Question

Which of the following does not represent a unit cell for the given lattice

• A. Cell 1
• B. Cell 2
• C. Cell 3
• D. Cell 4

Answer 1

Answer: (D)

Cell 4

Answer 2

A unit cell must have all its corners at equivalent lattice points. In the given centered square lattice, all lattice points are equivalent. Cells 1, 2, and 3 have corners that are all lattice points of the same type (or can be considered equivalent in the Bravais lattice definition). Cell 4, however, has two corners that are "grid points" (e.g., (4,0), (4,-1)) and two corners that are "center points" (e.g., (3.5,-0.5), (4.5,-0.5)). Since these are not equivalent positions relative to the overall lattice structure when defining the boundaries of a unit cell, Cell 4 cannot be a valid unit cell.