On the use of two-time correlation functions for X-ray photon correlation spectroscopy data analysis

Area of Science:

• Physics
• Materials Science

Background:

• Multi-time correlation functions are essential for studying non-equilibrium processes.
• Two-time correlation functions are frequently employed in X-ray photon correlation spectroscopy for out-of-equilibrium systems.
• One-time correlations are often derived from two-time correlations at varying sample ages, but this approach lacks uniqueness.

Purpose of the Study:

• To scrutinize two distinct methods for analyzing two-time correlation functions.
• To discuss the implications of these analysis methods on correlation times and functional shapes.
• To provide clarity on the interpretation of correlation data in non-equilibrium systems.

Main Methods:

• Analysis of two distinct methods for evaluating two-time correlation functions.
• Application of three illustrative examples to demonstrate the impact of analysis choices.
• Comparison of derived correlation times and functional shapes based on different analytical approaches.

Main Results:

• The analysis reveals that the extraction of one-time correlations from two-time functions is not a unique process.
• Different analysis methods can lead to variations in the calculated correlation times.
• The functional shape of correlations can also be influenced by the chosen analysis technique.

Conclusions:

• The choice of method for analyzing two-time correlation functions significantly impacts the derived correlation times and functional shapes.
• Careful consideration of analysis techniques is crucial for accurate interpretation of non-equilibrium dynamics.
• This work highlights the importance of method selection in X-ray photon correlation spectroscopy and similar techniques.