The characteristic that defines crystals as opposed to glass is order. Crystals are ordered matter. They are constructed as an ordered stacking of molecules or groups of atoms and molecules. They always have a unit, called the unit cell, which can be an atom, a molecule or a group of atoms or molecules, which is repeated periodically in the space filling a volume.
Periodic order, periodicity, is one of the fundamental properties of a crystal. It shouldn’t be difficult to understand this concept of matter ordered periodically. We see it in flooring, in wallpapering or in the brick walls of houses. We use it whenever we want to cover a surface. For example, a brick wall:
|In this wall the distance between each block or brick is always the same. This distance is called period and, as we can see, it changes with direction. The property of matter organised in this way is called periodicity. It’s as easy as that!||In this classic brick-laying arrangement, the bricks are also placed at an identical distance but the period values change. The structure is different but it is also periodic – that is, it is also crystalline.|
Those bricks are the equivalent of what we call unit cell crystallography. To create a crystalline structure you only have to imagine changing those bricks into molecular units. We’re going to help you imagine it by representing each repetitive unit of a molecular crystal as a brick cube from a construction set.
|The unit cell we have chosen is that of pyrite, a very common iron sulphide, a very pretty mineral that is gold in colour.|
|If we place blocks or cells next to each other to form a row, we get a periodic distribution in one direction.|
|If we pack several of these rows in a perpendicular direction, we get a periodic plane in two directions. This is a two-dimensional crystal.|
|Finally, if we stack blocks or unit cells in the third direction, we get a three-dimensional periodic stacking of identical elements.|
This is a crystal. The only difference is that a one-centimetre pyrite crystal contains around 100000000000000000000000 unit cells instead of the three hundred and forty-three in the illustration.
Now, imagine that you find yourself inside this crystalline structure. Place yourself in an iron atom and look around. Then move to another iron atom of another cell and you’ll see that your surroundings are the same. This is another property of crystals: homogeneity.
Now try to move in a particular direction. You will have to negotiate the links that join the atoms with difficulty. Stop and change the direction of movement. Now you’ll see that the difficulty of moving has also changed. This is another highly important property of crystals: anisotropy.
One of the more attractive properties of crystals is their polyhedric beauty. They are solids with a morphology limited by plane faces and straight edges and come together in sharp vertices. In nature, pyrite, the mineral whose structure we have just created, is found in the form of beautiful crystals with different forms. We are going to show how all of these forms are a consequence of the internal periodicity of the crystal.
|Pyrite cubes are very simple to create by stacking the blocks or unit cells so that they delimit a three-dimensional cube with six perfectly plane faces.|
But if we allow the faces to be stepped, then they can form other, different faces. Remember crystals are made up of millions of identical little blocks. Although in detail the faces are stepped, those steps would be imperceptible to human sight.
|For example, if we make the crystal faces perpendicular to the vertices of the unit cell, the resulting crystalline form is the octahedron.|
|If we make the external faces of the crystal perpendicular to the edges of the cube then we get another type of shape, the pentagonal dodecahedron.|
Whether a mineral crystallizes with one form or another, or with combinations of forms, depends on the crystallization conditions. The angles that the different faces of a crystal form depend exclusively on the dimensions of the unit cell, for which they are always constant for a specific compound. This is what is called the Law of constancy of interfacial angles of a crystal.
In nature there are more than four thousand different minerals – that’s four thousand different crystalline structures. And hundreds of thousands of other crystalline structures have been and continue to be obtained in the laboratory crystallizing natural products and new synthesis compounds.
All of these hundreds of thousands of structures can be classified into 230 different groups thanks to another fundamental property of crystals: symmetry.