a
high-density, supercooled amorphous liquid droplet and to a bulk crystal. We
find a consistent under-coordination of the liquid relative to the average
coordination number in the bulk crystal. We use our order parameter to analyze
the geometrically frustrated growth of a Frank--Kasper phase and discover how
structural defects compete with the formation of crystallographic sites that
are higher-coordinated than the liquid environments. The here-presented method
for classifying order on a particle-by-particle level have broad applicability
to future studies of structural self-assembly and crystal growth, and they can
aid in the design of building blocks and for targeting pathways of formation of
novel soft-matter structures.
