Inverse Transformation: Unleashing Heterogeneous Dynamics with an Alternative Approach to XPCS Data Analysis
Ross N. Andrews, Suresh Narayanan, Fan Zhang, Ivan Kuzmenko, Jan Ilavsky
X-ray photon correlation spectroscopy (XPCS), as an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering vector-dependent sample dynamics at smaller length scales. The penetrating power of X-rays enables probing dynamics with XPCS in a broad array of materials, including polymers, glasses and metal alloys, where attempts to describe the autocorrelation function with simple exponential decay usually fail. The prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions, which implicitly assumes homogeneous dynamics. In this paper, we propose an alternative analysis scheme based on inverse Laplace or Gaussian transform for elucidation of heterogeneous distributions of dynamic time scales, an approach analogous to the CONTIN algorithm widely accepted in the DLS analysis of polydisperse and multimodal systems. Using a few examples, we demonstrate that the inverse transform approach not only generates equivalent dynamic time scales for dynamically homogeneous materials, but also reveals hidden multimodal dynamics for dynamically heterogeneous materials, thereby unleashing the full potential of XPCS in revealing dynamics of complex materials.