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Hi there.

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00:00:22,790 --> 00:00:23,750
I'm Brian.

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00:00:23,750 --> 00:00:26,960
We're going to be doing problem
number 7 of the 2009

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00:00:26,960 --> 00:00:29,880
final examination.

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00:00:29,880 --> 00:00:33,460
So the way I like to approach
these problems is to identify

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00:00:33,460 --> 00:00:35,720
what I think is important to
know before attempting them.

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00:00:35,720 --> 00:00:37,670
Things that you should review
that will help you

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00:00:37,670 --> 00:00:39,320
successfully navigate
the problem.

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00:00:39,320 --> 00:00:42,430
I call this the what
I need, W I N.

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00:00:42,430 --> 00:00:44,470
So for this particular problem,
which I think of as

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00:00:44,470 --> 00:00:47,590
the phase diagram problem, you
need three things critically

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00:00:47,590 --> 00:00:50,610
in order to successfully
complete it.

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00:00:50,610 --> 00:00:53,240
Number one you need to have a
general understanding of what

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00:00:53,240 --> 00:00:56,400
a phase diagram is, how to read
it, how to write it, how

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00:00:56,400 --> 00:00:58,890
to interpret the information
it gives you.

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00:00:58,890 --> 00:01:02,430
You can find a lot of this in
chapter 9 of Shackleford.

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00:01:02,430 --> 00:01:04,670
Along the same lines you should
probably know how to go

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00:01:04,670 --> 00:01:07,230
in between binary and unary
phase diagrams. How they are

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00:01:07,230 --> 00:01:10,150
related at least. In this
problem it's not absolutely

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00:01:10,150 --> 00:01:11,490
necessary to know this.

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00:01:11,490 --> 00:01:14,440
But in similar problems we might
ask, this is critical to

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00:01:14,440 --> 00:01:17,050
understand how these two
are interrelated.

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00:01:17,050 --> 00:01:19,850
The second thing you should
know is some language like

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00:01:19,850 --> 00:01:21,610
critical point and
triple point.

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00:01:21,610 --> 00:01:24,700
Where these are and what they
mean on the phase diagram.

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00:01:24,700 --> 00:01:27,210
And the third thing is the
phase coexistence.

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00:01:27,210 --> 00:01:29,160
So what does that
actually mean?

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00:01:29,160 --> 00:01:30,780
How do you find it on
the phase diagram?

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00:01:30,780 --> 00:01:36,180
So with these three particular
points, I'd review them and

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00:01:36,180 --> 00:01:37,720
then I would recommend
attempting the problem

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00:01:37,720 --> 00:01:39,370
afterwards.

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00:01:39,370 --> 00:01:42,040
So we're going to start
the problem.

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00:01:42,040 --> 00:01:43,280
We're going to start
over here.

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00:01:43,280 --> 00:01:47,160
I'm actually going to start this
from a reverse direction.

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00:01:47,160 --> 00:01:49,520
And review really quick what
a binary phase diagram is.

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00:01:49,520 --> 00:01:51,850
because this is actually the
phase diagram which you will

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00:01:51,850 --> 00:01:55,560
see most often as you progress
in your career as a scientist

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00:01:55,560 --> 00:01:56,940
or an engineer.

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00:01:56,940 --> 00:01:58,270
This is something you'll
see a lot of the time.

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00:01:58,270 --> 00:02:00,940
It'll have either one element
and another element.

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00:02:00,940 --> 00:02:03,940
Or one compound and another
compound along the axis.

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00:02:03,940 --> 00:02:08,220
And it shows the different
phases which exist at certain

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00:02:08,220 --> 00:02:10,200
temperatures and compositions.

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00:02:10,200 --> 00:02:12,720
So in general it's important
to sort of understand

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00:02:12,720 --> 00:02:13,970
what a phase is.

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00:02:13,970 --> 00:02:18,800
So a phase, is a chemically and
a structurally homogeneous

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00:02:18,800 --> 00:02:21,790
material given certain
state conditions.

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00:02:21,790 --> 00:02:25,540
So a phase diagram depicts
picks all these phases.

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00:02:25,540 --> 00:02:29,380
It's the master plot of phases
that are in equilibrium given

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00:02:29,380 --> 00:02:32,620
a particular set of
state conditions.

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00:02:32,620 --> 00:02:34,560
When I say state conditions
I'm actually referring to

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00:02:34,560 --> 00:02:37,410
things like temperature,
pressure, I even sometimes

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00:02:37,410 --> 00:02:41,110
consider composition to be one
of those state conditions.

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00:02:41,110 --> 00:02:45,210
So in a binary phase diagram,
what we're looking at is the

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00:02:45,210 --> 00:02:48,100
temperature versus
the composition.

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00:02:48,100 --> 00:02:51,040
So if you have some composition
of silicon and

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00:02:51,040 --> 00:02:53,850
germanium at some temperature,
you know exactly what phase it

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00:02:53,850 --> 00:02:55,255
should be at thermodynamically.

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00:02:55,255 --> 00:02:58,090
It doesn't actually mean it
will be, but it should be.

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00:02:58,090 --> 00:03:00,750
So that's what a binary phase
diagram looks like.

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00:03:00,750 --> 00:03:03,050
So this is something you'll
see a lot and this is

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00:03:03,050 --> 00:03:05,230
something you probably will
become used to seeing a lot as

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00:03:05,230 --> 00:03:06,620
you go on in your years.

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00:03:06,620 --> 00:03:08,530
We're going to come back
to this in a second.

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00:03:08,530 --> 00:03:10,210
But first, for now, we're going
to it actually attempt

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00:03:10,210 --> 00:03:11,540
the problem that's given.

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00:03:11,540 --> 00:03:14,810
And then I'll tie both of
those together for you.

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00:03:14,810 --> 00:03:17,310
So let's go over and
let's actually look

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00:03:17,310 --> 00:03:18,070
at the problem now.

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00:03:18,070 --> 00:03:20,350
We'll go back to that
in a second.

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00:03:20,350 --> 00:03:23,090
We're asked to draw a unary
phase diagram for silicon.

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00:03:23,090 --> 00:03:25,190
And we're given some critical
information.

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00:03:25,190 --> 00:03:28,800
Specifically on the problem
we're given the triple point,

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00:03:28,800 --> 00:03:30,910
we're given the critical
point, and we're

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00:03:30,910 --> 00:03:32,280
asked to draw this.

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00:03:32,280 --> 00:03:34,610
Not to scale, of course,
but what it should

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00:03:34,610 --> 00:03:36,650
generally look like.

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00:03:36,650 --> 00:03:39,840
So the first thing I do
is label my axes.

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00:03:39,840 --> 00:03:42,630
Pressure, temperature.

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00:03:42,630 --> 00:03:44,260
And then we're given
certain data.

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00:03:44,260 --> 00:03:45,900
So I'm just going to throw it
down right in the beginning.

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00:03:45,900 --> 00:03:48,230
We're given pressure and
temperature for triple point.

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00:03:48,230 --> 00:03:49,570
We're given pressure
and temperature for

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00:03:49,570 --> 00:03:50,530
the critical point.

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00:03:50,530 --> 00:03:52,300
So I'm going to put those
points down right now.

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00:03:52,300 --> 00:03:54,350
Because I know that's
part of the answer.

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00:03:54,350 --> 00:03:56,160
So let me first put down
the triple point.

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00:03:56,160 --> 00:04:05,880
We're told the triple point
occurs at 0.15 atm.

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00:04:05,880 --> 00:04:12,530
And we're told that that is at a
temperature of 1415 celsius.

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00:04:12,530 --> 00:04:14,700
So temperatures are going
to be in celsius and our

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00:04:14,700 --> 00:04:16,690
pressures are going to
be in atmospheres.

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00:04:19,590 --> 00:04:23,680
So we're going to go up
to find this point.

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00:04:23,680 --> 00:04:25,020
In fact I'm going to give
it a different color.

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00:04:31,550 --> 00:04:33,160
That is our triple point.

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00:04:33,160 --> 00:04:35,870
I'm next going to plot the
critical point here.

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00:04:35,870 --> 00:04:40,100
We're told that that occurs
at a pressure of 6,600.

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00:04:40,100 --> 00:04:41,570
So not to scale of course.

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00:04:41,570 --> 00:04:43,170
But that's going to be somewhere
all the way up here.

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00:04:48,800 --> 00:04:55,760
Now we're told that that is
at a temperature of 4880.

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00:04:55,760 --> 00:04:58,330
So here's a point here.

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00:04:58,330 --> 00:04:59,645
So we've just put
two points down.

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00:04:59,645 --> 00:05:01,500
But that's not enough to
complete the problem.

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00:05:01,500 --> 00:05:03,150
It doesn't actually answer
all the questions.

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00:05:03,150 --> 00:05:06,630
The problem actually also asks
us to provide the normal

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00:05:06,630 --> 00:05:10,590
boiling point and the normal
melting point of silicon.

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00:05:10,590 --> 00:05:12,570
So you're not actually given
those temperatures because

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00:05:12,570 --> 00:05:13,350
you've got to be clever.

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00:05:13,350 --> 00:05:15,880
And all the students in our
class are given a periodic

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00:05:15,880 --> 00:05:17,150
table during the exam.

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00:05:17,150 --> 00:05:18,780
So I would encourage you to
have a periodic table with

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00:05:18,780 --> 00:05:20,020
this type of data.

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00:05:20,020 --> 00:05:22,720
So if you look at the periodic
table for silicon you can then

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00:05:22,720 --> 00:05:24,510
find your melting point
and you can find

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00:05:24,510 --> 00:05:26,370
your boiling point.

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00:05:26,370 --> 00:05:30,520
So this data, a normal melting
point and a normal boiling

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00:05:30,520 --> 00:05:32,460
point will occur at
1 atmosphere.

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00:05:32,460 --> 00:05:35,840
Let me just put 1 atmosphere
on the pressure here.

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00:05:35,840 --> 00:05:37,090
Again not to scale.

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00:05:41,900 --> 00:05:44,500
So anything that occurs at this
particular pressure, this

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00:05:44,500 --> 00:05:47,250
isobaric line, is going
to be normal.

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00:05:47,250 --> 00:05:53,730
So our normal melting point
occurs at 1414, which is right

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00:05:53,730 --> 00:05:56,050
next to 1415.

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00:05:56,050 --> 00:05:57,730
There we go.

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00:05:57,730 --> 00:06:01,700
And our normal boiling
point occurs at 3265.

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00:06:01,700 --> 00:06:03,690
These are approximate numbers.

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00:06:03,690 --> 00:06:04,940
So we'll put that here.

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00:06:07,760 --> 00:06:10,940
And now if you've seen a unary
phase diagram before, which I

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00:06:10,940 --> 00:06:12,530
hope you have during your
studying, you'll know that it

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00:06:12,530 --> 00:06:15,530
looks somewhat like a y shape.

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00:06:15,530 --> 00:06:17,340
So one thing we're going to do
now is we're going to connect

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00:06:17,340 --> 00:06:18,260
these dots.

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00:06:18,260 --> 00:06:20,640
We know that at very high
temperatures we're going to

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00:06:20,640 --> 00:06:23,510
have what's a gas, basically.

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00:06:23,510 --> 00:06:26,160
And at very low temperatures
we're going to have something

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00:06:26,160 --> 00:06:28,090
like a solid.

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00:06:28,090 --> 00:06:30,340
And we have some liquid
in the middle.

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00:06:30,340 --> 00:06:33,220
And the way we're going to
delineate these phases is to

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00:06:33,220 --> 00:06:34,470
connect these dots.

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00:06:44,170 --> 00:06:46,850
And this is what our unary
phase diagram is

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00:06:46,850 --> 00:06:48,410
going to look like.

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00:06:48,410 --> 00:06:51,760
So in order to complete this
problem-- it was actually not

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00:06:51,760 --> 00:06:54,230
too bad of a problem-- all you
have to do is label some

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00:06:54,230 --> 00:06:56,640
particular aspects
of this graph.

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00:06:56,640 --> 00:07:00,400
So number 1, we have a solid
region, we have a gas region.

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00:07:00,400 --> 00:07:02,500
That implies this must
be the liquid region.

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00:07:02,500 --> 00:07:04,140
I'll put an L there.

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00:07:04,140 --> 00:07:08,860
You're asked to identify 1,
2 and 3 component regions.

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00:07:08,860 --> 00:07:11,270
Or three 1-phase regions,
2-phase regions.

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00:07:11,270 --> 00:07:14,640
So number 1, you could have
chosen for a 1-phase region,

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00:07:14,640 --> 00:07:17,960
you can chosen a point here in
the gas, a point here in the

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00:07:17,960 --> 00:07:20,890
liquid, or a point here
in the solid.

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00:07:20,890 --> 00:07:23,470
I'll just choose
one in the gas.

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00:07:23,470 --> 00:07:28,290
So something here, let's call
that i, for answering part i.

161
00:07:28,290 --> 00:07:32,090
You could have chosen a point
along any of these lines for a

162
00:07:32,090 --> 00:07:33,100
2-phase equilibrium.

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00:07:33,100 --> 00:07:36,370
Which implies that at that
point, so at that specific

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00:07:36,370 --> 00:07:39,990
pressure and at that specific
temperature, you have both

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00:07:39,990 --> 00:07:40,710
phases of equilibrium.

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00:07:40,710 --> 00:07:42,280
Let me just choose one
and explain it.

167
00:07:42,280 --> 00:07:45,250
So let's choose something
here.

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00:07:45,250 --> 00:07:48,355
Between 0.15 and 1.

169
00:07:48,355 --> 00:07:50,350
So let's choose this point.

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00:07:50,350 --> 00:07:52,940
There we are.

171
00:07:52,940 --> 00:07:56,500
So at this point, at whatever
pressure we're at and whatever

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00:07:56,500 --> 00:07:59,970
temperature we're at here, we
have both liquid and gas in

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00:07:59,970 --> 00:08:00,570
equilibrium.

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00:08:00,570 --> 00:08:02,540
They both coexist. You're
not tending

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00:08:02,540 --> 00:08:03,970
towards one or the other.

176
00:08:03,970 --> 00:08:05,370
They're both there.

177
00:08:05,370 --> 00:08:09,560
So that's part B, the 2-phase
coexistence area.

178
00:08:09,560 --> 00:08:11,300
So we put that here.

179
00:08:11,300 --> 00:08:12,660
i i.

180
00:08:12,660 --> 00:08:14,190
And the third part
is the 3-phase

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00:08:14,190 --> 00:08:15,680
coexistence, which is--

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00:08:15,680 --> 00:08:18,540
almost you can pull it out of
the name-- the triple point.

183
00:08:18,540 --> 00:08:20,820
At the triple point-- and
there's only one of these--

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00:08:20,820 --> 00:08:23,530
you have all three,
gas, liquid and

185
00:08:23,530 --> 00:08:25,680
solid coexisting together.

186
00:08:25,680 --> 00:08:26,960
So we've already sort
of made that.

187
00:08:26,960 --> 00:08:29,740
That was our blue dot.

188
00:08:29,740 --> 00:08:30,940
1, 2, 3.

189
00:08:30,940 --> 00:08:33,090
That's that point right there.

190
00:08:33,090 --> 00:08:34,140
So not to scale.

191
00:08:34,140 --> 00:08:34,940
But this is the answer.

192
00:08:34,940 --> 00:08:36,110
This is full credit.

193
00:08:36,110 --> 00:08:38,690
One thing that's really
interesting to note is that on

194
00:08:38,690 --> 00:08:41,847
this particular answer we have
a negative slope on our

195
00:08:41,847 --> 00:08:44,240
solid-liquid coexistence line.

196
00:08:44,240 --> 00:08:46,320
Now you've probably seen this
before in your studying and it

197
00:08:46,320 --> 00:08:48,000
occurred with water.

198
00:08:48,000 --> 00:08:50,400
Most materials actually will
have a positive slope.

199
00:08:50,400 --> 00:08:52,860
If you think about it it's
sort of counterintuitive.

200
00:08:52,860 --> 00:08:56,070
What this implies is that if I'm
at a constant temperature

201
00:08:56,070 --> 00:08:59,670
and as I raise my pressure I'm
going to go from the solid to

202
00:08:59,670 --> 00:09:00,680
the liquid.

203
00:09:00,680 --> 00:09:03,170
Intuitively, we would think that
the solid is more densely

204
00:09:03,170 --> 00:09:05,970
packed and therefore as we
increase the pressure we're

205
00:09:05,970 --> 00:09:07,590
going to tend towards a solid.

206
00:09:07,590 --> 00:09:10,590
That's not the case in water and
in this problem is not the

207
00:09:10,590 --> 00:09:13,370
case with the data we're
given for silicon.

208
00:09:13,370 --> 00:09:15,740
In this case as we raise the
pressure we're actually

209
00:09:15,740 --> 00:09:16,630
turning into a liquid.

210
00:09:16,630 --> 00:09:18,410
It's kind of counterintuitive.

211
00:09:18,410 --> 00:09:21,550
Another way of actually saying
that is the liquid phase at

212
00:09:21,550 --> 00:09:24,850
this particular temperature
is more dense

213
00:09:24,850 --> 00:09:26,240
than the solid phase.

214
00:09:26,240 --> 00:09:28,270
And you see that with water,
which is why ice

215
00:09:28,270 --> 00:09:30,020
floats on top of water.

216
00:09:30,020 --> 00:09:32,390
So that is our unary diagram.

217
00:09:32,390 --> 00:09:34,710
That is the full credit
on this problem.

218
00:09:34,710 --> 00:09:37,360
I do want to tie it in really
quick though, with what a

219
00:09:37,360 --> 00:09:38,160
binary diagram is.

220
00:09:38,160 --> 00:09:41,040
Because this is a very important
concept to get and a

221
00:09:41,040 --> 00:09:42,440
potential problem.

222
00:09:42,440 --> 00:09:45,160
So we're going to go back
over to binary phase

223
00:09:45,160 --> 00:09:46,410
diagram over here.

224
00:09:49,750 --> 00:09:52,810
And so what we're looking at on
this binary phase diagram

225
00:09:52,810 --> 00:09:55,590
is actually, it's the
temperature versus the

226
00:09:55,590 --> 00:09:57,920
composition at a specific
pressure.

227
00:09:57,920 --> 00:10:00,920
Now for a binary phase diagram
you're going to assume--

228
00:10:00,920 --> 00:10:02,500
unless you're told otherwise--

229
00:10:02,500 --> 00:10:05,740
that it occurs at 1
atm, 1 atmosphere.

230
00:10:08,420 --> 00:10:10,970
If I want to go between the
binary and the unary that we

231
00:10:10,970 --> 00:10:14,670
just looked at, you need
to add your third axis.

232
00:10:14,670 --> 00:10:16,570
So if we had a third axis--

233
00:10:16,570 --> 00:10:17,470
let me draw that here.

234
00:10:17,470 --> 00:10:18,720
This is going to
be our z-axis.

235
00:10:21,850 --> 00:10:23,240
There's the z.

236
00:10:23,240 --> 00:10:27,070
We know that if we put a
pressure along this axis,

237
00:10:27,070 --> 00:10:29,520
we're going to be able to
extract what we had for our

238
00:10:29,520 --> 00:10:30,300
unary diagram.

239
00:10:30,300 --> 00:10:33,500
So let me do that for you.

240
00:10:33,500 --> 00:10:38,050
I'm going to call this
the pressure axis.

241
00:10:38,050 --> 00:10:41,480
Going back in and out
of the board.

242
00:10:41,480 --> 00:10:43,720
And actually this is at 1 atm.

243
00:10:43,720 --> 00:10:45,360
Which implies at some
point farther

244
00:10:45,360 --> 00:10:48,000
back we have the origin.

245
00:10:48,000 --> 00:10:49,290
You can just do this
lightly so it

246
00:10:49,290 --> 00:10:50,520
doesn't get too confusing.

247
00:10:50,520 --> 00:10:51,870
We have an origin for
our pressure.

248
00:10:51,870 --> 00:10:54,120
So at this point we
have 0 pressure.

249
00:10:54,120 --> 00:10:55,950
We don't work with negative
pressures.

250
00:10:55,950 --> 00:10:57,000
0 pressure.

251
00:10:57,000 --> 00:11:00,920
Which implies-- let me just
draw the Cartesian form of

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this-- so we have composition,
we have

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temperature, we have pressure.

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That's our x, y, z.

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Now what happens is that as we
increase pressure what happens

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to, for example, this point?

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Now what is this point?

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This point is the point
where we go from the

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solid to the liquid.

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That's the melting point.

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What happens to the melting
point as we increase or

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decrease our pressure?

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Well that information is given
on our unary phase diagram.

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Let's go back really quickly.

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As we increase our pressure we
can see that what's going to

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happen with our point is
it's going to go up.

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So what basically we have to
do is we need to take-- you

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have to think
three-dimensionally--

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00:11:46,610 --> 00:11:50,360
and take this graph and you're
going to take it an spin it

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and put it on to one of
those planes there.

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So we're going to get an idea.

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This is something that I would
challenge you, the listener,

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to do and think about and do
on your paper after you've

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completed this problem
successfully.

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I'm going to draw
it right now.

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00:12:02,705 --> 00:12:04,290
And I'm going to let you
look at it and think

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about it, what it means.

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So let me do that.

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Let's take a look now.

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This is our temperature axis.

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Here's t.

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Here's p.

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00:12:15,110 --> 00:12:18,370
Remember unary was p versus
t, so you've got

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to do a little flipping.

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00:12:19,770 --> 00:12:21,020
But let me just draw it now.

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00:12:29,912 --> 00:12:31,640
It kind of goes up
to the words.

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00:12:31,640 --> 00:12:33,490
But you get the idea.

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00:12:33,490 --> 00:12:35,640
This is-- if you do a little
flipping and I challenge you

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00:12:35,640 --> 00:12:37,680
to do that, some
three-dimensional thinking--

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00:12:37,680 --> 00:12:40,710
this is the unary phase plot
that we gave for our answer.

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00:12:40,710 --> 00:12:43,390
And the point I'm trying to
make is that you can go in

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between your unary and your
binary diagrams by

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00:12:47,650 --> 00:12:48,630
understanding that.

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For example, binary diagram is
at a constant pressure and

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00:12:52,710 --> 00:12:56,050
your unary diagram, unary
means that it has one

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00:12:56,050 --> 00:12:58,190
material, one composition.

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00:12:58,190 --> 00:13:01,590
So in this particular problem
I've created germanium to be

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00:13:01,590 --> 00:13:03,170
our b element.

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00:13:03,170 --> 00:13:07,210
And we're operating here
with pure silicon.

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So you can go in between
if you have the

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00:13:08,880 --> 00:13:10,380
grasp of that concept.

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00:13:10,380 --> 00:13:12,720
So I would challenge you
to think about that.

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00:13:12,720 --> 00:13:14,510
If you've gotten the problem
right and you understand this

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00:13:14,510 --> 00:13:17,570
concept, I think you're good
to go on phase diagrams.