About the HCP Atomic Radius Calculator
This tool estimates the atomic radius for an element with a hexagonal close-packed crystal structure using its c/a ratio, density, and atomic weight. It is useful for materials science students, engineers, and researchers who want to connect bulk density data with HCP lattice dimensions.
How to use this calculator
- Enter the HCP c/a ratio for the material.
- Enter the material density in g/cm³.
- Enter the atomic weight in g/mol.
- Click Calculate Radius to compute the radius and lattice parameters.
- Use Reset to restore the magnesium-like default values.
How it works
The calculator first uses the density relation for a conventional HCP unit cell containing 6 atoms. With atomic weight A, density ρ, and Avogadro’s number NA, the unit-cell volume is Vc = nA/(ρNA), where n = 6.
Example calculation
Using the default magnesium-like values, c/a = 1.633, density = 1.738 g/cm³, and atomic weight = 24.305 g/mol. The cell volume is about 1.3915 × 10^-22 cm³, giving a ≈ 0.32099 nm and c ≈ 0.52418 nm. The atomic radius is r = a/2 ≈ 0.1605 nm, or about 160.5 pm.
Frequently asked questions
Why does the calculator use 6 atoms per HCP unit cell?
It uses the conventional HCP unit cell, which contains 6 atoms when corner, face, and interior atom contributions are counted.
What is the ideal c/a ratio for HCP crystals?
The ideal hard-sphere HCP c/a ratio is about 1.633, but real materials can be higher or lower depending on bonding and structure.
Why is the atomic radius equal to a/2?
In the close-packed basal plane, neighboring atoms touch along the a direction, so the center-to-center distance is a and the hard-sphere radius is half of that.
Does temperature affect the result?
Yes. Density and lattice parameters change with temperature, so use density and crystal data measured at the same or similar temperature when possible.