Cubic Cell Calculator
Calculate lattice parameters for cubic crystal structures from atomic radius
Calculate Cubic Cell Parameters
Radius of the atoms in the crystal structure
Type of cubic crystal lattice structure
Cubic Cell Results
Lattice type: Simple Cubic (SC)
Formula used: a = 2r
Input radius: 0.000 Å
Coordination number: 6
Crystal Structure Analysis
Example Calculations
Aluminum (FCC)
Atomic radius: 1.43 Å
Structure: Face-centered cubic
Formula: a = 4r/√2
Calculation
a = 4 × 1.43 Å / √2
a = 5.72 Å / 1.414
a = 4.045 Å
Iron (BCC)
Atomic radius: 1.24 Å
Structure: Body-centered cubic
Result: a = 2.86 Å
Cubic Crystal Types
Simple Cubic
1 atom per unit cell
Coordination number: 6
Packing factor: 52.4%
Body-Centered
2 atoms per unit cell
Coordination number: 8
Packing factor: 68.0%
Face-Centered
4 atoms per unit cell
Coordination number: 12
Packing factor: 74.0%
Common Examples
Simple Cubic (SC)
Polonium (Po)
Body-Centered (BCC)
Iron (Fe), Chromium (Cr)
Tungsten (W), Molybdenum (Mo)
Face-Centered (FCC)
Aluminum (Al), Copper (Cu)
Gold (Au), Silver (Ag)
Nickel (Ni), Lead (Pb)
Crystallography Tips
FCC and HCP are closest-packed structures
Higher coordination means more stability
Packing factor affects material density
Atomic radius values from X-ray diffraction
Understanding Cubic Crystal Structures
What is a Unit Cell?
A unit cell is the smallest repeating unit that contains all the structural information of a crystal. When unit cells are stacked together in three dimensions, they form the complete crystal structure. Cubic unit cells are characterized by having all angles equal to 90° and all edges of equal length.
Why Calculate Lattice Constants?
- •Determine crystal structure from atomic data
- •Predict material properties and behavior
- •Design new materials with desired properties
- •Analyze X-ray diffraction patterns
Lattice Formulas
Simple Cubic (SC)
a = 2r
Atoms touch along cube edges
Body-Centered Cubic (BCC)
a = 4r/√3
Atoms touch along cube diagonals
Face-Centered Cubic (FCC)
a = 4r/√2
Atoms touch along face diagonals
Note: The lattice constant 'a' represents the edge length of the cubic unit cell. All formulas assume hard sphere atoms in contact.