X-Ray Diffraction

Bragg peaks · structure factor · powder pattern

λ = 1.54 Å
a = 3.52 Å
Physics: Bragg's law: 2d·sinθ = nλ. Structure factor F(hkl) = Σf_j·exp(2πi(hx_j+ky_j+lz_j)) determines peak intensity. FCC selection rule: hkl all odd or all even; BCC: h+k+l = even; diamond: (h+k+l)=4n or all odd. Atomic form factor f(Q) = Fourier transform of electron density, decreases with Q. Powder diffraction averages over all orientations → rings that become peaks in 2θ scan. Rietveld refinement fits full diffraction pattern to extract lattice parameters, atomic positions, site occupancies. Cu Kα1 λ=1.5406 Å is standard laboratory source.