(1997)3946 3.3.Ox (a nism of oxidation into alumina preforms would corre- spond to the mcchanism of oxidation of the basc Al-Mg alloy. According to Venugopalan et al. [15, the nto free space is controlled by oxygen transport through the near-sur face alloy layer. This is consistent with a situation where the weight gain rate decreases with time and is Oxygen atmosphere independent of oxygen pressure. When the transport of oxygen controls the rate, the weight gain rate per unit Location of area ()(oxidation rate) is given by the following Metal expression [15] W16D(x-X1) where W is the weight gain rate, A is the cross sectional area, Do is the diffusion coefficient of oxygen in molten aluminum, X. is the mole fraction of dissolved oxygen Oxygen atmosphere in the alloy film at the mgo/alloy film interface, XI is Alumina L。 cation of the mole fraction of dissolved oxygen in the alloy film Metal alumina front at the Al2O3 alloy film interface, L is the thickness of channel he alloy film, and Vm is the molar volume of the alloy For the directed oxidation of Al-Mg alloys without a preform, the cross-sectional area of the melt, A, is equal to 154 mm. When oxidation occurs into an Al2O, preform, A represents the cross sectional area of Fig. 6. Schematic diagram showing the movement of the oxidation the void space between the alumina particles(Avoid) and front from(a)to(c), as directed oxidation of Al-Mg alloy proceeds is estimated to be 69.3 mm2(in the absence of wetting hrough an Al, O, preform Wetting between the Al-melt and the Al,O, particles would increase the cross-sectional area from Avoid to each curve in Fig. 4 in the growth stage and are given Aw. As a first approximation, it is assumed that the Table 2. values for increase in cross-sectional area is proportional to the n Table 3. USing these values in Eq (6), Aw and k can surface area per unit volume of the particle(3/R for be estimated for various particle sizes as shown in spherical particles). Aw would then be given by Table 4. In the initial period of the grow expression. ncreases with decreasing particle size as can be ob- served from Table 4. This would indicate that wetting A,=kx (4) of the AlO; particles by the Al melt(or secondary nucleation of Al2O3 on the existing AlO, particles here k is a measure of the volume associated with the occurs in the initial period of the growth stage. How- oxidation interface and R denotes the Al)O, particle ever, wetting alone cannot extend the oxidation front radius. The rate of oxygen transport across the alloy unless Mgo is present at the melt surface over the layer can then be estimated from underlying Al2O3 product. It is also seen froIn Table 4 Wnre 16D(YI-XI that k decreases with decreasing particle size. This implies that the volume associated with the extended where Jpre denotes the weight gain rate per unit area for infiltration into an AlO, preform and Wpre denotes the W gain rate as a function of Al,O, particle size, at 30000 s, fo corresponding wcight gain rate. Eq. (5)can be re-writ- n of Al-Mg alloy into A2O, preforms at 1450 K Average particle size of R2(um) 2 Weight gain rate 16D( -Xi alumina, R(um) (gm-2s-) The maximum values of Wpre/Avoid can be deter 0.019 mined for each particle size from the initial slope of44 H. Vemgopalan, T. DebRoy ; Materials Science and Engineering AU.2 (1997) 39-46 3.3. Oxygen trimspout In the initial period of the growth stage, the mecha￾nism of oxidation into alumina preforms would corre￾spond to the mechanism of oxidation of the base Al-Mg alloy. According to Venugopalan et al. [15], the growth kinetics of Al-Mg alloys into free space is controlled by oxygen transport through the near-sur￾face alloy layer. This is consistent with a situation where the weight gain rate decreases with time and is independent of oxygen pressure. When the transport of oxygen controls the rate, the weight gain rate per unit area (J) (oxidation rate) is given by the following expression [ 151: where Wis the weight gain rate, A is the cross sectional area, D, is the diffusion coefficient of oxygen in molten aluminum, XT, is the mole fraction of dissolved oxygen in the alloy film at the MgO/alloy film interface, XL’ is the mole fraction of dissolved oxygen in the alloy film at the Al,O,/alloy film interface, L is the thickness of the alloy film, and Y, is the molar volume of the alloy. For the directed oxidation of Al-Mg alloys without a preform, the cross-sectional area of the melt, A, is equal to 154 mm’. When oxidation occurs into an Al,O, preform, A represents the cross sectional area of the void space between the alumina particles (Avoid) and is estimated to be 69.3 mm2 (in the absence of wetting). Wetting between the Al-melt and the Al,O, particles would increase the cross-sectional area from Avoid to A,. As a first approximation, it is assumed that the increase in cross-sectional area is proportional to the surface area per unit volume of the particle (3/R for spherical particles). -4, would then be given by the expression: where k is a measure of the volume associated with the oxidation interface and R denotes the A&O, particle radius. The rate of oxygen transport across the alloy layer can then be estimated from Eq. (3) as: (5) where JPre denotes the weight gain rate per unit area for infiltration into an Al,O, preform and W,,, denotes the corresponding weight gain rate. Eq. (5) can be re-writ￾ten as: W A prc _ w x 1~QPt, - x3 Avoid Avoid LVm (6) The maximum values of Wpre/Avoid can be deter￾mined for each particle size from the initial slope of Oxygen aimosphorc 0 on0 --t-Alumina particle Oxygen atmosphere / Location of alumina front Oxygen atmosphere Location of alumina front Fig. 6. Schematic diagram showing the movement of the oxidation front from (a) to Cc), as directed oxidation of Al-Mg alloy proceeds through an A&O, preform. each curve in Fig. 4 in the growth stage and are given in Table 2. Values for D,, XL, Xk’, L, and I/, are given in Table 3. Using these values in Eq. (6), A, and k can be estimated for various particle sizes as shown in Table 4. In the initial period of the growth stage, A, increases with decreasing particle size as can be ob￾served from Table 4. This would indicate that wetting of the AlzO, particles by the Al melt (or secondary nucleation of Al,O, on the existing A&O, particles) occurs in the initial period of the growth stage. How￾ever, wetting alone cannot extend the oxidation front unless MgO is present at the melt surface over the underlying AlzO, product. It is also seen from Table 4 that k decreases with decreasing particle size. This implies that the volume associated with the extended Table 5 Weight gain rate as a function of Al,O, particle size, at 30000 s, for infiltration of Al-Mg alloy into AllO, preforms at 1450 K Average particle size of alumina, R (pm) Weight gain rate (gm-“s-l) 8 2.83 0.015 16 4 0.018 110 10.5 0.019