Calculate unit cell properties for cubic crystal structures (SC, BCC, FCC) in materials science and crystallography
Last updated: April 2026 | By Patchworkr Team
The edge length of the cubic unit cell (1 Å = 10⁻¹⁰ m)
If provided, calculates the required lattice parameter
V = a³
r = a/2 | Atoms = 1 | Coordination = 6 | Packing = 52.4%
r = (√3/4)a | Atoms = 2 | Coordination = 8 | Packing = 68.0%
r = a/(2√2) | Atoms = 4 | Coordination = 12 | Packing = 74.0%
PF = (N × V_atom) / V_cell
A cubic unit cell is the smallest repeating structural unit of a crystalline solid that exhibits cubic symmetry. In crystallography, the unit cell is like the "building block" that, when repeated in three dimensions, creates the entire crystal structure. The cubic system is one of seven crystal systems and is characterized by three equal-length axes (a = b = c) that meet at 90-degree angles.
There are three main types of cubic unit cells: Simple Cubic (SC), where atoms are located only at the corners of the cube; Body-Centered Cubic (BCC), which has an additional atom at the center of the cube; and Face-Centered Cubic (FCC), which has additional atoms at the center of each face. Each structure has different atomic packing efficiency, coordination numbers, and physical properties.
The packing fraction indicates how efficiently atoms fill space in the structure. FCC has the highest packing fraction (74%), making it the most efficient cubic structure, followed by BCC (68%) and SC (52%). The coordination number tells how many nearest neighbors each atom has, which affects bonding and material properties. Common examples include iron (BCC), copper (FCC), and polonium (SC).
Step 1: Select the type of cubic unit cell: Simple Cubic (SC), Body-Centered Cubic (BCC), or Face-Centered Cubic (FCC).
Step 2: Enter the lattice parameter (a), which is the edge length of the cube, typically measured in Ångströms (Å). For reference, 1 Å = 10⁻¹⁰ meters = 0.1 nanometers.
Step 3: Optionally, enter the atomic radius (r) to calculate what lattice parameter would be required for that atomic size in the selected structure.
Technical Details: The calculator computes the unit cell volume (a³), the number of atoms per unit cell (considering fractional atoms at corners, faces, and body center), the coordination number (nearest neighbors), and the atomic packing fraction (percentage of volume occupied by atoms). For SC, atoms touch along cube edges. For BCC, atoms touch along body diagonals. For FCC, atoms touch along face diagonals.
Scenario: A materials scientist is studying copper (Cu), which crystallizes in a face-centered cubic (FCC) structure with a lattice parameter of 3.615 Ångströms at room temperature.
Unit Cell Volume: 47.24 ų
Atoms per Cell: 4 atoms
Coordination Number: 12 (each atom touches 12 neighbors)
Packing Fraction: 74.0% (highly efficient packing)
Atomic Radius: 1.278 Å
This high packing fraction contributes to copper's excellent ductility and malleability, as atoms can slide past each other along close-packed planes. The high coordination number also contributes to copper's good thermal and electrical conductivity, as each atom has many neighbors for electron and phonon transfer.
FCC has 8 corner atoms (each shared by 8 cells = 1 atom total) plus 6 face atoms (each shared by 2 cells = 3 atoms total), giving 1 + 3 = 4 atoms per unit cell.
The coordination number is the number of nearest neighbor atoms that touch a given atom. Higher coordination generally means stronger bonding and higher melting points.
Iron (at room temperature), chromium, tungsten, molybdenum, and vanadium all crystallize in BCC structures. These metals tend to be harder and less ductile than FCC metals.
Packing fraction (or atomic packing factor) is the percentage of unit cell volume occupied by atoms, treating them as hard spheres. The remaining space is void/empty space between atoms.
SC has the lowest packing fraction (52.4%) and coordination number (6), making it less stable. Only polonium naturally forms SC structure at room temperature among elements.
Yes! Iron transforms from BCC (room temp) to FCC (above 912°C) to BCC again (above 1394°C). These phase transitions are crucial in steel heat treatment and metallurgy.
The lattice parameter (a) is the physical dimension of the unit cell edge. For cubic cells, all three edges are equal. It's typically measured using X-ray diffraction techniques.
Understanding crystal structure helps predict mechanical properties, electrical conductivity, thermal expansion, and phase transformations. It's essential for alloy design, semiconductor engineering, and materials selection.
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