In this video we're going to look at how
we would draw a
cooling curve
and we start with a liquid mixture
and cool it down. We start with the liquid mixture
at 1600 Kelvin and a mole fraction 0.7 so that's right around here
that's our starting point. In order to understand behavior let's look at a couple regions.
The yellow region
corresponds to a mixture of a liquid
and solid silicon so we pick some point in this region
then the lever rule will tell us how much
liquid is present with this composition in equilibrium with solid silicon
The orange region corresponds to two solids in equilibrium so
again picking a point corresponds to
solid silicon equilibrium
with this compound Mg2
Si. So this is a stoichiometric compound and we have two solid phases in
equilibrium in this
orange region. So let's
look what happens if at our starting point you start removing heat
at a constant rate, well we're gonna cool down the liquid till we get to this point
so we would see on our diagram the temperature
would decrease. How fast depends on what the heat capacity is
for the liquid and then at this point which is
close to 1600 Kelvin we start making
solid silicon in equilibrium with the liquid
and as we continue to cool down
we make more solid silicon and we change of course the composition of the liquid
because removing
just silicon from the liquid and we'll continue till we get to this point where
we have
solid silicon and liquid
in equilibrium and so on our cooling diagram we're going to see
the temperature changing more slowly
once we start making the solid-phase
and so for here just say
temperature's decreasing but we're removing more energy because of the phase change.
Now we get to this point, now we're looking at a slightly different
situation,
this is eutectic. Now as we
continue to remove energy we have a liquid at the eutectic composition in
equilibrium with silicon
We're going to stay at constant temperature while we remove the rest of the
energy.
And so first on the cooling diagram this means we're gonna be at constant
temperature, so this is
actually horizontal and this is the
formation of this compound
and pure silicon equilibrium in the eutectic liquid
disappears so that when we continue to remove energy
we move down to this point which is this much
this composition pure silicon this composition is the compound.
Only thing we're changing is that we're lowering the temperature we have no further
phase change
and so now we're looking at changes due to heat capacity and depending what the
heat capacity of the solid is determines the slope of this line
and so the details are not
strictly correct because I didn't look up heat capacities and
heat melting etc. but the important points are here
the temperature decreases based on heat capacity as it does here
at this point it's a liquid this is the heat capacity of the two solids
here we have the formation of the compound
and additional pure silicon. At the eutectic point the temperature does not
change
Here the temperature decreases as we form
silicon solid from the liquid mixture
Let's look at one more example of
cooling curve for the same diagram and we're going to now start with a different
composition. We're going to start with an overall
silicon mole fraction 0.33
and at 1500 Kelvin. So that means we're starting here
Now as we cool down of course we have the same behavior we saw
before that temperature's going to decrease because of
there's a heat capacity for liquid we're removing energy and heat capacity term
is what that slope would be
and what the scales are of course on the diagram.
We get to this point, now
everything in terms a phase change takes place at one temperature because
below this what we have is this compound Mg2
Si. So now we're going to have a horizontal line
corresponding to whatever the delta H
for this compound the heat of fusion
and then once we've made all the compound at this temperature which is
about 1360 Kelvin
then we will cool down the solid
and this again will be heat capacity of the solid.
So again this is horizontal and once
we passed the horizontal constant temperature
solidification now we just have to pure compound and we're just
cooling it down and how fast depends on its heat capacity.