Wavelength & resolution shows why light fails and X-rays and electrons succeed. Bragg's law shows how a crystal turns a wavelength into a measurable diffraction angle.
Photon wavelength from E = hc/λ; electron wavelength from the relativistic de Broglie
relation λ = hc / √(eV·(2m_e c² + eV)) with m_e c² = 511 keV. A typical
chemical bond is ≈1.5 Å, so a probe needs λ ≲ ~2 Å to resolve atoms. Bragg's law
nλ = 2d·sinθ gives constructive interference — a diffraction spot — only when the
extra path between planes is a whole number of wavelengths.