Enter XRD input data
Use direct d-spacing or derive d from common lattice systems. Results appear above this form after submission.
Example data table
These example rows illustrate typical reflections calculated with Cu Kα radiation, λ = 1.5406 Å.
| Material | System | hkl | Lattice input | d-spacing (Å) | Approx. 2θ (deg) |
|---|---|---|---|---|---|
| Silicon | Cubic | (111) | a = 5.431 Å | 3.135589 | 28.4421 |
| Silicon | Cubic | (220) | a = 5.431 Å | 1.920148 | 47.3023 |
| TiO₂ Anatase | Tetragonal | (101) | a = 3.784 Å, c = 9.515 Å | 3.516152 | 25.3094 |
| ZnO | Hexagonal | (102) | a = 3.2495 Å, c = 5.2069 Å | 1.911069 | 47.5408 |
Formula used
Bragg relation
nλ = 2d sinθ
The calculator solves for θ, then reports the measurable peak position as 2θ.
d-spacing by crystal system
Direct: d is entered directly.
Cubic: d = a / √(h² + k² + l²)
Tetragonal: 1/d² = (h² + k²)/a² + l²/c²
Orthorhombic: 1/d² = h²/a² + k²/b² + l²/c²
Hexagonal: 1/d² = (4/3)(h² + hk + k²)/a² + l²/c²
Additional reported terms
q = 4πsinθ / λ
sin²θ is often useful for indexing and peak comparison workflows.
How to use this calculator
- Select the calculation mode that matches your data source.
- Enter the X-ray wavelength, such as 1.5406 Å for Cu Kα.
- For lattice modes, provide valid lattice constants and Miller indices.
- Choose the main diffraction order n and the maximum order series.
- Set the instrument scan window in degrees 2θ.
- Press Calculate Peak Position to show the result block above the form.
- Review the summary table, series table, and Plotly peak chart.
- Use the CSV or PDF buttons to export the calculated values.
FAQs
1) What does the calculator actually predict?
It predicts the Bragg angle θ and the measurable diffraction location 2θ for a selected reflection. It also reports d-spacing, q, and scan-window visibility.
2) Why is 2θ shown instead of θ alone?
Most diffractometers record detector position as 2θ. Showing both values helps connect theory to the instrument’s observed peak position.
3) When should I use direct d-spacing mode?
Use direct mode when d-spacing is already known from indexing, standards, or prior analysis. The calculator then converts that spacing into diffraction angles.
4) What happens if nλ / 2d is greater than 1?
That reflection order is not physically allowed for the given wavelength and spacing. The calculator flags it because arcsin cannot be evaluated beyond one.
5) Are the plotted peak heights real intensities?
No. The chart emphasizes peak positions, not measured counts. Relative heights are visual placeholders so positions remain easy to compare across orders.
6) Can this page replace full phase identification?
No. It helps predict positions and check indexing logic. Full phase analysis still requires pattern matching, intensity interpretation, background treatment, and instrument calibration.
7) Why include q and sin²θ?
These quantities are useful in reciprocal-space analysis and reflection indexing. They also help compare peaks across different wavelengths or crystal systems.
8) Which wavelength should I enter?
Enter the wavelength used by your instrument or source line. A common laboratory value is Cu Kα at 1.5406 Å, but other sources are valid.