Question

The smallest repeating unit of a crystal lattice is called

• A. Unit cell
• B. Primitive cell
• C. Wigner–Seitz cell
• D. Crystal system

Hint:

Think of a unit cell as a decorative wall tile. By placing identical copies of this tile side-by-side, you can cover an entire wall (the crystal lattice) perfectly.

Answer 1

The Correct Option is A

Concept: A crystal structure is formed by a periodic, three-dimensional spatial arrangement of atoms, ions, or molecules. To simplify the mathematical and geometric tracking of these complex systems, the entire infinite structure is partitioned into small, identical building blocks called unit cells.

Step 1: Defining the Unit Cell and its properties.
A unit cell is defined as the smallest structural subdivision of a crystal lattice that retains the complete symmetry and structural characteristics of the overall crystal. By shifting this basic geometry repeatedly along its primary axes (lattice translation vectors \(\vec{a}, \vec{b}, \vec{c}\)), the entire long-range periodic lattice can be constructed seamlessly without creating any gaps or overlaps.

Step 2: Distinguishing from other concepts.
Let us analyze why the general definition points specifically to the standard unit cell over the other choices:
• Unit cell: This is the standard, broadest definition for the repeating block. It can be primitive (containing 1 lattice point) or non-primitive/conventional (containing multiple lattice points, like FCC or BCC, which are preferred because they preserve the full geometric symmetry of the system).
• Primitive cell: This is a specific subset of a unit cell that contains exactly *one* net lattice point. While it is a smaller unit cell, it is not always chosen as the standard repeating unit because its shape often obscures the higher orthogonal rotational symmetries of the lattice.
• Wigner–Seitz cell: A highly specialized type of primitive cell constructed around a single lattice point by drawing perpendicular bisector planes to all neighboring points. It is predominantly utilized in advanced solid-state band physics.
• Crystal system: A broad classification grouping scheme (such as cubic, tetragonal, monoclinic) based on axial lengths and angles, rather than a physical repeating physical volume element. Hence, the overarching general term for the smallest repeating unit is the Unit cell.