Modeling of Young's modulus, hardness and stiffness of chromium zigzag multilayers sputter deposited

Sculptured thin films exhibiting a zigzag microstructure behave as a field of “microsprings”. Two theoretical approaches are presented to predict hardness, Young's modulus and stiffness of these coatings taking into account the film's geometry (zigzag) and the bulk material properties. Both models are based on the deformation of a single zigzag period caused by a normal force. In the first model (simple model), the column diameter is neglected during the deformation (no difference between the curvature radius of internal and external fibre). These differences are taken into account in the second model (enhanced model). The column section is not perfectly circular and so, both models are developed for circular and square sections. Models are tested on chromium zigzag multilayers sputter deposited with a constant thickness close to 1 μm and with half-period thickness Λ / 2 ranging from 50 to 1000 nm. Geometrical parameters are determined from Scanning Electron Microscopy observations. These parameters are used to calculate the theoretical values of Young's modulus, hardness, and stiffness. Experimental values of Young's modulus (ranging from 86 GPa for single layers up to 250 GPa for the film composed of 10 periods 100 nm thick) and hardness (ranging from 2 GPa for single layers up to 14 GPa for the film composed of 10 periods 100 nm thick) of chromium thin films are measured by nanoindentation. A quite good agreement is obtained between experimental and computed values. Such comparison proves that the proposed models are valuable to predict some mechanical properties of multilayers with a zigzag microstructure.