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Simulation of atomic force microscopy operation via three-dimensional finite element modelling

Numerical modelling of atomic force microscopy cantilever designs and experiments is presented with the aim of exploring friction mechanisms at the microscale. As a starting point for this work, comparisons between finite element (FE) models and previously reported mathematical models for stiffness calibration of cantilevers (beam and V-shaped) are presented and discrepancies highlighted. A colloid probe (comprising a plain cantilever on which a particle is adhered) model was developed, and its normal and shear interaction were investigated, exploring the response of the probe accounting for inevitable imperfections in its manufacture. The material properties of the cantilever had significant impact on both the normal response and the lateral response. The sensitivity of the mechanical response in both directions was explored and it was found to be higher in terms of normal rather than lateral sensitivity. In lateral measurements, generic response stages were identified, comprising a first stage of twisting, followed by lateral bending, and then slipping. This was present in the two cantilever types explored (beam and V-shaped). Additionally, a model was designed to explore the dynamic sensitivity by comparing the simulation of a hysteresis loop with a previously reported experiment, and the results show good agreement in the response pattern. The ability to simulate the scan over an inclined surface representing the flank of an asperity was also demonstrated.