in this video I will be talking about
nucleation in crystal growth
nucleation which results in a crystal is
a liquid vapour or solution to solid
phase transition the resulting crystal
can grow in various ways for example
through a liquid that freezes on the
surface of the crystal or deposition
which is a gas so let's face transition
a few examples of this are the growth of
calcite minerals and buyer ice crystals
a pirate' crystal is shown here on the
screen the formation of a snowflake is a
very good example of nucleation and
crystal growth combined the snowflake
starts out with nucleation where water
droplet nucleates and grows into a
snowflake this is a special example of
crystal growth because water vapour
crystallizes directly via the process of
deposition I will talk more about this
example later nucleation can occur in
two different ways namely homogeneous
and heterogeneous nucleation homogeneous
nucleation occurs when a pure liquid
nucleates
because that's been cooled sufficiently
surprisingly enough sufficiently cool
does not mean the freezing temperature
of the pure liquid depending on the
liquid it needs to be cooled down a
certain amount further for example
homogeneous nucleation of water occurs
with the chance of 99.9 percent at about
minus 35 to minus 43 degrees Celsius
depending on the size of the water
droplet but there's a very low chance of
freezing at minus 10 degrees Celsius but
if water is not pure it can with a high
probability also nucleate at minus 10
degree Celsius this is because of dust
particles in the water allowing it to
nucleate at a higher temperature this
process is called heterogeneous
nucleation the process of crystal growth
is driven by a degree of super cooling
this is necessary because the nucleation
barrier needs to be lowered by means of
thermal fluctuations so the higher the
degree of super cooling is the bigger
the thermal fluctuations are our two
major growth mechanisms non-uniform
natural growth and uniform normal growth
non-uniform lateral growth advances in
steps of the uniform normal growth a
thoughts in a continuous way the main
criterion which decides between the two
growth mechanisms is this diffusivity of
the surface
a diffused surface changed from one
place to another in a continuous way and
thus allows for uniform normal growth
across the crystal alternatively sharp
service reached a major change
properties discontinuous leads to
non-uniform lateral growth even when the
supercooling is active the surface will
reach a metastable equilibrium between
steps which it does not indicate uniform
normal growth in order for snow click
before supercooled water droplets must
first nucleate from an ice crystal this
can happen in two ways either through
homogeneous or heterogeneous nucleation
in order for a crystal to form through
homogeneous nucleation temperature must
be minus 35 degrees Celsius or lower so
in most case it's unlikely a snowflake
forms in this way since the temperature
in a cloud juice is not this low so
snowflakes mostly formed by a
heterogeneous nucleation meaning a dust
particle is needed inside the droplet of
water in order for it to nucleate
because of the dust particle temperature
needed for the water droplet to nucleate
comes higher mu minus 6 degrees once the
droplet has nucleated and thus an ice
crystal has formed starts to grow
because of the deposition of water
vapour on the surface of the ice crystal
water molecules from the water vapour
align themselves in a certain way in the
ice crystal namely in a way which
maximizes attracted forces and minimizes
repulsion
this causes the hexagonal shape of the
snowflake the Grove of an ice crystal
after nucleation takes about half an
hour after which the ice crystal is
heavy enough to fall out of the cloud
and become a snowflake now for the
theoretical explanation of homogeneous
and heterogeneous nucleation when the
drop of size R is nucleated this leads
to a change in free energy as seen here
the first part is the negative
contribution proportional to the volume
of the droplet because the mixture is
initially unstable the second part is
the positive contribution proportional
to the surface area because an interface
needs to be made with interfacial energy
there is a certain value R star for rich
droplets above this radius are stable
and below are unstable it means that the
energy required to form a critical new
it showed at the bottom left and your
current probability of this activation
process is shown on the bottom right
this is basically the method of
argumentation that can be used to
describe homogeneous nucleation at
Virginia's nucleation is a bit more
complicated
if the surface of a different solid is
present it lowers the activation energy
for nucleation crystal nucleus nucleus
against the solid with a certain angle
this contact angle depends on the
tensions between the catalyst and solid
catalyst and liquid and liquid and solid
we now find a similar change in free
energy with different energy
contributions because the interface
described by this formula if the contact
angle is less than 90 degrees this
seriously decreases the degree under
cooling that is necessary