Complex Modeling and Nanostructure Determination

Novel materials are at the heart of the next generation of energy, environmental, and health technologies. The structure of such materials is often complex.  And many of them are composites, exhibiting complex ordering on multiple length scales. To truly harness the power of such materials, we must understand the relationship between atomic structure and macroscopic properties. However, the atomic structure of highly complex materials can be extremely difficult to solve.

The structure of bulk materials can generally be described with crystal models, which require only tens or hundreds of parameters, while X-ray diffraction data typically yields information on hundreds or thousands diffraction peaks. Thus, a unique structural solution can often be found. However, for complex materials, the number of degrees of freedom in a suitable structure model is often larger than the number of independent data points obtained from experiment. Thus, the problem is inherently ill-posed, making a unique structural solution impossible.

Complex Modeling
Complex Modeling

For these structural problems, a single experimental technique cannot provide sufficient information to guarantee that the problem is well-posed. Thus, to obtain unique structural solutions for complex materials, a new paradigm of analysis is needed, an infrastructure that can combine different information sources and models into a coherent framework to solve problems using global optimization. Within this framework, a material with unknown structure could be probed with various experimental tools, such as X-ray diffraction (XRD), transmission electron microscopy (TEM), Small Angle Scattering (SAS), Raman spectroscopy, etc., to yield an array of data sets that would then be fed into a global optimizer. Additionally, theoretical inputs, such as density functional theory or molecular dynamics calculations, as well as constraints on the variables, could be integrated into the optimization. Thus, while each single experimental or theoretical input may not generate enough information to produce a solution, together the pieces of information make a more complete picture of the problem we want to solve.

The software framework Diffpy-CMI is an open-source project which provides tools for doing complex modeling. To read more and download the software, please go to for more information.