Fractal geometry supporting 2D silica networks: sample generation and its mechanical properties

  • Ochoa Ontiveros, Lilian Aurora (University of Wuppertal)
  • Bamer, Franz (RWTH Aachen)

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Fractal geometry, a mathematical framework that studies intricate and irregular shapes characterized by intrinsic self-similarity, provides a powerful alternative representation of complex structures beyond classical Euclidean geometry. Unlike traditional geometry, fractal geometry can accurately capture the repeating patterns and fine details observed in many natural and synthetic materials. In this study, fractal curves are proposed as a spatial underlying pattern to systematically introduce a controlled degree of disorder into initially crystalline two-dimensional silica networks, thereby generating defective model structures that resemble amorphous materials. These 2D silica structures, modelled following Zachariasen’s theory of random networks, are constructed by sequences of topological flip transformations. These transformations are identified as Stone-Wales defect flips, and selectively alter bond connectivity while preserving the fundamental coordination: each silicon atom connected to three adjacent oxygen atoms. These silica structures have been used for experimental imaging and computational visualization of defective hexagonal lattice structures and two-dimensional amorphous materials. The defect generation protocol simulates an experimental process involving incremental kinetic energy increases to trigger the flips, harmonic potential-based local relaxations after each transformation, and a final relaxation with a Yukawa potential to ensure physical plausibility of the resulting network. The resulting disordered networks maintain essential ring topology constraints and retain recognizable imprints of the underlying fractal patterns. The identification and prediction of the elementary mechanical processes in disordered materials has been a significant research point, therefore, the mechanical characterization through tensile and shear testing on the generated samples reveals that the fractal generator’s properties significantly influence the emergent mechanical responses, affecting network stiffness, anisotropy and strength. This work highlights the potential of fractal-guided topological engineering as a versatile route to design disordered silica-like materials, providing novel perspectives for defect engineering in low-dimensional disordered solids.