Interactive diffraction explorer

Detected peaks

These widths are measured at half prominence. They are not automatically fitted FWHM and are not used for Scherrer/Williamson–Hall calculations. Fit peaks or provide validated FWHM values in the Structure tab.

Uploaded pattern worksheet

Every uploaded row can be viewed. Select the 2θ and intensity columns, then Add selected pattern. Preview search does not filter analysis.

Peak fitting & deconvolution

At most six components and 3,000 points per fit. Constant residual baseline is fitted. Optional centers use automatically estimated amplitude and width starts.

Validated peak ledger

Use fitted peaks, or paste validated measurements below. All FWHM values must be in degrees 2θ. Assign HKL yourself for lattice calculations.

Scherrer estimates coherent-domain size, not microscopy particle diameter. Instrument correction, strain, anisotropy and profile choice affect estimates. Williamson–Hall requires at least three resolved widths and an appropriate isotropic model.

Pattern comparison

Second pattern is interpolated onto the active pattern over the common range; no extrapolation. Comparison uses the processed intensities.

User reference peak matching

Position-only reference coverage is an exploratory match, not phase identification or quantitative phase analysis. No licensed diffraction database is included.

Illustrative cubic reflection generator

Geometric cubic Bragg positions with centering selection rules only; equal illustrative intensities, no atomic structure factors. h, k, l ≤ 6.

XRD workflow & scientific limits

1. Import the diffraction table. Review its worksheet and select degrees 2θ/intensity columns before adding.
2. Set zero shift, range, background and optional smoothing. Process all patterns and inspect peak detection.
3. Fit narrow peak ranges to obtain model-specific FWHM. Add fit components to the structure ledger.
4. Provide wavelength and measured instrumental broadening; select an appropriate correction. Assign HKL only when justified.
5. Calculate d-spacing, Scherrer, Williamson–Hall and selected lattice metrics. Inspect residuals and export settings.

First-order Bragg law: d = λ/(2 sinθ). Scherrer: D = Kλ/(β cosθ), where β is corrected FWHM in radians of 2θ. Gaussian correction uses √(βobserved² − βinstrument²); Lorentzian correction uses subtraction. Williamson–Hall uses β cosθ versus 4 sinθ, with intercept Kλ/D and slope ε. It is an unweighted isotropic uniform-deformation estimate. No uncertainty in λ, K or instrumental-width estimates is propagated.

Smoothing can alter widths. Pseudo-Voigt fitting is a Gaussian/Lorentzian mixture; choosing a simple width correction does not constitute full instrumental profile deconvolution. Unresolved instrument-limited widths produce unavailable size estimates. Negative WH intercept or slope is flagged rather than forced to a physical result.

Not implemented: Rietveld/Le Bail/Pawley refinement, automatic indexing, structure solution, texture refinement, quantitative phase fractions, automated crystalline/amorphous fraction, PDF/database search, CIF structure factors, Kα₂ stripping, 2D detector integration, proprietary RAW/RAS/BRML formats or full commercial XRD equivalence. Basic XRDML accepts one intensity scan with 2Theta start/end or explicit positions.

Methods references: IUCr crystallite-size and instrumental-broadening discussion; IUCr diffraction peak-profile discussion.