Elsevier

Acta Materialia

Volume 58, Issue 14, August 2010, Pages 4804-4813
Acta Materialia

Application of classical nucleation theory to phase selection and composition of nucleated nanocrystals during crystallization of Co-rich (Co,Fe)-based amorphous precursors

https://doi.org/10.1016/j.actamat.2010.05.015Get rights and content

Abstract

Classical steady-state nucleation theory is applied to Co-rich Fe,Co-based alloys to provide a rationale for experimental observations during the nanocrystallization of Co-rich (Co,Fe)89Zr7B4 and (Co,Fe)88Zr7B4Cu1 amorphous precursors. The amorphous precursor free energy is estimated using density functional theory. This simple theory suggests: (i) strain or interface energy effects could explain a tendency for a body-centered cubic (bcc) phase to form during crystallization. Dissolved glass formers (Zr,B) in crystalline phases may also contribute; (ii) similar face-centered cubic (fcc) and hexagonal close-packed (hcp) free energies could explain the presence of some hcp phase after crystallization even though fcc is stable at the crystallization temperature; (iii) nanocrystal compositions vary monotonically with the Co:Fe ratio of the amorphous precursor even when multiple phases are nucleating because nucleation is not dictated by the common tangency condition governing bulk phase equilibria; and (iv) Fe-enrichment of the bcc phase can be attributed to a relatively small free energy difference between the amorphous and bcc phases for high Co-containing alloys.

Section snippets

Motivation and relevant experimental background

Fe- and Co-based soft magnetic nanocomposites are obtained by partial (primary) crystallization of an initially amorphous precursor to form a composite microstructure of Fe,Co-based nanocrystals embedded in a glass former enriched amorphous matrix [1], [2], [3], [4]. The small grain size of the nanocomposite microstructure is critical for obtaining desirable soft magnetic properties [5]. Recent investigations of primary crystallization in high Co-containing (Co,Fe)89Zr7B4 and (Co,Fe)88Zr7B4Cu1

Binary model

Classical nucleation theory states that the nucleus of a product phase, β, formed through thermal fluctuations must be larger than a critical size to spontaneously grow. Formation of a critical nucleus involves overcoming the activation barrier for nucleation, ΔGβ. ΔGβ and the steady-state nucleation rate, Iβ, are expressed for a spherical precipitate as [26]:ΔGβ=16πσδ,β33(ΔGβ+Wδ,β)2,Iβ=Kβe-ΔGβkTσδ,β is the interfacial free energy between the parent phase, δ, and the product phase, β. ΔGβ

Model results

The free energies of the liquid phase and the disordered bcc, fcc and hcp phases of the binary FeCo system [39], [40] were taken from the BINARY SGTE Alloy Database using Thermocalc™. In Fig. 2, the free energy curves are presented as a function of composition for T = 1400 °C and T = 450 °C, along with the most recent binary phase diagrams [41]. The former temperature is reasonable for solidification of a highly undercooled liquid, while the latter roughly corresponds to a temperature at which

Conclusions

Steady-state classical nucleation theory has been applied to Co-rich Fe,Co-based alloys under a number of simplifying assumptions. This simple theory offers some explanations for experimental observations noted in the introduction for crystallization of (Fe,Co)89Zr7B4 and (Fe,Co)89Zr7B4Cu1 amorphous precursors.

Observation 1

The strain and/or interface energy effects could be significant enough to account for the preferential nucleation of the bcc phase with Co:(Fe + Co) ratios >XT0 of the binary bcc and fcc

Acknowledgements

D.C. Berry and B. Wang are acknowledged for performing the differential scanning calorimetry presented in this work. The authors also gratefully acknowledge M.A. Willard of the Naval Research Laboratories for helpful discussions relevant to the work described here. P.R.O. acknowledges support from a National Defense Science and Engineering Graduate Research Fellowship throughout the preparation of this manuscript. Funding from the National Science Foundation is also acknowledged (NSF Grant #

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