“…Several of these alloy systems have shown considerable nanometer-scale grain size stability in experiments, including Ni-P, Ni-W, Fe-Zr, and W-Ti. [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.…”