Lattice, basis and unit cell
Crystal structure · Physics
Study notes
Step 1: Choose a crystal structure. Let’s use a simple cubic lattice. Step 2: Define the lattice vectors: a1 = (a,0,0), a2 = (0,a,0), a3 = (0,0,a), where a is the lattice constant. Step 3: The basis: a single atom at the origin (0,0,0). Step 4: Unit cell: a cube with side a. Step 5: Count atoms in the unit cell. In a simple cubic lattice, each corner atom is shared by 8 cells, so each contributes 1/8. 8 corners × 1/8 = 1 atom per unit cell. Result: The simple cubic unit cell contains exactly one atom.