Simulation Study of Heterogeneous Nucleation at Grain Boundaries During the Austenite-Ferrite Phase Transformation: Comp
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INTRODUCTION
AN understanding of the solid-state transition between the austenite (c) and ferrite (a) phases is of critical importance in the processing and heat treatment of steels. Despite the fact that the c to a transformation has been well studied, the details of the solid-state nucleation event remain unclear. In the 1950s, Clemm and Fisher[1] proposed a geometric model (the spherical cap model) to describe the heterogeneous nucleation process. By assuming all interfacial energies are isotropic, Clemm and Fisher calculated the activation energy of nucleation for different defect sites and showed that the critical work of formation decreases in the order of GB faces, triple lines (edges), and quadruple points (corners).[1] To calculate the activation energy required for nucleation at grain boundaries, it is necessary to know (1) the volume of the nucleus, (2) the surface area of the nucleus, and (3) the matrix grain boundary area which has been replaced by the emerging nucleus. However, the critical nucleation energy predicted by this model is in poor agreement with experimental measurements,[2,3] and later studies[4,5] have
HUAJING SONG, Postdoctoral Researcher, and JEFFREY J. HOYT, Professor (Department Chair), are with the Department of Material Science and Engineering, McMaster University, Hamilton, ON, L9H4L7, Canada. Contact e-mail: [email protected] RONGPEI SHI, Postdoctoral Researcher, and YUNZHI WANG, Professor, are with the Department of Material Science and Engineering, The Ohio State University, Columbus. Contact e-mail: [email protected] Manuscript submitted March 31, 2016. METALLURGICAL AND MATERIALS TRANSACTIONS A
pointed out that both the grain boundary energy and phase boundary energy have strong orientation dependence, i.e., anisotropic. Lee and Aaronson were the first to consider crystallography during the solid-state nucleation process.[4,6,7] The authors developed a faceted-spherical cap geometry to describe the shape of a grain boundary nucleus. The model demonstrated that a low-energy facet in the matrix will minimize the total interfacial free energy subject to the constraint of a constant volume, thereby decreasing the critical energy for the nucleation process. Additional interphase boundary studies supported the faceted-spherical cap geometry by demonstrating that special crystallographic orientation relationships (OR) can create small fully coherent regions at the interphase boundary, which significantly reduces the interfacial energy.[8–10] Although classical nucleation theory (CNT) was proposed more than a century ago,[11] the nucleation rates derived based on the above geometric models usually exhibit a huge discrepancy when compared to measured values.[2,12,13] For example, Lange et al.[2] used both transmission electron microscopy (TEM) and scanning electron microscopy (SEM) to count ferrite diffraction spots arising from nucleation on austenite grain boundaries in high-purity Fe-C alloys. The authors detected a very high ferrite nucleation rate, around 102-105 nuclei per cm2 of
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