Stability of binary nanocrystalline alloys against grain growth and phase separation

Grain boundary segregation has been established through both simulation and experiments as a successful approach to stabilize nanocrystalline materials against grain growth. However, relatively few alloy systems have been studied in this context; these vary in their efficacy, and in many cases the stabilization effect is compromised by second phase precipitation. Here we address the open-ended design problem of how to select alloy systems that may be stable in a nanocrystalline state. We continue the development of a general “regular nanocrystalline solution” model to identify the conditions under which binary nanocrystalline alloy systems with positive heats of mixing are stable with respect to both grain growth (segregation removes the grain boundary energy penalty) and phase separation (the free energy of the nanocrystalline system is lower than the common tangent defining the bulk miscibility gap). We calculate a “nanostructure stability map” in terms of alloy thermodynamic parameters. Three main regions are delineated in these maps: one where grain boundary segregation does not result in a stabilized nanocrystalline structure, one in which macroscopic phase separation would be preferential (despite the presence of a nanocrystalline state stable against grain growth) and one for which the nanocrystalline state is stable against both grain growth and phase separation. Additional details about the stabilized structures are also presented in the map, which can be regarded as a tool for the design of stable nanocrystalline alloys.