Stability of immiscible nanocrystalline alloys in compositional and thermal fields

Alloying is often employed to stabilize nanocrystalline materials against microstructural coarsening. The stabilization process results from the combined effects of thermodynamically reducing the curvature-dominated driving force of grain-boundary motion via solute segregation and kinetically pinning these same grain boundaries by solute drag and Zener pinning. The competition between these stabilization mechanisms depends not only on the grain-boundary character but can also be affected by imposed compositional and thermal fields that further promote or inhibit grain growth. In this work, we study the origin of the stability of immiscible nanocrystalline alloys in both homogeneous and heterogeneous compositional and thermal fields by using a multi-phase-field formulation for anisotropic grain growth with grain-boundary character-dependent segregation properties. This generalized formulation allows us to model the distribution of mobilities of segregated grain boundaries and the role of grain-boundary heterogeneity on solute-induced stabilization. As an illustration, we compare our model predictions to experimental results of microstructures in platinum-gold nanocrystalline alloys. Our results reveal that increasing the initial concentration of available solute progressively slows the rate of grain growth via both heterogeneous grain-boundary segregation and Zener pinning, while increasing the temperature generally weakens thermodynamic stabilization effects due to entropic contributions. Finally, we demonstrate as a proof-of-concept that spatially-varying compositional and thermal fields can be used to construct dynamically-stable, graded, nanostructured materials. We discuss the implications of using such concepts as alternatives to conventional plastic deformation methods.