the wavelength requirement for diffraction
You cannot see a virus with a searchlight or read fine print with a boxing glove — the tool has to be finer than the thing it probes. Diffraction obeys the same rule. To read out the atomic structure of a crystal, the wave you shine on it must have a wavelength comparable to the spacing between atoms, roughly an angstrom (0.1 nanometre). That is the wavelength requirement, and it decides which kinds of waves can do the job at all.
The requirement drops straight out of Bragg's law. Rearranged, sin theta = n lambda / (2 d), and since sin theta can never exceed 1, you get lambda <= 2 d for even the first order to appear. If lambda is much larger than the plane spacing d, no angle exists that satisfies Bragg's law and there is simply no diffraction. Visible light, with wavelengths around 5000 angstrom, is thousands of times too coarse to be diffracted by atomic planes a couple of angstroms apart — which is exactly why we cannot photograph atoms with a light microscope.
Three kinds of radiation do have the right wavelength and so are the workhorses of structural science. X-rays around 0.5 to 2 angstrom scatter off the electron clouds. Electrons, accelerated in a microscope to sub-angstrom wavelengths, scatter off the electrostatic potential and interact so strongly that samples must be ultrathin. Neutrons of thermal energies also land near an angstrom and scatter off nuclei and magnetic moments. Different probes, one shared entry ticket: a wavelength on the scale of the atomic spacing.
For planes spaced d = 2 angstrom, Bragg needs lambda <= 4 angstrom. Copper X-rays (1.54 angstrom) pass easily; a beam of visible green light (5000 angstrom) fails by a factor of over a thousand, so it cannot diffract from atomic planes at all.
Only wavelengths at or below about 2d can diffract; this is why X-rays, electrons, and neutrons — not light — reveal atomic structure.
The requirement is lambda <= 2 d, not lambda = d. A wavelength somewhat below the spacing works and in fact lets more reflections appear; a wavelength far above it kills diffraction entirely.