No abstract

No abstract

No abstract

Modern materials under study for next generation technologies in energy conversion and storage, environmental remediation, and health are highly complex, often heterogeneous and nano-structured. Here we refer to these as real materials. A full understanding of the structure requires us to go beyond crystallography and to study the local structure, which is a major experimental and theoretical challenge [1].Although we have been able to solve the structure of crystals for more than 100 years, when the structure of the material is not periodically long-range ordered, as is the case in real-materials in general, we need characterization methods that extend crystallography, and for nano-materials we are finding that we even need to replace crystallography. Microscopy and imaging is playing a critical role in this endeavor, of course. However, in this talk we focus on the nanostructure problem: obtaining the 3D coordinates of atoms in space with high precision, which goes beyond obtaining images.A recent issue that we have been encountering is that as the structure becomes more complex at the nanoscale, the amount of information in the scattering tends to decrease due to the overlap of broad scattering peaks and the inability to obtain information from single particles. At the same time, the complexity of the structural model needed to describe the structure increases. At some point the structure inverse problem becomes ill-posed and there is not a unique structural model consistent with the data but, in principle a large number of, degenerate solutions. This is illustrated in Fig. 1 where simulations of nanoparticle clusters have been generated consistent with atomic pair distribution function (PDF) data. Each dot gives the fitting figure of merit for a cluster generated during the reconstruction. On the x-axis is the agreement factor between the PDF calculated for the nanoparticle and measured data. On the y-axis is another figure of merit related to surface energy that measures the compactness of the candidate simulated nanoparticle. There is a large number of dots that have as good or better agreement with the data than the correct solution indicating that there is a large number of degenerate models when we just use the PDF data to measure against. We can also use some kind of physical plausibility of the model to differentiate between good and bad models, and one such measure is the mean number of bonds per atom. This measure discriminates against models that have lowcoordinated atoms extending out from the surface. Even taking these two measures together we do not find a unique solution. We believe that this problem of model degeneracy is quite widespread, though maybe not widely appreciated.To address this problem of the posedness of the inverse problem we have been developing an approach called "Complex Modeling" that allows multiple datasets to be complexed or considered together in a multi-modal fit [2]. I will describe this approach in the talk. In this mode we want to give multiple 172

No abstract