A simple model for determining alloy composition with large glass forming ability in ternary alloys
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ARK, Graduate Student, Department of Metallurgical Engineering, and D.H. KIM, Associate Professor, Center for Nanocrystalline Materials, Department of Metallurgical Engineering, are with Yonsei University, Seoul 120-749, Korea. W.T. KIM, Associate Professor, is with the Center for Noncrystalline Materials, Department of Physics, Chongju University, Chongju 360-764, Korea. Manuscript submitted January 5, 2000. 200—VOLUME 32A, JANUARY 2001
can select alloy compositions in order to reduce experimental efforts. Egami and Waseda[6] have proposed a criterion for minimum solute content in a binary alloy to form amorphous structure by rapid solidification, which can be written as follows: Cmin B
冟
冟
(vB ⫺ vA) ⫽ Cmin B vA
冟冢 冣 冟 rB rA
3
⫺ 1 ⬇ 0.1
[1]
is the minimum solute content, and vi and ri where Cmin B (i ⫽ A, B) are atomic volume and atomic radius, respectively. The model is based on atomic scale elasticity theory. Above a certain level of effective atomic mismatch, the crystalline solid solution loses its stability and glass can form during rapid solidification. The larger the atomic size difference, the smaller the amount of solute required to form an amorphous structure. The model was applied successfully in many binary alloy systems, but the model can give only minimum solute content for glass formation during rapid solidification. The preceding model was simply extended to the ternary alloy system by adding each solute contribution as follows:[8] Cmin B
冟
冟
冟
冟
(vB ⫺ vA) (vC ⫺ vB) ⫹ Cmin ⬇ 0.1 C vA vA
[2]
This model was used to predict the glass forming range in Co-TM-B systems (TM ⫽ Ti, Zr, Hf, Cr, Mo, W, V, Nb, Ta, and Mn).[7] Also, several glass forming alloys such as Al90FexCe10⫺x and Mg-TM-X satisfied this criterion.[8,9] Again, this model can give information on the compositional range for glass formation during rapid solidification. Considering that dense atomic packing in the liquid may stabilize the liquid phase and that atomic size differences play an important role in increasing the packing density, there may be an optimum ratio between two solute contents if the total solute content is fixed in a ternary alloy. The chemical contribution of solute to stabilizing liquid structure is ignored. Then the effect of atomic size difference can be represented as follows: CB
冟
冟
冟
冟
(vB ⫺ vA) (v ⫺ vB) ⫹ CC C ⫽P vA vA
[3]
where Ci is the concentration of solute i and P is a parameter, representing effective atomic mismatch. As we can see, the parameter P is dependent on both the relative concentration of solute atoms and total solute content. Figure 1 shows variations of ⌬Tx observed in many different Mg-Cu-Y amorphous alloys by Kim et al.[10] The graph shows a maximum ⌬Tx of 60 K in Mg65Cu25Y10. To find the optimum alloy composition, a wide composition range was surveyed. Table I summarizes the alloy compositions ⌬Tx and parameter P calculated by Eq. [3] with atomic sizes of Mg, Cu, and Y.[11] Figure 2 shows the same ⌬Tx data replotted as a function of the parameter P. Each symbol in the fig
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