Kavli Affiliate: Vinothan N. Manoharan
| First 5 Authors: Jessica H. Sun, Abigail Plummer, Grace H. Zhang, David R. Nelson, Vinothan N. Manoharan
| Summary:
Conical surfaces pose an interesting challenge to crystal growth: a crystal
growing on a cone can wrap around and meet itself at different radii. We use a
disk-packing algorithm to investigate how this closure constraint can
geometrically frustrate the growth of single crystals on cones with small
opening angles. By varying the crystal seed orientation and cone angle, we find
that — except at special commensurate cone angles — crystals typically form a
seam that runs along the axial direction of the cone, while near the tip, a
disordered particle packing forms. We show that the onset of disorder results
from a finite-size effect that depends strongly on the circumference and not on
the seed orientation or cone angle. This finite-size effect occurs also on
cylinders, and we present evidence that on both cylinders and cones, the defect
density increases exponentially as circumference decreases. We introduce a
simple model for particle attachment at the seam that explains the dependence
on the circumference. Our findings suggest that the growth of single crystals
can become frustrated even very far from the tip when the cone has a small
opening angle. These results may provide insights into the observed geometry of
conical crystals in biological and materials applications.
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