# Primitive vectors of bcc

• potatowhisperer
In summary, the conversation discusses the difficulties in visualizing the direction of primitive vectors in BCC crystal structures and asks for the steps and conditions to determine these directions. It is noted that any unit cell containing one basis is considered a valid primitive unit cell, and that for more complicated structures there may be multiple atoms in the basis. One possible solution is to take the vectors from the origin to two corners and the body center, as there are three ways to choose two out of three corners due to the cubic symmetry. The BCC cubic unit cell is chosen because it represents the symmetry well, while for other primitive unit cells the symmetry is less obvious. The same applies for FCC structures.

#### potatowhisperer

hello
i have browsed this forum for topics about this, and i found them very enlightening and helped a lot in terms of finding the length of the primitive vectors , the problem that i have is with the direction of said primitive vectors , while in fcc they are more or less easy to visualize in BCC they are not .
so my question is , how is the direction in BCC of the primitive vectors found ? i mean what are the steps and conditions followed to get those directions ?

There are several possible solutions.
In general any unit cell that contains exactly one basis is a valid primitive unit cell.

For the basic BCC structure the basis is one atom.
For more complicated crystal structures there may be more than one atom. E.g. for rock salt, NaCl, the primitive unit cell must contain one Na and one Cl atom.
For the diamond structure the primitive unit cell must contain two atoms, as they are not related by a simple translation.

One possible solution is to take the vectors from the origin to two corners and to the body center. You see immediately that there are 3 ways to pick 2 out of 3 corners...
This is due to the cubic symmetry.
In fact, the reason the BCC cubic unit cell is chosen is because it nicely represents the symmetry. For any of the possible primitive unit cells the symmetry is much less obvious. The same is true for FCC.

## 1. What are primitive vectors of bcc?

Primitive vectors of bcc (body-centered cubic) are three vectors that define the unit cell of a bcc crystal lattice. They are used to describe the arrangement of atoms in a bcc crystal structure.

## 2. How are primitive vectors of bcc different from other crystal lattices?

Bcc crystal lattices have a unique arrangement of atoms, with a body-centered cubic unit cell. This means that there is an atom at the center of the unit cell, as well as at each corner. The primitive vectors for bcc are different from other crystal lattices in that they define this specific arrangement of atoms.

## 3. How are the primitive vectors of bcc calculated?

The primitive vectors of bcc are calculated using the lattice parameters, which describe the size and orientation of the unit cell. These parameters can be determined experimentally or mathematically, and are used to calculate the primitive vectors.

## 4. What is the significance of primitive vectors in bcc crystals?

The primitive vectors of bcc are important because they define the basic building blocks of the crystal structure. They determine the shape and symmetry of the unit cell, which in turn affects the physical and mechanical properties of the material.

## 5. Are primitive vectors of bcc the same as lattice vectors?

No, primitive vectors of bcc and lattice vectors are not the same. Lattice vectors are used to describe the arrangement of atoms in any crystal lattice, while primitive vectors specifically refer to the unique arrangement of atoms in a bcc crystal lattice.

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