Visual physics and mathematics/Crystal structures

A very little grain of salt


Each line represents a bond between two ions in a crystal of NaCl (sodium chloride = ordinary salt). Blue and green distinguish the two kinds of ions. It is a centered cubic crystal. Each Na+ ion is surrounded by 8 close neighbors Cl-. Likewise, each Cl- ion is surrounded by 8 close neighbors Na+. Two nearby ions always have opposite charges, because opposite charges attract each other while charges of the same sign repel each other.

Crystal galaxies
What would we see if we were small enough to be inside a crystal and see its atoms as stars, or if we looked up at the sky in a crystal galaxy?



Cubic galaxy



Diamond sky

A bright line of stars reveals that the line of vision (the line from the center of the eye to the center of the object) is in a plane of stars. These planes are like the faces of a precious stone:



The simple cubic structure
The simple cubic structure is the simplest crystal structure:





The repetition of the same
The simple cubic structure is a stack of cubes in the three directions of space. A crystal structure is obtained by the repetition of the same cell, not necessarily cubic, in one or more directions of space.

A crystal structure can be in two dimensions:



A stack of identical spheres has the structure of a crystal.

A frieze has the structure of a one-dimensional crystal:



The face-centered cubic structure


This structure is obtained by repeating a face-centered cubic cell:



The diamond structure


This structure is obtained by repeating the following cell:



Promenades inside a diamond: