Modulation of contact resonance frequency in friction force microscopy on the atomic scale

摘要

Friction is one of the physical phenomena, which maybe is one of the greatest challenges to theudscientic and industrial communities and has a direct linkage to energy eciency and environmentaludcleanliness of all moving mechanical systems. In everyday life, one rarely thinks about friction orudappreciates its importance, but there is no doubt that it is a major cause of energy loss. Hence,udthe prospect of further understanding and reducing friction in engineering systems has real-life andudeconomic implications for not only preserving our limited energy resources, but also in saving ourudplanet from hazardous emissions for generations to come.udOn the macroscopic scale, the da Vinci-Amonton laws are common knowledge (1. friction isudindependent of the apparent contact area, 2. friction is proportional to the normal load and 3. fric-udtion is independent of velocity). With the invention of the Atomic Force Microscope in 1986, audmodern eld of tribology developed which made it possible to investigate friction on the micro-udscopic scale. Experiments with small contacts have shown that the abovementioned empirical lawsudare not always correct. Reasons may be related to a larger surface-to-volume ratio and the greaterudimportance of adhesion, surface chemistry and surface structure. By these means, a better under-udstanding of the phenomenon of friction is required, to learn how to quantify and eventually how toudcontrol friction.udThe central topic of this thesis concerns friction on the atomic scale. With the Friction ForceudMicroscope, that is operated in ultra high vacuum and at room temperature, the friction of audsingle asperity contact between a sharp probing tip and a udat surface has been investigated. Thisudis in contrast to the friction between two bodies on the macroscopic scale, where the contact isudformed by a multitude of asperities. This single asperity is dragged over the surface by a support.udWhile the support is moving with constant velocity, the tip apex itself typically exhibits a stick-slipudmotion, where the tip periodically sticks in a potential well, until the pulling force is high enoughudto overcome the static force and to induce a slip event, where the tip jumps into an adjacentudpotential well. The stick-slip process has been studied and analysed profoundly by experimentsudand numerical calculations by means of the tip motion on the surface lattice, also with respect of the limit cases of the superlubricity regimes.udThe inuduence of the applied load on the stick-slip motion was experimentally and numericallyudinvestigated and indicates that the friction force is decreasing when reducing the load, until the loadudreaches a critical threshold, below which the system enters the superlubricity regime. Numerical calculations indicate that a reduction in load enlarges the stability regions, where the tip apexudposition is in a potential well, and thus facilitates the tip to follow a trajectory with lower energyudbarriers.udThe eect of mechanical actuation of the cantilever on friction has also been analysed experimen-udtally and numerically. Numerical model calculations have been performed in two dimensions basedudon an integrator solving the Newton equation of motion. For the actuation in normal direction, theudstability regions are shown to periodically expand and contract, and similar to a decreasing loadudallows the tip trajectory to explore regions on the potential energy surface with lower energy barri-uders. Mechanical actuation of the cantilever in normal direction was already shown experimentallyudby others to reduce the friction, an actuation of the torsional vibration mode is now demonstratedudto also reduce the friction force.udThe inuduence of the temperature on the stick-slip motion is investigated numerically by im-udplementing Brownian motion of the tip apex, and indicates that the thermal noise allows the tipudapex to overcome an energy barrier on the potential energy surface slightly earlier compared toudthe case at zero temperature and thus reduces the friction force. An increasing temperature isudshown to decrease friction until a critical temperature is reached, above which the system entersudthe superlubricity regime, similar to the load and actuation dependence of friction.udThe tip trajectory has been analysed in detail by numerical and analytical calculations withudsubject to the scan direction and oset, which allows to describe and quantify the angular de-udpendence of static and kinetic friction for square and hexagonal lattice symmetries. Since the tipudtrajectory is not directly accessible in experiments, a method has been introduced which combinesudthe horizontal and vertical deudections to determine the tip path also in experiments. Hence, severaludaspects of the stick-slip process were analysed thoroughly, which give new insight and an improvedudunderstanding of the friction on the atomic scale.udThe second important topic of the thesis concerns resonance frequencies of a cantilever inudcontact. The contact resonance frequency depends on several parameters such as load, contactudarea, material properties of the tip apex and sample material, and can be measured and tracked in the experiment. The rst mode of the normal and torsional contact resonance frequencies indicateuda maximum when the contact is not stressed in the lateral direction. The contact resonanceudfrequencies are decreasing shortly before a slip event, around which the contact resonances drop toudits initial values, but can not be accurately followed, owing to the nite phase locked loop responseudtime. Thus, the contact resonances may be used as an indicator of a forthcoming slip event.udSuch a behaviour might also be relevant for macro-slip events, such as earthquakes, where early warning systems are still missing. The contact resonance technique also appears to be sensitiveudto atomic defects. Atomic defects are detected for the normal and torsional modes, which are notudclearly detected in the lateral force or in the vertical deudection channels. Additional excitationudof the sliding system at the contact resonance reduces the friction and gives further informationsudabout the mechanical properties of the asperity contact and the sample material. Since the contactudresonance frequency of the normal and torsional mode oscillations are tracked simultaneously toudthe lateral force, a contact resonance map is generated in addition to the friction force map, whichudis presented on the atomic scale for the rst time.udIn summary, several aspects of friction, especially the stick-slip process, and contact dynamics,udincluding the contact resonance frequencies, have been thoroughly investigated on the atomic scale.