solid state chemistry - Confusion in unit cells of crystal system

Unit cells are divided into two main types

1. Primitive


2. Non-primitive

Primitive includes simple cubic lattice whereas non-primitive includes fcc bcc end centered..

Among the seven types of crystal systems orthorhomic crystal system posses both primitive as well as non-primitive unit cells i.e. face centred body centred rnd centred and simple cubic but the cubic system posses primitive , body centred and face centred arrangements only.

My question is if face centred is possible in cubic system why is not end centred type of unit cell arrangement possible in cubic system if there is no sort of hindrance in vacant space as in orthorhombic which posses all types of unit cell arrangements.

Answer

First, a note: the classification of crystal systems, or the reduction of possible lattice types into primitive Bravais lattices, has nothing to do with “space available” or “hindrance”. It is purely a mathematical property having to do with the symmetry of the lattices.

To answer your question, the base-centered cubic lattice is not a Bravais lattice, because it is equivalent to a simple tetragonal lattice: