I suppose most of you have seen a crystal at one time or another,
probably in a natural history museum or in a chemical bottle.
Here is an unusually big crystal
dug out of a clay pit in Brazil.
Here's a smaller one,
broken from the side of a cleft in a rock in Arkansas.
But crystals aren't always big, beautiful things like this.
As a matter of fact, crystals are everywhere.
The salt you use to flavor your food for example.
It consists of little crystals of sodium chloride.
You can see their shapes by looking at them
through a magnifying glass.
Little cubical crystals of sodium chloride.
Snow, here are some enlarged pictures of single snowflakes.
Each is a single crystal of water.
Here's a crystal I like especially well,
probably because I made it myself.
It's a crystal of alum.
As a matter of fact, you can make a crystal just like it.
I put some directions in the film notes
in case you want to do it yourself.
You buy the alum you need at a drugstore
and grow the crystal in mason a jar.
If you do do this i'm sure you'll be very much impressed by one thing:
the crystal keeps growing, maybe for a week.
It keeps getting bigger,
but all the time it has plane faces...
meeting in sharp edges.
You can see I haven't ground the faces on this crystal
or polished them at all.
This is just the way the beast grows.
It almost seems as if you were getting something out of nothing.
Something with a shape all its own,
which it decides all by itself throughout its career.
In order to grow a single perfect crystal as big as this,
you have to take pains and let everything happen slowly.
But you can see what's actually happening
by letting things happen a little bit faster,
and looking at the business under the microscope.
I'm going to take a solution of alum
which is just itching to deposit crystals
and make a little pool of it on the microscope slide...
and then add a few little crystals of alum
to give the alum something to deposit on...
and then get myself in focus
and let 'er rip.
There they are, you can actually see them grow
if I turn now to a higher magnification.
The little crystals keep pretty much the same shape as they grow,
just getting bigger.
Naturally they all sit down on the microscope slide
on one of their biggest faces.
So you see the shape of the crystal
depends mostly on what the crystal is made of, and not on its size,
so long as it's free to grow in all directions.
Now crystals don't only grow out of solutions.
They grow out of gases.
Snowflakes, water crystals grow that way,
and one of the places,
one of the most important places where crystals grow
is out of melted materials when you cool them.
Here I've got another powder you can get at the drugstore,
called salol,
which melts to a convenient temperature.
I'll put a little of it on a microscope slide.
I'll carry it over here to the hot plate...
and melt it.
And now let's go over here to the microscope.
There's one growing, turning very slowly in the liquid as it grows
because it hasn't quite sat down on the slide yet.
It seems almost to push those flat faces ahead
through the part that's still melted.
Of course you know that the whole crystal isn't moving
and shoving its front along.
The liquid next to the face is becoming solid
and adding itself to the face.
But it's doing this in such a way
that the stuff added on also forms a flat face,
so the crystal keeps its shape while it grows.
Now, I'll melt this, but
carefully on the hot plate so as to leave just
a little rounded blob of crystal.
That rounded blob will be a single crystal,
but it won't have flat faces,
and I want you to see what happens
when this cools down again under the microscope.
There it goes
growing the faces it wants to have,
filling in the hollows
and squaring off the rounded corners
so that its boundaries are all flat again.
Notice now what happens when two crystals
bump into each other so to speak.
They don't push each other around,
they just stop growing where they meet,
because they've used up all the stuff to grow with there.
So the boundary between two crystals
isn't necessarily one of the natural faces
on either of them.
The boundary line just depends on
how the crystals happened to come together.
When the whole thing is finally frozen
you have a dense mass of crystals.
Maybe no single one of them shows any of its natural faces,
but the whole mass is made up of crystals just the same.
Almost all rocks are made up this way.
Granite is a good example.
Here's a hunk of it.
Let's take a close look at it.
You can see grains of the different colored minerals
which make up granite.
Here's a gray strain of quartz,
here's a grain of pink feldspar,
and the little black flecks are grains of a kind of mica.
And each of these grains will be a single-crystal.
Notice that the three things don't mix together in the solid.
They crystallize out in separate grains.
Before i get through you'll begin to see why.
When you came in,
I was melting some bismuth in a crucible over here,
and it's been cooling,
and crystals ought to have formed on the sides of the crucible,
so that when i pour off the part of the bismuth that's still melted,
you can see them.
Sometimes you can show up the crystals
in a finished piece of metal
by polishing the surface and then etching it carefully
with something that will eat away the metal.
Here's a cast brass door handle
which the manufacturer had polished,
and then over the years
the sweat on people's hand etched it,
and now you can see the boundaries between some of the crystals
which make up that door handle.
In those pieces of metal,
the crystals are much smaller than these crystals
because they've been broken up
when the metal was drawn, or rolled, or hammered into shape.
But the metal is crystalline just the same.
Well, so almost all solid things are made of crystals.
In fact if you ask a physicist these days
to define a solid, he'll probably say
a solid is a bit of matter that is crystalline.
Of course that doesn't seem to get them very far
because somebody is sure to ask what do you mean by crystalline.
But he's got an answer to that one.
The answer comes in two parts.
The first part says all matter is made of atoms.
The second part says in crystalline matter
the atoms are arranged in regular order.
I want to talk a little more about what he means by this,
and show you a little of the evidence for it.
The idea is that the crystal is a pattern of atoms,
a regularly repeated pattern of atoms
like the regularly repeated pattern of the wallpaper.
If the atoms were flat
and made a two dimensional crystal
they might be taking up an orderly arrangement,
like this arrangement of pennies on the table.
In three dimensions,
they might be making an arrangement like these bearing balls,
closely packed together.
Of course, these close packed arrangements
aren't the only arrangements the atoms might take.
They're just simple examples of what I mean.
Now already perhaps
you can see what these two ideas -
the idea that the crystal is made of little units,
atoms or molecules, all alike,
and that those little units
are arranged in the crystal in a regular array -
you can see how those two ideas
would explain what you've been looking at under the microscope.
For instance, those alum crystals
kept the symmetrical shape as they grew.
Now suppose you had a two dimensional crystal,
like with a pattern of atoms like the arrangement of pennies.
There are more atoms and solution, all around it,
but since the arrangement is symmetrical in the crystal,
you expect pennies to add themselves on at the same rate here,
and here,
and here, and so on,
because conditions are the same with all those places.
The crystal will grow symmetrically
and keep its shape
so long as nothing gets in the way
and prevents more atoms from reaching the surfaces.
Let me show you another kind of evidence for these two ideas.
It's the kind of evidence which doesn't come from the process of growth.
It comes from the properties of the finished crystal.
This is the evidence of cleavage.
If you ever handled mica, you're acquainted with cleavage.
The mica crystals you find in nature
come apart easily in one direction
and not in any other,
so that you can split them into extremely thin tough sheets.
The mica acts as if it was made like a book,
with a lot of leaves of tough paper,
but if you actually try it,
you'll get the feeling that there's no limit
to the thinness of those leaves of paper.
You'll feel that if you were skillful enough,
you could split each leaf of the mica in two,
and then each of those in two again, and so on.
It makes you guess that the atoms in the mica
are arranged in great sheets,
but the atoms are bonded together very tightly in the sheet,
and the bonding forces between the sheets are very small.
Just the arrangement of atoms in sheets like that is a kind of orderliness.
There aren't many crystals that cleave as well as mica.
Alum for example doesn't cleave at all,
bus a great many crystals do cleave amazingly well.
Let me show you the cleavage in this crystal.
It's a crystal of nickel sulfate hexahydrate.
It cleaves parallel to this face.
I'll put the thing down on a little plaster seen to hold it in place.
I'll take a single edge razor blade,
and direct the blade parallel to the face,
and give the back of the blade smart tap.
She comes apart.
And now look at that,
as flat as you please.
You may say: oh you picked a special place in the crystal.
But look,
I can cleave it again,
parallel to that same face,
and get a thin plate out of the thing.
So it isn't a special place in the crystal.
It's a special direction in the crystal.
Now, maybe you'll say
all that isn't any special direction,
you've got a sharp razor blade and you're cutting the thing apart with it.
Alright, if that's what you think,
let me try the same stunt in a different direction.
I turn my razor blade in a different direction
and I whack it,
and nothing much happens,
until I whack it a lot harder,
and finally, of course, the thing busts
and there's no nice flat face.
It's just broken apart like anything else.
Now let me show you the cleavage in another crystal,
a crystal of sodium nitrate.
Here's a crystal
that cleaves in three directions, not just one.
I can cleave it here, like this...
and I can cleave it here, like this...
and here, like this.
By the way, you can grow both of these crystals,
nickel sulfate and sodium nitrate,
by recipes given in the film notes
in case you want to play around with the stuff yourself.
Sodium nitrate has a lot of interesting properties.
It has most of the properties of the mineral calcite.
When big crystals of calcite
were first discovered about 300 years ago,
in a quarry in Iceland,
the scientists of that day got hold of some
and their studies of the stuff
made the first big start in our understanding of crystals.
As I say, sodium nitrate and calcite have many properties in common.
In particular, they both cleave the same way.
When those earlier scientist saw the way calcite cleaves,
they had the idea
that maybe calcite was made of tiny building blocks,
all alike,
and all having the shape of little cleavage blocks of calcite.
You may be inclined to laugh at this
and say the calcite, like all matter, must be made of atoms,
and atoms don't look like building blocks.
Okay, you're telling me.
What do the atoms look like?
Little hard round iron pellets?
Don't let me fool you with those pennies
and bearing balls I've been showing you.
They just show where the atoms are,
not what the atoms look like.
For all I know, the atoms look like four leaf clovers.
I want to emphasize that those early scientists
produced both of the main ideas
which go into the picture of a crystal that we have today.
First, they were saying
crystals have an ultimate fine structure:
the building blocks.
We would call them small groups of atoms instead of blocks,
but the difference is really more a matter of words
than of anything else.
Second, they were saying
that structure has a regular array.
The blocks are stacked up in a regular order,
and they keep stacking up in regular arrangement
as the crystal grows.
It turns out that you can think of any crystal,
not only crystals which show cleavage, but any crystal,
as made of little blocks, stacked up in regular array,
without overlapping, on top of one another,
and side by side,
if you choose the right shape of block.
In the case of alum the right shape of block is a cube,
and you can think of the alum crystal
as made of little cubes,
all stacked up,
on top of one another, without overlapping, this way.
Notice that I've made the main faces
on the model of the alum crystal
by stepping back the cubes as I piled them up.
At first you might think that would mean
that the faces would be pretty rough.
But you got to remember that these little cubes
are really only a few atoms wide.
Their sides are only about one ten-millionth of a centimeter long,
and you wouldn't feel that roughness,
or even see it under the microscope.
One of the things that gave early support to the building block idea
was the fact that all crystals of the same stuff
have the same angles between corresponding faces.
The crystals might be very different in size,
they might have grown at different rates on different faces,
so that they have different overall shapes,
like these two alum crystals.
Nevertheless, the angles between corresponding faces
of all crystals are the same,
so long as the crystals are made of the same material.
It also suggests very strongly
that each material forms its own building block,
which gets repeated again and again
as the crystal grows.
Most crystals can't be made out of cubic building blocks
as alum can.
Their building blocks don't have the same length on the different directions.
For example, here is the arrangement of atoms
in the cubic building block for iron.
It's fairly simple.
Now look at this model of the building block for garnet.
It represents an elaborate grouping of a hundred sixty atoms.
But this study isn't easy,
don't get the idea you can turn on the x-rays
and out rocks the answer.
It's a very specialized kind of study.
But once we know what arrangements atoms take in crystals,
we can begin to add why they take those arrangements.
We're really only just beginning to get that kind of knowledge.
Now, turn back for a moment to the microscope
and remind yourself of what is happening while a crystal grows.
Atoms are constantly arriving at the surfaces
and adding themselves onto those surfaces in an orderly way,
and they're doing this at an amazing rate of speed.
The crystals you're looking at are going fairly fast.
Suppose a crystal grew at the rate
of only a couple of millimeters a day, which is fairly slow.
You can calculate
that about a thousand layers of molecules
would have to be laid down per second on the surface of that crystal.
And all the molecules have to be laid down
in the right sort of order.
I want to borrow a trick from Sir Lawrence Bragg
to give you just a rough idea
of some of the things that we think must go on as the crystal grows.
Sir Lawrence blows soap bubbles.
He blows them in a pan of soapy water,
tiny bubbles which rise to the surface
and collect in rafts.
The bubbles behave a little like atoms because
when they're floating on the water
they attract one another a little,
and when they touch,
they stick to one another quite strongly, as atoms do.
But again, like the atoms,
they have a squashy sort of size,
so that they take up space.
Watch how the bubbles collect together into an orderly arrangement.
It's the same as the arrangement of pennies I showed you,
the so-called close-packed arrangement.
Notice that the rafts are made of large parts.
All of the parts have the same sort of order,
but the orderliness of the parts is turned in different directions,
so that there are grain boundaries between the parts.
This is like a solid made of lots of crystals
which started growing in different places and finally joined.
It's like the salol after it's all solidified,
or that brass door handle.
When you think of how fast the atoms have to get into order,
much faster than this,
the more astounding their achievement seems to be.
But this will give you some little idea
of what a hustle and bustle must really have to go on
on an atomic scale.
Sometimes, when the molecules are very big
and have an irregular shape,
they're too sluggish to get themselves arranged in the order.
Then they congeal into a glass.
A glass is very much like a liquid,
but it's like a liquid in which the molecules
are no longer able to move past each other.
It has patterns of order in the midst of disorder.
The disorder is frozen in place so to speak,
and can't get itself rearranged into order.
Liquids and glasses are pretty disorderly arrangement of molecules,
and gases are the most disorderly arrangements of all.
The only order in gases
is the arrangement of atoms grouped in each molecule of the gas.
Later in this course, you'll learn more about gases.
But already you can see why gases
are still very much alike in a great many ways,
whereas there are so many different kinds of solids.
The only way gases can differ
is in the kinds of molecules they are made up.
But solids can differ also
in the kind of orderliness which those molecules take up
in the crystals which comprise the solid.
I can show you this selectiveness
actually happening in some of the materials you already looked at.
I'll melt some salol on the hot plate over here.
There...
I bring it over to the microscope and let it cool down,
so that it wants to crystallize,
then I'll seed the salol
with a tiny crystal of alum.
Nothing happens.
No salol will crystallize on it.
Now I'll seed the melt...
with a few little crystals of salol,
and you can see the salol crystals grow,
leaving the alum crystal unaffected.
The orderliness of alum is not the right kind of orderliness for salol,
and the salol simply waits
until the right kind of orderliness is presented to it.
And I think now you can see what I promised you would see about granite,
why it is that the three different ingredients,
quartz feldspar, and mica,
form three separate kinds of crystals in the granite,
and don't form just a single crystal
in which the molecules of quartz, feldspar and mica all take part together.
It's because those three kinds of molecules
normally form crystals with three different kinds of order.
When the three kinds of molecules are all together,
they can't find a kind of order which is common to all three of them,
so they crystallise out separately,
each in its preferred way.
You know, after 20 years of growing crystals,
I still find the whole business nearly miraculous.
You go to the microscope to watch it,
and it happens again,
and you know that the atoms are at work,
busily, almost unerringly constructing something,
something regular, something orderly,
constructing something, which from an atom's point of view,
is simply enormous.
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