Prof: So as we ended
last time, we said despite
Earnshaw,
which says you can't have these
Lewis structures,
might there really
be shared-pair
bonds and lone-pairs,
and how do we know;
we have to look,
or feel.
So last time we tried feeling
with scanning probe microscopy
-- AFM, STM, SNOM.
They're really great.
You can see atoms;
you can see molecules,
but you can't see bonds.
Okay, so what's the key word
here?
Students: Lux.
Prof: Lux, right?
So maybe we'll see it,
if we can't feel it.
Now this is the entrance to
this building,
the old delivery entrance out
on Prospect Street.
And you know there's
interesting stuff all over the
building.
Up here on top there's a fluted
filter paper and a funnel,
but hidden back in the shadows
is something that's a little
surprising to you,
back there, which is a
microscope.
What science do you associate
that with?
Students: Biology.
Prof: Biology,
not chemistry,
right?
What's it doing?
Well at least it's back in the
shadows there.
But maybe the eyeball up there
says we can see the things we
can't feel.
Okay?
This is a picture -- does
anybody recognize this?
Student: Flea.
Prof: You know what it's
from?
Student: Bubonic plague?
Prof: It's from Robert
Hooke's great book,
Micrographia,
from 1665.
It's a wonderful book.
The page is about this big.
And imagine the person who had
fleas, seeing that for the first
time.
It's exquisite, this drawing.
And he said in the book:
"But Nature is not to be
limited by our narrow
comprehension;
future improvements of glasses
may yet further enlighten our
understanding,
and ocular inspection may
demonstrate that which as yet we
may think too extravagant either
to feign or to suppose."
So if he had a microscope that
could do that in 1665,
we must have a microscope now
that's powerful enough to see
bonds, right?
And in fact we do.
In fact, there's a brand new
one that they promise will come
online next Tuesday in a room
about 100 yards over that way,
and the trick it uses is the
same one Newton used to measure
the distance of the air gap for
Newton's rings,
or that Hooke explained by the
pulses, right?
And it's interference that
comes from scattering.
So you've seen oil on water,
thin layers of oil on water,
and you see rainbows in them.
Why?
Okay, so light comes in and
scatters from two surfaces,
that let's say are 200
nanometers apart.
Okay?
So the path difference between
the one that reflects from the
top and the one that reflects
from the bottom,
the difference is 400
nanometers;
one goes 400 nanometers further
than the other.
Now suppose that happened to be
one wavelength.
Right?
Then if that purple light that
came in, one going further than
the other, they would come out
exactly one wave apart.
So it would be as if it were a
single wave and they would
reinforce one another and you'd
see the purple light strongly.
Okay?
But if the wavelength
difference were half -- if the
path difference were half the
wavelength, like for red light
--
Oh-oh.
What do we do here, Elaine?
Better get it quick,
before something comes up.
You're a good sport.
<<Technical
adjustments>>
OK.
Thank you.
Prof: If it's one
wavelength path difference,
then it reinforces and we get a
nice strong wave coming out.
Okay?
But if it's half-a-wavelength
difference, like for the red
light, then they cancel.
One is a maximum when the other
is a minimum,
and they're zero.
Okay?
So you get no scattering.
So that's why you get different
colors, because the oil is
different thicknesses in
different parts of the slick.
Okay, so here's the new machine
that's right over here that's
supposed to come on -- new
machines actually;
there are two of them;
it was a package deal.
And that's Chris Incarvito
who's the director of the
Chemical Instrumentation Center
and the proud owner of these two
new machines.
So the one he's looking at
there is a user -- is to be
operated by users.
So it's just you sort of push
buttons and you get where the
atoms are in the molecule -- at
least that's the hope -- and it
costs about $200,000.
Okay, so there's a little
thread there that has a crystal
on, but you need a magnifying
glass to see it.
You won't see it with your eyes;
it's a tiny, tiny crystal.
Okay?
So here's an x-ray tube.
X-rays come down the pipe
there, hit the crystal and get
scattered, and are detected by
this CCD detector.
Okay?
And then from that information,
those scattered rays,
you get where the atoms are in
the molecule;
more precisely,
as you'll see,
where the electrons are in the
molecule, or in the crystal.
The other machine that he's
especially proud of costs $350K.
And why is it more expensive?
Because it collects more.
Instead of using that little
disc of a CCD,
it has a curved image plate.
Right?
So when the x-rays come down
here and hit the tiny crystal,
many more of them get collected
by the plate.
So it's more efficient.
So those will be coming soon.
And if all you have to do is
press a button and the structure
comes out, that seems fine.
But that's not the goal of this
course, to press a button.
We want to understand how such
a thing works.
Seeing individual molecules,
atoms, and maybe bonds,
there's a problem,
and the problem is wavelength.
Because you know in principle
you can't resolve things that
are closer together than the
wavelength of light,
and the wavelength of light
we've been talking about here is
400-800 nanometers.
Whereas what's the distance of
a carbon-carbon bond?
Anybody remember?
Student: 1.86.
Prof: One and a half
angstroms, right?
So three orders of magnitude
smaller than the wavelength of
light.
So this is a problem,
and it's why,
as you'll see,
you use x-rays,
because they have short
wavelengths.
Now to understand this we'd
have to know what light is.
So what is light?
You people have studied physics
and so on.
So what's light? Wilson?
Student: Who knows?
Prof: Who knows, okay.
Student: An
electromagnetic wave.
Prof: It's an
electromagnetic wave.
Okay.
Now I've seen -- indeed it is
-- I've seen waves on the ocean,
right?
Does it mean that
electromagnetic waves are like
those waves?
In what way is an
electromagnetic wave a wave?
What's wavy about it?
Well you can make a graph
that's a wave,
that involves light.
So here what we're going to
plot is the force on a charge.
The charge is at a particular
position.
We'll have the charge over
there on the right;
it's fixed there,
and we're going to measure the
force on it that'll make it
accelerate up or down.
Okay?
Oops.
It doesn't work quite the way
it does on mine.
Please let me know when that
happens.
No maybe it's going to work.
>
What that first thing did was
went up and down,
up and down,
up and down.
Okay?
But if you plot it then as a
function of time,
it's a wave.
Right?
The field, at a particular
point, as a function of time,
is a wave.
It goes up and down and up and
down.
Okay, now so we plot the field,
or the force on a charge at one
position as a function of time.
But there's another way of
making a plot that also shows
light as a wave,
which is to show the field at
different places at the same
time.
Right?
So we're going to change it and
now the horizontal axis is the
position but it's at a
particular instant.
So as the thing goes along
there are different forces at
different positions,
okay?
And again, that will be a wave.
So that's the sense in which
light is a wave.
And what is it that we're
plotting?
We're plotting the electric
field.
So light is associated with an
electric field that goes up and
down.
Right?
And you can plot it in time or
in space and get a wave.
So that's the sense in which
it's a wave.
It's also, incidentally,
a magnetic field;
it's electromagnetic.
Maxwell dealt with things like
that.
And there's a magnetic field
perpendicular to the electric
field,
but we don't care about it,
at least not until next
semester when we talk about
nuclear magnetic resonance,
because the electric field is
so much stronger in its effect
on molecules.
Now, its effect is on charges;
on electrons,
on protons, therefore on
nuclei.
Now, accelerated electrons
scatter light.
So here comes the light in.
We'll see if this works.
Okay, so it makes the electron
go up and down,
as the light goes by.
But up and down moving of
electrons, accelerating
electrons, is what
creates electric fields.
Right?
That's what an antenna is,
is electrons moving back and
forth.
So when the original light
comes through and hits the
electron and makes it vibrate up
and down,
that electron vibrating emits
radiation,
electromagnetic radiation,
in all directions;
all directions except this
direction, and stronger the more
you're perpendicular to the
direction it's going up and
down.
But anyhow it scatters the
light.
So most of the light still goes
through the direct beam,
but a little bit of it gets
scattered;
much less would be scattered --
a single electron wouldn't
scatter very much,
you'd need lots of electrons to
scatter a lot,
and they have to be cooperating.
Okay?
Now you tell me,
why are we interested in
electrons scattering light?
There are just as many protons
in a sample as there are
electrons.
Why don't we worry about the
protons scattering light?
Student: Electrons are
a lot less massive.
Prof: So what?
Student: They move a
lot more easily.
Prof: Ah,
the electrons are what moves.
You need the moving charge to
generate the scattered light.
The lightest positive charged
things are -- of normal
particles -- are a thousand
times heavier than the
electrons.
So they don't move very much.
It's the electrons that scatter
the light.
So with x-rays,
you see electrons,
not nuclei.
Okay, they're too heavy.
Now then, but you need a lot of
electrons to scatter enough to
see, and they have to cooperate.
Right?
So here we have ripples on a
pond;
you've all seen that kind of
thing with a little bit of rain
falling.
And so suppose you had two
spots that are generating
ripples,
two electrons let's say,
and they give off circular
waves here,
in two dimensions,
and they interfere with one
another.
But you can see a pattern is
emerging,
and when you're very,
very far away from these,
compared to the distance
between the electrons,
as indeed you are in these
samples we're talking about
where you have an infinitesimal
crystal and the detector plate
is a substantial distance away
--
right?
-- the electrons are really
close to one another.
So you're way,
way, way far away on the scale
of the distance between the
electrons.
Okay?
And now you can see what
pattern there is for high points
and low points,
for waves.
Okay?
Because you can see here that
there's a pattern like that,
that goes along the maxima.
Everybody see that?
And halfway in between those
dashed yellow lines,
there's no change at all;
nothing's happening there.
Right?
And if you go out very,
very far away,
you can see that asymptotically
these approach these straight
lines that originate between the
electrons,
or on the crystal in a real
case.
So what you have coming out of
the crystal are straight rays of
light, x-ray light.
Okay?
And the angles at which they
come out depend on where the
electrons are.
If the electrons are closer
together or further apart or
displaced in this direction,
you'll get different patterns
of the ripples.
So somehow it must be possible,
or there must be a connection
between the positions of the
electrons and where these rays
are coming out.
Right?
And if you can go backwards,
to go from where the rays come
out, to where the electrons
were, then you've solved the
problem.
Right?
You're not creating an image,
the way you would with a normal
microscope.
You're trying to interpret the
scattering.
So the angular intensity
distribution,
at great distance,
depends on the scatterer
distribution at the origin;
that is, in the crystal.
Now, if you have normal light,
and a lens like Hooke's
microscope, then you can use
these lenses to refocus it.
So the same information is
coming out.
The sample there is emitting
these rays, but a lens collects
them and refocuses them to make
an enlarged image that you then
observe.
The problem is that you can't
do that with x-rays.
People are making efforts now,
with nanofabrication kind of
things,
to make things that will act
like lenses for x-rays,
and they've made some steps,
but nothing like you would need
to actually observe electrons in
a crystal.
Okay?
Be sure to read -- there's a
webpage -- have some of you read
it so far?
-- that has to do with what I'm
lecturing on now,
which will help you a lot I
think;
so look for that.
So we're interested in seeing
molecules, atoms,
bonds, collectively,
by x-ray crystallography.
That is, we're not seeing the
image of individual electrons,
we're seeing the scattering
that comes from all the
electrons acting together.
So we're not seeing them one at
a time, we're seeing something
collective about them.
So that, for example,
a real sample,
or a sort of fake sample,
of benzene,
which had a bunch of -- six
carbon atoms in a ring,
might look like this at any
given time.
It's sort of regular but things
are a little bit one way or the
other, vibrating and so on.
Now you wouldn't see this in
x-ray, because everything is
cooperating in what you're
getting.
You'd see some sort of average
of all of them,
and it would be a little bit
smeared because of that.
Right?
You don't see -- with scanning
probe microscopy,
with these sharp tips,
you actually can feel
individual atoms,
and if one atom is someplace
else, you'll see it,
or feel it there.
That's not true in x-ray.
You see an averaged structure.
And it's averaged in two ways.
There's blurring,
from motion and from defects.
There's one benzene molecule
missing there.
It's time-averaged because it
took you time to collect these,
this information.
With synchrotrons and really,
really intense beams,
people are trying to get faster
and faster data collection,
but still what you see is
time-averaged on the scale of
how fast atoms are moving in
your sample.
So it's time-averaged,
what you get.
And it's also space-averaged,
right?
It's as if you put them all on
top of one another,
that's what you would see,
but some are displaced a little
one way, the other,
and so on.
So it's a little fuzzy.
Okay?
And this is an advantage for
scanning probe microscopy,
which operates in real space,
actually feels individual
things.
Okay, so x-rays were discovered
in 1895 by Röntgen,
using Crookes' tube that we
talked about.
Okay?
And he took a picture of his
wife's hand there,
Frau Röentgen's hand,
in 1896.
But what he sees is not a
picture that you can blow up,
like with a microscope,
because it's just a shadow.
All the bones do is stop the
x-rays that are going through.
So you don't get something
that's enlarged.
Right?
You're not going to be able to
use it the way you use medical
x-rays.
Okay.
But in 1912 Max von Laue
invented x-ray diffraction,
which is this scattering and
detect --
not trying to focus things,
not using a shadow,
but looking at these rays that
come out and trying to figure
out from them,
something about what the atoms
were.
And that's his diffraction
picture.
That's what you'd see on that
-- remember there was that round
CCD plate that's on this new
machine?
You might get a pattern that
looked sort of like that.
That was copper sulfate in 1912.
But the real breakthrough by
was William Lawrence Bragg,
who was 22 years old.
He had just graduated from
Cambridge University when he
determined the structure of a
crystal using Laue's x-ray
diffraction pattern.
So he figured out how to go the
other way, to go from the
x-ray's scattered pattern to
what the atoms were that were
doing it.
Right?
And he did this in 1912 when he
was 22-years-old,
and he got the Nobel Prize in
1915.
He's still the youngest Nobel
Laureate.
Right?
His son gave me permission to
use this picture.
He's a very nice guy,
lives in Cambridge.
Okay, then of course we've come
a long way from that.
I think you probably recognize
this picture,
right?
What is it?
Prof: It's the
scattering from DNA.
Is it a picture of DNA?
Students: No.
Prof: No it's not a
double helix.
What it is, is the way x-rays
come out when they hit the
double helix.
Okay?
And you have to figure
backwards, and that's what Crick
was able to do;
and we'll discuss how he did
that.
Okay, so that's 1952,40 years
after Bragg's discovery.
And then just in 2000,
not so long ago,
this has gone to the complete
structure of the ribosome at 2.4
angstroms resolution,
which was done here at Yale,
in this building and the next
building.
Okay, and that's what it looks
like.
It has twenty-five nanometers
across, 250 angstroms,
as long as whatever number that
is;
lots of carbon-carbon bonds.
And you see all those atoms.
There are greater than 100,000
atoms, not counting the
hydrogens.
Incidentally,
why is it easier to see other
atoms than to see hydrogens?
Student: They have
never counted them.
Prof: Because that's
where the electrons are.
Hydrogens come with only one
electron.
Other atoms come with lots of
electrons.
So it's hard to see hydrogens;
much easier to see the other
things.
Okay, now what can electron
diffraction show,
x-ray diffraction show?
That's what we want to know.
Can it show molecules?
Yes.
Can it show atoms?
Apparently;
I just showed you a picture.
But what we really want to know
is whether it can show bonds and
whether Lewis was right.
So to understand this,
we have to know how diffraction
works.
I mean, you could just be like
the people that will go and
punch the button on that
machine, but that's not what I
think you would be satisfied
with.
So I'll help you out.
So like all light,
x-rays are waves;
they just are very short.
So now I'm going to demonstrate
with a machine here,
which was designed for an
overhead projector,
but I believe it's going to
work here.
Okay, so here are our waves.
Okay, so here's a wave coming
in.
Okay?
And when it gets to this
position, it hits an electron
here and an electron here;
forget this one for now.
Okay, everybody got me?
At a given time,
these two electrons are being
pushed up;
then they're going to be pushed
down, as this wave passes by.
Okay, now as those two get
pushed up and down,
they give off waves in almost
all directions;
all directions for our purposes.
So they give off waves in all
different directions.
Right?
Now notice the one,
the part of that scattered
x-ray that goes straight
forward,
in the same direction the
original light came in,
is bound to be in-phase with
one another.
Right?
And we can test that with this
line here, because if they're
going right straight ahead,
this one is a maximum when this
one is a maximum.
Everybody with me on that?
And it'll keep that.
So you'll get scattering by
both of them cooperating,
coming out of it straight
ahead.
But how about if it's at an
angle?
Okay, so I can push this up and
change the angle.
How about at that angle,
how much light is going to be
coming out from these two
electrons?
Student: None.
Prof: None,
they exactly cancel each other,
right?
But if I go to this angle,
now they're just as strong as
they were originally,
right?
And then it'll go weak,
weak, weak, weaker,
weakest, nothing;
then stronger,
stronger, stronger,
stronger, very strong,
weaker, weaker,
weaker, weaker,
weaker, zero.
So there'll be a modulation --
as you go out at different
angles here,
going either up or down,
it'll be strong,
then nothing,
then strong,
then nothing,
strong then nothing.
Right?
So now what will determine,
what will determine how
frequently these angles recur,
at which reinforcement occurs?
Is that clear, the question?
What determines the angles?
Yeah -- pardon me?
Student: The wavelength.
Prof: Ah,
obviously the wavelength.
What if the wavelength were
very, very, very short?
Student: Lots of angles.
Prof: Then you'd get
lots of them.
You wouldn't have to do it very
much before the next one came
in, if they were very -- what
else determines it,
besides the wavelength.
Yes John?
Student: The distance
between the two of them.
Prof: The distance.
That's what we're really
interested in,
is using this;
knowing the wavelength of the
x-rays, using this to measure
distance.
Okay?
Now let's forget the one on the
bottom here.
Let's put this one in.
Okay?
Now -- oh okay,
for reference let's look at the
bottom a second.
So the first reinforcement came
here, between the top one and
the bottom one.
Everybody with me?
How about for the top one and
the middle one,
where did the first one come?
You had to go to a higher
angle, there,
to get reinforcement between
the top and the middle.
Right?
So the closer things are
together, the fewer the angles
are.
Everybody with me on that?
Notice that's a reciprocal
relationship.
The closer things are in what
we call 'real space,' the
distance between the electrons,
the further apart are the rays
that come out,
in angle.
Okay?
So it's backwards.
Closer together,
further apart,
in what's called 'reciprocal
space.'
Okay, now suppose you had a
whole row of electrons that were
evenly spaced.
Okay?
So here's the first,
the second, the third.
Now we'll take all three of
them.
Right?
And what you notice is that as
we go out it gets weaker,
weaker, weaker,
weaker, weaker,
weaker, weaker,
weaker, weaker.
Now when we get to the angle
here, where the first and the
third were very strong,
what do we see now?
The one in the middle cancels
the first one,
and if it were a very long row
of them,
the fourth one would -- here
the second one cancels the first
one --
the fourth would cancel the
third,
the sixth would cancel the
fifth, and so on,
and you wouldn't get anything.
Right?
But then you'd get it again
when you got to the second.
The one that would've been the
second angle,
if it was just one and three,
will be strong,
because this one halfway in
between will reinforce.
Right?
So closer together,
further apart.
And if you have a whole row of
equally spaced things,
they'll all be together,
according to whatever the
distance between successive ones
is.
Yes, Shai?
Student: What are the
chances that electrons are going
to be spaced evenly along --
Prof: Ah,
what could cause electrons to
be spaced exactly evenly?
Student: A crystal.
Prof: A crystal;
x-ray crystallography, right?
So that's why you use crystals.
Okay, that's what we want to
say here, I think.
<<Technical
adjustments>>
Prof: Okay,
so that's the wave machine.
And if you want to do it in the
privacy of your room,
you can go to this website at
Stonybrook and download
something that allows you to run
a Java applet that does sort of
this kind of thing.
This, if you blow it up in
there, the waves look sort of
funny there,
at the atoms,
and the reason is because
you're measuring the phase
perpendicular to different
directions of the wave.
That's just to help you out,
if you try this and have -- and
are confused by that.
Okay, now there are -- so
suppose you have just an
arbitrary set of electrons,
and the waves coming in and
hitting them,
what directions will you get
reinforcement in?
Well there are two directions
that you're guaranteed,
no matter what the spacing is,
and that's this.
Here the light comes in and
goes out.
So the direct beam,
you have the same path,
because one of them gets hit
earlier,
but has a longer path coming
out, and the other one gets hit
later but has a shorter path
coming out.
So they're guaranteed to be
exactly in-phase if they're
scattering straight ahead.
Okay?
But only a little of the light
is getting scattered.
Most of it is the direct beam.
So you don't even notice the
difference, from that.
So that's not very exciting.
But there's another angle at
which you're sure that these two
are going to be in-phase,
and that's this angle.
Now how do we get to that angle?
I've lost some of the -- since
you downloaded it there's some
more stuff in here now.
But -- so now I can't quite
remember, let me just try.
Okay, so this blue line here is
called the scattering vector,
and that's how different the
arrow coming out is from the
arrow going in.
Right?
That's just a funny
mathematical or geometric thing
that people have defined;
they call it the scattering
vector.
Right?
Now this length is exactly the
same as that length.
This length is exactly the same
as that length,
and when you turn at a given
angle,
those two will -- the vector
between those will be
perpendicular to the direction
they're going,
and they'll be in-phase again.
Right?
And if you draw the line that
connects the two points,
notice the scattering vector is
perpendicular to that line.
So you say that this incoming
wave was scattered perpendicular
to this line.
That's how a mirror works.
Right?
That angle is called the
specular angle,
because speculum is the
Latin word for mirror.
Right?
So you're bound to get
reinforcement at the specular
angle, and you know that from
having looked at mirrors.
Okay, now suppose there were
another electron on that same
line or plane.
Okay?
For the same reason it's
guaranteed to be in-phase.
So everything on that plane
will scatter in-phase at that
particular angle.
They'll all reinforce one
another.
Great.
So all electrons on a plane
perpendicular to the scattering
vector, scatter in-phase at the
specular angle.
Now suppose you have a whole
bunch of electrons and you have
to figure out how they're going
to reinforce or cancel one
another.
There's a trick you can use.
You see if you can discern a
set of planes that are evenly
spaced, that contain all,
or almost all,
of the electrons you're
interested in.
Okay, now if you look at this
pattern, you can see that
there's a set of planes,
equally spaced,
that passes through all of
them.
Can you perceive it?
There.
Okay, there are three electrons
on the first plane,
four on the second,
two on the third and one on the
fourth.
Okay?
Now why is that handy?
Okay, so there's the scattering
vector, perpendicular to these
planes, and all the electrons on
any one plane will scatter
in-phase with one another.
Okay, so it's as if there were
a single electron three times
bigger,
or four or two or one,
on those successive planes,
because they're all going to be
in-phase with one another.
So we could pretend they're all
at one point,
on any given plane.
Okay?
So now all we have to worry
about is the phase relationship
from one plane to the next.
Got that?
If they were in-phase from one
plane to the next,
as well as on the planes,
then everything will be
in-phase and you'll get really
bright reflection coming out at
that scattering angle.
Okay?
Now, so let's think -- so it's
as if we had these collected
electrons all lying on the
scattering vector and we want to
know whether they're in-phase
with one another.
Okay, so here's light that
comes in and out at a certain
angle from the first one;
three electrons worth of
scattering from that,
the ones that were on that
plane -- okay?
-- and four from the second
plane.
Now are the three and the four
in-phase with one another?
What condition would have to
apply in order for those to be
in-phase with one another?
They have different path
lengths, but if the paths differ
by an integral number of
wavelengths,
then they'll be in-phase with
one another and reinforce.
Okay?
So there's the path difference
in red.
If that happens to be --
suppose the wavelength of the
light,
and the angle of the scattering
-- which also determines that
path difference,
as you can see -- suppose that
the wavelength and the angle are
such that that happens to be one
wavelength?
Okay, so those are in-phase
with one another;
all seven will be scattering
together.
Right?
How about the next one,
with two electrons,
how about its phase?
What was the condition we
talked about,
up here at the top?
Student: Evenly.
Prof: Evenly spaced.
So what do you know about the
next one?
Student:
>
Prof: It's going to be
in-phase too,
two waves behind the first one.
Right?
It'll be two wavelengths behind
the first one,
exactly, at some angle.
Right?
And the next one will be three
wavelengths behind.
So all these electrons are
going to be scattering in-phase
at that particular angle.
So you get a really strong
reflection coming out.
Right?
It'll be as if it were all the
electrons working together.
So the net in-phase scattering
is as if there were ten
electrons doing the scattering.
That's great, right?
Now suppose that the first path
difference, instead -- suppose
you had a different wavelength
or a different angle.
So the first,
between the three and the four,
suppose the difference in path
was half a wavelength.
Then how would it differ?
<<Students speak over one
another>>
Prof: How about between
the first and the second.
Wilson?
Student: Cancel.
Student: The first and
the second?
Prof: The first and the
second, would they exactly
cancel and get zero?
Student: There'd be one
left.
Prof: Why?
Student: There's one --
Prof: Ah,
there are three in the first
and four in the second,
right?
So you got plus three but minus
four.
How about the next one?
Speak up gang.
Students: Plus two.
Prof: Plus two.
And the last one?
Students: Minus one.
Prof: Minus one.
And what's the net scattering?
Student: Nothing.
Students: Zero.
Prof: Zero.
Okay?
So you can see how this is a
neat trick to work.
If you can see in the pattern a
bunch of planes which would
contain the electrons,
then you can figure out in a
particular direction,
how strong the scattering would
be.
Now, we're going to do an
experiment and it requires the
room to be dark.
And so I'm going to start
turning the lights off and ask
Filip to get into position to do
stuff in the dark here.
Okay, and turn this one off.
Okay.
Now I'll show you first what
we're going to do.
So pull out the little thing
there.
And there's a laser that's
focused right here,
but it's too bright,
because the other things we're
going to see are very dim,
which is why we had to turn the
lights off.
So I'm going to put this black
tube there, with a little hole
in the end.
Hopefully I can get it
positioned so that most of the
laser will go inside here and we
won't see it very well.
Let me get it positioned right.
It's a moving target so it's
not so easy.
Okay now, so here's the view
from the ceiling.
There's the screen,
and this laser is coming from
the back of the room and hitting
the screen, right here.
Okay?
Now what Filip is going to do
is put things called diffraction
masks,
which are just slides,
thirty-five millimeter slides,
and he's going to put them in
the path of the light.
And that's, the distance from
Filip to here,
is 10.6 meters;
I measured it.
Okay?
And so put in the first slide
please.
And see this?
Those are all deflections at
different angles.
And what's doing the scattering
is a slide that looks like this.
Okay?
A jail window, right?
Okay, so what it's giving is a
row of dots.
Now I'm going to ask Filip to
do two things here.
First, rotate the slide around
this axis, so rotate it like
this.
What do you think will happen?
You see, right?
The row of spots is
perpendicular to the direction
of the lines.
Okay?
And now I'm going to ask him to
do something else.
I'm going to ask him to twist
the slide like this,
which changes the effective
distance between these.
And notice what happens as he
makes them closer?
Twisting makes them look closer
together, right?
What happens to the spots?
Student: Farther apart.
Prof: Does that surprise
you?
Student: That's that
reciprocal --
Prof: That's that
reciprocal relationship.
When things get closer together
the angles get bigger.
Okay, now things are going to
get darker here.
So I'm going to do some things.
Turn that out and also get the
room light.
Well no, I want to show you
something here first.
Okay, so I'm going to show you
what the masks are going to be
and then we'll show you the
effect from the masks.
Okay, so the next -- so here's
a question for you to work for
homework.
What is the spacing of the
lines on Filip's slide?
How far are the bars in the
jail window apart on that slide,
in order to give a spacing here
-- oh I did the wrong,
I was premature with that -- in
order to get that 10.8
centimeter spacing here,
at a distance of 10.6 meters,
with 63 nanometer wavelength
light?
Okay?
You can use that to find the
distance between the bars on his
slide,
and I want you to do that,
because if you can do it then
you understand how this works.
Okay, but the next one he's
going to show -- not yet but
he'll put it in -- is one that's
a similar spacing,
but of pairs of lines.
There's a pattern being
repeated, pairs of lines.
Okay?
And then he's going to go to a
whole bunch of hexagons of dots,
which we will call benzene,
but it's not exactly like
benzene would be,
a benzene gas,
because they're all oriented
exactly the same way.
Right?
So it's oriented benzene;
that's the next one we're going
to look at.
And then we're going to look at
this one, which is also oriented
benzene.
Can you see the difference in
the pattern between the one on
the top and the one on the
bottom?
Those red lines are a hint.
Student: They're
connected.
Prof: In the bottom
they're all pairs of hexagons,
that are distributed randomly,
where in the top they're
individual ones.
Now then he's going to show you
this one.
How's that different?
Student: Quadrupled.
Prof: It's quartets of
hexagons.
And finally he's going to show
you this one,
which is a crystal of hexagons,
and in a crystal they truly
would be oriented.
Okay?
And then we're going to -- the
pièce de
résistance,
at the end of this sound and
light show, is going to be that.
You know what that is?
It's a light bulb filament,
that he's going to hold up in
the path of this;
so a helix.
Okay, now we're ready to do the
trick.
So we'll mute that and do this,
and if you have a laptop open
you'll need to close it because
we got to --
it's not very bright,
so we have to make it as dark
as possible,
and I have to find my way back
there and close my laptop.
Okay you ready Filip?
Teaching Fellow: Yes.
Prof: Okay,
so first it's going to be pairs
of jail bars.
So how does it look different
from what we saw before?
Student: Like triplets.
Student: Like different
lights in there.
Prof: It's the same kind
of dots but their intensity is
modulated.
They're not just evenly --
they're not just all the same or
slowly dying away as you move
out to right or left.
They come in a pattern.
Okay, now let's do the next one.
This is the one that's benzene,
but randomly,
a random collection of benzene.
So how would you describe that?
Student: A snowflake.
Prof: It looks like a
snowflake.
Oh, my laptop has come on.
>
Go figure.
I'm putting things to cover the
lights up here.
Okay, so it's a snowflake.
Now we're going to look at
pairs of benzenes.
How is it different?
It's still the snowflake.
<<Students speak over one
another>>
Prof: But there are bars
across it.
Everybody see that?
Student: Yes.
Prof: Can we stop the
green blink back there or put
something across it?
That's good.
Okay, now we're going to do
quartets of benzenes.
How does that look?
How would you describe that?
<<Students speak over one
another>>
Prof: It's now got bars
going in both directions,
not just horizontaloid but also
verticaloid;
they're actually vertical I
think, but not quite.
Okay, now a lattice of benzenes.
Isn't that great?
So it takes the same -- it's
the same underlying pattern,
the snowflake,
but it concentrates all the
light that would've been spread
out,
into very, very fine points.
Remember when it was just
pairs, we put bars across,
but it was the same amount of
light coming out,
so that it got focused sort of,
and when we have a whole
lattice it gets fabulously
focused.
I can see things quite far out
from the middle here,
because I'm so close to the
screen.
I'll hold my hand up but you
can't see my hand.
>
They go way out.
So that's what a crystal is.
The crystal takes the same
underlying pattern,
that comes from the molecule,
and focuses it into intense
points at many,
many angles.
So it's like looking at the
scattering from a single
molecule but looking at it
through a pegboard.
You know what a pegboard is?
In a tool shop you used to put
a pegboard up.
It's a piece of masonite or
something that had holes in it,
regularly, and you could put
little hooks in it to hang your
hammer and your saw and whatnot.
So it's as if you have,
you're looking through such a
pegboard at that underlying
pattern.
And now we're ready for the
pièce de
résistance,
which is the light bulb
filament, which is hard to see.
This is why we really needed
the lights out.
We needed it for the snowflake
too because it was so -- so what
do you see for the light bulb
filament?
Students: An X.
Prof: You see an X,
right?
Can people in the back see the
X?
And there are dots along the
arms of the X.
Okay?
So that does it,
you can open your laptops again
now and we'll try to get some
lights back on.
Sorry for straining your eyes.
<<Technical
adjustments>>
Prof: Okay,
so there's the scattering from
these things and we can -- now
so let's try to understand it.
So this was the slide with
randomly positioned but oriented
benzenes.
It turns out that random
positioning generates the same
diffraction as a single pattern
but gives it more intensity.
If we'd just put one hexagon
there you wouldn't have seen
enough from it.
Okay, so here's the pattern you
got from isolated benzenes,
which is that snowflake
pattern.
Right?
And when we had a lattice made
of those,
you saw the same underlying
pattern,
but only at little -- only at
regularly spaced spots that had
to do with how far apart the
hexagons were from one another,
and much more intense,
because all the light that
would be scattered all over the
screen here is focused in those
little dots.
Okay, now the thing that
generated this snowflake was
benzene, or what we're calling
benzene, the hexagon.
Okay, now can you see what we
need in order to understand?
What do you look for in order
to see what directions will give
you scattering?
Ah sorry, I was having so much
fun we went over.
So we'll talk about this next
week.
Thanks.
And thanks Elaine.