Torsional and lateral eigenmode oscillations for atomic resolution imaging of HOPG in air under ambient conditions

Combined in-plane and out-of-plane multifrequency atomic force microscopy techniques have been demonstrated to be important tools to decipher spatial differences of sample surfaces at the atomic scale. The analysis of physical properties perpendicular to the sample surface is routinely achieved from flexural cantilever oscillations, whereas the interpretation of in-plane sample properties via force microscopy is still challenging. Besides the torsional oscillation, there is the additional option to exploit the lateral oscillation of the cantilever for in-plane surface analysis. In this study, we used different multifrequency force microscopy approaches to attain better understanding of the interactions between a super-sharp tip and an HOPG surface focusing on the discrimination between friction and shear forces. We found that the lateral eigenmode is suitable for the determination of the shear modulus whereas the torsional eigenmode provides information on local friction forces between tip and sample. Based on the results, we propose that the full set of elastic constants of graphite can be determined from combined in-plane and out-of-plane multifrequency atomic force microscopy if ultrasmall amplitudes and high force constants are used.