Crystal Structure Input Form
Example Data Table
| Structure | Radius (Å) | a (Å) | c (Å) | Atoms per Cell | Coordination | APF |
|---|---|---|---|---|---|---|
| Simple Cubic | 1.20 | 2.40 | 2.40 | 1 | 6 | 0.5236 |
| Body-Centered Cubic | 1.25 | 2.8868 | 2.8868 | 2 | 8 | 0.6802 |
| Face-Centered Cubic | 1.28 | 3.6204 | 3.6204 | 4 | 12 | 0.7405 |
| Hexagonal Close-Packed | 1.30 | 2.6000 | 4.2458 | 6 | 12 | 0.7405 |
Formula Used
Simple cubic: a = 2r, nearest neighbor = a, and Z = 1.
Body-centered cubic: a = 4r / √3, nearest neighbor = √3a / 2, and Z = 2.
Face-centered cubic: a = 2√2r, nearest neighbor = a / √2, and Z = 4.
Hexagonal close-packed: a = 2r, c = (c/a) × a, and conventional Z = 6.
Cell volume: cubic cells use V = a³. HCP uses V = (3√3 / 2)a²c.
Atomic packing factor: APF = total atomic sphere volume / unit cell volume.
Theoretical density: ρ = ZM / (NAV), where M is atomic mass and V is cell volume.
Plane spacing: cubic spacing uses dhkl = a / √(h² + k² + l²). Hexagonal spacing uses 1/d² = 4(h² + hk + k²)/(3a²) + l²/c².
How to Use This Tool
Choose the crystal structure you want to study.
Select whether you know atomic radius or lattice parameter a.
Enter the length value and choose the correct unit.
Add atomic mass to estimate the theoretical density.
Adjust the c/a ratio when using the hexagonal option.
Pick the supercell size for a denser 3D visualization.
Press Visualize Structure to generate metrics and plots.
Use the CSV button for tabular data export.
Use the PDF button to save the displayed output.
Frequently Asked Questions
1. What does this tool calculate?
It calculates lattice parameters, packing factor, theoretical density, nearest neighbor distance, selected plane spacings, atoms per unit cell, and a 3D structure view.
2. Which crystal structures are supported?
The tool supports simple cubic, body-centered cubic, face-centered cubic, and hexagonal close-packed structures.
3. Why does HCP need a c/a ratio?
HCP geometry depends on two lattice dimensions. The c/a ratio controls cell height relative to the basal edge and changes volume, density, and spacing values.
4. What is atomic packing factor?
Atomic packing factor measures how much of the unit cell volume is occupied by atoms modeled as hard spheres. Higher values indicate tighter packing.
5. Why is the displayed density theoretical?
The formula assumes a perfect crystal without defects, impurities, thermal expansion, or vacancies. Real samples may differ from the predicted value.
6. Can I use lattice parameter instead of radius?
Yes. Select the lattice input mode and enter parameter a. The tool converts it to an equivalent atomic radius for the chosen structure.
7. What does the 3D plot show?
The 3D plot shows atom centers in a repeated supercell. It helps you compare symmetry, packing, and spacing patterns visually.
8. What export formats are included?
You can export the calculated summary as CSV and save the visible result section as a PDF document.