Effects of Alloying on Nanoscale Grain Growth in Substitutional Binary Alloy System: Thermodynamics and Kinetics
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NANOCRYSTALLINE materials exhibit many unique properties which are normally superior to their coarse-grained counterparts, and therefore have great potentials in a variety of applications.[1–5] However, due to a high volume fraction of grain boundaries (GBs), the driving force for grain coarsening of the nanocrystalline materials is rather high, and the thermal stability of this kind of materials is poor. Many pure nanocrystalline metals, e.g., Sn, Pb, Al, Mg, Cu, and Pd, etc.,[6–9] are subjected to apparent grain coarsening even at room temperature. This strongly hinders the applications of these materials. Therefore, enhancing thermal stability of nanocrystalline materials is a fundamentally important issue regarding the applications of nanocrystalline materials.
According to the classical grain growth theory,[10,11] the velocity of grain growth (dD/dt) is expressed by the product of driving force (P = c/D) and GB mobility (MGB), dD c ¼ MGB P ¼ MGB dt D
½1
Accordingly, the enhanced thermal stability of nanocrystalline materials can be achieved by either reducing the driving force or reducing the GB mobility. It has been demonstrated widely that both of the above two strategies can be achieved by alloying foreign elements.[11–13] Therefore, understanding the alloying effects on grain growth of nanocrystalline materials will be essentially important for enhancing their thermal stability. So far, plenty of efforts and progresses[12–26] have been reported in evaluating the alloying effects both thermodynamically and kinetically. However, several issues are still required to be clarified, which are summarized briefly below. A. Thermodynamic Description for Grain Growth of Nanocrystalline Alloy System
HAORAN PENG, Ph.D. Candidate, YUZENG CHEN, and FENG LIU, Professors, are with the State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an, Shaanxi, P.R. China. Contact e-mail: [email protected] Manuscript submitted November 28, 2014. Article published online September 8, 2015 METALLURGICAL AND MATERIALS TRANSACTIONS A
Thermodynamic descriptions of a nanocrystalline alloy system have been carried out by Weissmu¨ller,[12,27] and other authors,[13–19,28–33] yielding a conclusion that the minimum of Gibbs energy of a system corresponds to a zero GB energy caused by solute segregation. VOLUME 46A, NOVEMBER 2015—5431
Basically, the reported models assume an equilibrium solute distribution* in the bulk and GB phases, and thus *The equilibrium solute distribution referred in the context is not equivalent to the equilibrium state of the system but only means the solute distribution in bulk and GB follows the equilibrium GB segregation equation.
follow the equilibrium GB segregation equation, e.g., Mclean’s model.[34] This means, at a given state, namely, a given D, the solute molar fractions in the bulk (Xb) and GBs (XGB) are determined by the equilibrium GB segregation equation. However, for an actual grain growth process, the nonequilibrium system prevails, and in turn, t
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