journal article·2023-05-23Open access

Concurrent multi-peak Bragg coherent x-ray diffraction imaging of 3D nanocrystal lattice displacement via global optimization

Siddharth Maddali, Travis D. Frazer, Nazar Delegan, Katherine J. Harmon, Sean E. Sullivan, Marc Allain, Wonsuk Cha, Alan Dibos, Ishwor Poudyal, Saugat Kandel, Youssef S. G. Nashed, F. Joseph Heremans, Hoydoo You, Yue Cao, Stephan O. Hruszkewycz

npj Computational Materials· Volume 9· Issue 1

Abstract

Abstract In this paper we demonstrated a method to reconstruct vector-valued lattice distortion fields within nanoscale crystals by optimization of a forward model of multi-reflection Bragg coherent diffraction imaging (MR-BCDI) data. The method flexibly accounts for geometric factors that arise when making BCDI measurements, is amenable to efficient inversion with modern optimization toolkits, and allows for globally constraining a single image reconstruction to multiple Bragg peak measurements. This is enabled by a forward model that emulates the multiple Bragg peaks of a MR-BCDI experiment from a single estimate of the 3D crystal sample. We present this forward model, we implement it within the stochastic gradient descent optimization framework, and we demonstrate it with simulated and experimental data of nanocrystals with inhomogeneous internal lattice displacement. We find that utilizing a global optimization approach to MR-BCDI affords a reliable path to convergence of data which is otherwise challenging to reconstruct.
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Research context

OpenAlex topics: Advanced X-ray Imaging Techniques · Advanced Electron Microscopy Techniques and Applications · Crystallography and Radiation Phenomena

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (42)

Show source-provided references
1. Robinson, I. K., Vartanyants, I. A., Williams, G. J., Pfeifer, M. A. & Pitney, J. A. Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction. Phys. Rev. Lett. 87, 195505 (2001).10.1103/PhysRevLett.87.195505 ↗
2. Miao, J., Ishikawa, T., Robinson, I. K. & Murnane, M. M. Beyond crystallography: Diffractive imaging using coherent x-ray light sources. Science 348, 530–535 (2015).10.1126/science.aaa1394 ↗
3. Fienup, J. R. Phase retrieval algorithms: a comparison. Appl. Opt. 21, 2758–2769 (1982).10.1364/AO.21.002758 ↗
4. Marchesini, S. et al. X-ray image reconstruction from a diffraction pattern alone. Phys. Rev. B 68, 140101 (2003).10.1103/PhysRevB.68.140101 ↗
5. Marchesini, S. Invited article: A unified evaluation of iterative projection algorithms for phase retrieval. Rev. Sci. Instrum. 78, 011301 (2007).10.1063/1.2403783 ↗
6. Kawaguchi, T. et al. Gas-induced segregation in pt-rh alloy nanoparticles observed by in situ bragg coherent diffraction imaging. Phys. Rev. Lett. 123, 246001 (2019).10.1103/PhysRevLett.123.246001 ↗
7. Singer, A. et al. Nucleation of dislocations and their dynamics in layered oxide cathode materials during battery charging. Nat. Energy 3, 641–647 (2018).10.1038/s41560-018-0184-2 ↗
8. Hruszkewycz, S. O. et al. Strain annealing of sic nanoparticles revealed through bragg coherent diffraction imaging for quantum technologies. Phys. Rev. Mater. 2, 086001 (2018).10.1103/PhysRevMaterials.2.086001 ↗
9. Pateras, A. et al. Combining Laue diffraction with Bragg coherent diffraction imaging at 34-ID-C. J. Synchrotron Radiat. 27, 1430 (2020).10.1107/S1600577520009844 ↗
10. Newton, M. C., Leake, S. J., Harder, R. & Robinson, I. K. Three-dimensional imaging of strain in a single ZnO nanorod. Nat. Mater. 9, 120 (2009).10.1038/nmat2607 ↗
11. Hofmann, F. et al. Nanoscale imaging of the full strain tensor of specific dislocations extracted from a bulk sample. Phys. Rev. Mater. 4, 013801 (2020).10.1103/PhysRevMaterials.4.013801 ↗
12. Wilkin, M. J. et al. Experimental demonstration of coupled multi-peak bragg coherent diffraction imaging with genetic algorithms. Phys. Rev. B 103, 214103 (2021).10.1103/PhysRevB.103.214103 ↗
13. Newton, M. C. Concurrent phase retrieval for imaging strain in nanocrystals. Phys. Rev. B 102, 014104 (2020).10.1103/PhysRevB.102.014104 ↗
14. Gao, Y., Huang, X., Yan, H. & Williams, G. J. Bragg coherent diffraction imaging by simultaneous reconstruction of multiple diffraction peaks. Phys. Rev. B 103, 014102 (2021).10.1103/PhysRevB.103.014102 ↗
15. Kandel, S. et al. Using automatic differentiation as a general framework for ptychographic reconstruction. Opt. Express 27, 18653–18672 (2019).10.1364/OE.27.018653 ↗
16. Maddali, S. et al. General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I. J. Appl. Crystallogr. 53, 393–403 (2020).10.1107/S1600576720001363 ↗
17. Li, P. et al. General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II. J. Appl. Crystallogr. 53, 404–418 (2020).10.1107/S1600576720001375 ↗
18. Unser, M., Thevenaz, P. & Yaroslavsky, L. Convolution-based interpolation for fast, high-quality rotation of images. IEEE Trans. Image Process 4, 1371–1381 (1995).10.1109/83.465102 ↗
19. Larkin, K. G., Oldfield, M. A. & Klemm, H. Fast fourier method for the accurate rotation of sampled images. Opt. Commun. 139, 99–106 (1997).10.1016/S0030-4018(97)00097-7 ↗
20. Thévenaz, P., Blu, T. & Unser, M. Interpolation revisited [medical images application]. IEEE Trans. Med. imaging 19, 739–758 (2000).10.1109/42.875199 ↗
21. Godard, P., Allain, M., Chamard, V. & Rodenburg, J. Noise models for low counting rate coherent diffraction imaging. Opt. Express 20, 25914–25934 (2012).10.1364/OE.20.025914 ↗
22. Godard, P. On the use of the scattering amplitude in coherent x-ray bragg diffraction imaging. J. Appl. Crystallogr. 54, 797–802 (2021).10.1107/S1600576721003113 ↗
23. Kandel, S. Using automatic differentiation for coherent diffractive imaging applications. PhD thesis dissertation, (2021).
24. Saad, D. Online algorithms and stochastic approximations. Online Learn. J. 5, 6–3 (1998).
25. Duchi, J., Hazan, E. & Singer, Y. Adaptive subgradient methods for online learning and stochastic optimization. J. Mach. Learn. Res. 12, 2121–2159 (2011).
26. Maddali, S. mrbcdi: Differentiable multi-reflection bragg coherent diffraction imaging for lattice distortion fields in crystals. https://github.com/siddharth-maddali/mrbcdi.
27. Paszke, A. et al. Pytorch: An imperative style, high-performance deep learning library. In Adv. Neural. Inf. Process. Syst. (eds H. Wallach, H. Larochelle, A. Beygelzimer, F. d’Alché-Buc, E. Fox, & R. Garnett) 32, pages 8024–8035. (Curran Associates, Inc., 2019).
28. Fienup, J. R. & Wackerman, C. C. Phase-retrieval stagnation problems and solutions. J. Opt. Soc. Am. A 3, 1897–1907 (1986).10.1364/JOSAA.3.001897 ↗
29. Kingma, D. & Ba, J. Adam: A method for stochastic optimization. arXiv preprint https://arxiv.org/abs/1412.6980 (2014).
30. Phillips, R. Crystals, Defects and Microstructures: Modeling Across Scales. (Cambridge University Press, 2001).10.1017/CBO9780511606236 ↗
31. Ulvestad, A., Menickelly, M. & Wild, S. M. Accurate, rapid identification of dislocation lines in coherent diffractive imaging via a min-max optimization formulation. AIP Adv. 8, 015114 (2018).10.1063/1.5017596 ↗
32. Fuchs, F. et al. Silicon carbide light-emitting diode as a prospective room temperature source for single photons. Sci. Rep. 3, 1637 (2013).10.1038/srep01637 ↗
33. Lohrmann, A. et al. Single-photon emitting diode in silicon carbide. Nat. Commun. 6, 7783 (2015).10.1038/ncomms8783 ↗
34. Cochrane, C. J., Blacksberg, J., Anders, M. A. & Lenahan, P. M. Vectorized magnetometer for space applications using electrical readout of atomic scale defects in silicon carbide. Sci. Rep. 6, 37077 (2016).10.1038/srep37077 ↗
35. Atatüre, M., Englund, D., Vamivakas, N., Lee, S.-Y. & Wrachtrup, J. Material platforms for spin-based photonic quantum technologies. Nat. Rev. Mater. 3, 38–51 (2018).10.1038/s41578-018-0008-9 ↗
36. Miao, K. C. et al. Electrically driven optical interferometry with spins in silicon carbide. Sci. Adv. 5, eaay0527 (2019).10.1126/sciadv.aay0527 ↗
37. Bourassa, A. et al. Entanglement and control of single nuclear spins in isotopically engineered silicon carbide. Nat. Mater. 19, 1319–1325 (2020).10.1038/s41563-020-00802-6 ↗
38. Nelder, J. A. & Mead, R. A simplex method for function minimization. Comput J. 7, 308–313 (1965).10.1093/comjnl/7.4.308 ↗
39. Kandel, S. et al. Efficient ptychographic phase retrieval via a matrix-free levenberg-marquardt algorithm. Opt. Express 29, 23019–23055 (2021).10.1364/OE.422768 ↗
40. Scheinker, A. & Pokharel, R. Adaptive 3d convolutional neural network-based reconstruction method for 3d coherent diffraction imaging. J. Appl. Phys. 128, 184901 (2020).10.1063/5.0014725 ↗
41. Cherukara, M. J. et al. AI-enabled high-resolution scanning coherent diffraction imaging. Appl. Phys. Lett. 117, 044103 (2020).10.1063/5.0013065 ↗
42. Harder, R. Deep neural networks in real-time coherent diffraction imaging. IUCrJ 8, 1–3 (2021).10.1107/S2052252520016590 ↗