A relaxation method for the energy and morphology of grain boundaries and interfaces

Citations of this article
Mendeley users who have this article in their library.


The energy density of crystal interfaces exhibits a characteristic "cusp" structure that renders it non-convex. Furthermore, crystal interfaces are often observed to be faceted, i.e., to be composed of flat facets in alternating directions. In this work, we forge a connection between these two observations by positing that the faceted morphology of crystal interfaces results from energy minimization. Specifically, we posit that the lack of convexity of the interfacial energy density drives the development of finely faceted microstructures and accounts for their geometry and morphology. We formulate the problem as a generalized minimal surface problem couched in a geometric measure-theoretical framework. We then show that the effective, or relaxed, interfacial energy density, with all possible interfacial morphologies accounted for, corresponds to the convexification of the bare or unrelaxed interfacial energy density, and that the requisite convexification can be attained by means of a faceting construction. We validate the approach by means of comparisons with experiment and atomistic simulations including symmetric and asymmetric tilt boundaries in face-centered cubic (FCC) and body-centered cubic (BCC) crystals. By comparison with simulated and experimental data, we show that this simple model of interfacial energy combined with a general microstructure construction based on convexification is able to replicate complex interfacial morphologies, including thermally induced morphological transitions.




Runnels, B., Beyerlein, I. J., Conti, S., & Ortiz, M. (2016). A relaxation method for the energy and morphology of grain boundaries and interfaces. Journal of the Mechanics and Physics of Solids, 94, 388–408. https://doi.org/10.1016/j.jmps.2015.11.007

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free