Grain Boundary Transitions in Binary Alloys

Abstract

A thermodynamic diffuse interface analysis predicts that grain boundary transitions in solute absorption are coupled to localized structural order-disorder transitions. An example calculation of a planar grain boundary using a symmetric binary alloy shows that first-order boundary transitions can be predicted as a function of the crystallographic grain boundary misorientation and empirical gradient coefficients. The predictions are compared to published experimental observations.

Structural short-range forces between solid-melt interfaces

“…Fig. 19 shows the same data on a logarithmic scale, together with the analytical prediction of the slowest decaying quartic interaction term, which stems from the [110] and [101] density waves; here we note that for the prediction of the decay range also the rotation of the interface normal by θ has to be taken into account in expression (25). More explicitly, due to the rotation invariance established by the box operator, for each interface either the reciprocal lattice vectors (related to the lattice orientation) or the interface normal vector have to be rotated according to the grain misorientation.…”

“…On the theoretical side we mention in particular discrete lattice models 17 as well as molecular dynamics (MD) simulations [18][19][20][21][22][23] . Several continuum descriptions have been pushed forward, including those based on phase field models [24][25][26][27] with either an orientational order parameter 24,25 or multiorder parameter models 26,27 ; these order parameters are needed to distinguish between the different grain orientations. More recently, the phase field crystal (PFC) method has been introduced 28,29 , allowing to describe the atomic structure and thus the local lattice orientation via the crystal density field.…”

Phase transitions in stable nanocrystalline alloys

“…[8][9][10][11][12][13] While these models are able to identify systems with potential stability through energetic considerations of grain boundary segregation, the accurate accounting of entropic effects has been limited by assumptions needed to make the analytical models tractable, i.e., dilute limit or regular solution assumptions. A number of analytical [20][21][22][23] and atomistic models 24,25 have been developed for determining the change in free energy associated with grain boundary segregation under a variety of conditions, but typically do not allow the grain size to change during disordering. Thus the process of how a thermodynamically stable nanocrystalline state would disorder remains obscured; since the nanocrystalline state is stabilized by the enthalpic benefits of grain boundary segregation, it should still favor a higher entropy state at elevated temperatures (e.g., a solid solution phase).…”

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

“…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.…”