Sampling Volumes in Powder Diffraction Experiments

Faculty: Alican Noyan

In a recent study, our faculty member Alican Noyan applied data science methods to a materials science problem. In many real-world experiments, we rarely have access to the entire population, we only collect data from a sample. This idea, familiar to anyone who has dealt with sampling bias or data quality issues, also applies to experiments in physics and materials science.

In collaboration with Columbia University, Alican developed a statistical model that estimates how many particles in a solid sample actually contribute useful information during a diffraction experiment—a method used to study material structure. The model combines geometric probability with Bernoulli statistics and the Lorentz-Scherrer equation to describe how sampling efficiency depends on particle size and the angular conditions of the experiment. Monte Carlo simulations—familiar to our students from the second year statistics course—were used to test the model, simulating millions of particles to quantify how experimental parameters affect data quality and uncertainty.

Figure 1

Diffraction geometry used in the simulations.

The surprising insight? Only a small fraction of particles may contribute to the measured signal. Understanding how this undersampling happens helps researchers design better experiments and highlights the importance of statistical thinking in any scientific field.

This study is a reminder that data science has a wide range of applications demonstrating its value across many scientific and technical fields.

Publications