Simultaneous Deconvolution of In-Plane and Out-of-Plane Forces of HOPG at the Atomic Scale under Ambient Conditions by Multifrequency Atomic Force Microscopy

Multifrequency atomic force microscopy (AFM) is shown to be an excellent tool for imaging crystal structures at atomic resolution in different spatial directions. However, determining the forces between single atoms remains challenging, particularly in air under ambient conditions. Developed here is a trimodal AFM approach that simultaneously acquires torsional and flexural frequency-shift images and spectroscopic data to transfer these observables into in-plane and out-of-plane forces between single bonds of highly oriented pyrolytic graphite (HOPG) at atomic resolution in air under ambient conditions based on the Fourier method. It is found that the cantilever mean deflection is an excellent indicator to understand that strong attractive interactions between the tip and the surface of HOPG in dynamic AFM imply a local lift of the topmost carbon layer when using higher eigenmodes for the topographical feedback. Cross-talk between torsional and flexural-oscillation modes is shown to be negligible. Interestingly, significant differences are observed in the in-plane forces depending on the orientation of the carbon bonds relative to the direction of torsional oscillation.

Automated summary

Multifrequency atomic force microscopy is proven to be a powerful tool for imaging crystal structures at atomic resolution in different spatial directions. A new trimodal AFM approach has been developed to determine in-plane and out-of-plane forces between single bonds of highly oriented pyrolytic graphite with atomic resolution in air under ambient conditions. Additionally, the cantilever mean deflection is identified as a critical indicator for strong attractive interactions between the tip and HOPG surface, with negligible cross-talk between torsional and flexural oscillation modes.