How are XRD patterns simulated?

X-ray diffraction (XRD) patterns are simulated from the crystal structure using kinematic diffraction theory.

Simulation Process

1. Identify reflections: For a given crystal structure, all allowed Bragg reflections (hkl) within the measured 2-theta range are enumerated based on the lattice parameters
2. Compute structure factors: For each (hkl) reflection, the structure factor F(hkl) is calculated from the atomic positions, element-specific scattering factors, and thermal displacement parameters
3. Apply corrections: Lorentz-polarization factor, multiplicity factor, and Debye-Waller factor are applied
4. Generate pattern: Peak positions (from Bragg's law) and intensities (from |F(hkl)|^2 with corrections) are combined and broadened with a pseudo-Voigt profile

Default Parameters in MatCraft

• Radiation: Cu K-alpha (wavelength = 1.5406 Angstroms)
• 2-theta range: 10 to 90 degrees
• Peak broadening: 0.1 degree FWHM (idealized)

Uses

• Phase identification: Compare simulated patterns with experimental XRD measurements to confirm phase identity
• Fingerprinting: Each crystal structure produces a unique diffraction pattern
• Quality check: Verify that the computed crystal structure matches known experimental patterns

Limitations

Simulated patterns assume a perfect, infinite crystal. Real samples have finite size broadening, strain effects, preferred orientation, and background signals that are not modeled.