Do Directional Primary and Secondary Crack Patterns in Thin Films of Maghemite Nanocrystals Follow a Universal Scaling Law?

Cracks due to a shrinking film restricted by adhesion to a surface are observed in nature at various length scales ranging from tiny crack segments in nanoparticle films to enormous domains observed in the earth's crust. Here, we study the formation of cracks in magnetic films made of maghemite (gamma-Fe2O3) nanocrystals. The cracks are oriented by an external magnetic field applied during the drying process which presents a new method to produce directional crack patterns. It is shown that directional and isotropic crack patterns follow the same universal scaling law with the film height varying from micrometer to centimeter scales. Former experimental studies of scaling laws were limited to small variations in height (1 order of magnitude). The large variation in height in our expriments becomes possible due to the combined use of nanocrystals and electron microscopy. A simple two-dimensional computer model for elastic fracture leads to structural and scaling behaviors, which match those observed in the experiments.