Egberts, PhilipMathias, Thomas2023-09-122023-09-122023-09-04Mathias, T. (2023). Cantilever tip radius estimation through Contact Resonance Atomic Force Microscopy (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.https://hdl.handle.net/1880/116983https://doi.org/10.11575/PRISM/41827The mechanical characteristics of materials, particularly those of composite materials, can be mapped spatially and quantified using Contact Resonance Atomic Force Microscopy (CR-AFM). This technique operates by measuring the changes in resonance frequency as an AFM cantilever tip comes into contact with a sample surface. Such frequency shifts are primarily related to contact stiffness, although it can also influence other factors such as viscoelasticity. While several theories aim to connect the modal shape and resonant frequency of the AFM cantilever with contact stiffness, no direct application of these models has been developed to directly transform the resonant frequency into a physical mechanical property measurement. Instead, the majority of experimental studies utilising CR-AFM calibrate the frequency conversion factor relating to contact stiffness using a known reference sample, bypassing the direct use of these cantilever models. This thesis brings into focus two novel aspects aimed at enhancing and refining the CR-AFM technique: using thermal resonance to monitor the oscillation modes of an AFM cantilever during an experiment and establishing a connection between cantilever dynamics theory and the calibration of CR-AFM data that eliminates the requirement for normalisation to a known sample. In the first segment of this thesis, cantilever thermal displacement time series data is transformed into frequency space utilising the short-time Fourier transform(STFT) and continuous wavelet transform (CWT). It will be demonstrated that only the STFT calculations are capable of delivering the time-frequency resolution necessary to track AFM modal vibrations, at least currently. The application of the STFT allows for real-time tracking of the contact resonance frequency and Quality factor throughout a force spectroscopy experiment. The ensuing analysis reveals the fluctuations in contact resonance frequency over the course of this experiment. However, utilising cantilever analytical models to interpret this data using known contact mechanics models resulted in nonphysical estimates. Further studies are underway to reconcile the often problematic assumptions made in contact mechanics for AFM measurements with dynamic, STFT measurements. The experimental findings underscore the reasons why normalisation or calibration of CR-AFM results to samples with known stiffness has been prevalent until now. Despite progress, the comprehensive understanding of the contact mechanics and vibration theory necessary to analyse the dynamics of AFM cantilevers in such experiments remains an open challenge.enUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Atomic Force MicroscopeContact ResonanceMechanical PropertiesEngineering--MechanicalEngineeringMaterials Sciencemaster thesis