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

Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49  |  Page 50  |  Page 51  |  Page 52  |  Page 53  |  Page 54  |  Page 55  |  Page 56  |  Page 57  |  Page 58  |  Page 59  |  Page 60  |  Page 61  |  Page 62  |  Page 63  |  Page 64  |  Page 65  |  Page 66  |  Page 67  |  Page 68  |  Page 69  |  Page 70  |  Page 71  |  Page 72  |  Page 73  |  Page 74  |  Page 75  |  Page 76  |  Page 77  |  Page 78  |  Page 79  |  Page 80  |  Page 81