This group's research involves experimental studies in the equilibrium and non-equilibrium statistical mechanics of disordered solids and complex materials (gels, foams, colloids, etc.). These form three frequently overlapping segments: impedance fluctuations and microstructure, kinetics of defects in solids, and x-ray dynamical light scattering.
Due to the central limit theorem, Gaussian fluctuations are expected for most systems in thermodynamic equilibrium. All correlation functions of order greater than two of Gaussian random processes can be expressed in terms of first- and second-order correlation functions; therefore non-Gaussianity is quantified by the deviation of high-order statistics (i.e. order greater than two) from the expectation for Gaussian noise.
Non-Gaussian noise is often associated with the presence of correlations between microscopic fluctuations. One important example of this behavior occurs in the vicinity of a second-order phase transition, where the divergence of the correlation length mandates that fluctuations be non-Gaussian. Large non-Gaussian fluctuations are also present in steady-state driven systems with non-linear response functions. Careful study of the high-order statistics of fluctuations can give insight into the microscopic properties of complex systems.
Recent work has both resolved and raised important questions concerning the high-order statistics of 1/f resistance noise. The metal-insulator transition in percolation resistor networks is a canonical example of a second-order phase transition; hence, the resistance fluctuations as a function of variations in network topology are strongly non-Gaussian. Resistance noise in conductors near the percolation threshold has previously been envisioned as a fundamentally different situation in which one has Gaussian noise from a fixed-topology resistor network where each discrete element has statistically-independent fluctuations.
Howver, Prof. Seidler and coworkers at NEC Research Institute demonstrated that this sharp distinction between the dynamic- and static-configuration treatments is not appropriate for many materials. Local resistivity fluctuations result in a sampling of some subset of the phase space of configurations of the resistor network. When these fluctuations are not small the dynamical redistribution of current in the sample leads to long-range non-linear statistical couplings between the contributions to the total sample noise power from otherwise statistically-independent fluctuators. This results in non-Gaussian noise. Although the divergence of the noise power in conductors near the percolation threshold has been studied by several groups, no systematic study of the high-order statistics exists. This group will pursue this experiment using both thin-film and composite systems. In the long term, this work will evolve into investigations of the high-order statistics of impedance noise on both sides of the metal-insulator transition. Applications of impedance fluctuation spectroscopy for characterization of the microstructure of composite conducting materials and polycrystalline ferroelectric films will also be pursued.
The bulk properties of materials depend not only on their crystalline nanostructure, but also on their microstructure defined by domain walls, twin boundaries, and other planar defects. The dynamics of this microstructure under appropriate stresses are particularly important. For example, domain wall motion in ferromagnets determines their usefulness in power transformers and magnetic recording heads, while the recent explosion of microelectronics applications of ferroelectrics has generated renewed interest in their domain wall dynamics.
Ferroelastics (which include many ferroelectrics as a subclass) are low-symmetry martensitic materials which can reversibly rearrange their domain wall (usually twin boundary) configurations to minimize internal stress. Many insulating ferroelastics are appealing for fundamental studies of domain wall kinetics due to their large optical birefringence and large accessible range in domain wall velocities (spanning slow thermally-activated motion to driven linear response).
The goal of this research thrust is to correlate the well-characterized macroscopic mechanical properties of ferroelastics with the details of the microscopic interaction of domain walls with crystal defects. Observation of the domain wall motion on large length scales is straightforward with a polarized-light optical microscope. Measurements of the evolution of the roughness of the domain walls will be made by both optical-wavelength diffraction and dynamical light scattering (DLS). The propagation of light through the crystal provides a sensitive direct measurement of domain wall kinetics. The high-order statistics of the DLS signal will be investigated as a possible method to quantify spatial correlations between depinning events.
This final success of this project will depend directly on a correct treatment of the problems of both quasi-stationarity and non-ergodicity of the scattered light. To gain experience with these issues, experiments will first be performed on better-characterized complex materials where non-ergodicity has been carefully treated in the past.
The latest generation of x-ray source synchrotrons have opened up the possibility of x-ray dynamical light scattering (XDLS) studies of structural fluctuations on Angstrom length scales and micro-second time scales. Such a technique would provide a new window on many problems of long-standing interest in both condensed matter physics and material sciences, including: fluctuations at structural phase transitions in solids, thermal kinetics of point defects in solids, annealing phenomenon, and glass formation. However, several complications must be quantitatively understood before the potential of this technique can be realized. The most serious of these is the problem of non-ergodicity of the scatterers. Although non-ergodicity has been carefully studied in optical-wavelength DLS of diffusing species in gels, the (hopefully similar) difficulties in interpretation of XDLS spectra caused by the existence of a crystalline lattice of scatterers have not yet been treated.
Hence, in the short term, carefully chosen control experiments to determine the role of scattering from the largely time-invariant crystalline lattice in the interpretation of XDLS experiments will be performed. One appealing family of experiments involves simultaneous measurement of resistance noise and XDLS spectra for simple metals with thermally-diffusing or electromigrating interstitials. Experimental tests for the Gaussianity of the scattered field which do not make direct use of heterodyning will also be developed. In the long term, the focus of the XDLS experiments in my lab will likely shift to studies of ordering kinetics of solid-to-solid phase transitions.