# Crystal lattice structure finder for unit cells, packing factor, and density
This crystal lattice structure finder helps connect the picture of a unit cell with the calculations that students and materials scientists usually need next. You can inspect metallic, ionic, covalent, and ceramic structures, then calculate atomic packing factor, coordination number, atoms per cell, atomic radius from lattice parameter, cell volume, cell mass, and theoretical density from real material presets or custom inputs.The interactive viewer is designed for the common difficulty in crystallography: boundary atoms are visible, but only a fraction of each boundary atom belongs to the selected cell. Rotating the model makes the difference between corner sites, face sites, and interior sites easier to see before you use the numerical formula.# Simple cubic, FCC, and HCP compared
| Structure | Net atoms per cell | Coordination number | Atomic packing factor | Typical examples |
|---|---|---|---|---|
| Simple cubic | 1 | 6 | 52.36% | Alpha polonium is the classic elemental example. |
| Face-centered cubic | 4 | 12 | 74.05% | Copper, aluminum, nickel, silver, gold, and many ductile metals. |
| Hexagonal close-packed | 6 | 12 | 74.05% | Magnesium, alpha titanium, zinc, cobalt, and beryllium. |
# Atomic packing factor formula
Atomic packing factor is the fraction of unit cell volume occupied by hard-sphere atoms. It is calculated as APF = volume of atoms in the cell / unit cell volume. For simple cubic this becomes pi / 6 because one atom of radius a/2 fits into the cubic cell. FCC and ideal HCP both reach about 0.7405, which is the maximum packing fraction for equal spheres.Packing factor is not the same as density. APF describes how efficiently identical spheres fill space, while density also depends on molar mass and lattice dimensions. A light HCP metal and a heavy FCC metal can have similar packing factors but very different densities.# Theoretical density formula used by the calculator
The calculator uses rho = nM / (NA Vcell). In this equation, n is the number of atoms or formula units per cell, M is molar mass in grams per mole, NA is Avogadro constant, and Vcell is the unit cell volume in cubic centimeters. Cubic cells use a^3. Hexagonal cells use (3 sqrt(3) / 2) a^2 c, with c supplied through the c/a ratio.Because lattice constants are usually tabulated in angstroms, the calculator converts angstroms to centimeters before computing density. A small change in lattice constant can noticeably affect density because volume scales with the third power for cubic cells.# How to use lattice presets for metals and minerals
- Copper and aluminum: compare two FCC metals with the same net atoms per cell but different molar masses and lattice constants.
- Magnesium and alpha titanium: inspect HCP packing and see how c/a ratio changes the hexagonal cell volume.
- Alpha polonium: study the rare simple cubic structure and its lower packing efficiency.
- Halite: practice formula-unit density with a mineral-style NaCl conventional cell instead of a single-element metal.