Equation 6


and σ is the nucleus-melt interfacial energy, ∆H is the latent heat of solidification, ∆T is the degree of undercooling and Ts


is defined in Table 1.


Taking into account Eqns. (5) and (6), the graphite substrate site size at a given undercooling, ∆Τ can be calculated from:


Equation 7


All of the particles larger than, l become active nuclei as soon as the temperature falls24


fication temperature, Ts.


and at the end of graphite eutectic solidification respectively. Notice that within the tb


and to ,te tive for nucleation purposes. At the time tm ∆Tm undercooling, all sites with lm to tm


From Equation (7) it is found that as undercooling, ∆T in- creases, the nucleation size, l decreases. Figure 2b shows a cooling curve, T(t) where the arrow indicates the maximum undercooling, ∆Tm


defines the time at the onset time interval or ∆T = 0 to ∆T =


≤ l ≤ ∞ sizes become ac- , the degree of un-


dercooling drops enabling graphite particles and substrates below the equilibrium solidi- fication (Fig.2b), Tm Equation 10 Ns


(the number of all of the graphite nucleation sites in the melt) and b (a function of mainly the nucleus-melt interfa- cial energy and of the wetting angle) are known as the nucle- ation coefficients.


is the minimal temperature at the onset of eutectic solidi- Where; Equation 9


time interval no active sites are present in the set of graphite undissolved particles and substrates. As a result any nucleation events are stopped at tm of active sites for nucleation, Nnuc the n(l) curve in the lm


with l ≥ lm the tm


to te . Thus, the number, can be described by:23 ≤ l ≤ ∞ (0 ≤ ∆T≤ ∆Tm


is given by the area below ) range and it


Equation 8


sizes to be active. In turn, this indicates that within


Figure 3. Schematic representation of a heterogeneous nucleus on a substrate.


Figure 2. (a) Size distribution for graphite nucleation sites and (b) cooling curves T(l) and Ti


inoculated iron melts. 38


(l) for base and


Figure 4. A graphic representation of the ProductLog[x] function for x ≥ 0.


International Journal of Metalcasting/Summer 10


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