First-Order Interfacial Transformations with a Critical Point: Breaking the Symmetry at a Symmetric Tilt Grain Boundary

First-order interfacial phaselike transformations that break the mirror symmetry of the symmetric $\sum 5(210)$ tilt grain boundary (GB) are discovered by combining a modified genetic algorithm with hybrid Monte Carlo and molecular dynamics simulations. Density functional theory calculations confirm this prediction. This first-order coupled structural and adsorption transformation, which produces two variants of asymmetric bilayers, vanishes at an interfacial critical point. A GB complexion (phase) diagram is constructed via semigrand canonical ensemble atomistic simulations for the first time.

Figure 1

Simulation of a GB phaselike transformation with increasing $\mathrm{\Delta }{\mu }_{\mathrm{Ni}}(\equiv {\mu }_{\mathrm{Ni}}-{\mu }_{\mathrm{Ni}}^{(\text{pure})})$ at a fixed temperature of $T=0.373$ $T_m$, showing (a) a nominally clean GB at a low $\mathrm{\Delta }{\mu }_{\mathrm{Ni}}$ of $-0.56\mathrm{eV}/\mathrm{atom}$, (b) coexistence of two complexions at the transformation threshold $\mathrm{\Delta }{\mu }_{\mathrm{Ni}}$ of $-0.435\mathrm{eV}/\mathrm{atom}$, and (c) a bilayer complexion (with disorder) at a high $\mathrm{\Delta }{\mu }_{\mathrm{Ni}}$ of $-0.385\mathrm{eV}/\mathrm{atom}$. The corresponding GB structures at $T=0\mathrm{K}$ without thermal noises (obtained by the modified GA) are shown in Supplemental Fig. S6 [35].

Figure 2

Simulated GB complexion (phase) diagrams. (a) The computed map of GB adsorption from hybrid $\mathrm{MC}/\mathrm{MD}$ simulations. (b) The computed map of GB excess disorder. The solid purple line represents first-order phaselike transformations and ends at a GB critical point.

Figure 3

The first-order phaselike transformations predicted from atomistic simulations. (a) GB excess in Ni (in number of equivalent (210) atomic layers) vs the chemical potential difference ($\mathrm{\Delta }{\mu }_{\mathrm{Ni}}\equiv {\mu }_{\mathrm{Ni}}-{\mu }_{\mathrm{Ni}}^{(\text{pure})}$) computed by both the hybrid $\mathrm{MC}/\mathrm{MD}$ simulation at $T=0.4T_m$ and the modified GA at $T=0\mathrm{K}$. (b) The simulated GB atomic configurations (both top and side views) that correspond to the four points labeled in panel (a). (c) The variation of GB excess in Ni with the normalized bulk composition at four different temperatures computed from hybrid $\mathrm{MC}/\mathrm{MD}$ simulations. The abrupt adsorption transition (from “${\mathrm{\Gamma }}_{\mathrm{Ni}}=0$” to “${\mathrm{\Gamma }}_{\mathrm{Ni}}=2$ monolayers” at 0 K) shown in panel (a) occurs concurrently with a structural transition that breaks the mirror symmetry of the symmetric tilt GB, with a relative translation of the two abutting grains by a distance of $0.3a_{\text{bcc}}$ along the vertical direction in panel (b) and asymmetric adsorption of the second Ni layer on (only) one abutting grain. In addition, the two abutting grains are closer (by $\sim 0.21a_{\text{bcc}}$) after the structural transformation but there is no relative translation perpendicular to the projection plane. See Supplemental Fig. S6 for the detail of this structural transformation at $T=0\mathrm{K}$ obtained by the GA. Similar transformations occur at finite temperatures with increasing effects of interfacial disordering and the transformation becomes continuous at high temperatures.

Figure 4

DFT verification of the first-order transformation from the clean GB to the asymmetric bilayer complexion in Ni-doped Mo $\sum 5(210)/[001]$ symmetric tilt GB. (a) GB energy computed by DFT vs the chemical potential difference ($\mathrm{\Delta }{\mu }_{\mathrm{Ni}}\equiv {\mu }_{\mathrm{Ni}}-{\mu }_{\mathrm{Ni}}^{(\text{pure})}$). Illustrations of (b) the bilayer GB structure produced by the modified GA and [(c),(d),(e)] several other possible GB structures (named as $M1$, $M2$, and $M3$, respectively). DFT calculations demonstrated that the asymmetric bilayer is the most stable adsorption structure among these four possible configurations.