Triangular and Fibonacci number patterns driven by stress on core/shell microstructures.

Fibonacci number patterns and triangular patterns with intrinsic defects occur frequently on nonplanar surfaces in nature, particularly in plants. By controlling the geometry and the stress upon cooling, these patterns can be reproduced on the surface of microstructures about 10 micrometers in diameter. Spherules of the Ag core/SiOx shell structure, possessing markedly uniform size and shape, self-assembled into the Fibonacci number patterns (5 by 8 and 13 by 21) or the triangular pattern, depending on the geometry of the primary supporting surface. Under proper geometrical constraints, the patterns developed through self-assembly in order to minimize the total strain energy. This demonstrates that highly ordered microstructures can be prepared simultaneously across large areas by stress engineering.