## 2 Results and Discussion
### Ultrafast X-ray Diffraction Measurements  
In the following, we demonstrate UXRD experiments conducted on two different samples using our optimized femtosecond X-ray source. Figure 2: (**a**) The fluctuation of generated Cu-K\({}_{\alpha}\) X-ray flux within 100 min (blue dot) corresponding to the average output (red line). (**b**) The laser pump intensity dependence of the generated X-ray photon flux. (**c**) The reflection geometry of X-ray diffraction, in which the generated X-ray is passing through a tantalum slit and diffracted off a single-crystal Au film. The integration time of the measured diffraction pattern is 20 s. (**d**) The transmission geometry of X-ray diffraction, in which the generated X-ray is collected by a polycapillary X-ray optics and then diffracted off a polycrystalline Cu tape. The integration time of the measured diffraction pattern is 300 s.  
We first study a 200 nm thick Au (111) single crystal film grown on the mica substrate. The dynamics are triggered by a 400 nm pump pulse with an energy of 200 \(\upmu\)J. The corresponding penetration depth is 17 nm [10; 23] and the diameter of the optical pump spot on the sample is 2 mm, which is much larger than the width of the X-ray strip on the sample to ensure the homogenous excitation in the probed regime. To achieve a good signal-to-noise ratio, each Bragg diffraction image at different delay times is obtained by two-cycle accumulations. The exposure time of each image of one cycle is 20 s. The diffraction patterns include irradiated area and non-irradiated area of the film, and the latter is used as the reference for normalization. The electron-lattice interaction in Au-film after femtosecond optical excitation has been widely studied in detail [10; 24; 25; 26; 27]. When the optical pulse irradiates into the surface layer of the film, the deposited laser energy is first absorbed by the surface electrons, leading to the heating of electrons to a very high temperature in an ultrashort period, and then heating the lattice by the electron-lattice interaction. On the other hand, the optical excitation induces a large transient elastic force at the surface [24], which only lasts during the early electron nonequilibrium (1 ps to 2 ps), and the blast wave generated by this elastic force will propagate into the depth with the sound velocity, inducing strain wave along its path. The measured transient 0-20 scan curves for the delay time ranging from \(-\)140 ps to 390 ps are presented in Figure 3a. The white dotted line indicates the change in the center of the Bragg peak, which is extracted based on the single Gaussian function fitting. The variation of inter-atomic spacing of a 200-nm Au (111) crystal as a function of the pump-probe time delay is shown in Figure 3b. A shift of the diffraction angles and a slight broadening are observed when \(t>0\) ps. A shift towards a smaller diffraction angle indicates lattice expansion, and the maximum shift is reached at 60 ps after excitation [10]. Following the maximum lattice expansion, we have fitted the experimental data using the sine-damping function:  
\[y=\ y_{0}\ +\ Ae^{-\frac{x}{t_{0}}}\sin(\pi-\frac{x-x_{x}}{w})\]  
where \(y_{0}\) is the fitting constant (7.9 \(\times\) 10\({}^{-4}\)), \(w\) is the oscillation period (59.5 ps), \(t_{0}\) is the decay lifetime (120.5 ps), and \(A\) is the oscillation amplitude (7.8 \(\times\) 10\({}^{-4}\)). The fitting result with an R-square of \(-\)0.96 indicates that damped oscillations appear with a period of 121 ps, implying lattice breathing along the surface normal [9; 24]. The measured characteristic time (121 ps) is in good agreement with the theoretical calculation: \(\tau_{ac}=2d/c_{\rm s}=123\) ps, where \(d=200\) nm is the sample thickness and \(c_{\rm s}=3.24\) km/s is the longitudinal velocity of the acoustic wave in gold. Such oscillations stem from the blast waves traveling back and forth through the film along the (111) direction and the damping in oscillations amplitude is due to the finite acoustic transmission into the substrate.