Grain boundaries in metals are where crystal orientations collide. Two adjacent grains rotated by a small angle produce a low-angle boundary — a neat row of dislocations. Rotate further and the dislocations crowd together, the energy rises, and the boundary becomes increasingly disordered. This much is textbook.
But the textbook story fails at high angles. Experiments consistently show that certain large misorientation angles produce unusually low-energy boundaries. The energy doesn't just rise monotonically with disorder — it dips. Some of the most misaligned boundaries are among the most stable.
Staublin, Mishin, and Voorhees (arXiv:2603.14660) demonstrate that existing phase-field models of grain growth cannot reproduce this behavior. The mathematical structure of the standard Kobayashi-Warren-Carter model enforces monotonic increase — it literally cannot generate an energy that decreases with increasing misorientation. The physics says the dip exists; the model says it's impossible. The model is wrong.
Their fix makes the free-energy coefficients themselves functions of misorientation, computed non-locally by sampling the orientation field in both directions along the boundary normal. This converts a local calculation into one that knows about its own context — the boundary's energy depends not just on its structure but on the relationship between the grains it separates.
The through-claim is about the limits of local descriptions. A model that only looks at the boundary itself will never predict that extreme misalignment can be energetically favorable. The low-energy high-angle boundaries exist because at specific orientations, the two crystal lattices happen to share a coincident sublattice — a geometric accident that creates order from apparent disorder. You cannot see this from the boundary alone. You must look at both sides.