Materials for engineering, 3rd Edition - (Malestrom)

Structure of engineering materials 9
and substituting equation [1.3] gives:
r c = (2γ SL T m /L)(1/∆T) [1.6]
indicating that r c decreases with increasing undercooling.
For small degrees of undercooling, therefore, r c is large and there is only
a low probability that a large embryo will be formed in the liquid in a given
time by random thermal motion of the atoms. There is thus likely to be only
a low number of successful nuclei per unit volume of liquid. For high degrees
of undercooling, r c is small and the probability of forming such a nucleus is
now very high, so that a high number of successful nuclei per unit volume of
liquid will be observed. The implication of these effects upon the resultant
microstructure will be considered next.
Growth of nuclei. Once stable nuclei are formed in the liquid, they grow
at the expense of the surrounding liquid until the whole volume is solid.
Most crystal nuclei are observed to grow more rapidly along certain
crystallographic directions, causing spike-shaped crystals to develop. Further
arms may branch out sideways from the primary spikes, resulting in crystals
with a three-dimensional array of branches known as dendrites, as shown in
Fig. 1.5(a).
Dendrites grow outwards from each crystal nucleus until they meet other
dendrites from nearby nuclei. Growth then halts and the remaining liquid
freezes in the gaps between the dendrite arms, as shown in Fig. 1.5(b). Each
original nucleus thus produces a grain of its own, separated from the
neighbouring grains by a grain boundary, which is a narrow transition region
in which the atoms adjust themselves from the arrangement within one grain
to that in the other orientation.
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1.5 (a) Drawing of a dendrite and (b) schematic view of the freezing
of a liquid by nucleation and growth of dendrites.