Critical nanoring diameter vs nanotube diameter for single-walled nanorings with armchair configurations without torsion, armchair configurations with torsion, and zigzag configurations with torsion.
Critical nanoring diameter vs nanotube diameter for double-walled nanorings with armchair configurations without torsion, armchair configurations with torsion, and zigzag configurations without torsion.
The relationship of the critical diameter of the nanoring vs the number of walls .
The final stable cross sections for different nanotube configurations and nanoring diameters after relaxation. (a) with , (b) with , and (c) with .
The deformation sequence of a nanoring with an initial diameter of without torsion. During energy relaxation, the ring diameters shrink markedly. The ripples first develop on the compressive side of the outer wall, and subsequently buckle causing the failure of the ring.
The deformation sequence of a nanoring with an initial diameter of with torsion. The failure process is similar to the case. However, the ripple density along the circumferential direction is reduced with the inclusion of torsion.
The number of ripples of the outer tube vs the nanoring diameter of the type without torsion. The diameters of the nanorings in the inset are 7.86, 11.79, and 15.72 nm.
The effect of the wall-wall spacing on the stability of double-walled rings.
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