The Materials Complexity Frontier: Applied Math and Computational Challenges

1. The Materials Complexity Frontier: Applied Math and Computational Challenges S.J.L. Billinge Department of Applied Physics and Applied Mathematics Columbia University, CMPMS, Brookhaven National Laboratory

2. Complicated Problems Complex materials will lie at the heart of the solutions to many of society’s most pressing problems • Sustainable Energy • Environmental remediation • Health

3. Complex materials • Photovoltaics with improved efficiency • Nanoparticles in the light collecting layer • High energy density batteries • Electrodes • Electrolytes • Fuel cells for transportation applications • Electrodes • Electrolytes • Catalysts • Hydrogen storage • Sequestration • Functionalized mesoporous materials Image credits: 10.1126/science.1185509 U. Uppsala

4. The Nanostructure Problem • We want to engineer materials at the nanoscale • But we can’t even solve the atomic structure at the nanoscale: The nanostructure problem

5. The comprehension problem • The nanostructure problem is a concrete example of what I call The Comprehension Problem Data -> Knowledge -> Robust Understanding

6. The Crystal Structure Problem • Problem: • Here is a crystal, what is its structure? • Solution: • Give it to your grad student • She puts it on the x-ray machine • …Pushes the button • Machine tells you the structure Crystallography is largely a solved problem From LiGaTe2: A New Highly Nonlinear Chalcopyrite Optical Crystal for the Mid-IRL. Isaenko, et al., J. Crystal Growth, 5, 1325 – 1329 (2005)

7. The Nanostructure Problem • Problem: • Here is a nanoparticle, what is its structure? • Solution: • Give it to your grad student • She puts it on the x-ray machine • …Pushes the button

8. Complex materials • Photovoltaics with improved efficiency • Nanoparticles in the light collecting layer • High energy density batteries • Electrodes • Electrolytes • Fuel cells for transportation applications • Electrodes • Electrolytes • Catalysts • Hydrogen storage • Sequestration • Functionalized mesoporous materials Image credits: 10.1126/science.1185509 U. Uppsala

9. The Nanostructure Problem • Problem: • Here is a nanoparticle, what is its structure? • Solution: • Give it to your grad student • She puts it on the x-ray machine • …Pushes the button

10. Structure Solution from PDF Example: C60 • 60 atoms => n(n-1)/2 = 1770 pair-vectors • We know the lengths (not the directions) of ~18 unique distances • We have an imperfect measure of the multiplicities of those distances • We don’t have any symmetry information to help us Is the problem well conditioned or ill conditioned? Is there a unique solution?

11. 60 atoms ~64 atoms C60 Ultra-small CdSe NPs

12. Successology

13. Problem Well posed problem: Information in the PDF data ILL POSED Problem! Degrees of freedom in the model Bits of information

14. Structure Solution

15. Complex Modeling Solution • c = a + ib – complex number mixes real and imaginary parts • m = e + it – complex modeling mixes experiment and theory in a coherent computational framework • Billinge and Levin, Science 2007 • exoscale Computing • Compl-

16. Joking aside Main applied math challenges: • Heterogeneous data • Reliability of results • Tolerating systematic errors/aberrations Main computational challenges: • Expensive forward calculations (e.g., DFT!), now in a regression loop

17. Complex Modeling infrastructure: Diffpy-CMI www.diffpy.org Official release of Diffpy-CMI v0.1 (Complex Modeling Infrastructure) on 3/31/14 (284 downloads)

18. Robustness (degeneracy/convergence) of modeling results “HPC” enabled brute-force search of structure solution phase-space of CdSe Quantized growth nanoparticles

19. How does the addition of Small Angle Scattering Data affect the results? • SAXS data from NSLS X9B on CdSe particles dissolved in toluene • tetrahedral CdSe model has SAXS residuum 0.008 • clusters generated from PDF optimization have poor fit to the SAXS data • validate uniqueness of the tetrahedral structure models.

20. Materials modelers, please don’t get too smug • Ultra-stable Au144 nanocluster

21. Now do all that in quasi-real time: in-situ, in-operando experiments • We can see precursor species in solution • We can measure Nanoparticle structural parameters => Let’s do in-situ studies of synthesis • collaboration with the group of Bo Iversen (Aarhus) Image credit ChristofferTyrsted

22. Or spatially resolved • Computed tomography nano-diffraction • 103 more data than a regular ct-scan

23. Data Rates at modern synchrotron facilities • Courtesy Ray Osborne, APS, ANL

24. These data rates are not exceptionally high • But there are complex data assessment, reduction and modeling steps that must be carried out in quasi-real time requiring particular architecture and access mode. • Solving this problem will revolutionize how scattering scientists do their experiments. Imagine a doctor interpreting an MRI scan from thousands of frames of the raw nuclear spin relaxation data….

25. To make significant progress in Complex Materials • Use theoretical/computational and experimental data synergistically • Validate robustness of solutions • Increase reproducibility of all computational results • Couple data acquisition, assessment, reduction and modeling more closely • …..automate discovery using data analytics approaches These are applied math, software and architectural issues: Compl-exoscale computing!