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The lattice constant is the edge length of a crystal’s unit cell, the fundamental repeating unit that defines the crystal lattice. In cubic systems the unit cell is a cube, so a single lattice constant suffices to describe all three dimensions. The size of this cube is governed by how many atoms fit into the cell and how they are arranged. Visualising the atoms as hard spheres helps to understand the geometric relationships that set the lattice constant.

Identify the Space Lattice

Determine whether the cubic crystal is simple cubic (SC), face‑centered cubic (FCC), or body‑centered cubic (BCC). In an SC lattice, atoms sit only at the cube corners. An FCC lattice places atoms at each corner and at the center of every face. A BCC lattice has an additional atom in the cube’s center. For instance, copper adopts an FCC lattice, iron a BCC lattice, and polonium a SC lattice.

Find the Atomic Radii

Obtain the atomic radius (r) for the element in question. The periodic table provides reliable values: polonium’s radius is 0.167 nm, copper’s is 0.128 nm, and iron’s is 0.124 nm.

Calculate the Lattice Constant

Use the appropriate formula based on the lattice type:

• SC: a = 2 × r
• FCC: a = (4 × r) / √2
• BCC: a = (4 × r) / √3

For example, polonium’s SC lattice constant is a = 2 × 0.167 nm = 0.334 nm.

References

• University of Pennsylvania: Structure of Metals – Close Packing