Overview: The spectral model of grain boundary segregation

Grain boundaries are comprised of a wide variety of different atomic sites, and each of those sites has its own local environment, energetics, and tendency to attract or repel the solute elements dissolved in an alloy. The chemical segregation of solutes to grain boundaries is a classical and pervasive problem in materials science, but treatment of the full spectrum of grain boundary sites in a generalized polycrystalline ensemble has not been rigorously possible until recently. This overview article holistically summarizes the recent rapid developments in such spectral modeling, and foreshadows those coming in the future. Beginning from self-consistent definitions of the thermodynamic site properties (enthalpy and excess entropy of segregation), considering the solute interactions at non-dilute concentrations, and treating the statistical mechanics of configurational entropy, we elaborate the use of a full, multi-variate segregation isotherm that can be applied to any binary alloy system. We review the existing computational methods of determining those spectra, and survey spectral databases developed for thousands of alloys at various levels of accuracy. Preferred sets of spectral parameters are provided for appropriately simplified versions of the segregation isotherm, to facilitate wide usage of the model. We proceed to highlight the key successes of the spectral model, including its validation against full atomistic Monte Carlo simulations and a variety of experiments. Alloy design efforts that use spectral data to target interesting segregation behaviors are illustrated, including extensions to complex cases like ternary alloys with solutes that collaborate to fill grain boundary sites, and nanocrystalline alloys with stable grain boundaries. The state of the spectral model is sufficiently robust that significant physical problems with historical, non-spectral models are now coming more clearly to light; the time is right for broader replacement of historical models with spectral ones.