Energy Dissipation in Atomic Force Microscopy and Atomic Loss Processes

Abstract

Atomic scale dissipation is of great interest in nanomechanics and atomic manipulation. We present dissipation measurements with a linearized, ultra-small amplitude atomic force microscope which is capable of measuring dissipation at chosen, fixed separations. We show that the dynamic dissipation in the noncontact regime is of the order of a few 10-100 meV per cycle. This dissipation is likely due to the motion of a bistable atomic defect in the tip-surface region. In the contact regime we observe dc hysteresis associated with nanoscale plasticity. We find the hysteretic energy loss to be 1 order of magnitude higher for a silicon surface than for copper.

Measurement of energy dissipation between tungsten tip and Si(1 0 0)-(2×1) using sub-Ångström oscillation amplitude non-contact atomic force microscope

“…In case of small amplitude, far below the first resonance frequency, the measured interaction stiffness (negative of the force gradient between tip and sample), k int , is given by [12] …”

“…In the real experimental setup, however, there is a phase difference, but this is corrected by nulling the lock-in phase, prior to the measurement. The relation of the change in the phase and energy dissipation per cycle as the sample approaches to the tip can be given by [12] …”

“…Measurement of tip-sample forces and dissipation of energy as a function of separation [5][6][7] is also possible and will probably shed light into a number of interesting problems like atomic manipulation, atomic scale friction, etc. We have recently built a highly sensitive nc-AFM using small oscillation amplitudes (0.25 Å ) [8] for imaging [9][10][11] and force/dissipation-distance spectroscopy [12]. Employment of sub-Å ngström oscillation amplitudes has a number of advantages over large oscillation amplitudes used by most of other groups and simplifies the analysis considerably.…”

Controlled ionic condensation at the surface of a native extremophilemembrane

“…S1 in supplemtary data). When A is sufficiently small, the surface interaction potential probed by 70 the AFM tip can be approximated as locally parabolic 43 , and tip-sample force F ts becomes: F ts ≈ F ts0 -k ts z, where z is the tip-sample distance and k ts is the local tip-sample force gradient called "tip-sample interaction stiffness". The cantilever-tip system is then described by the harmonic 75 oscillator model with a linear damping factor that accounts for the viscoelasticity of the medium.…”

“…Near resonance and at small amplitudes, k ts can be expressed as a function of the free oscillation amplitude A 0 , the phase shift relative to the driving signal φ, and A, namely: k ts =k A 0 cosφ /A, where k is the 80 cantilever stiffness. 43 It should be noted that due to the low quality factor of the cantilver oscillation in liquid (typically 2-5), the use of the harmonic oscillator model becomes contentious when the tip oscillates very close to the smaple (<1 nm). Practically, direct tip-sample coupling leads to the 85 loss of a well defined resonance (over-damping) and unambiguous interpretation of the data becomes difficult.…”