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Research over the years has shown that the formation of the Fe$_3$Si phase inFINEMET (Fe-Si-Nb-B-Cu) alloys leads to superior soft magnetic properties. Inthis work, we use a CALPHAD approach to derive Fe-Si phase diagrams to identifythe composition-temperature domain where the Fe$_3$Si phase can be stabilized.Thereafter, we have developed a precipitation model capable of simulating thenucleation and growth of Fe$_3$Si nanocrystals via Langer-Schwartz theory. Foroptimum magnetic properties, prior work suggests that it is desirable toprecipitate Fe$_3$Si nanocrystals with 10-15 nm diameter and with thecrystalline volume fraction of about 70 \%. Based on our parameterized model,we simulated the nucleation and growth of Fe$_3$Si nanocrystals by isothermalannealing of Fe$_{72.89}$Si$_{16.21}$B$_{6.90}$Nb$_{3}$Cu$_{1}$ (composition inatomic \%). In numerical experiments, the alloys were annealed at a series oftemperatures from 490 to 550 \degree C for two hours to study the effect ofholding time on mean radius, volume fraction, size distribution, nucleationrate, number density, and driving force for the growth of Fe$_3$Sinanocrystals. With increasing annealing temperature, the mean radius ofFe$_3$Si nanocrystals increases, while the volume fraction decreases. We havealso studied the effect of composition variations on the nucleation and growthof Fe$_3$Si nanocrystals. As Fe content decreases, it is possible to achievethe desired mean radius and volume fraction within one hour holding time. TheCALPHAD approach presented here can provide efficient exploration of thenanocrystalline morphology for most FINEMET systems, for cases in which theoptimization of one or more material properties or process variables aredesired.

Metastable Phase Diagram and Precipitation Kinetics of Magnetic Nanocrystals in FINEMET Alloys