Nucleation and Growth

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Nucleation and Growth

• What is it and how does it relate to phase
  equilibria.

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What exactly is Nucleation and Growth?
Nucleation is a process by which random
interaction of molecules of a certain composition
come together to form the initial regular
structural pattern in the crystalline solid. The
nuclei starts as just a few molecules connected.
Once a nuclei has formed there is a tendency for
them to be reabsorbed because these newly formed
nuclei are very small and have a large surface
area with respect to volume. This means that a
large percentage of the atoms in the nuclei are
on the surface with unsatisfied chemical bonds.
In order for a nuclei to survive and not be
reabsorbed, it must undergo rapid growth beyond
its critical size. Creating the surface area of
the nucleus requires energy and this is why
nucleation is not a spontaneous occurrence, but
is actually endothermic. The critical size is
the point when the nuclei will no longer
spontaneously be reabsorbed into the solution.
Nuclei can commonly grow to in excess of ten
microns in diameter. Growth is a process by
which existing nuclei of material grow into
larger particles. Growth can occur at artificial
nucleation sites, which may be added purposely or
be introduced do to contaminants in the melt or
solution. Growth of nuclei is spontaneous due to
the fact that the atoms become more ordered and
therefore their entropy is decreased.
So what does this have to do with phase diagrams?
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The answer is more than you would think.
The graph at the left illustrates one possible
path of a solution. Concentration of the solute
in question above Cs will result in the growth
of existing nuclei and above Css nucleation will
occur.
This shows us that the concentration of the
solute in question determines whether or not
nucleation or growth occurs and the concentration
of the precipitate changes when nucleation starts
to occur.
The concentration is raised through the middle of
II by the addition of the component in question.
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So nucleation and growth controls the
crystallization paths and more importantly the
liquid composition.
By performing a isoplethal analysis or by
examining a crystallization path on a ternary
phase diagrams with knowledge of nucleation and
growth, not only can the solid composition be
determined, but some insight can be given into
particle size and size distribution.
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How can this be applied to phase diagram analysis.
The point X is in the primary crystallization
field of B. This means initially particles of B
nucleate and grow followed by precipitation.
Once enough B is precipitated out of the liquid,
there is then a sufficient concentration of BC in
the liquid phase for nucleation of BC to occur,
so for a time both B and BC are precipitating
out. Then at point P, the final liquid
composition, A, B, and BC are all in sufficient
concentration for nucleation and growth. When
taking a close look at the concentration of each
component over time, a feel for the particle size
and size distribution can be attained. The
distribution of particle sizes of B should be
spread out over a wide range of sizes due to the
fact that nucleation and growth was occurring
throughout the entire duration of the cooling
process, which means some nuclei had much longer
periods of growth then others. BC size
distribution would tend to be more compact then
B, but there should still be a range of particle
sizes. The distribution of particle sizes of A
would be very small or nonexistent due to the
fact that the nucleation of particles of A was
followed by very little time for growth. The
average particle size of A should be the smallest
with BCs average particle size being a bit
larger and the average particle size of B being
quite a bit larger than BC. This entire
analysis is just one possibility, the only point
when nuclei form could be when the solid first
appears.
The blue line is the path of the liquid
composition when cooling the liquid from
composition X.
How exactly can this information be applied to
tailor a ceramic powder?
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Real world applications
With the use of titration or some other way of
controlling the concentration of a specific
component in a solution, the particle size and
size distribution can be controlled. If a large
particle size distribution is desired, keep the
concentration of the solute in question above the
concentration required for nucleation for a long
period of time. To achieve a powder with large
particles, but a tight distribution of sizes,
allow the concentration of the component in
question to exceed that required for nucleation
for only a very short period of time followed by
a long period in which the concentration is large
enough for growth. By doing this each nuclei
will have a long and equal period of growth.
This can also be achieved by never allowing the
concentration of the component in question to
exceed the level for nucleation to occur, but
instead adding artificial nucleation sites. This
eliminates any variation in the amount of time
for particle growth and should therefore result
in a slightly more compact particle size
distribution. To precipitate out small particles
with a rather small variation in size, add all of
the component to be precipitated out at once,
this way many nuclei will form all at once. By
the time the concentration of the component that
is precipitating out gets below that required for
nucleating, the number of nuclei is very large
such that each nuclei grows very little before
the concentration of the component in question is
essentially zero.
Above is an example of a concentration versus
time for precipitating large particles with a
small distribution of sizes.
Above is an example of concentration versus time
for precipitating a powder with a large
distribution of sizes.
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Summary
Nucleation and Growth controls particle size and
size distribution in precipitated powders and is
therefore important in ceramic engineering
because the characteristics of a finished ceramic
piece is related to the particle size and size
distributions of the powder that was used to make
it.
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