Free XRD Analysis Tool — Online X-Ray Diffraction Analyzer

The angle between the primary un-scattered X-ray beam and the direction of the diffracted beam. In powder diffraction experiments, detectors scan along this $2\theta$ arc to measure scattered intensities. The position of these peaks corresponds directly to crystal lattice d-spacings through Bragg's law.

A fundamental equation of diffraction, formulated as $\lambda = 2d \sin\theta$, where $\lambda$ is the radiation wavelength, $d$ is the crystallographic interplanar spacing, and $\theta$ is the angle of incidence. It describes the conditions for constructive interference of X-rays scattered from atomic planes.

Crystallographic Information File (CIF) is a standard text format for representing atomic structures. It documents lattice parameters, space groups, symmetry constraints, and fractional coordinates, enabling simulation engines to compute theoretical diffraction patterns and match phase identities against scan results.

The average size of a single coherent crystalline domain inside a larger grain or powder sample. It is different from particle size, as a single physical particle can contain multiple boundaries. It is calculated from reflection broadening using the Scherrer equation.

The perpendicular distance between parallel planes of atoms within a crystal structure. Measured in Angstroms (\AA), d-spacing determines peak locations. Spacings shrink as the diffraction angle increases, representing planes with higher Miller indices.

Full Width at Half Maximum (FWHM) represents the width of a reflection peak at 50% of its maximum intensity. It is a critical metric for estimating grain boundaries and structural microstrains, as smaller domains produce broader peaks.

Integers ($h, k, l$) that define specific planes of atoms in a crystal lattice. In diffraction, they index reflection peaks. The structure factor calculations use these indices to calculate how atoms constructively interfere along these specific plane orientations.

The physical dimensions and shapes of the unit cell, defined by three lengths ($a, b, c$) and three angles ($\alpha, \beta, \gamma$). They govern the lattice volume and interplanar d-spacings, dictating the exact angle coordinates where reflections can occur.

A system of notation in crystallography for planes in crystal lattices. They are defined as the reciprocals of the fractional intercepts of the plane with the unit cell axes, reduced to lowest integer terms. In XRD, they identify the plane families causing diffraction.

The widening of diffraction peaks beyond instrument-induced limits. Peak broadening is caused by physical factors, primarily small crystallite sizes (coherent domains) and internal lattice strains (dislocations, vacancy defects, stacking faults).

The process of matching experimental diffraction profiles against database records of known chemical compounds. By comparing peak positions and intensities, researchers determine the mineral composition of unknown powder mixtures.

An advanced mathematical methodology that fits a complete theoretical model of the crystal structure to a whole measured diffraction scan. It refines atomic coordinates, thermal factors, and instrument factors using least-squares algorithms to determine accurate crystal geometries.

A formula relating crystallite size to peak broadening: $D = K\lambda / (\beta \cos\theta)$. $\beta$ is the FWHM in radians, $\lambda$ is the X-ray wavelength, and $K$ is the shape factor. It is widely used to evaluate nanocrystalline sizes under 100 nm.

A description of the 3D symmetry of a crystal, representing how unit cells repeat under translation, rotation, reflection, and screw axis translations. The space group dictates reflection rules, indicating which HKL planes can produce constructive diffraction peaks.

A linear regression method used to separate size and strain broadening. By plotting $\beta \cos\theta$ against $\sin\theta$ for multiple peaks, the slope indicates the lattice microstrain, and the y-intercept indicates the average grain size.