Tracking the surface atomic motion in a coherent phonon oscillation

X-ray photoelectron diffraction is a powerful tool for determining the structure of clean and adsorbate-covered surfaces. Extending technique into ultrafast time domain will open door to studies as diverse direct determination electron-phonon coupling strength in solids mapping atomic motion surface chemical reactions. Here we demonstrate time-resolved using ultrashort soft x-ray pulses from free electron laser FLASH. We collect Se $3d$ patterns over wide angular range optically excited $\mathrm{Bi}{}_{2}\mathrm{Se}{}_{3}$ with resolution 140 fs. Combining these multiple scattering simulations allows us track near-surface atoms within first 3 ps after triggering coherent vibration ${A}_{1g}$ optical phonons. Using fluence $4.2\phantom{\rule{0.28em}{0ex}}\mathrm{mJ}/{\mathrm{cm}}^{2}$ 1.55 eV pump laser, find resulting vibrational amplitude two interlayer spacings be on order 0.01 \AA{}.