| Autor: |
Sun JH; Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA., Plummer A; Princeton Center for Complex Materials, Princeton University, Princeton, New Jersey 08540, USA., Zhang GH; Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA., Nelson DR; Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA., Manoharan VN; Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA. |
| Abstrakt: |
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. |
