Minimizing segregation during the controlled directional solidification of dendritic alloys
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Liquidus
Solidus
[pct H]␣ k⫽ [pct H]L
850* 866 882 898 914 930 933**
19.90 24.80 30.85 38.61 47.77 59.66 62.23
0.8281 0.8039 0.9178 1.222 1.880 3.323 3.752
0.0416 0.0324 0.0297 0.0318 0.0394 0.0557 0.0603
*Eutectic temperature. **Melting point of aluminum
phase) and  (the silicon particles). Hydrogen is partitioned between the eutectic phases according to [pct H]E ⫽ [pct H]␣ ␣ ⫹ [pct H] (1 ⫺ ␣)
[14]
where ␣ is the mass fraction of ␣ in the eutectic-solid, based on the Al-Si phase diagram (␣ ⫽ 0.889), [pct H]E is the solubility of hydrogen in the eutectic mixture, and the symbols of the remaining solubilities are the same as before. From Table I, [pct H]␣ ⫽ 8.281 ⫻ 10⫺7 pct. Equation [5] is used to calculate the solubility of hydrogen in the eutectic; it is [pct H] ⫽ 4.446 ⫻ 10⫺5 pct. Hence, the solubility of hydrogen in the eutectic solid is 0.5671 ⫻ 10⫺5 pct. Thus, when the eutectic solidifies, the equilibrium partition ratio for hydrogen is 0.2849.
The authors acknowledge support provided by a subagreement between the University of Texas at El Paso and The University of Arizona, which allowed us to participate in the Materials Corridor Council Strategic Plan, United States Department of Energy Cooperative Agreement No. DEFC04-01AL67097. The authors also thank Professor P.N. Anyalebechi, Grand Valley State University, for sharing his publications on the solubility of hydrogen in aluminum alloys. REFERENCES
Fig. 3—Partition ratio of hydrogen during the solidification of Al-7 pct Si alloy, according to the assumptions of Scheil-type and equilibrium solidification.
temperature, and 933 K, the melting point of aluminum. Using the known Al-Si phase diagram[3] for the concentration of Si, the corresponding solubilities of hydrogen along the hypoeutectic liquidus and solidus of the Al-Si system and the equilibrium partition ratios of hydrogen were calculated. The results are summarized in Table I. The results of Table I assume that the concentration of Si in ␣ is its equilibrium concentration. In cast alloys, however, the average concentration of Si in ␣ is less than its equilibrium concentration because of dendritic microsegregation during solidification. Hence, the partition ratio is not uniquely given by temperature, as could be construed by Table I. Assuming no diffusion of Si in ␣ during solidification, the partitioning of hydrogen between the liquid and the solid was calculated to yield its partition ratio for an alloy of A1-7 pct Si. The results are shown in Figure 3, along with the case of equilibrium solidification. Silicon increases the activity coefficient of hydrogen in ␣; hence, both the solubility of hydrogen in ␣ and the partition ratio of hydrogen with lesser silicon (i.e., the Scheil case) are greater than the solubility and partition ratio for the equilibrium case. The solidified eutectic comprises ␣ (the aluminum-rich 3876—VOLUME 33A, DECEMBER 2002
1. P.N. Anyalebechi: in Light Metals 1998, B. Welch, ed., TMS, Warrendale, PA, 1998, pp. 827-42. 2. M. Ichimura and Y. Sasajima: J. Jpn.
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