BrightKidz Library
Subjects
A crystal grows in layers, and the layers stay parallel Three six sided shapes sit in a row. Each one is drawn as a set of outlines nested inside each other like the rings in a tree stump. The shape on the left has two rings, the middle one has three, and the one on the right has four. Every ring in a set has exactly the same six sided shape as the one inside it, only larger, so the sides of the outer rings run parallel to the sides of the innermost core.

Why a Crystal Has Flat Faces

About 18 minutes

You already know that the flat faces of a crystal are the outside of a pattern too small to see, and that the pattern is atoms stacked in the same small arrangement over and over.

That one sentence quietly leaves two questions lying around, and this article is about both of them.

Why flat? A pattern of atoms is not a chisel. Nobody is smoothing anything.

And why those flats? A crystal does not come out as a random lump with random sides. It comes out with the same angles, every time, in every specimen — and that turns out to be the most useful fact in the whole subject.

Blocks cannot make a curve

Start with the flatness, because it is the easier half.

Get a box of identical building blocks and stack them. Now try to build a smooth slope. You cannot. You can make a level top, because the blocks sit in rows. You can make a clean diagonal, because a stack that steps across by exactly one block each time comes out perfectly straight.

Anything in between comes out as a staircase.

Why a stack of identical blocks can only have some flat sides Two shapes built out of identical small squares. The shape on the left has a flat top along a row of squares, and a clean slope where each square steps across by exactly one square, so both of those edges come out perfectly straight. The shape on the right is trying to make a gentler slope, and because the squares can only step by whole squares it comes out as a staircase instead. A dashed straight line drawn over the staircase shows the smooth edge that shape cannot make. both of these are flat runs the pattern allows this one cannot be flat the dashed line is what it cannot make Identical blocks, stacked. Only some directions come out smooth.
Identical units, stacked. A few directions come out perfectly smooth. Every other direction is steps, however carefully you build.

That is the whole reason a crystal has flat faces and not curved ones. It is not being carved. It is being built, out of parts that are all the same size and can only sit in certain places — and a thing built that way has some directions that come out smooth and a great many that do not.

The smooth directions become faces. The rest never get the chance.

The one thing that never varies

Now the harder half, and the discovery that started the whole science.

In 1669 a scientist called Nicolaus Steno got hold of a lot of quartz crystals and did something nobody had thought was worth doing. He measured the corners.

Quartz turns up in wildly different shapes. Long and needle-like, short and stubby, chipped, lopsided, some the size of a grain and some the size of your arm. Steno measured them anyway, and found that the angle where two faces meet came out at 120 degrees every single time.

Not roughly. Not usually. Every crystal, whatever it looked like.

Three quartz crystals of different sizes, all with the same corner angle Three six sided shapes drawn side by side, each one an end on slice through a quartz crystal. They are all different sizes and none of them is regular: every side is a different length and no two shapes look alike. One corner on each shape is marked with a short line across it and labelled one hundred and twenty degrees. The three marked corners are identical even though the three shapes are not. 120° 120° 120° every side a different length bigger, and a different shape again small and lopsided Nothing about the shape is fixed. The corner is. Every quartz crystal anyone has measured, at any size, gives 120° at this corner.
Three quartz crystals sliced across and drawn end-on. Every side is a different length and no two shapes match. Every corner is 120 degrees.

Table salt does the same thing with a different number. Salt grains are cubes, so their faces meet at 90 degrees — and the first article already asked you to tip some onto dark paper and look. Now you know what you were looking at. That 90 was not a coincidence of the grain you happened to pick. It is what salt does.

This is the part worth holding on to. The size of a crystal tells you nothing. The shape tells you almost nothing. The angle tells you what it is. For well over two hundred years, long before anyone could show that atoms were real, a protractor and a good eye were how people worked out what was inside a rock.

Why the shape can change while the angle cannot

So why does the angle survive when nothing else does?

Because of how a crystal gets bigger. It does not stretch and it does not swell. It grows the way a wall gets taller: by having another layer laid on the outside. Atoms arrive from the liquid or the gas around it, find a spot on the pattern, and lock into place.

And a new layer laid flat on an existing face is parallel to it. It has no choice. It is sitting on the face, following the same rows of atoms.

Adding layers to a growing crystal A small eight sided core sits in the middle of the picture. Four of its sides are flat, running level or upright, and four are cut corners set at a slant. Layers can be added around the core one at a time, and each new layer keeps every side exactly parallel to the side it was built on. The slanted corner sides move outward much faster than the flat ones, so with each layer the corners get shorter, and by the last layer they have vanished altogether and the shape is a plain square. The flat sides never change direction at any point. the flat sides meet at 90 degrees, at every layer growing fastest, and vanishing growing slowest The bold shape in the middle is the crystal you started with. Watch the slanted corners, not the flat sides.

Add layers to a young crystal one at a time and watch what happens to the shape.

The shape changes enormously between the first ring and the last. The directions of the sides never move at all. Every ring runs parallel to the one inside it, because every ring was built on top of it.

That is why the angle outlives the shape. The angles were settled by the pattern before the crystal was big enough to see, and no amount of growing can argue with them.

The faces you can see are the slow ones

Watch that slider again, and this time watch only the four slanted corners.

They are growing faster than the flat sides — much faster. And they are the ones that disappear.

That sounds like it must be a mistake, and it is the best thing in this article. A face that grows quickly races outward, and as it does, the two faces on either side of it close in behind and meet. The fast face runs out of room and shuts. Meanwhile the slow, lazy faces have nowhere to go but sideways, so they spread out and take over the whole crystal.

As a rule, then: the faces you can see and hold and measure on a finished crystal are, mostly, the slowest-growing surfaces it had. The energetic ones grew themselves out of existence early on and left no trace.

A young crystal has some faces growing fast and some growing slowly. Which ones are still there on the finished crystal?

Next time you pick up something with flat faces and sharp edges, put your thumb in one of the corners. That angle was decided by the arrangement of atoms inside, before the crystal was big enough for anyone to notice, and nothing that happened afterwards was allowed to change it.