A crystal is built up of lots of atoms in a repeating pattern. The gaps between the atoms are about the same size as an x-ray so you can fire an x-ray into the crystal and it will bounce off the atoms. If it were smaller, it wouldn’t hit them, if it were too big it wouldn’t be able to get in the gaps. You can then measure the angle the x-ray has bounced off at and work out where your atoms are. Depending on what element the atom is, the x-rays will bounce off differently. Once you’ve worked out where some of your atoms are, because the crystal structure repeats, you can multiply up those atoms to get your whole crystal.
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