Energy Loss Triggered by Atomic-Scale Lateral Force

Abstract

We perform bimodal atomic force microscopy measurements on a Br-doped NaCl (001) surface to investigate the mechanisms behind frequency shift and energy dissipation contrasts. The peculiar pattern of the dissipated energy in the torsional channel, related to frictional processes, is increased at the positions of Br impurities, otherwise indistinguishable from Cl ions in the other measured channels. Our simulations reveal how the energy dissipates by the rearrangement of the tip apex and how the process is ultimately governed by lateral forces. Even the slightest change in lateral forces, induced by the presence of a Br impurity, is enough to trigger the apex reconstruction more often, thus increasing the dissipation contrast; the predicted dissipation pattern and magnitude are in good quantitative agreement with the measurements.

Dissipation signals due to lateral tip oscillations in FM-AFM

“…However, it should be noted, that the frequency ratio is chosen such that a moderate resonance is responsible for the rather high dissipation rate (which means that with a slightly detuned frequency, one would exceed the threshold of 0.01 eV per cycle, but one could also get lower values). It shows two maxima to the left and to the right of one maximum in the topography (comparable to the experimental finding in [ 42 ]). As the lateral force is responsible for the dissipation here, these maxima occur where the partial derivative of the potential energy in lateral direction is highest.…”

A Fourier method for estimating potential energy and lateral forces from frequency-modulation lateral force microscopy data

“…This is true in our setup, where we use a qPlus sensor [18] in the first flexural mode [11]. When lateral forces are detected with the torsional mode of a soft sensor [10,19,20], then the motion of the normal mode must also be taken into account [14]. Even when only the first flexural mode is laterally excited, the typical Δf curve for FM-LFM data along the direction of tip oscillation (required to calculate force and energy) has many more inflection points than typical FM-AFM data, causing it to fall directly into the set of curves for which the force and energy deconvolution by either the Sader-Jarvis method or Matrix method is ill-posed (see figure 1(b) in [9]).…”

Coupled molecular and cantilever dynamics model for frequency-modulated atomic force microscopy

“…However, agreement between theoretical predictions and experimental dissipation rates has remained a challenge [ 4 ] in many cases. The detailed reaction path for a given system can be quite complicated, involving different types of hysteresis [ 5 ] and additional effects such as lateral tip displacements [ 6 – 7 ].…”

“…Molecular dynamics (MD) simulations [ 1 ] with material specific interatomic potentials are computationally less demanding. They can take the finite frequency of the approach and retraction of the tip into account [ 20 – 21 ] and have also been applied to torsional cantilever oscillations, where the tip moves parallel to the sample surface [ 6 ]. In these simulations the tip motion is represented in a parametric way, e.g., by prescribing a sinusoidal trajectory normal or parallel to the surface.…”

“…It is not feasible to include the full extent of an AFM cantilever nor that of a substrate within an atomistic simulation. As in previous studies [ 1 , 6 , 20 – 22 ] the simulation must be restricted to a small volume around the crucial region of interaction between the tip and the substrate. This is sketched in Fig.…”