Simulations of Cracks Supported by Experiments: The Influence of the Film Height and Isotropy on the Geometry of Crack Patterns

Here, we show that cracks give valuable information on the height and the isotropy of nanocrystal films. Two-dimensional crack patterns are systematically studied by simulations and experiments varying the height and the anisotropy of the applied stress. The simulations are carried out using a bundle-spring network model, which allows studying the influence of height on crack patterns. For the experiments, a model system made of magnetic γ-Fe₂O₃ nanocrystals is used, which enables a change in the anisotropy of the stress by applying a magnetic field during the drying process. The crack pattern morphology is investigated by simulations using square, hexagonal, and isotropic spring arrangements and applying an isotropic or unilateral stress. The average crack distance as a function of the film height studied by simulations follows a universal scaling law, confirming the experimental data. We show that this implies that the morphology of the crack pattern does not change with the height. The frequency of crack fragments as a function of the number of their sides or neighbors is analyzed for isotropic crack patterns obtained from the simulations using various spring arrangements. Finally, the theoretical results are compared to the experiments. The observed linear scaling of crack distances with height is in good agreement with the theory. The frequency of crack fragments as a function of the number of sides and neighbors does not significantly change with height, except for very thin layers. The simulations show that the experimental frequencies indicate the isotropy of the nanocrystal films.