Researchers from Oak Ridge National Laboratory (ORNL), North Carolina State University (NC State), and the National Institute of Standards and Technology (NIST) have used Bayesian statistical methods to develop a novel approach for materials characterization and as a result, to gain new insights into material structures.
This research work is expected to accelerate the development of many new materials for use in various applications.
We want to understand the crystallographic structure of materials – such as where atoms are located in the matrix of a material – so that we have a basis for understanding how that structure affects a material’s performance. This is a fundamentally new advance that will help us develop new materials that can be used in everything from electronics and manufacturing to vehicles and nanotechnologies.
Jacob Jones, Professor, NC State
The initial step in analyzing a material’s crystallographic structure is to bombard a material sample with photons, electrons, or other subatomic particles.
This bombarding process is performed using technology such as the Advanced Photon Source at Argonne National Laboratory or the Spallation Neutron Source at ORNL. When the bombarded particles are scattered by the material, researchers will be able to measure the energy and angle of these particles.
Then Things get Really Tricky.
Generally, a material’s crystallographic structure is studied by analyzing the data obtained from scattering experiments using statistical techniques known as “least squares fitting”. Due to limitations of this technique, researchers are able to only study a material’s structure.
These techniques fail to provide a complete description of the variability or uncertainty within a materials structure. This is because the techniques do not make use of probabilities to describe answers.
Least squares is a straightforward technique, but it doesn’t allow us to describe the inferred crystallographic structure in a way that answers the questions that the materials scientists want to ask. But we do have other techniques that can help address this challenge, and that’s what we’ve done with this research.
Alyson Wilson, Professor, NC State
The fact is that, the space between atoms is not constant and it is not the same throughout a sample. This condition is true for all the aspects of a material’s structure.
“Understanding that variability, now possible with this new approach, allows us to characterize materials in a new, richer way,” Jones says.
This is Where Bayesian Statistics Comes into Play.
For example, atoms vibrate, and the extent of the vibration is controlled by their temperature. Researchers want to know how those vibrations are influenced by temperature for any given material. And Bayesian tools can give us probabilities of these thermal displacements in a material. This approach will allow us to analyze data from a wide variety of materials characterization techniques – all forms of spectroscopy, mass spectrometry, you name it – and more fully characterize all kinds of matter. Honestly, it’s very exciting.
Jacob Jones, Professor, NC State
“We also plan to use these techniques to combine data from different types of experiments, in order to offer even more insights into material structure,” Wilson says.
The paper, “Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis,” is featured in the Nature journal Scientific Reports. Key authors of the paper are Chris Fancher, who is a postdoctoral researcher at NC State, and Zhen Han, a former Ph.D. student at NC State. Co-authors include Igor Levin of NIST; Katharine Page of ORNL; Brian Reich, an associate professor of statistics at NC State; and Ralph Smith, a Distinguished Professor of Mathematics at NC State.
The work was carried out with support from the Kenan Institute for Engineering, Technology and Science at NC State, the Eastman Chemical Company-University Engagement Fund at NC State, the National Science Foundation under grant DMR-1445926, and the U.S. Department of Energy’s Office of Science under contract number DE-AC02-06CH11357.