Quantum Simulation of Fractal Fracture in Amorphous Silica

In order to design new materials at atomic-length scales, there is a need to connect the fractal nature of fracture surfaces at the atomic scale using quantum mechanics modeling with that of the experimental data of fracture surfaces at macroscopic-length scales. We use a semi-empirical quantum mechanics simulation of fracture in amorphous silica to calculate a parameter identified as a critical characteristic length, a0, which has been experimentally derived from the fractal nature of fracture for many materials that fail in a brittle matter. To our knowledge, there are no known simulation models other than our related research that use the fractal parameter a0 to describe the fractal fracture of the fracture surface using quantum mechanical simulations. We provide evidence that a0 can be calculated at both the atomic and macroscopic scale, making it a fundamental property of the structure and one of the elements of fractal fracture. We use a continuous random network model and reaction coordinate method to simulate fracture. We propose that fracture in amorphous silica occurs due to bond reconfiguration resulting in increased strain volume at the crack tip. We hypothesize two specific configurations leading to fracture from a four-fold ring reconfiguration to three-fold ring or (newly observed) five-fold ring configurations resulting in a change in volume. Finally, we define a reconfiguration fracture energy at the atomic level, which is approximately the value of the experimental fracture surface energy.