The X-ray free electron lasers (XFEL) can enable diffractive structural determination of protein crystals or single molecules that are too radiation-sensitive for conventional X-ray analysis. However the electronic form factor could have been modified during the ultrashort X-ray pulse due to photoionization and electron cascade caused by the intense X-ray pulse. For general X-ray imaging techniques, to minimize radiation damage effect is of major concern to ensure faithful reconstruction of the structure. Here we show that a radiation-damage-free diffraction can be achieved with an atomic spatial resolution, by using X-ray parametric down-conversion (XPDC), and two-color two-photon ghost diffraction. We illustrate that the formation of the diffraction patterns satisfies a condition analogous to the Bragg equation, with a resolution that could be as fine as the lattice length scale of several Angstrom. Because the samples are illuminated by the optical photons of low energy, they can be free of radiation damage.
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