Grain boundary order-disorder transitions

The conditions for grain boundary (GB) structural transitions are determined from a diffuse interface model that incorporates structural disorder and crystallographic orientation. A graphical construction and numerical calculations illustrate the existence of a first-order GB order–disorder transition below the bulk melting point. When thermodynamic conditions permit their existence, disordered GB structures tend to be stable at higher temperatures and are perfectly wet by liquid at the melting point, while ordered grain boundaries are meta-stable against preferential melting. We calculate GB phase diagrams which are analogous to those for liquid–vapor phase transitions. The possibility that a grain boundary (GB) may start to melt below the bulk melting point has long been speculated. The existence of its free surface counterpart, surface melting, has been confirmed by experiments [1–3]. Indirect evidence of GB premelting has been accumulated over decades from observations of abrupt changes in macroscopic properties such as GB diffusivities, dihedral angles, sliding and migration rates [4–8]. However, only limited direct evidence of GB premelting has been published. Hsieh and Baluffi imaged boundaries in pure aluminum by TEM [9]. They concluded that GB preferential melting does not occur below 0.999Tm. Recent direct observations confirm GB premelting in colloidal crystals [10] and in multi-component metallic systems [11]. Numerous atomistic calculations and simulations have been performed to study GB premelting, including lattice-gas models [12, 13], molecular dynamics (MD) [14–21], and Monte Carlo (MC) simulations [22, 23]. Although atomistic methods provide direct and often accurate calculations of GB structures and energies, such calculations are not feasible to predict GB behavior over a range of temperature, stress, chemical potentials, misorientations, and inclinations. Using a diffuse interface model developed by Kobayashi, Warren and Carter (KWC) [24, 25], we present an analysis of GB structures in the framework of classical interfacial thermodynamics. The analysis produces predictions of stability of different GB structures from general characteristics of thermodynamic data. For material systems with fixed stoichiometry, the KWC model uses two coarse-grained field variables to describe a two-dimensional polycrystalline structure: a local crystallographic orientation field, hð~xÞ, and a local crystallinity field, gð~xÞ, which characterizes structure disorder. Readers are referred to the appendix in Ref. [26] for discussion on coarse-graining schemes to calculate g and h. For a GB plane in which both fields are uniform, g and h reduce to functions of a single spatial variable x. Although the GB is diffuse in this model, its position can be identifies as a narrow region where g is significantly less than 1; h changes abruptly at the minimum of g(x) as illustrated in Fig. 1. M. Tang (&) Æ W. C. Carter Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA e-mail: [email protected] R. M. Cannon Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA J Mater Sci (2006) 41:7691–7695 DOI 10.1007/s10853-006-0608-4 123 Grain boundary order-disorder transitions Ming Tang Æ W. Craig Carter Æ Rowland M. Cannon Received: 29 April 2006 / Accepted: 20 June 2006 / Published online: 31 October 2006 Springer Science+Business Media, LLC 2006