The enumeration and transformation of dislocation dipoles II. The transformation of interstitial dipoles into vacancy dipoles in an open dislocation array

Abstract

If the presence of crystal surfaces permits some of the dipole content of a dislocation array to leave the crystal to form intrusions or extrusions on the surface, then the dipole strength of the array, as defined in part I, can change by glide processes. It is confirmed that the energy difference between vacancy and interstitial dipoles of equal height due to nonlinear elasticity is a possible cause of the conversion of interstitial dipoles to vacancy dipoles by slip, with the consequent production of extrusions at the crystal surface. The energy difference increases with decreasing dipole height and may account for the observed preponderance of small vacancy dipoles. However, the gain in energy resulting from the conversion of interstitial dipoles to vacancy dipoles is offset by long-range elastic energy stored in the field of the ‘fibre stress’—the average tensile stress in the band resulting from the bias. This leads to an equilibrium bias in dipole population and causes the fibre stress to increase as cyclic straining reduces the height of the dipoles.

Acknowledgements

Thanks are due to Dr Vlad Stolojan for carrying out the Monte Carlo integration. The authors are grateful to Robinson College, Cambridge, for support.

Notes

‡ We do not consider processes that can convert a dipole into an array of loops. The role of such processes is not currently well understood, although Kratochvil and Sedlácek (2003) have recently discussed dislocation pattern formation in terms of loops. However, Antonopoulos et al. (1976) and Tippelt et al. (1997) observed extensive dipolar arrays (arrays of loops at least ten times as long as they are wide) in persistent slip bands, to which this paper should apply.

† Note a typographical error in the original paper; the integrand in equation (A 4) of the paper by Brown (1977) should be raised to the third power. The sign is also corrected here.

† Experiment shows that the dipoles are spaced apart about ten times their height. Using equations (2) and (3), one finds an effective stress of about one tenth of the saturation stress itself acting on a screw dislocation linking neighbouring dipoles of average height but of opposite sign.