This document discusses nucleation of liquid and freezing in alloys. It explains that nucleation of liquid occurs more easily than nucleation of solid, as the nucleus of liquid has a lower total surface energy than a single solid-liquid interface. During freezing of an alloy, the composition of the solid changes from the initial equilibrium composition to match the overall composition of the liquid, with a spike in the liquid immediately next to the solid interface.

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3. Nucleation of Liquid:
 The solidification of metals occurs by
nucleation & growth. Same is also true for
melting.
 Nucleation of solid phase during freezing is
much more difficult process than formation of
nuclei of liquid phase during melting.
 Metals do not superheat to any appreciable
extent before they are liquefied, whereas some
super cooling occurs almost every time a metal
is frozen.
 In melting most metals do not normally
superheat, although superheating of the order
of 0.1k has been reported for gallium.

4. Cont’d….
 Nucleation in melting occurs on the surfaces of
solids .
 In this case, the nucleus , consisting of a
region of the liquid phase , will be enveloped
by two different surfaces .
 One side is liquid-solid interface and other is
gas-liquid interface.
 The total surface energy of this pair of surfaces
is smaller than that of a single solid-gas
interface .
Γgs > Γsl + Γgl

5. Cont’d….
 The fig(a) represents a liquid nucleus at an
early stage of development & fig(b) of the
same nucleus at slightly later time.
 Spreading of the liquid nucleus along the
surface, in these figures, decreases the
area on gas solid interface .
 As a result, there is a decrease in surface
energy so any rise of temperature above
the equilibrium melting temperature causes
a decrease in volume free energies .

6. Cont’d…..
 It can be seen that both surface and
volume free energies favor melting for even
the slightest amount of super heating.
 There is also another factor, diffusion rate
also increases with rising temperature.
 The rate of a melting reaction should
therefore tend to increase with super
heating.

7. Freezing in Alloys:
 Consider an isomorphous-alloy system with the
phase diagram shown in fig(a). In this system
at temperature T1 , solid of composition (a) is
in equilibrium with liquid of composition (b).
 Let it now be assumed that fig(b) represents a
volume of liquid of composition (b) placed in a
long tabular mold & that heat is only removed
from left end of the mold so that heat flow is
linear & from right to left.
 Under these conditions, freezing will start at
the left end of the liquid and the small volume
element (dx) may be taken to represent the
first solid to form.

8. Cont’d…….
 The freezing of this volume element will take
place at temperature T1 and the composition
of the solid will correspond to point (a) in fig(a)
 If this layer of solid is frozen in a relatively
short period of time with negligible solid-state
diffusion, we can assume that it is formed from
the liquid layer adjacent to the interface and
not from the entire volume of the liquid.
 Since the solid contains a higher ratio of A to B
atoms than does the liquid layer from which it
forms, the latter is depleted in A atoms and
enriched in B atoms.

9. Cont’d…..
 This composition change in the liquid just
ahead of the interface increases as more solid
is formed , but the increase eventually stops
when a steady state condition is attained.
 The change in composition of the liquid next to
the interface is a similar change in the
composition of the solid that can form from
this layer of liquid.
 Thus If the composition of the liquid
correspond to point d in fig (a), than the solid
that freezes must have the composition of
point c.

10. Cont’d….
 The indicated freezing process can only occur if
the temperature at interface is lowered from
T1 to T2.

11.  The concentration of an excess of B atoms in
the liquid adjacent to the interface reaches a
maximum when when the liquid next to the
solid attains the composition of point e.
 At this instant the solid is able to freeze solid of
composition b.when this occur, the steady
state has been attained and the solid, which is
formed from the liquid layer enriched in B atoms is
the same as the liquid drawn into this layer.
 At this time, the temperature at the interface
must be T3.

12. Cont’d….
 Notice that, In both cases, the composition of the
solid rises from its original value a to that of the
original liquid b. At the interface there is also a
sudden rise in composition to the value e as one
passes from solid into liquid.
 Following this sudden rise, the composition in the
liquid decreases exponentially back to the value to
the original liquid, which is b.
 It is important to note that in the above discussion
it is implied that there are no liquid convection
currents. In the presence of such currents it is not
possible to attain as large a concentration of B
atoms in advance of the interface.

13. cont’d….
 There are other factors that may also limit the
magnitude of the composition change in the
liquid at the interface .
 However, for our purposes we can assume that
the distance composition curves shown in fig(c)
are representative of what can actually happen
under similar conditions during the freezing of
an alloy.