Theoretical Aspects of Spinodal Decomposition in Fe-C
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I.
INTRODUCTION
THERE is vast experimental evidence that shows carbon redistribution during the room-temperature aging of Fe-C martensite, giving rise to fine modulations in carbon content across martensite. Two main processes have been proposed in the literature to account for this observation: (i) carbon segregation into the vicinity of defects,[1] and (ii) spinodal decomposition.[2] Both processes lead to a reduction in the free energy of the supersaturated solid solution in ferrite. However, a clear distinction must be made between the two. As discussed in previous studies by the current authors,[3,4] both defect segregation and spinodal decomposition are strongly related to the thermodynamic description of the ferrite phase. Carbon segregation to defects is a well-understood phenomenon, and has been extensively modeled, particularly in the context of strain aging.[5,6] On the other hand, spinodal decomposition in Fe-C systems still remains unclear. With the advances in experimental techniques, the topic has recently drawn significant interest from the scientific community.[7–9] Most of the spinodal decomposition literature has been focused on
B. KIM is with the Department of Engineering, Lancaster University, Lancaster LA1 4YW, UK and also with the Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands. Contact e-mail: [email protected] J. SIETSMA and M. J. SANTOFIMIA are with the Department of Materials Science and Engineering, Delft University of Technology Manuscript submitted July 20, 2017. Article published online January 3, 2019 METALLURGICAL AND MATERIALS TRANSACTIONS A
the experimental work on Fe-Ni-C systems, as exemplified by References 2, 4, 7 and 8 However, evidence for spinodal decomposition occurring in the iron-carbon binary system is scarce. Ren and Wang[10] presented a theoretical analysis of the spinodal decomposition in Fe-C systems, and experimentally showed the occurrence of spinodal decomposition in a Fe-1.83wt. pct C system[11] by means of electron microscopy. More recently, Naraghi et al.[12] aimed to incorporate the carbon-ordering processes occurring during martensite aging in the Fe-C system into ThermoCalc. In agreement with the earlier postulation by Taylor et al.,[2] Naraghi et al.[12] showed that for Fe-C, the overall system’s free energy was the highest for disordered dissolution of carbon in BCC. The energy was then shown to decrease successively by Zener-ordering and spinodal decomposition. It is emphasized that spinodal decomposition explicitly requires the presence of a miscibility gap caused by the characteristic double-minima Gibbs free energy curve (discussed in Section II). Within the spinodal, a system is regarded as being thermodynamically unstable with respect to compositional fluctuations. Therefore, in order to lower the system’s free energy, the system decomposes into a mixture of two stable compositions on either side of the miscibility gap.[13] In the case of Fe-C, spinodal decomposition w
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