Analysis for Free Dendritic Growth Model Applicable to Nondilute Alloys
- PDF / 367,123 Bytes
- 7 Pages / 593.972 x 792 pts Page_size
- 4 Downloads / 200 Views
UCTION
THE free dendritic growth in an undercooled alloy melt as a main subject in the research of solidification theory has fueled increasing attention in past decades.[1–3] In the original free dendritic growth model (LGK model),[4] Lipton et al. assumed local equilibrium condition with no interfacial kinetic effect and adopted a morphological stability criterion along with an equation for the total undercooling to predict the radius of curvature and the velocity at the tip. In order to describe high Pe´clet number conditions, i.e., deviations from the local-equilibrium state, some models[5–8] were proposed later. Among them, the Boettinger–Coriell–Trivedi (BCT) model[7] received wide acceptance due to its relative simplicity as well as the ability to describe rapid solidification by introducing the thermodynamic driving force, the kinetic undercooling, and Aziz’s solute trapping model. Several simplifying assumptions, however, restrict the application of the BCT model. One of them is the assumption of straight solidus and liquidus. It leads to a significant discrepancy in model predictions for alloys with the retrograde-type solidus and curved liquidus. Divenuti and Ando eliminated this limitation and developed a model (DA model)[8] with curved (real) phase SHU LI, Associate Professor, is with the College of Applied Science, Harbin University of Science and Technology, Harbin 150080, Heilongjiang, People’s Republic of China. JIONG ZHANG, formerly Undergraduate Student with the Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Department of Applied Physics, Institute of Advanced Materials Physics, School of Science, Tianjin University, Tianjin 300072, People’s Republic of China, is now Graduate Student with the Department of Physics and Astronomy, University of Missouri-Columbia, Columbia, MO 65201. PING WU, Professor, is with the Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Department of Applied Physics, Institute of Advanced Materials Physics, School of Science, Tianjin University. Contact e-mail: [email protected] Manuscript submitted May 11, 2009. Article published online June 13, 2012 3748—VOLUME 43A, OCTOBER 2012
boundaries, based on the BCT model. Another assumption in the BCT model is the equilibrium solute diffusion in bulk liquid. That is the BCT model does not take into account the relaxation effect of nonequilibrium liquid diffusion, which is supported by experiments[9–11] and theories.[12] Galenko and Danilov (GD model)[13] and Wang et al.[14] incorporated the relaxation effect into the BCT model with and without linear phase boundary assumptions, respectively. These two models have a finite value for the solutal diffusion velocity in bulk liquid in contrast with the previous models, in which the relaxation time is neglected and thus the diffusion velocity is infinite. All of the preceding models are restricted to dilute alloys. Consequently, the range of application is limited. Most importantly, the dilute assumption can bring on remar
Data Loading...
