X-ray Diffraction: Theory & Applications

Explore how x-ray diffraction reveals crystal structures and enables chemical, structural, stress, and particle size analyses, powered by high-energy x rays with phase-contrast diffraction.

Explain how x-rays form from rapid electron deceleration. Describe continuous spectrum and characteristic x-rays, including k alpha and k beta lines, Moseley’s law, and filters.

Understand absorption edge as a jump in mass absorption coefficient guiding filters and monochromators in x-ray diffraction, with beam geometry and detectors enabling powder and texture analyses.

Explore x-ray diffraction from constructive interference of waves scattered by periodic crystal planes, derive Bragg's law using interplanar spacing d, and introduce the reciprocal lattice.

Derive diffraction conditions from the reciprocal lattice point and phase difference. Detail Bragg and Laue conditions, Ewald construction, and the sphere of reflection with Laue, rotating crystal, and powder methods.

Explore how stereographic projection translates crystal plane angles into a 2D map using poles on a reference sphere, great and small circle traces, and the wolf net tool.

Use the Wulff net to measure angles between crystal planes, trace planes on the projection, and rotate poles about normal or inclined axes with standard projections and zonal relations.

Explore the main x-ray diffraction methods—Laue with white radiation, rotating crystal, and powder using the Debye Sherrod method—analyzing transmission, back-reflection, and cone patterns on films.

Explore how peak intensity in x-ray diffraction depends on polarization, atomic scattering and structure factors, multiplicity, Lorentz polarization factors, absorption, and temperature factors, tied to lattice spacing and atom positions.

Explore x-ray diffraction concepts by explaining how finite crystals broaden peaks and applying the Scherrer formula to determine particle size using variance and integral breadth methods.

Explore precise lattice parameter measurement with x-ray diffraction using Bragg's law, high-angle data, and extrapolation methods to obtain true lattice constants.

Explore precise lattice parameter measurements in non-cubic crystals, splitting lines into hkl groups for a and zero-zero-one lines for c, and apply least squares to minimize random errors.

Determine phase boundaries in x-ray diffraction by constructing tie lines and applying disappearing phase and parametric methods to map the solvus line.

Explore how x-ray diffraction reveals stress and enables chemical analysis in metals, distinguishing uniform macro strain that shifts diffraction peaks from non-uniform microstrain that broadens them, and identifying residual stress.

Analyze texture with x-ray diffraction to reveal macro texture, fiber components, and orientation distributions, differentiating random from textured materials and linking deformation and recrystallization textures to anisotropic properties and applications.

Explore how the orientation matrix converts crystal to specimen coordinates, defines orthonormal properties, and links ideal orientation, pole figures, Euler angles, Miller indices, and reference-sphere projections.

Explore how Euler angles describe orientation through rotation sets, build orientation matrices, and model texture via orientation distribution functions in Euler space.

Explain pole figure measurement using a four-axis goniometer with Bragg angle setup, tilting to 70-80 degrees and spinning about the normal. Cover iterative reconstruction, defocusing correction, and reference-sample calibration for accurate orientation distribution.