Pick your Cubic Cell Type (simple, BCC, or FCC), choose a Calculation Type, then enter either the Atomic Radius or Edge Length along with the Atomic Mass to get your Primary Result — plus the Coordination Number, Packing Efficiency, and Atoms per Unit Cell for that crystal structure.
Primary Result
--
Coordination Number
--
Packing Efficiency
--
Atoms per Unit Cell
--
The three types of cubic cells are Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). SC has atoms only at the corners, BCC has an additional atom at the center, and FCC has atoms at the corners and face centers.
In a cubic cell, all three lattice parameters (a, b, c) are equal, and all angles are 90°. The lattice parameter 'a' represents the edge length of the cubic unit cell.
The lattice constant depends on the cubic structure: For SC: a = 2r, for BCC: a = 4r/√3, and for FCC: a = 2√2r, where 'a' is the lattice constant and 'r' is the atomic radius.
Different cubic structures have different arrangements of atoms. The formulas account for how atoms touch along different directions - edge, body diagonal, or face diagonal - depending on the crystal structure.
These calculations are based on ideal hard sphere models and provide good approximations for many materials. Real crystals may have slight deviations due to factors like thermal vibrations and electronic interactions.
This calculator is designed for metallic crystals with single atom types. For ionic crystals with different sized cations and anions, specialized calculations considering both ion sizes are needed.
The coordination number (number of nearest neighbors) varies by structure: Simple Cubic has 6, Body-Centered Cubic has 8, and Face-Centered Cubic has 12 nearest neighbors.
Packing efficiency is the fraction of space occupied by atoms. It's 52.4% for SC, 68.0% for BCC, and 74.0% for FCC structures, calculated from the volume of atoms divided by unit cell volume.