Single crystal
If want to quantitatively calculate various physical properties of a material, e.g., their electronic structure or heat capacity, we need to know about its crystal structure; how the atoms and molecules are arranged inside the material. In our everyday life, we deal with various single crystals. We all have seen the cubic crystals of common salt or sugar. Some of you have seen the quartz crystal, or some beautiful crystalline stones. Crystals grow in nature; they can even grow in our body. For example, gallstones, kidney stones, they are all single crystals.
So what is the definition of single crystal?
We call a piece of solid is single crystal, if it is made up of repeated translation of a pattern unit. We call this pattern unit basis, which may be a single atom or a group of atoms. The repetition is continued throughout the entire solid and in three dimensions.
Ideally, there should be no grain boundaries or any impurity present in a single crystal. Size of the solid has to be much larger compared to the size of the pattern unit. Size of the pattern units are in the order of few angstroms, while we consider the size of a bulk single crystal is of the order of millimeter or centimeter.
Why is single crystal formed?
Why the atoms gather in a regular pattern? Because this particular arrangement gives the system lowest possible energy.
How can we say that a piece of solid is a single crystal?
The repeated arrangement of atoms in a crystal can be experimentally verified by x-ray diffraction. Laue x-ray diffraction pattern (which we will discuss later in detail) lets us find out the symmetry of the atomic arrangement, and thus determining the crystal structure.
Also, the internal geometry of a crystal shows up in many ways. The binding force of atoms in a solid is anisotropic; the binding force of atoms is stronger in certain directions while weaker in some other directions. Therefore, there are some particular planes along which the crystal can be broken very easily. These are called cleavage planes.
When a crystal is cracked or broken, it breaks along the cleavage planes. So when we see a piece of Sugar or Salt, it may not be a perfect cube, but the angle between the faces are always exactly 90 degrees.
Another reason the internal geometry shows up at the surface, is because how the crystals grow. Imagine a crystal is growing out of a liquid solution. There are atoms floating all around, and finally settling down in the growing crystal when it finds a position of least energy. You can appreciate certain direction in which the crystal will grow faster than some other directions, therefore growing into some kind of geometrical shape.
Because of these reasons the outer shape of a crystal reflects some of the internal character of the atomic arrangement.