Nanotribology: tip–sample wear under adhesive contact
Introduction
Friction and wear between two sliding solids are very common processes in nature, but they are also among the most complex and least understood. Considerable success has been achieved recently in the quantitative measurement of friction forces on the atomic scale and in understanding the underlying macroscopic mechanism in the case of sliding friction without wear. This result has been made possible by considerable improvements in the characterization of interfaces. Moreover, the rapid development of atomic force microscopes (AFMs) and the availability of large computer resources have made possible quantitative predictions for the tribological processes. Successes on both the experimental and theoretical sides have opened up a new research field called nanotribology [1].
From an experimental point of view, the AFM is a rather versatile instrument that can be used to investigate how surface materials are moved or removed on the micro and nano scale; for example, in scratching and wear and nanofabrication/nanomachining. By scanning the sample in two dimensions with the AFM, wear scars are generated on the surface. Primarily, wear depth is a function of normal load. At loads below a critical value, elastic deformations are responsible for low wear. For higher normal loads, wear depth is expected to increase with normal load value. But wear is not only the prerogative of the sample: the tip of the AFM probe also experiences wear. This paper investigates the complex wear process of probe tips by taking into consideration the variation of tip mass as a consequence of adhesive interaction between the tip and sample.
Section snippets
The model
It is well known that, in the non-contact operating mode (NC-AFM), for small oscillations the cantilever can be considered as a damped harmonic oscillator characterised by a spring stiffness k and effective mass m*. The resonance frequency of the system is ν=k/m*. A variation of the effective tip mass leads to a shift in the resonance curve for the cantilever. Unfortunately, the shift in the resonance curve is not only due to variation of the tip mass but also due to external force gradients.
Wear rate
In this section a quantitative evaluation is given of the wear rate of material transfer when a probe tip is in adhesive contact with a sample surface in a mesoscopic approach. In order to have a general framework for the whole process, internal degrees of freedom are not considered. For the sake of simplicity, single components of material transferred are considered to have atomic mass, although in a more realistic approach a cluster of atoms should be considered [6].
As already mentioned,
Numerical results
In our simulation we consider a fixed number of atomic layers, about 200 atoms/layer exposing a [001] face, in which each layer is separated by y0, the vertical distance from the next neighbour. Moreover, σ=1/ny0 is a decay factor for the probability of having a transition to the tip. Assuming the value of 0.2 nm for the layer spacing, it is reasonable to conclude that, for n≈5÷6 layers, the decay factor σ varies between 0.8 and 1 nm−1. This value is in good agreement with the result obtained in
Conclusions
A general approach to the problem of wear in IC-AFM operating mode due to adhesive tip–sample interaction, under the form of the transfer of material from the sample to tip probe, has been developed. The objectives and results of the present paper can be summarized as follows:
- 1.
Irreversible material transfer between a tip probe and a sample in adhesive contact is considered from theoretical and numerical points of view through statistical methods. A double-well potential transition simulates the
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