# Recent Advances in Ultrafast Structural Techniques
## 3 Structural Techniques Involving Ultrashort Electron Pulses
### Bright Compact Direct Current (DC) FED Setups
A detailed analysis of the evolution of Bragg and CDW peaks, and optical measurements provides an atomically resolved movie highlighting the interplay between electronic and nuclear degrees of freedom. (**b**) Intense perturbation of the electronic system gives rise to smearing of the electron density modulation (\(t<0.1\) ps), driving the lattice towards the undistorted state (\(t<0.3\) ps). At the same time, the energy is transferred from the electronic subsystem to phonons, resulting in the recovery of the electron density modulation and thermal disordering of the lattice (\(t<1\) ps). The CDW order is nearly recovered at \(t<4\)ps, after which time the sample is thermalized at a somewhat higher temperature. Figure adapted from Reference [183] with permission from Springer Nature. (**c–d**) Transient optical properties and structural transitions in phase-change material Ge\({}_{2}\)Sb\({}_{2}\)Te\({}_{5}\) (GST). (**c**) Diffraction patterns of crystalline and amorphous states recorded with 92-keV fs-electron pulses. (**d**) Below-threshold dynamics in crystalline GST showing the time evolution of diffraction peaks and the extracted temperature rise. Figure adapted from Reference [190] with permission from Springer Nature. (**e–m**) Collective modes coupled to charge transfer in Me\({}_{4}\)P[Pt(dmit)\({}_{2}\)]\({}_{2}\). (**e**) Experimental diffraction pattern of Me\({}_{4}\)P[Pt(dmit)\({}_{2}\)]\({}_{2}\) at 90 K. (**f**) Simulated diffraction showing the contributions of individual reflections and selected peaks. (**g**) Simulated difference pattern for the thermal phase transition: charge-separated phase \(\rightarrow\) high-temperature (metallic) phase. (**h**) Differential FED data [I\({}_{\text{on}}\)(t) - I\({}_{\text{off}}\)] at different \(t\) following photoexcitation. (**i**) Snapshots of the structural dynamics constructed from the FED data. (**j**) Temporal profiles of the relative intensity changes of selected diffraction peaks. (**k-m**) Dynamics of key structural modes involved in the photoinduced phase transition of dimers initially neutral (blue) and divalent (red), compared with the thermal phase transition (dashed orange lines). Figure adapted from Reference [223] with permission from Science AAAS. In all aforementioned FED experiments, the temporal resolution was in the range of \(\approx\) 100 - 350-fs. In pursuit of a different DC fs-electron gun concept capable of producing sub-100-fs, and ideally sub-30-fs multi-electron bunches, Petruk et al. [224] found that \(\Delta\)t\({}_{\text{P}}\) is governed the strength of the electric field at the cathode's surface since most of the temporal broadening occurs during the initial stage of electron propagation [225]. Hence, a more general expression for Equation (16) follows, Equation (17):  
\[\Delta\text{t}_{\text{P}}\ \approx\ \frac{\Delta\text{p}_{0}}{\text{e}|\text{E}_{ \text{g}}|} \tag{17}\]  
where \(\left|\text{E}_{\text{g}}\right|\) is the magnitude of the geometrical electric field at the cathode's surface, i.e., in the area where electrons are born.] Equation (17) stresses the need to achieve both high electric field strengths and low initial momentum (or energy) spread at the cathode's surface in order to minimize the temporal broadening caused by \(\Delta\)p\({}_{0}\) as well as additional broadening arising from instabilities in the high-voltage power supply [224]. Note that \(\Delta\)p\({}_{0}\) affects both the temporal and spatial resolutions (see definition of L\({}_{\text{x}}\) in Equation (6)). Figure 17 illustrates a new DC fs-electron source concept capable of generating multi-electron bursts as short as 30 fs (12 fs rms). The idea here is to shape the cathode in order to increase the  
Figure 16: **Structural transitions at surfaces, measurements in reflection geometry. ****(a–c)** Fs-reflection high-energy electron diffraction (RHEED) patterns and surface structures. Diffraction patterns at T = 30 K before (**a**) and 6 ps after (**c**) laser excitation.