Geometric frustration of hard-disk packings on cones
Jessica H Sun1, Abigail Plummer2, Grace H Zhang3
1Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
Physical Review. E
|December 20, 2023
Summary
Crystal growth on cones is geometrically frustrated by closure, forming seams and disordered packing. This frustration is a finite-size effect dependent on circumference, impacting single crystal formation.
Area of Science:
- Materials Science
- Crystallography
- Computational Physics
Background:
- Crystal growth on curved surfaces presents unique challenges.
- The closure constraint on conical surfaces can lead to geometric frustration.
Purpose of the Study:
- Investigate how geometric frustration impacts single crystal growth on cones.
- Analyze the role of cone angle and seed orientation in crystal formation.
- Understand the factors leading to disordered particle packing.
Main Methods:
- Utilized a disk-packing algorithm to simulate crystal growth.
- Varied crystal seed orientation and cone angle parameters.
- Developed a model for particle attachment at the crystal seam.
Main Results:
- Crystals typically form an axial seam on cones, except at commensurate angles.
- Disordered particle packing emerges near the cone tip.
- Onset of disorder is a finite-size effect dependent on circumference, not seed orientation or cone angle.
- Defect density increases exponentially with decreasing circumference on both cones and cylinders.
Conclusions:
- Single crystal growth can be frustrated on small-angle cones due to geometric constraints.
- Circumference is a critical factor in crystal defect formation on conical and cylindrical surfaces.
- Findings offer insights into biological and material conical crystal structures.
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