Thermodynamics of hydrogen in Al-Si alloys
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Thermodynamics of Hydrogen in Al-Si Alloys
[pct H]0 ⫽ [pct H]␣ ␣ ⫹ [pct H] (1 ⫺ ␣)
D.R. POIRIER and P.K. SUNG The solubility of hydrogen in Al-Si alloys can be used to model the formation of porosity in most of the aluminum casting alloys. Anyalebechi[1] summarized the data on the solubility of hydrogen in liquid and solid Al-Si alloys and reduced the data to interaction coefficients that can be used to calculate the effect of silicon on the activity and concentration of hydrogen in the subject alloys. The interaction coefficients for the solid alloys, however, apply to the mixtures of two phases and not to the individual phases (i.e., the aluminum-rich solid solution (␣ ) and the silicon particles (Si)). In order to model solidification behavior, the solubilities of hydrogen in the liquid, ␣, and the eutectic-solid (␣ ⫹ Si) are needed, so an analysis of the solubility data, reviewed by Anyalebechi and originally published by Ichimura and Sasajima,[2] was carried out. The analysis also leads to the equilibrium partition ratio for hydrogen in solidifying hypoeutectic Al-Si alloys. The solubility of hydrogen in solid aluminum is deduced from Figure 9 of Reference 2 as 6672.4 ⫹ 3.8637 T
ln CH ⫽ ⫺
6672.4 ⫺ 5.4605 T
Anyalebechi[1] reviewed many determinations of the solubility of hydrogen in solid aluminum; he recommends ln [pct H] ⫽ ⫺
6830.2 ⫺ 5.1725 T
[3]
Equations [2] and [3] are plotted in Figure 1, where it can be seen that they give similar results. For 300 ⬍ T ⬍ 500 K, the solubility according to Eq. [2] is 3 to 27 pct greater than that according to Eq. [3]. For T ⱖ 600 K, the results with Eq. [2] are slightly less. In the solidification
D.R. POIRIER, Professor, and P.K. SUNG, Assistant Research Professor, are with the Department of Materials Science and Engineering, The University of Arizona, Tucson, AZ 85721. Contact e-mail: [email protected] Manuscript submitted April 2, 2002. 3874—VOLUME 33A, DECEMBER 2002
ln [pct H] ⫽
A ⫹B T
[5]
where A and B are constants. The form of Eq. [5] is reasonable, since the concentration is dilute. In order to account for the hydrogen in the ␣ phase, along the Al-Si solvus, the activity of hydrogen, aH, can be expressed as aH ⫽ fH [pct H]␣
[6]
where fH is the activity coefficient of hydrogen. The activity and activity coefficient depend on the temperature, T, and the concentration of Si along the Al-Si solvus. For dilute solutions of hydrogen in ␣, it is assumed that ln fH ⫽
[2]
[4]
where the subscript 0 represents the alloy as a whole, the subscripts ␣ and  represent the respective phases, and ␣ is the mass fraction of ␣. It is presumed that the solubility of hydrogen in Si follows the relationship as a function of temperature:
[1]
where CH is the concentration of hydrogen in the original units of Reference 2, 3.14 ⫻ 10⫺8 m3 kg⫺1 Pa⫺0,5, and T is in K. For our purposes, it is convenient to write the solubility in weight percent and to define the solubility as the concentration of hydrogen in equilibrium with 1 atm pressure of H2. With the conversion,
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