Linus Pauling: Another example of a silicate, a silicate with different properties is provided by asbestos. This is a hard rock. It consists,
it has nearly the same composition as the feldspar, Mg3Si2O5OH4. If I take hold of this rock, I can pull it apart into little, minute, very thin fibers. The reason for this, of course,
is that the atoms are arranged along long lines, or are bonded along, just to the one axis in the crystal. This is another
form of asbestos. It is a form in which there are sheets that are rolled up into minute cylinders that run in this direction,
and they are piled so loosely together that they fall apart.
Then there are minerals such as mica. Here I have a specimen of mica. It is pseudo-hexagonal. These are natural faces.
It has the black phase present in granite. In mica, the atoms are held together by strong bonds in layers, and these layers
are only loosely attached to one another. I might be able, just by using my fingernail, to get hold of a few million of these
layers and by pulling to separate them from the rest of the crystal, pull it apart in this way. The layers are strong within
the sheet, but they are very loosely superimposed on one another in this crystal.
Now, another example - a metal. Metals have peculiar properties that are characteristic of them. They can be deformed in
a special way. They are malleable, which means that they can be hammered out into sheets. They are ductile, which means
that they can be drawn out into wires.
Here is a piece of copper, a sheet of copper. I can bend it, and it distorts without breaking. It is tough in this respect;
tough and strong. Other metals are still tougher and still stronger – the structural metals. Here are some octahedral crystals,
crystals with octahedral-faced development, of native copper; copper as it occurs in nature. We know the structure of the
metal copper. It is illustrated by the model over here at the end of the table. Here, each of these spheres represents a
copper atom. We know that in a crystal of copper, in the little grains of copper that make up the sheet of the copper metal,
or a copper wire, the atoms are arranged in the way that is shown here, a way such that each atom has twelve neighbors. If
I look at this atom, I can see that that there are six neighbors that surround it in the same plane. Then there are three
in contact with it in the plane below and three in the plane above. This way of arranging spheres in space is one of the
closest-packed ways. There’s no way of getting a given number of spheres into a smaller volume than by arranging them in
closest packing. Each copper atom is 2.55 angstrom away from its neighbor. We may say that the effective diameter of the
copper atom in copper metal is 2.55 angstrom. One angstrom is a 100 millionth of a centimeter, 10 to the minus-8 centimeters.
This crystal of copper with this structure is a cubic crystal. The octahedron is closely related to the cube, and the tetrahedron,
you see here we have a tetrahedron, is also closely related to the cube. This is the way in which cannonballs are sometimes
piled in front of the courthouse on the lawn, in the tetrahedron.
If you are skeptical about the tetrahedron in relation to the cube, I may make a drawing. Here we have a representation of
a cube. If I now connect the corners that are not adjacent to one another, I can connect these corners with one another and,
in this way, get a drawing of a tetrahedron in a different orientation from this one. Well, I think that I can prove that
this has cubic symmetry in a different way. If I start removing copper atoms from this model, I obtain, after awhile, I reach
a state where I can lift out a group that have been fastened together and, you see, that here we have fourteen atoms, obviously
in a cubic arrangement. There are eight at the corners of the cube, indicated here, and then six others that occupy the centers
of the six faces of the cube. The copper crystal has cubic symmetry; each atom is bonded to the twelve surrounding atoms.
