Posted: March 24th, 2017

Explain how every crystal lattice has a unit cell that has the shape of a parallelopiped and is “primitive” in the sense that it contains only one lattice point.

A crystal consists of a building block (an atom or group of atoms) that is repeated periodically through space. (a) Describe the difference between the “crystal lattice”, the arrangement of lattice points in space, and the “crystal structure”, the arrangement of atoms in space. (b) Explain how every crystal lattice has a unit cell that has the shape of a parallelopiped and is “primitive” in the sense that it contains only one lattice point. (c) Given (b), why do we often choose a unit cell that contains more than one lattice point (for example, the face-centered cubic and body-centered cubic cells)?