Example Data Table
| Material model |
Structure |
a value |
Unit |
Atomic mass |
Atoms per cell |
| Copper model |
Face Centered Cubic |
0.3615 |
nm |
63.546 |
4 |
| Iron model |
Body Centered Cubic |
0.2866 |
nm |
55.845 |
2 |
| Diamond carbon model |
Diamond Cubic |
0.3567 |
nm |
12.011 |
8 |
| Magnesium model |
Hexagonal Close Packed |
0.3209 |
nm |
24.305 |
6 |
Formula Used
Cubic cell volume: V = a³
Custom lattice volume: V = abc × √(1 + 2cosαcosβcosγ − cos²α − cos²β − cos²γ)
HCP conventional volume: V = 3√3a²c / 2
Mass per cell: m = nM / NA
Density: ρ = mass per cell / volume in cm³
Atomic packing factor: APF = n × (4πr³ / 3) / V
Void fraction: Void = 1 − APF
Radius estimates: SC r = a / 2, BCC r = √3a / 4, FCC r = √2a / 4, Diamond r = √3a / 8, HCP r = a / 2.
How to Use This Calculator
- Select the crystal structure that matches your material model.
- Enter lattice edge a. Add b, c, and angles for custom cells.
- Choose the correct length unit.
- Enter atomic mass in grams per mole.
- Enter a custom radius only when you want to override the estimated radius.
- Press calculate to view results above the form.
- Use CSV or PDF buttons to save the same calculated output.
Understanding Crystal Structure Results
Crystal structure data describes how atoms repeat in a solid. A unit cell is the smallest repeating block. Its sides and angles define the lattice. When those values are known, useful material properties can be estimated quickly.
Why Unit Cell Volume Matters
Volume is the base value for most results. Cubic cells use a simple edge cubed rule. Triclinic cells need all three edges and angles. Hexagonal close packed cells use a conventional hexagonal volume. A correct volume keeps density and packing results reliable.
Density And Mass Per Cell
The calculator estimates mass per cell from atoms per cell and atomic mass. It uses Avogadro’s constant. The mass is then divided by the cell volume in cubic centimeters. This gives theoretical crystal density. It is useful for comparing a model with measured density.
Packing Factor Meaning
Atomic packing factor shows how much of the cell is filled by atoms. Simple cubic packing is low. Body centered cubic packing is higher. Face centered cubic and ideal hexagonal close packed structures are very efficient. A higher value means less empty space inside the model.
Radius Choices
Some structures have direct radius relationships. Simple cubic uses half the edge. Body centered cubic uses the body diagonal. Face centered cubic uses the face diagonal. Diamond cubic uses a smaller fraction of the body diagonal. Custom cells may need a measured radius from diffraction data.
How To Read The Output
Check the selected structure first. Then review atoms per cell, cell volume, density, radius, packing factor, and void fraction. A packing factor above one usually means the radius or cell type is wrong. A density far from known data may mean the atomic mass, atom count, or unit was entered incorrectly.
Practical Use
This calculator helps students, engineers, and lab users test crystal assumptions. It can compare cubic, hexagonal, and custom lattices. It also creates export files for records. Use consistent units. Keep enough precision. Verify unusual structures with trusted crystallography data before using results for design decisions.
Limitations
The result is an ideal estimate. Real samples may include strain, defects, vacancies, impurities, and temperature effects. Use the output as a clear first check, not as a final laboratory certification alone.
FAQs
What does this crystal structure calculator find?
It finds unit cell volume, mass per cell, theoretical density, estimated radius, packing factor, and void fraction. It supports common cubic cells, hexagonal close packed cells, and custom lattice geometry.
Can I use a custom unit cell?
Yes. Choose custom lattice. Then enter a, b, c, alpha, beta, gamma, and atoms per cell. The calculator uses the general lattice volume equation.
What happens if I leave atomic radius blank?
The calculator estimates radius for standard structures. It uses known geometric relations for simple cubic, body centered cubic, face centered cubic, diamond cubic, and hexagonal close packed models.
Why is my packing factor above one?
A packing factor above one usually means a wrong radius, wrong unit, wrong atom count, or wrong structure choice. Atoms cannot fill more than the entire unit cell volume.
Does this calculate real measured density?
No. It estimates theoretical density from an ideal unit cell. Real density can differ because of defects, impurities, temperature, porosity, and measurement conditions.
Which structures are included?
The form includes simple cubic, body centered cubic, face centered cubic, diamond cubic, hexagonal close packed, and custom lattice options.
Can I export the results?
Yes. After entering values, use the CSV button for spreadsheet data. Use the PDF button for a simple report file with the calculated results.
Which units should I use?
Use the unit that matches your lattice data. The calculator accepts meters, micrometers, nanometers, angstroms, and picometers. Keep radius units consistent too.