Model unit cells quickly with clean inputs for common crystal lattices here. Get atomic packing, coordination, d‑spacing, and Bragg angles in seconds accurately now.
| Structure | Input | Unit | Atomic weight (g/mol) | Key output |
|---|---|---|---|---|
| FCC | r = 0.124 | nm | 63.546 | a ≈ 0.351 nm, APF ≈ 0.740, density ≈ 8.9 g/cm³ |
| BCC | a = 2.87 | Å | 55.845 | r ≈ 1.24 Å, APF ≈ 0.680, density depends on A |
| HCP | a = 2.95, c/a = 1.633 | Å | 47.867 | c ≈ 4.82 Å, APF ≈ 0.740, CN = 12 |
Crystal symmetry controls slip, diffusion paths, and electronic band structure. A unit cell provides a compact way to quantify this geometry and compare metals, ceramics, and semiconductors across experiments.
Simple cubic has 1 atom per cell and coordination number 6. Body‑centered cubic has 2 atoms per cell with coordination 8. Face‑centered cubic has 4 atoms per cell and coordination 12. Hexagonal close‑packed has 6 atoms per conventional cell and coordination 12.
For hard‑sphere models the calculator applies SC a=2r, BCC a=4r/√3, and FCC a=4r/√2. For HCP, a=2r and c is either entered or derived from c/a. The ideal close‑packed ratio is about 1.633, but real values vary by element and temperature.
Atomic packing factor (APF) estimates how much of the cell is occupied by atoms. SC is about 0.524, BCC about 0.680, and both FCC and ideal HCP about 0.740. Higher APF generally correlates with lower free volume and often higher ductility in close‑packed metals.
Theoretical density uses ρ=(n·A)/(Nₐ·V), where n is atoms per cell, A is atomic weight in g/mol, and V is cell volume in cm³. This quickly checks whether a chosen lattice constant is realistic; large deviations can indicate porosity, alloying, or an incorrect phase assignment.
For cubic systems d=a/√(h²+k²+l²). For hexagonal systems, 1/d²=(4/3)(h²+hk+k²)/a² + l²/c². With a wavelength λ and order n, Bragg’s law nλ=2d sinθ yields θ. A common lab wavelength is Cu Kα, 1.5406 Å.
Use one consistent length unit for r, a, c, d, and λ. Nanometers and ångströms are typical: 0.1 nm equals 1 Å. Enter Miller indices as integers and avoid the (0 0 0) case. For HCP, provide c if you have measured data; otherwise use c/a.
Nearest‑neighbor distance should match the touching condition implied by the structure, and APF should fall in the expected range above. If Bragg reports “no solution,” nλ exceeds 2d. Adjust indices, order, or wavelength to reach a feasible diffraction angle. For metals, lattice constants typically sit between 2.5 and 4.5 Å. For ionic ceramics, larger cells are common. Compare your computed density and d‑spacings with reference cards to confirm phase purity and identify preferred orientation. before finalizing a materials model.
Choose a lattice, pick radius or lattice-constant mode, and enter r or a. For HCP, also provide c or a c/a ratio. The calculator then returns a, r, volume, APF, and nearest-neighbor distance.
Enter atomic weight in g/mol and a realistic lattice constant. Density uses atoms per unit cell, Avogadro’s number, and cell volume converted to cm³. Results are theoretical and assume a perfect crystal without defects or porosity.
Bragg’s law requires nλ ≤ 2d. If you pick a high order, a long wavelength, or a small d-spacing, the arcsine argument exceeds one. Reduce n, use a shorter wavelength, or choose lower-index planes.
In the ideal hard-sphere limit, both FCC and HCP have APF about 0.740 and coordination 12. Real materials can deviate slightly because bonding and temperature change effective radii and lattice constants, but the close-packed picture remains useful.
Use the same length unit you selected for lattice parameters. For example, Cu Kα is 1.5406 Å, which is 0.15406 nm. Consistent units prevent incorrect Bragg angles and d-spacing values.
The calculator uses the hexagonal d-spacing relation with (h k l) in three-index form. It combines the basal-plane term (h²+hk+k²) with the c-axis term l²/c². Avoid all zeros because that plane is undefined.
Yes. After a successful calculation, use Download CSV for spreadsheet work or Download PDF for a quick report. Exports include your latest inputs and the full results table shown on screen.
Accurate crystal metrics help design materials and experiments better.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.