Elastically mediated interactions between grain boundaries and precipitates in two-phase coherent solids

Ye-Chuan Xu, Pierre-Antoine Geslin, and Alain Karma
Phys. Rev. B 94, 144106 – Published 24 October 2016
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Abstract

We investigate analytically and numerically the interaction between grain boundaries and second phase precipitates in two-phase coherent solids in the presence of misfit strain. Our numerical study uses amplitude equations that describe the interaction of composition and stress [R. Spatschek and A. Karma, Phys. Rev. B 81, 214201 (2010)] and free-energies corresponding to two-dimensional hexagonal and three-dimensional BCC crystal structures that exhibit isotropic and anisotropic elastic properties, respectively. We consider two experimentally motivated geometries where (i) a lamellar precipitate nucleates along a planar grain boundary that is centered inside the precipitate, and (ii) a circular precipitate nucleates inside a grain at a finite distance to an initially planar grain boundary. For the first geometry, we find that the grain boundary becomes morphologically unstable due to the combination of long-range elastic interaction between the grain boundary and compositional domain boundaries, and shear-coupled grain boundary motion. We characterize this instability analytically by extending the linear stability analysis carried out recently [P.-A. Geslin, Y.-C. Xu, and A. Karma, Phys. Rev. Lett. 114, 105501 (2015)] to the more general case of elastic anisotropy. The analysis predicts that elastic anisotropy hinders but does not suppress the instability. Simulations also reveal that, in a well-developed nonlinear regime, this instability can lead to the break-up of low-angle grain boundaries when the misfit strain exceeds a threshold that depends on the grain boundary misorientation. For the second geometry, simulations show that the elastic interaction between an initially planar grain boundary and an adjacent circular precipitate causes the precipitate to migrate to and anchor at the grain boundary.

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  • Received 28 July 2016

DOI:https://doi.org/10.1103/PhysRevB.94.144106

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ye-Chuan Xu1,2, Pierre-Antoine Geslin1,3, and Alain Karma1,*

  • 1Physics Department and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA
  • 2Department of Materials Physics, School of Physics and Optoelectronic Engineering, Nanjing University of Information Science & Technology, Nanjing, China
  • 3Univ Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622, Lyon, France

  • *a.karma@neu.edu

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Issue

Vol. 94, Iss. 14 — 1 October 2016

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