Terms Of Friction Force Research Articles

Amplitude-dependent internal friction in dilute copper—aluminium alloys with three kinds of peaks

Amplitude-dependent internal friction is measured on 99.999% Cu and dilute Cu—Al alloys, annealed and lightly prestrained. The measurements are made with an inverted torsion pendulum, at temperatures between 300 K and 90 K, and at about 1.6 Hz. Three kinds of peaks are observed: (1) the peak in the amplitude dependence, which is shifted to higher amplitude, and the peak height increases, either with increasing concentration or with decreasing temperature; (2) the peak in the concentration dependence, which exhibits the ‘peaking effect’; the peak is shifted to higher concentration, and the peak height increases, as the amplitude increases; (3) the peak in the temperature dependence, which is shifted to lower temperature, and the peak height increases as the amplitude increases. These results are interpreted in terms of frictional forces and the associated relaxation of dislocations oscillating in random solid solution.

Atomic-scale wear properties of muscovite mica evaluated by scanning probe microscopy

Atomic-scale wear properties of muscovite mica were evaluated in terms of friction force and surface topographic changes using a scanning probe microscope. Friction from a load of 100–300 nN generated a 1-nm-deep wear groove which corresponded to the depth from the surface of one cleavage plane to the surface of the next periodic cleavage plane. The atomic image of the bottom surface of the wear groove corresponds to the basal plane of mica.

Numerical integration of the Langevin equation: Monte Carlo simulation

Monte Carlo simulation techniques are derived for solving the ordinary Langevin equation of motion for a Brownian particle in the presence of an external force. These methods allow considerable freedom in selecting the size of the time step, which is restricted only by the rate of change in the external force. This approach is extended to the generalized Langevin equation which uses a memory function in the friction force term. General simulation techniques are derived which are independent of the form of the memory function. A special method requiring less storage space is presented for the case of the exponential memory function.

Muon capture in atoms, crystals and molecules

The slowing down and capture of negative muons in solids is discussed on the basis of classical equations of motion where the energy dissipation is described in terms of frictional forces. Transport equations determining the energy distribution of the muons in the target are formulated and solved for various models. Using a statistical model of the atom it is shown that the muons are captured typically at energies of a few tens of electron volts, that the angular momentum distribution of the muons at capture is almost statistical, and that this distribution is not expected to be qualitatively changed by the subsequent cascade to the tightly bound orbits. In mixtures of atoms with atomic numbers Z 1 and Z 2 the capture ratio is to a good approximation proportional to the atomic concentration and, in the statistical model, proportional to ( Z 1 Z 2 ) 7 6 . Calculations are also performed with more accurate atomic models, and it is shown that capture ratios as well as angular momentum distributions are influenced by the ionicity of the atomic bonds and the atomic shell structure. No systematic study of these effects has been made but the few results obtained seem to be in reasonable agreement with experiments.