Characterisation methods

Every characterisation method has a resolution limit set by the wavelength or probe it uses, and that single fact organises the whole toolkit. Visible light has a wavelength around 500 nanometres, so an optical microscope — no matter how well built — cannot resolve details smaller than roughly that, which rules out seeing individual atoms (spaced tenths of a nanometre apart) by definition, not by poor engineering. Magnification past that point produces a bigger blur, not more detail.

Different probes push the limit down by using something with a shorter wavelength. X-rays have wavelengths comparable to atomic spacing, which is why X-ray diffraction can probe crystal structure — but it does not produce a picture. A crystal's regular, repeating lattice scatters X-rays into a pattern of sharp spots whose positions and intensities encode the lattice's symmetry and spacing; recovering the atomic arrangement from that pattern is a calculation, not a photograph. Electron microscopy uses electrons, whose wavelength at practical energies is shorter still, and can form real-space images resolving individual atoms directly — a genuinely different kind of information from a diffraction pattern, obtained by a genuinely different physical process.

Spectroscopy is different again: rather than resolving position, it uses the sample's bonding and electronic structure to determine what it is made of and how it is bonded, at no particular length scale at all. Choosing a characterisation technique is therefore not a question of "which is best" but of matching the probe to the specific question — position at the nanometre scale asks for microscopy, crystal symmetry asks for diffraction, chemical identity asks for spectroscopy, and a full study of a new material typically needs several of them together.