Find interplanar spacing using Bragg relations or cubic lattice indices. Review outputs with unit checks. Save reports, compare values, and study diffraction behavior easily.
Bragg law: nλ = 2d sinθ.
Rearranged spacing form: d = nλ / (2 sinθ).
Cubic crystal relation: d = a / √(h² + k² + l²).
Use Bragg law when diffraction data is known. Use the cubic relation when the lattice constant and plane indices are known.
| Method | Sample Input | Spacing d |
|---|---|---|
| Bragg law | 1.5406 A, n=1, theta=14.22 deg | 3.1358 A |
| Bragg law | 1.5406 A, n=1, theta=22.50 deg | 2.0129 A |
| Bragg law | 1.5406 A, n=1, theta=28.30 deg | 1.6248 A |
| Cubic lattice | a=5.431 A, (111) | 3.1356 A |
| Cubic lattice | a=5.431 A, (220) | 1.9201 A |
| Cubic lattice | a=5.431 A, (311) | 1.6375 A |
The distance between crystal layers is called interplanar spacing. It describes how far one atomic plane sits from the next. This value matters in solid state physics, materials science, and X-ray diffraction studies. A small spacing changes the diffraction angle. A larger spacing shifts the pattern in another direction. Accurate spacing helps identify unknown crystals.
Scientists use layer spacing to study crystal structure. Engineers use it to inspect metals, ceramics, and semiconductors. Students use it to connect theory with lab work. The value also helps compare a measured sample with reference data. That makes crystal spacing useful in quality control and research.
Bragg’s law links wavelength, angle, order, and spacing. When X-rays reflect from parallel planes, strong peaks appear only at special angles. The relation is nλ = 2d sinθ. Here, n is diffraction order, λ is wavelength, θ is the Bragg angle, and d is layer spacing. This calculator rearranges that relation to solve for d quickly.
For cubic materials, spacing can also come from the lattice constant and Miller indices. The formula is d = a / √(h² + k² + l²). This is useful when the unit cell dimension is known. It gives direct spacing for a selected plane. It is common for simple cubic, body centered cubic, and face centered cubic studies.
This tool returns spacing in meters, nanometers, angstroms, and picometers. It also reports reciprocal spacing. That helps users compare results across lab notes and published tables. The calculator keeps the workflow simple. You enter the known values, choose a method, and read the spacing immediately. Export options then help save or share the result.
Check units before solving. Confirm whether your angle is θ or 2θ. Use realistic diffraction orders. For Miller indices, do not enter all zeros. For best results, compare the answer with a known reference pattern. That step reduces entry mistakes and improves confidence. A clear calculation also makes reports easier to review later.
If two methods are available, compare them when your sample permits. Similar values support consistency. Large differences often signal unit errors, wrong indices, or an incorrect diffraction angle entry.
It is the distance between adjacent crystal planes. Scientists often label it as d. It helps describe structure and interpret diffraction patterns.
Theta is the Bragg angle used inside the formula. Many instruments report 2theta directly. This calculator lets you choose either format.
Use Bragg law when you know wavelength, diffraction order, and diffraction angle. It is common in X-ray diffraction work and lab analysis.
Use the cubic formula when the crystal is cubic and you know the lattice constant plus the Miller indices of the plane.
Yes. Higher orders can occur in diffraction. Still, first order is often used because it is simple and commonly reported in examples.
Crystal spacings are very small. Angstrom units match atomic scale distances well. They keep the reported values easy to read.
The cubic formula becomes invalid because the denominator becomes zero. At least one Miller index must be non-zero for a real plane.
CSV files help with spreadsheets and data review. PDF files help with sharing, printing, or attaching a clean calculation summary to reports.
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.