# Aren't unit cell and the relevant crystal similar?

"A crystal is formed by a large number of repetitions of basic pattern of particles in space.

The basic structural unit which when repeated in three spatial directions generates the crystal structure is called unit cell."

Problem:

Assume I take some same perfect geometrical cubes and arrange them in all three dimensional directions, a larger box similar to the smaller ones will be introduced.

From this assumption and the information above it, I deduce that a unit cell should be similar to the relevant crystal. That means, the only difference would be lying between their size.

If this is the case, why consider the geometry of unit cell and not directly the respective crystal? We know in the assumption above; the fundamental cubical boxes would be determined by same geometrical information as would the derived cubical box.

That is; if the lengths of three axes of cube are represented by letters $a,b$ and $c$ and the angles between axes are represented by Greek letters $\alpha$, $\beta$ and $\gamma$ then for a cube,

$$a=b=c$$$$\alpha=\beta=\gamma=\pi^c$$

This information is general. It is for all size of cubes. Then, why to define a unit cell and think it simpler to handle with than the crystal?

• The unit cell doesn't really define the crystal shape. The 3D crystal shape depends on a multitude of factors. I think 2500 odd shapes have been detected for the 3D crystals of the mineral calcite. mnh.si.edu/earth/text/2_2_1_4.html – MaxW Dec 22 '15 at 18:10
• The Bravais lattice and the unit cell combine to make a space group. See here: chemistry.stackexchange.com/questions/28507/… for more details. – Jon Custer Dec 22 '15 at 19:18
• A crystal is not similar to its unit cell, nor does the textbook say so. See, you are made out of a large number of atoms; do you look like an atom? Certainly not! – Ivan Neretin Dec 22 '15 at 19:58
• The symmetry limitations (rotations, reflections and mirror images) of the unit cell also limit the crystals. So calcite won't ever form a perfect cube like pyrite can. But as you can see from the number of different calcite crystals the symmetry limitations don't prevent a great deal of variety in the 3D crystal shape. – MaxW Dec 22 '15 at 21:05
• @Man_Of_Wisdom OK, a crystal may grow like that. But it may do otherwise as well. Draw a small square. Draw 4 more similar squares, and attach them to all sides of the initial square. What you see is not similar to the smaller box. Continue by adding more repeating unit cells to all sides of the new figure. This is still a crystal with the same unit cell, but it does not look quite like yours. – Ivan Neretin Dec 23 '15 at 7:02