# Calculation of tribological effects of modern materials on the atomic level

Simulations techniques offer the possibility of several and even unusual material combinations on different length scales to calculate and take prognoses about their friction properties. This white paper we will discuss the possibilities of the atomic description of tribological effects.

# Introduction

The focus of engineering on the issues of energy- and cost-efficiency through the control of friction and wear in equipment and components requires an always better understanding of the underlying mechanisms. Tribological effects take place at the surfaces and interfaces, respectively. We distinguish between different mechanisms of friction, namely adhesion, microploughing and hysteresis. The results of the abrasion mechanism: adhesive failure, abrasive failure and fatigue (see fig. 1). These effects are observed in the tribology on different length scales (see fig. 2)

# Tribological effects are classified on the length scale levels

- of unitribology (~1m). At this magnitude the efficiency (degree of efficiency) of an everyday machines is described. The tribological properties are determined by the respective interaction of the individual parts...
- on the decitribology scale (~1dm). At this magnitude the tribology of the components of a machine is described that are in (frictional and wear) contact with each other. These effects are determined by the interaction...
- on the macrotribology scale (~1mm). Here the interactions between the surfaces are described with the materials still treated as continua (homogeneous, not as single atoms) and the interactions will be approximated by characteristic material parameters, as their elasticty- and shear modulus. In turn, the parameters are determined by the features of the components...
- on the microtribology scale (~1 µm). On this length scale effects are in focus, where the interactions of individual granular fragments of the components ( texture, roughness) is already dealt with. The precise description of the interaction within and between the fragments is finally achieved by the description of the interaction...
- on the nanotribology scale (~1nm). Here the atomic composition of the materials is finally important. The stoichiometry, the chemical composition of the components and consequential the following molecular interactions determine the parameters, as they mostly empirically enter into the larger length scales. On the nanotribology scale, the macroscopic properties like hardness and elastic moduli are now calculated, based on atomic interactions. Likewise, the interactions at the surfaces of friction pairs are calculated on the atomic level.

The constantly improving possibilities of surface treatment allow to tailor the material combinations. However, the selection of optimal combinations of friction pairs is costly because of the variety of available materials. For optimal use of the technical options it is necessary to confine all the possible combinations on basis of theoretical forecasts. The current simulation techniques offer the possibility of treating several (even ununsual) combinations on different length scales on the computer. Depending on the length scale, the available methods for the simulations range from electronic structure calculation on the nanometer scale over quantum and classical molecular dynamics up to monte- carlo and finite elements methods for macrotribology issues.

# An example: run-in procdure of different material combinations

In these simulations run-in procdure of two friction pairs are examined. The simulations are performed by atomic scale modelling. The influence of the chemical bonds between the atoms and the concrete surface structure on the friction behavior is visualized.

## Details of the simulations

The modelling of the atoms was made by Lennard-Jones potentials which are characterized by different adhesion parameters and atomic masses. The temperature during the simulation was 25 °C.

The calculations were performed using the MD package lammps on single Opteron processors with ~ 2.0GHz with a computing time of about 2 minutes, at a simulation time of 300fs (120000 steps with 0.0025fs). For simplicity, the configurations are two-dimensional. For three-dimensional calculations, the computing time increases approximately linearly with system size.

## Results friction pair soft / hard

In the following illustrations, a carrier substrate (in red) is partially coated with relatively soft and atomically lighter material (blue) is rubbed with an opposite material that is signifitantly harder (even red). An example of the underlying situation would be a cobalt coating on a germanium substrate. The upper left image represents the initial situation. Subsequently, the two surfaces are rubbed against each others. The various images show snapshots of the process. The rubbing procdure is repeated several times, as in a bearing. It is seen that in the course of the simulation, the blue substance is smeared out on the carrier and after a few cycles, no more significantly altered. Similarly, the pollution of the grinding surface is visible (blue atoms settle on the lower surface). In the beginning, this process may be characterised as abrasive wear, followed by a combination of adhesive wear and adhesive friction.

### Time steps of the run-in procdure

The individual images show the calculated run-in procdure of the friction pair of soft vs. hard materials in chronological order from top left to bottom right.

## Results friction pair hard vs. hard

As a second example, a friction pair of two similarly hard materials has been investigated. In the following figures the results of this study are shown. This situation corresponds to,e.g., the friction of silicon on copper. During this simulation, although, the light gray coating as well as the carrier substrate surface ground a little and both areas are mutually contaminated, but the major effect is the displacement of the light gray hemisphere in friction direction. For better visibility of this behavior in both panels markers are set at the original locations (in white). This process is nearly pure micro ploughing.

### Time steps of the run-in procedure

The individual images show the calculated run-in procdure of the friction pair of hard vs. hard material in chronological order from top left to bottom right.

# Interest / Questions ...

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# Further reading ...

on the tribological basics you can read further:

G. Mennig, M. Lake: Verschleißminimierung in der Kunststoffverarbeitung - Phänomene und Schutzmaßnahmen, Kapitel II

Hanser Fachbuch, 2007

on the topic of atomic scale simulationen of friction you my have a look at:

A. Koike, M. Yoneya: Molecular dynamics simulation of sliding friction of Langmuir- Blodgett monolayers

Journal of Chemical Physics 105(14), pp 6060-6067 (1996)

I. Stankovic, S. Hess, M. Kröger: Microscopic structure, dynmaics, and wear at metal-metal interfaces in sliding contact

Physical Review E 70, pp. 066139 (2004)

further calculations for example:

C.D.Lorenz, E.B. Webb III, M.J. Stevens, M. Chandros, G.S. Grest: Frictional dynamics of perflourinated self-assembled monolayers an amorphous SiO_{2} Tribology Letters, 19 (2), 93ff (2005)

on finite-element-methods:

K. Holmberg, H. Ronkainen, A. Laukkanen, K. Wallin: Friction and wear of coated surfaces - scales, modelling and simulation of tribomechanisms, Surf. Coat. Tech. 202, 1034ff (2007)