In the case of Al-Si alloys modified with strontium, at the beginning of nucleation of the eutectic phases, the concen- tration of strontium atoms in the liquid is quite low (about 0.02 wt% in an optimally modified Al-7%Si alloy)14
more-
over, the solubility of strontium in silicon is negligible.5, 6 Therefore the probability that strontium atoms interfere with the stacking of silicon atoms during formation of the nucleus to the extent that it alters the shape of the nucleus is negligi- bly small and, for all practical purposes, the shape of the sili- con nucleus in strontium-modified Al-Si alloys is the same as that in the un-modified alloys.
Once formed, the stability of the solid embryos in the liq- uid alloy depends on surface energy considerations because their formation leads to the creation of an interface between them and the liquid. Creation of this interface causes a posi- tive energy contribution to the total free energy of the sys- tem. For this reason, nucleation of the solid in the liquid re- quires a certain degree of under-cooling in order to provide the additional driving force that is needed to overcome this energy barrier. The preceding analysis is known as the clas- sical theory for homogeneous nucleation7 sented mathematically by Eq. (1)
and may be repre- Equation 1
+ solid), V is the volume and AS solid nucleus, ∆GB
In Eq. (1), ∆GHom
is the total free energy of the system (liquid is the surface area of the
is the free energy of the bulk which is
equal to the difference between the free energy of the solid and the free energy of the liquid, and γ is the solid/liquid interfacial energy. For five conjoined tetrahedrons each of edge length a, Eq. (1) gives
Equation 2
The presence of a catalytic surface in the Al-Si melt, e.g., pre-existing solid particles such as oxide bi-films,8 rous-rich particles,9
phospho- or pre-eutectic iron-rich particles,10, 11
may aid nucleation by providing surfaces on which silicon can easily form. In this way, the positive energy contribution of the surface that is created by the silicon embryo can be reduced. This is known as heterogeneous nucleation 7 may be represented mathematically by Eq. (3)
and Equation 3
In Eq. (3), f(S) is some function of S where S = cos δ and δ is the wetting angle of the liquid alloy on the catalytic particle. For an effective catalytic particle, f(S) is less than 1. Dif- ferentiating Eq. (3) with respect to a, and equating the result to zero allows determination of the critical nucleus size, a*
Equation 4
Substituting the critical nucleus size into Eq. (3) allows de- termination of the energy barrier to heterogeneous nucle-
48 Song et al.12 measured the effect of strontium on the interfacial
energy (γ) between an Al-Si eutectic melt and solid silicon and reported that strontium significantly decreases γ. Simi- larly, Nakae 13
reported that the interfacial energy between the
Al-Si eutectic liquid and solid silicon decreases upon addition of strontium. Therefore, and according to Eq. (5), strontium significantly lowers the energy barrier (∆G*
ation of eutectic silicon particles in hypoeutectic Al-Si alloys. In Eq. (5) ∆G*
energy of liquids, γ, is only a weak function of temperature 15 so when it comes to temperature-dependency, we can write
depends on γ and ∆GB Equation 6 In Eq. (6) GS
ing of the system. Eq. (6) states that the energy barrier for nucleation decreases sharply with increased under-cooling. Table I shows that addition of strontium to an Al-Si hypo- eutectic alloy is accompanied by significant under-cooling which supports the fact that strontium changes the nucle- ation environment of eutectic silicon. Experiments by Bian et al. with high temperature x-rays confirm the presence of Si-Si covalent bonds in liquid Al-Si alloys.16
the liquid, respectively so that (GS and GL
are the free energy of the solid and –GL
) is the under-cool- ) and aids nucle- . However, the interfacial
ation of the eutectic silicon particles, ∆G* Equation 5
More impor-
tantly, Bian et al. show that addition of strontium to these alloys decreases the number of these Si-Si covalent bonds. Since small aggregates of covalently bonded silicon atoms are potential nuclei of silicon (i.e., embryos), it follows that the presence of strontium in liquid Al-Si alloys reduces the number of silicon nuclei in the melt, and hence under- cooling always accompanies solidification of strontium- modified alloys. Similarly, recent synchrotron radiation x- ray micro-diffraction experiments by Shankar et al.17
show
that addition of strontium to hypoeutectic and near-eutectic Al-Si alloys reduces the average coordination number of silicon atoms, increases the average Si-Si inter-atomic distance, and changes the Si-Si-Si bond angle. All these changes in the structure of the liquid Al-Si alloy confirm Bian et al.’s assertion that strontium reduces the number of silicon nuclei during solidification of the eutectic phases in hypoeutectic Al-Si alloys. Further evidence that strontium reduces the number of silicon nuclei during solidification of the eutectic phases comes from McDonald et al. who found that adding strontium to hypoeutectic Al-Si alloys significantly increases the size of the eutectic grains (which suggests that strontium decreases the number of nucleation events of eutectic silicon).18
Hence, the presence of strontium in hypoeutectic Al-Si alloys has two opposing effects: (1) It aids nucleation of eutectic silicon by decreasing the interfacial energy of the liquid alloy; and (2) it hinders nucleation of eutec- tic silicon by decreasing the number of potential silicon
International Journal of Metalcasting/Winter 10
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