"Very small" in this context is less than the lattice spacings, which for a typical crystal can be on the order of the wavelength of an X-ray (i.e., there's ~ 0.1-100 ångströms between the crystal's diffracting planes, so "distance x" must be a fraction of that length).
A typical room is effectively a <https://en.wikipedia.org/wiki/Gas_in_a_box>. If the walls of your box are good X-ray detectors then an isotropically-radiating X-ray source somewhere near the middle of the room will evidence an essentially uniform energy loss at the detectors, and and weak reflection from air molecules back towards the source. However, if you substituted the air in the room with a crystal lattice, the energy loss would be much stronger at detectors in some directions, and there would be strong reflections back towards the source along some directions. See <https://physicsopenlab.org/2018/01/18/bragg-diffraction/> for some details.
Symmetry breaking is very important to the study of condensed matter physics, including solid matter, and arguably it’s the reason your room exists at all.
https://simple.wikipedia.org/wiki/Higgs_field https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking
Uhuh, but enough to be physically detectable?