Title: Local structure and lattice dynamics study of low dimensional materials using atomic pair distribution function and high energy resolution inelastic x-ray scattering
Description: Structure and dynamics lie at the heart of the materials science. A detailed knowledge of both subjects would be foundational in understanding the materials' properties and predicting their potential applications. However, the task becomes increasingly difficult as the particle size is reduced to the nanometer scale. For nanostructured materials their laboratory x-ray scattering patterns are overlapped and broadened, making structure determination impossible. Atomic pair distribution function technique based on either synchrotron x-ray or neutron scattering data is known as the tool of choice for probing local structures. However, to solve the \structure problem" in low-dimensional materials with PDF is still challenging. For example for 2D materials of interest in this thesis the crystallographic modeling approach often yields unphysical thermal factors along stacking direction where new chemical intuitions about their actual structures and new modeling methodology/program are needed.

Beyond this, lattice dynamical investigations on nanosized particles are extremely dicult. Laboratory tools such as Raman and infra-red only probe phonons at Brillouin zone center. Although in literature there are a great number of theoretical studies of their vibrational properties based on either empirical force elds or density functional theory, various approximations made in theories make the theoretical predictions less reliable. Also, there lacks the direct experiment result to validate the theory against. In this thesis, we studied the structure and dynamics of a wide variety of technologically relevant low-dimensional materials through synchrotron based x-ray PDF and high energy resolution inelastic x-ray scattering (HERIX) techniques. By collecting PDF data and employing advanced modeling program such as DiPy-CMI, we successfully determined the atomic structures of (i) emerging Ti3C2, Nb4C3 MXenes (transition metal carbides and/or nitrides) that are promising for energy storage applications, and of (ii) zirconium phenylphosphonate ion exchange materials that are proposed to separate lanthanide ions from actinide ions in nuclear waste.

Both material systems have two-dimensional layered nanocrystalline structure where we observed that the stacking of layers are not in good registry, also known as "turbostratic" disorder. Consequently the signals from a single layer of atoms dominate the experimental PDF{thus building up a single slab model and simulating PDF using Debye function analysis was sucient to capture the main structural features in the measured PDF data. The information on correlation length of layers along the stacking direction, however, is contained in low-Q diraction peaks in either laboratory x-ray or synchrotron x-ray scattering patterns. On the lattice dynamics side, we first investigated the trend of atomic bonding strength in size dependent platinum nanoparticles based on temperature dependent PDF data and measured Debye temperatures. An anomalous bond softening was observed at a particle size less than 2 nm. Since Debye model gives a simple quadratic phonon density of states (PDOS) curve, which is a simplified version of real lattice dynamics, we are motivated to measure full PDOS curves on three CdSe nanoclusters by using non-resonant inelastic x-ray scattering technique.

We observed an overall blue-shift of PDOS curves with decreased sizes. Our current exemplary studies will open the door to a large number of future structural and lattice dynamical studies on a much broader range of low-dimensional material systems.