Thermodynamic aspects of Cottrell atmospheres

Abstract

Using open system elastic constants, we can convert any of the many existing solved small-strain problems of stress fields of dislocation configurations to what the stresses and solute distribution equilibrium would be in alloys. We confine ourselves to small strain linear isotropic elasticity in which the solute atoms are centres of pure dilation and compute the inhomogeneous compositional distributions that are called Cottrell atmospheres, as well as the energy changes due to the segregation. We correct the misconception in the literature that the solute distribution does not affect the stress field of the dislocation and show that the atmosphere around an edge dislocation acts like an edge dislocation with a Burgers vector of opposite sign.

Keywords:

• dislocations
• elasticity
• grain boundaries
• alloys

Acknowledgement

My year in the Goldsmith Laboratory 1960-1961 was amazingly productive. Many fundamental aspects in this study originated then. I had the opportunity to learn about the Bitter-Crum theorem from Frank Nabarro himself, to solve the elastic problems associated with compositionally inhomogeneous crystals, attend all of Alan Cottrell’s eight lectures comprising his course on dislocation, and learn from his ability to simplify and make difficult concepts useful. Ten years later, the work begun in Cambridge became the amazingly rich thesis of the late Francis Larché.

Alan was a gracious host, but was occupied with the aftermath of two recent fires in the laboratory. Because furnaces had to be shut down every evening, the specimens I had brought to study could not be heat treated. What was a headache for Alan was serendipitous opportunity for me; I turned to theory and a more leisurely scholarly career.