The influence of elastic strain energy on the formation of coherent hexagonal phases

W. E. Mayo, T. Tsakalakos

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24 Scopus citations


The elastic strain energy function, Y (n), of coherent hexagonal phases has been derived for arbitrary directions, n, in a parent phase with arbitrary crystal structure. These calculations indicate that in all cases Y (n) exhibits transverse isotropy about the c axis. As a result, Y (n) has a pronounced effect on the morphology of the precipitating structures. In the case of hexagonal inclusions, three possible optimum shapes in reciprocal space are identified: 1) a rod parallel to the c axis, 2) a plate perpendicular to the c axis, and 3) a hollow conical shape with the axis of revolution parallel to c. The precise precipitate shape can be predicted by identifying the direction n o which minimizes the strain energy function, Y (n). Evaluation of Y (n) for η and ή MgZn2 precipitates in the ternary Al-Mg-Zn system correctly predicts the orientation and morphology of the particles. This method has also been extended to explore the morphology of the microstructure of hexagonal spinodal alloys. It is shown that the gradient energy term is generally anisotropic, and that together with the strain energy function, Y(n), has a strong influence on composition fluctuations. It is predicted that a one-dimensional periodic compositional variation along the [001] direction should be observed when Y [001] is a global minimum. In all other cases, the microstructure is complex and lacks periodicity.

Original languageEnglish (US)
Pages (from-to)1637-1644
Number of pages8
JournalMetallurgical Transactions A
Issue number10
StatePublished - Oct 1980

ASJC Scopus subject areas

  • Engineering(all)


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