The Khachaturyan theory of elastic inclusions: Recollections and results

Abstract

In keeping with the assignment, this paper has two parts. The first is a personal recollection of my interactions with Professor Armen Khachaturyan since he first visited Berkeley in the 1970s. The second part is a review of the Khachaturyan formulation of the theory of elastic inclusions, with emphasis on results found since his classic monograph on the Theory of Structural Transformations in Solids [Wiley, New York, 1983]. The focus here is on the shapes and habits of coherent inclusions. The basic theory is presented, briefly, to exhibit Khachaturyan's results for the strain and energy within a coherent inclusion and show that the elastic energy is minimal for a thin-plate morphology with a definite habit. The preferred habit of the thin-plate inclusion is then discussed and computed for inclusions with dyadic strain (including the dislocation loop) and coherent inclusions with orthorhombic or simpler symmetry. This is followed by a discussion of the evolution of precipitate shape during coarsening, including the theory of the spontaneous splitting of coarsening precipitates and the development of octahedral or tetrahedral shapes.

Keywords:

• elasticity
• inclusions
• phase transformations
• precipitation
• shape evolution

Acknowledgement

This work was supported by the National Science Foundation under Grant DMR 0706554 to the University of California, Berkeley.