The Bordoni relaxation revisited

Abstract

It is generally agreed that the Bordoni relaxation in fcc metals is caused by kink-pair formation in dislocations along close-packed lattice directions. None of the existing theoretical treatments using the line tension approach is however able to give an adequate description of this process. The bow-out of a segment must be described by a kink-chain, and its configuration is essentially controlled by the interaction energy of the kinks. This coordinate-space is multi-dimensional depending on the number n of the kink-pairs, their positions and their widths. When the kinks have high mobility (as expected in fcc metals) and assume equilibrium positions with respect to stress, the dimensions of the coordinate-space are reduced to two. The system in mechanical equilibrium can then be described by its enthalpy H ¯ ( σ , n ) , which generally can only be obtained by numerical methods. For each stress σ a number of mechanically stable configurations with different number n of kink-pairs exist. Thermodynamic equilibrium is the reached in the ground state, i.e. the state with lowest enthalpy H ¯ with an equilibrium number n ¯ ( σ ) of kink-pairs. The energy dissipation is caused by a phase-lag between σ( t) and n( t) in the neighbourhood of n ¯ . The generalized Paré condition does not apply for multiple kink-pairs and for an oscillating stress, even small, there are practically always a number of states accessible with different number of kink-pairs. For shallow bow-outs analytical solutions for H ¯ ( σ , n ) exist. It is then possible to derive the magnitude of the energy dissipation by numerically integrating the differential equation for the dislocation velocity. An essential role plays the asymmetry in the dislocation movement: The forward movement must always take place by thermally activated kink-pair nucleation, whereas the backward movement against a still positive stress will occur by kink-pair collapse, for which the energy barriers can be smaller. Due to the dissociation of dislocations in fcc lattices into two partials, a distribution of activation energies is expected.