Application of classical nucleation theory to phase selection and composition of nucleated nanocrystals during crystallization of Co-rich (Co,Fe)-based amorphous precursors
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, . and the steady-state nucleation rate, Iβ, are expressed for a spherical precipitate as [26]: 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 > 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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