a b s t r a c t a r t i c l e i n f oA grain boundary (GB) "phase" (complexion) diagram is computed via a lattice type statistical thermodynamic model for the average general GBs in Bi-doped Ni. The predictions are calibrated with previously-reported density functional theory calculations and further validated by experiments, including both new and old aberrationcorrected scanning transmission electron microscopy characterization results as well as prior Auger electron spectroscopy measurements. This work supports a major scientific goal of developing GB complexion diagrams as an extension to bulk phase diagrams and a useful materials science tool.© 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. 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. 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]. Thus, a potentially-transformative research is represented by the development of GB "phase" (a.k.a. complexion) diagrams as an extension to bulk phase diagrams and a generally-useful materials science tool. To support this goal, recent studies [9,10,13-16] have extended bulk CALPHAD (CALculation of PHAse Diagrams) methods to model coupled GB premelting and prewetting (a.k.a. the formation of nanoscale, impurity-based, quasi-liquid complexions) and subsequently constructed a class of "GB λ diagrams" to represent the thermodynamic tendency for general GBs to disorder at high temperatures. Although the predicted trends have been validated with direct high-resolution transmission electron microscopy (HRTEM) [9,[14][15][16][17][18][19] and proven useful for forecasting sintering behaviors [9,10,[13][14][15]20], these GB λ diagrams are not yet rigorous GB complexion diagrams with well-defined transition lines. 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]...