The self-assembly of strongly-coupled nanocrystal superlattices, as a convenient bottom-up synthesis technique featuring a wide parameter space, is at the forefront of next-generation material design. To realize the full potential of such tunable, functional materials, a more complete understanding of the self-assembly process and the artificial crystals it produces is required. In this work, we discuss the results of a hard coherent X-ray scattering experiment at the Linac Coherent Light Source, observing superlattices long after their initial nucleation. The resulting scattering intensity correlation functions have dispersion suggestive of a disordered crystalline structure and indicate the occurrence of rapid, strain-relieving events therein. We also present real space reconstructions of individual superlattices obtained via coherent diffractive imaging. Through this analysis we thus obtain high-resolution structural and dynamical information of self-assembled superlattices in their native liquid environment.

Studying the so-called ”hidden” phases of quantum materials—phases that do not exist under equilibrium conditions, but can be accessed with light—reveals new insights into the broader field of structural phase transitions. Using terahertz irradiation as well as hard x-ray probes made available by x-ray free electron lasers (XFELs) provides unique capabilities to study phonon dispersion in these materials. Here, we study the cubic peak of the quantum paraelectric strontium titanate (SrTiO3, STO) below the 110 K cubic-to-tetragonal tran- sition. Our results reveal a temperature and field strength dependence of the transverse acoustic mode in agreement with previous work on the avoided crossing occurring at finite wavevector, as well as evidence of anharmonic coupling between transverse optical phonons and a fully symmetric A1g phonon. These results elucidate previous optical studies on STO and hold promise for future studies on the hidden metastable phases of quantum materials.

This thesis focuses on how domain formation and local disorder mediate non-equilibrium order in the context of condensed matter physics. More specifically, the data supports c-axis CDW ordering in the context of the rare-earth Tritellurides. Experimental studies were performed on Pd:ErTe3 by ultra-fast pump-probe and x-ray free electron laser (XFEL). Ginzburg Landau models were used to simulate domain formation. Universal scaling analysis on the data reveals that topological defects govern the relaxation of domain walls in Pd:ErTe3. This thesis presents information on progress towards using light to control material domains.

For this thesis, the energy of the CXLS electron beam was measured and the beam’s energy jitter was calculated. It is essential to characterize the beam’s en- ergy and energy jitter in order to ensure that the powerful x-rays produced by CXLS will be of a consistent and desirable energy. The energy of the electrons within the electron beam can be calculated through utilizing basic physics prin- ciples and the geometry of the beamline. The energy of the beam for the data collected was found to be 3.426 MeV at POP module 1 and 12.3 MeV at POP module 9. The energy jitter of the beam was determined for four different angle settings of the VPSPD for linac 1 and found to be lowest when the linac 1 VPSPD was set to an angle of 97°. The energy jitter of the beam was 1.50e-03 MeV when the VPSPD for linac 1 was set to 97°.