Bravais Lattice

A Bravais lattice is simply a repeating pattern of arrangement of atoms with all points in pattern being equivalent. Alternatively, it is the lattice in which atoms present at all latice points are identical.

Determining lattice points

In a given lattice, we can select a random point and examine its surroundings. We will notice that, if a repeating pattern exists, there will be surrounding points to the reference point which have identical surroundings themselves. Once all such surrounding points are found, we have essentially found out a lattice, and the points that make this lattice are called lattice points.

Examples of Bravais lattice

The simplest example for a Bravais lattice is a square lattice.

Primitive vectors

Primitive vectors are the vectors with which a Bravais lattice can be re-constructed. Formally, a Bravais lattice (in three dimensions) can be defined with primitive vectors, as a collection of all and only those points in space that are reachable from origin with the position vectors defined as $$\bar r = n_{1}\bar a_{1} + n_{2}\bar a_{2} + n_{3}\bar a_{3}$$ where it is necessary for $n_{1}$, $n_{2}$, $n_{3}$ to be $0$ or a negative/positive integer. The three vectors used above are the primitive vectors. This experiment now aims at giving an understanding of defining primitive vectors.