Pleats in crystals on curved surfaces.

Area of Science:

• Materials Science
• Condensed Matter Physics
• Geometry

Background:

• Hexagonal crystals tile flat surfaces but struggle with curved ones.
• Topological defects (pentagons, heptagons) aid tiling of curved surfaces, like soccer balls.
• Spherical crystal surfaces exhibit defect scars, but general curved surfaces require new models.

Purpose of the Study:

• To investigate how crystal order is affected by varying positive and negative curvature.
• To explore the role of pleats (uncharged dislocation lines) in relaxing surface curvature.
• To understand defect formation and organization on complex curved surfaces.

Main Methods:

• Experimental investigation of crystal order on cylindrical capillary bridges with controlled negative curvature.
• Energetic calculations to model defect behavior and transitions.
• Observation of defect patterns including dislocations, pleats, scars, and heptagons.

Main Results:

• Observed transitions from no defects to isolated dislocations, then pleats, on negatively curved surfaces.
• Dislocations proliferated and organized into pleats, effectively relaxing curvature.
• Unseen isolated heptagons appeared alongside scars on these surfaces.

Conclusions:

• Pleats act as uncharged topological dipoles, relaxing curvature on surfaces.
• Crystal order can be precisely controlled by surface curvature, offering new insights into defect theories.
• Potential applications include engineering curved structures and developing novel soft lithography techniques.