# Basic cubic centered lattice

1. Aug 15, 2009

### Petar Mali

Do yoh have some nice picture to show why the primitive vectors of basic cubic lattice are

$$\vec{a}_1=\frac{a}{2}(-\vec{e}_x+\vec{e}_y+\vec{e}_z)$$

$$\vec{a}_2=\frac{a}{2}(\vec{e}_x-\vec{e}_y+\vec{e}_z)$$

$$\vec{a}_3=\frac{a}{2}(\vec{e}_x+\vec{e}_y-\vec{e}_z)$$

Thanks!

2. Aug 15, 2009

### kanato

3. Aug 17, 2009

### aanidaani

I'm afraid I don't have a diagram to show you, but it's pretty easy to visualize the primitive vectors by just thinking about it. A primitive vector simply connects two identical lattice points.

So, for instance, the a3 vector translates one-half a lattice parameter in the +x direction, one-half a lattice parameter in the +y direction, and one-half a lattice parameter in the -z direction. If you start at a corner atom in the BCC structure, this will take you to the body center.

I don't know if this helps at all--and it doesn't really answer your question--but it was useful to me when I first learned crystal structures.