Convert an XRD pattern from 2θ to d-spacing or Q (Beta)

Peak positions in 2θ depend on the X-ray wavelength, so a pattern measured with a cobalt or molybdenum tube doesn't line up with copper reference data, and papers or databases often list d-spacings instead. This page converts a diffraction pattern to d-spacing, to Q, or to the 2θ it would have with Cu Kα1, using the wavelength stored in your data file. d-spacing is preset.

How to convert 2θ to d-spacing

1. Upload the original data file: Bruker .raw or .brml, Panalytical .xrdml, .rd or .udf, Rigaku .ras, .rasx or .asc, or Bruker .uxd. These normally record the wavelength.
2. Choose the axis under X axis: d-spacing (Å), Q (Å⁻¹), or 2θ recalculated for Cu Kα1.
3. Check the wavelength: the result names the anode and the Kα1 value used for the conversion.
4. Download .xy, .xye, CSV or Excel with the new axis.

The formulas

With λ the Kα1 wavelength stored in the file and θ half the measured 2θ:

• d = λ / (2 sin θ), in ångström;
• Q = 4π sin θ / λ, in Å⁻¹;
• Cu-equivalent 2θ: the angle that gives the same d with Cu Kα1 (1.540598 Å), i.e. 2 · arcsin(1.540598 / λ · sin θ).

If a file stores no separate Kα1 value, the stored average wavelength is used, and failing that the standard Kα1 of the anode, labelled as such in the details.

Things to keep in mind

• Kα2 stays in the data. The whole pattern is converted with the Kα1 wavelength, so Kα2 shoulders remain where they were relative to the peaks. The conversion changes the axis, not the peak shapes.
• d runs backwards. High 2θ means small d, so the rows of a d-spacing file go from large to small d, in measurement order. The preview chart shows d decreasing to the right.
• Mo to Cu. Angles that would lie beyond 180° 2θ with Cu Kα1 can't exist; those points are left empty and the result says how many.
• Only 2θ scans are converted. Rocking curves and other ω or φ scans keep their axis, with a note.
• Plain text files such as an existing .xy or GSAS files carry no wavelength, so they stay in 2θ. Upload the instrument's original file instead.

The XRDML download always keeps the original 2θ positions and wavelengths, so the conversion never overwrites the raw measurement. Intensities can be normalised to 100 at the same time, which helps when overlaying patterns from different instruments.

Format details: Bruker RAW, XRDML, Rigaku RAS.

More about what this tool reads and writes: XRD Pattern Converter (RAW, BRML, XRDML, RAS).