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

Abstract

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.

Hydration Dynamics and the Future of Small-Amplitude AFM Imaging in Air

“…The recent work by Eichhorn and Dietz [ 3 ] is particularly suitable to investigate the problems that might emerge when (1) imaging in air with small or ultra-small amplitudes and (2) advancing the field of multifrequency AFM, where several cantilever modes are excited in multiple ways, i.e., flexural and torsional. The first point is relevant because (1) such small amplitudes are of the same order of magnitude or smaller than the water films that form on surfaces, i.e., ~0.1–1 nm, and (2) it shows that even recent research fails to report the actual regime of operation, i.e., how many regimes were available for imaging in the experiments and which regime was exploited.…”

“…It is likely, however, that as a systematic investigation of force reconstruction, aging, and imaging regime is carried out, new identities or useful expressions will emerge. Finally, the SASS regime can also be accessed and exploited in multifrequency AFM [ 3 , 53 ]. In this regime, sample indentation δ is minimal but non-zero.…”

“…The atomic force microscope can be operated in air, ultra-high vacuum (UHV), and liquid environments [ 1 ]. Nevertheless, a multiplicity of phenomena controlling cantilever dynamics [ 2 ], modes of operation [ 3 ], and feedback mechanisms [ 4 , 5 ] influence the possibilities and challenges encountered in each environment. This calls for attention in terms of the operation, utilization, and interpretation of data; for this reason, different theories have been developed and implemented in many cases [ 6 ].…”

“…Moreover, the user must cope with and understand the character of some dynamic variables, such as the sharpness of the tip [ 9 , 10 ], otherwise referred to as the tip radius, R, in high-resolution imaging applications. Perhaps counter-intuitively to the newcomer, the field has rapidly advanced in two extremes—in liquid [ 11 , 12 , 13 , 14 ] and UHV environments [ 15 ]—while several complex phenomena have hindered the imaging and quantification of phenomena in air [ 16 ] with similar resolutions, controls, or throughputs [ 3 ]. There has been research in air in terms of capillary interactions [ 17 ], spontaneous capillary condensation [ 16 ], and the way the air environment affects surfaces [ 18 ], molecules on it, and modes of imaging [ 3 , 19 , 20 , 21 ].…”

“…Perhaps counter-intuitively to the newcomer, the field has rapidly advanced in two extremes—in liquid [ 11 , 12 , 13 , 14 ] and UHV environments [ 15 ]—while several complex phenomena have hindered the imaging and quantification of phenomena in air [ 16 ] with similar resolutions, controls, or throughputs [ 3 ]. There has been research in air in terms of capillary interactions [ 17 ], spontaneous capillary condensation [ 16 ], and the way the air environment affects surfaces [ 18 ], molecules on it, and modes of imaging [ 3 , 19 , 20 , 21 ]. In terms of force measurements in air, most have focused on capillary interactions [ 22 ] arising from the formation and rupture of a capillary neck as a function of the relative humidity (RH), either experimentally [ 16 ] or theoretically [ 23 ].…”