Diffuse interface model for structural transitions of grain boundaries

Abstract

The conditions for structural transitions at the core of a grain boundary separating two crystals was investigated with a diffuse interface model that incorporates disorder and crystal orientation ͓Kobayashi et al., Physica D 140, 141 ͑2000͔͒. The model predicts that limited structural disorder near the grain boundary core can be favorable below the melting point. This disordered material is a precursor to a liquid phase and therefore the model represents grain boundary premelting. This model is shown to be isomorphic to Cahn's critical point wetting theory ͓J.W. Cahn, J. Chem. Phys. 66, 3667 ͑1977͔͒ and predicts first-and higher-order structural grain boundary transitions. A graphical construction predicts the equilibrium grain boundary core disorder, the grain boundary energy density, and the relative stability of multiple grain boundary "complexions." The graphical construction permits qualitative inference of the effect of model properties, such as empirical homogeneous free energy density and assumed gradient energy coefficients, on properties. A quantitative criterion is derived which determines whether a first-order grain boundary transition will occur. In those systems where first-order transition does occur, they are limited to intermediate grain-boundary misorientations and to a limited range of temperatures below the melting point. Larger misorientations lead to continuously increasing disorder up to the melting point at which the disorder matches a liquid state. Smaller misorientation continuously disorder but are not completely disordered at the melting point. Characteristic grain boundary widths and energies are calculated as is the width's divergence behavior at the melting point. Grain boundary phase diagrams are produced. The relations between the model's predictions and atomistic simulations and with experimental observations are examined.

Calculation and validation of a grain boundary complexion diagram for Bi-doped Ni

“…Grain boundaries (GBs) can undergo phase-like transformations, for example, premelting [1] or adsorption [2] transitions, which can influence a broad range of materials properties [3][4][5]. Thus, GBs can be treated as "interfacial phases" that are thermodynamically two-dimensional (2-D) despite that they have thermodynamically-determined interfacial widths as well as through-thickness compositional and structural gradients.…”

“…Thus, GBs can be treated as "interfacial phases" that are thermodynamically two-dimensional (2-D) despite that they have thermodynamically-determined interfacial widths as well as through-thickness compositional and structural gradients. A new term "complexion" was introduced to differentiate such 2-D interfacial phases from the conventional bulk phases defined by Gibbs [1,3,4,6,7].Phase diagrams are one of the most useful tools for materials engineering. Materials scientists have long recognized that phase-like behaviors at GBs can often control the fabrication processing, microstructural evolution, and materials properties [3,[6][7][8][9][10][11][12].…”

“…An early report in 1999 [21] also constructed a GB complexion diagram for Cu-Bi via a rather simple model that considered GBs as "quasi-liquid layers" to explain the GB segregation behaviors measured by Auger electron spectroscopy (AES), but more recent aberration-corrected scanning transmission electron microscopy (AC STEM) observed an ordered bilayer complexion in Cu-Bi instead [22]. GB complexion diagrams with first-order transition lines and critical points have been constructed using diffuse-interface (phase-field) [1,23,24] and latticetype [16,[25][26][27][28] models, which have not yet been validated with experiments systematically, particularly by direct HRTEM or STEM characterization.In this study, we computed a GB complexion diagram for average general GBs in Bi-doped Ni, for which a recent experimental study found ubiquitous formation of a bilayer complexion at virtually all general GBs at 700°C and 1100°C [29]. Furthermore, we calculated the GB transition lines for two special GBs based on the 0 K density functional theory (DFT) calculations reported in two prior studies [30,31] for Scripta Materialia 130 (2017) [165][166][167][168][169] …”

“…An early report in 1999 [21] also constructed a GB complexion diagram for Cu-Bi via a rather simple model that considered GBs as "quasi-liquid layers" to explain the GB segregation behaviors measured by Auger electron spectroscopy (AES), but more recent aberration-corrected scanning transmission electron microscopy (AC STEM) observed an ordered bilayer complexion in Cu-Bi instead [22]. GB complexion diagrams with first-order transition lines and critical points have been constructed using diffuse-interface (phase-field) [1,23,24] and latticetype [16,[25][26][27][28] models, which have not yet been validated with experiments systematically, particularly by direct HRTEM or STEM characterization.…”

“…Thus, GBs can be treated as "interfacial phases" that are thermodynamically two-dimensional (2-D) despite that they have thermodynamically-determined interfacial widths as well as through-thickness compositional and structural gradients. A new term "complexion" was introduced to differentiate such 2-D interfacial phases from the conventional bulk phases defined by Gibbs [1,3,4,6,7].…”