Novel materials have brought great impacts to our society, such as the ones we have seen in flexible LED displays, large storage batteries, and photovoltaic materials. To discover materials with an ever higher performance we need to understand the relationship between nanoscale structure and the material properties. The properties are highly dependent on ‘imperfections’ inside materials, such as defects, nanoscale structures, interfaces, surfaces, or multi-scale heterogeneities. X-ray diffraction has been a powerful tool to quantify the atomic arrangements of well-ordered materials (crystals), however, challenges are raised when applying this technique to materials with imperfections. The main issues are: loss of signal in the experiments and increased complexity of the structural solutions introduced by the imperfections. With these two issues together, the whole problem is then turned into an ill-posed inverse problem, i.e., we might not have enough information to uniquely assign one and only one structure based on signals measured from experiments.
In this project, we tackle the ill-posed inverse problem by reviewing and reformulating the entire problem with more mature mathematical setups and applying data analytical approaches to explore hidden information in data
To facilitate interactions with new theoretical models as well as data exploratory analysis, it’s crucial to have a platform that enables automated experimentation, generates rich metadata systematically, and processes data in real-time. A series of software packages, xpdAcq, xpdAn and xpdView, have been developed to achieve this goal. xpdAcq provides an easy-to-use user interface with an experimenter-centric syntax which minimizes the requirements of programming background from users. Experiments run with xpdAcq will be bundled with rich metadata. xpdAcq metadata includes information from various aspects of the experiment, ranging from sample temperature, detector information, sample composition, to parameters required for mathematical operations on the data. xpdAn provides a configurable analysis pipeline to process data in real-time where processed data will be pushed to a database with detailed logs. This enables exploratory data analysis later. xpdView is a data visualization tool that is tightly integrated with xpdAcq and xpdAn. It is designed to efficiently display information and help the experimenter make decisions on the fly.
Progress in Mathematics and data analytical approaches
Graph Theory is a field in math that describes detailed properties between a set of groups and its corresponding graphs. Graph Theory is a good entry point of formulating the ill-posed nanostructure inverse problem. Research on Distance Geometry, a sub-field of Graph Theory, has been explored to aid in the solution of nanostructure reconstructions. In this research, the inverse problem based on atomic pair distribution function (PDF) is formulated as an Unassigned Distance Geometry Problem.
With formal mathematical setup, we are able to explore the minimum information content required to reconstruct the structures and an algorithm that demonstrates this reconstruction process is being carried out in this research as well.
Please find slides summarizing current stage of this project here
This project is funded by the US National Science Foundation DMREF program.
This material is based upon work supported by the National Science Foundation under DMR Grant No. 1534910
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
The NSF award may be seen here