What's the difference between lattice vectors and basis vectors?

[Raziel2701]

Google has not been very useful, and Kittel has too little on crystallography. Actually, what's a good source on crystallography?

 

[daveyrocket]

A lattice vector is [itex]\vec{R} = n_1\vec{a}_1 + n_2\vec{a}_2 + n_3\vec{a}_3[/itex] where a1, a2 and a3 are the basis vectors (n's are integers). Generally there are three basis vectors, these form a linearly independent set from which you can construct any lattice vectors. The set of lattice vectors is the set of all lattice points in space. Of course, the basis vectors are also lattice vectors. Any linearly-independent trio of lattice vectors could be chosen as basis vectors. Or it could be a pair if you have a two-dimensional lattice.

Check Ashcroft and Mermin.. I think it has a little more than Kittel.