Determination of Solid Fraction from Cooling Curve
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TRODUCTION
UPON rapid solidification of undercooled melts, such as by melt fluxing or electromagnetic levitation,[1] the transformed fraction can be directly measured using differential thermal analysis, differential scanning calorimetry, synchrotron diffraction, or dilatometry experiments.[2] For solidification with negligible undercooling, all the preceding techniques can be used, whereas, for rapid solidification, delicately and repeatedly treating the sample is essential for achieving a high undercooling; in this case, most of the above techniques are limited due to the expensive facilities and the high sensitivity for measuring heat release. As an inexpensive approach, the cooling curve method provides consistent results to reflect the solidification process.[3–9] In the early 1980s, Levi and Mehrabian studied the cooling curves and the heat flow during rapid solidification of undercooled metal droplets, and interpreted the relationship among the solid fraction, the enthalpy heat, the specific heat, and the temperature history in detail.[3,4] Barth et al. used the cooling curves of nickel and iron melts to predict the enthalpy and the specific heat of undercooled melt.[5] Using the Newtonian cooling principle, C¸etin and Kalkanli presented a procedure for evaluating the latent heat of primary and eutectic solidification of gray cast iron.[6] For solidification of undercooled droplets in gas atomization, Vedovato et al. developed a model describing the cooling behavior.[7] For spherical undercooled liquid metallic samples, Saleh and Clemente proposed a model for analyzing the cooling curve.[8] Using an equiaxed solidification model, Gandin et al. predicted the cooling curve for solidification of Al-Cu alloys.[9]
Computer-aided–cooling curve thermal analysis (CA-CCA) is another important method to evaluate the solidification from thermal history.[10–13] Stefanescu et al. used the CA-CCA method by coupling the macroscopic heat transfer and microscopic kinetics to calculate the solid fraction during solidification.[10] Emadi et al. analyzed the cooling curve of Al-Si alloy using the CA-CCA method.[13] Recently, applying firstprinciples analysis of thermodynamics and heat flow, Gibbs et al. developed a method to study the cooling curves of Al-Si and Al-Ag alloys.[2,14] Yang et al. presented a numerical model to describe the cooling process of bulk-undercooled Cu-Ni melts.[15,16] In this study, we will introduce a new method to predict the transformed fraction directly from the cooling curves in term of baselines.* This method *The cooling curves without any transformation or latent heat release.
avoids explicit determination of thermal-physical parameters such as the heat transfer coefficient and the specific heat, as well as complicated calculations. To test this method, the experimental results from Ni-3.3 wt pct B and Fe-4.56 wt pct Ni alloy (by the present authors) and Al-7 wt pct Si alloy and Al-14 wt pct Cu alloy from Emadi et al.[13] and Gandin et al.[9] are used; the cooling curves are analyzed by the current method.
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THEORE
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