Bragg Calculator
Converts between the angle a reflection is observed at and the spacing of the lattice planes that produced it, through λ = 2d sin θ.
- You supply
- Either an angle (θ or 2θ) or a d-spacing, and the anodes you want it answered for.
- Reading it
- One row per anode, each quoted to the significant figures its own wavelength constant carries. n.a. means that radiation cannot reach the reflection at all: nothing with d < λ/2 diffracts.
Worked examples: NaCl (200) · quartz (101)
Input
Results
| Mo: | 0.84 Å |
|---|---|
| Cu: | 1.8 Å |
Wavelengths are Kα.
How this is calculated
Every other row is the same equation with that anode’s wavelength in place of this one. Results are quoted to the significant figures of whichever is coarser, your input or the wavelength constant.
Characteristic wavelengths
| Anode | Energy Kα / keV | Kα / Å in use | Kα1 / Å | Kα2 / Å | Kβ / Å |
|---|---|---|---|---|---|
| Ag | 22.11 | 0.560868 | 0.5594075 | 0.563789 | 0.497069 |
| Mo | 17.44 | 0.710730 | 0.709300 | 0.713590 | 0.632288 |
| Cu | 8.04 | 1.541838 | 1.540562 | 1.544390 | 1.392218 |
| Co | 6.93 | 1.790260 | 1.788965 | 1.792850 | 1.62079 |
| Fe | 6.40 | 1.937355 | 1.936042 | 1.939980 | 1.75661 |
| Cr | 5.41 | 2.29100 | 2.28970 | 2.293606 | 2.08487 |
Kα is the 2:1 weighted mean of Kα1 and Kα2, which is what an unmonochromated tube delivers — it is the right choice for ordinary laboratory data, and it is what this site uses unless you say otherwise. Choose Kα1 if a monochromator or a Johansson mirror removes the Kα2 component. Kα2 is not offered on its own, because no experiment runs on it alone — it is listed only because the Kα1/Kα2 splitting is why high-angle peaks look doubled. Kβ is what the filter or monochromator removes; compute with it to find out where the ghost peaks of an unfiltered pattern fall.
Kα is not an independent constant: it is (2 × Kα1 + Kα2) / 3, which reproduces every Kα value in this table to its own last digit.
Values taken from B. B. He, Two-Dimensional X-Ray Diffraction, John Wiley & Sons, Hoboken, NJ, Second edition, 2018.