Advanced XRD Peak Calculator

Analyze diffraction peaks using flexible physics inputs and clear outputs. Save reports fast and compare. Visualize XRD behavior with dependable calculations and export tools.

Calculator Inputs

Plotly Graph

The chart below shows a simulated Gaussian diffraction peak centered at the calculated 2θ position.

Example Data Table

Material Wavelength (Å) 2θ (deg) FWHM (deg) (hkl) Typical Use
Silicon 1.5406 28.44 0.12 (111) Semiconductor reference peak checks
Gold 1.5406 38.18 0.22 (111) Nanoparticle phase confirmation
Iron 1.5406 44.67 0.18 (110) Body-centered cubic analysis
Aluminum 1.5406 38.47 0.15 (111) Face-centered cubic indexing

Formula Used

1) Bragg’s Law

nλ = 2d sinθ

Use this relation to find d-spacing from peak angle, or find the diffraction angle from known plane spacing.

2) Scattering Vector

q = 4π sinθ / λ

This expresses the peak in reciprocal space and helps compare diffraction positions across measurements.

3) Cubic Lattice Parameter

a = d √(h² + k² + l²)

For cubic systems, the lattice parameter follows directly from d-spacing and the selected Miller indices.

4) Scherrer Size Equation

D = Kλ / (β cosθ)

This estimates crystallite size when line broadening is known. β must be in radians, and instrumental broadening should be corrected beforehand.

How to Use This Calculator

  1. Select whether you want to solve from 2θ or from d-spacing.
  2. Enter the X-ray wavelength in angstroms. Cu Kα commonly uses 1.5406 Å.
  3. Set the diffraction order, usually 1 for routine peak analysis.
  4. Provide either the peak position 2θ or the d-spacing, depending on the chosen mode.
  5. Enter FWHM if you want a Scherrer crystallite size estimate.
  6. Add h, k, and l for a cubic lattice parameter calculation.
  7. Press the calculate button to show results above the form.
  8. Use the CSV or PDF buttons to export the result table.

Frequently Asked Questions

1) What does this XRD peak calculator compute?

It calculates Bragg angle, peak position, d-spacing, scattering vector, cubic lattice parameter, and optional Scherrer crystallite size from common diffraction inputs.

2) Which wavelength should I enter?

Enter the wavelength used by your X-ray source. Cu Kα is commonly 1.5406 Å, but other sources such as Co Kα need their own values.

3) What is the difference between θ and 2θ?

θ is the Bragg angle between the beam and crystal plane. 2θ is the detector angle normally reported by diffractometers and peak lists.

4) When is the Scherrer size result useful?

Use it when peak broadening mainly comes from small crystallite size. Correct instrumental broadening first, or the calculated size may be underestimated.

5) Why do I need Miller indices?

Miller indices identify the reflecting plane. For cubic materials, they allow conversion from d-spacing into the lattice parameter using a simple geometric relation.

6) Can this calculator index every crystal structure?

No. The lattice-parameter step in this file assumes a cubic crystal. Bragg’s law and Scherrer calculations still work for other structures.

7) What makes a Bragg condition invalid here?

If nλ divided by 2d is greater than one, no real diffraction angle exists. That means the chosen wavelength, spacing, or order is incompatible.

8) What does the Plotly graph show?

It shows a simulated Gaussian peak around the calculated 2θ value. It is useful for visualization, not as a replacement for full profile fitting.

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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.