najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-6-723-731najo-601Research ArticlePHYSICSФИЗИКАNanocluster structure deduced from AC-STEM images coupled to theoretical modellingNanocluster structure deduced from AC-STEM images coupled to theoretical modellingSukutaK.SukutaK.

107 Reykjavík

107 Reykjavík

Van den BosscheM.Van den BosscheM.

107 Reykjavík

107 Reykjavík

PedersenA.PedersenA.

107 Reykjavík

107 Reykjavík

JónssonH.JónssonH.

107 Reykjavík, Iceland; Los Alamos, NM 87545, USA

107 Reykjavík, Iceland; Los Alamos, NM 87545, USA

hj@hi.isScience Institute and Faculty of Physical Sciences, University of IcelandScience Institute and Faculty of Physical Sciences, University of IcelandScience Institute and Faculty of Physical Sciences, University of Iceland; Center for Nonlinear StudiesScience Institute and Faculty of Physical Sciences, University of Iceland; Center for Nonlinear Studies20171208202586723731Copyright © Sukuta K., Van den Bossche M., Pedersen A., Jónsson H., 20252025Sukuta K., Van den Bossche M., Pedersen A., Jónsson H.Sukuta K., Van den Bossche M., Pedersen A., Jónsson H.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/601

Determining the atomic structure of nanoclusters is a challenging task and a critical one for understanding their chemical and physical properties. Recently, the high resolution aberration corrected scanning transmission electron microscope (AC-STEM) technique has provided valuable information about such systems, but the analysis of the experimental images has typically been qualitative rather than quantitative. A method is presented for detailed analsis of AC-STEM images combined with theoretical modelling to extract atomic coordinates. An objective function formed by a linear combination of a fit to the two-dimensional AC-STEM image plus an estimate of the cluster’s energy for adding information about the third dimension is used in a global optimization algorithm to extract the atomic coordinates. The method is illustrated by analyzing model images generated for the Garzón structure of the Au55 cluster, which is a metastable structure for the embedded atom method (EAM) potential function used here to estimate the total energy. As the method does not rely on the alignment of atom rows in the AC-STEM image, the partially disordered chiral structure of the Au55 can successfully be determined even when a significant level of noise is added to the images.

Determining the atomic structure of nanoclusters is a challenging task and a critical one for understanding their chemical and physical properties. Recently, the high resolution aberration corrected scanning transmission electron microscope (AC-STEM) technique has provided valuable information about such systems, but the analysis of the experimental images has typically been qualitative rather than quantitative. A method is presented for detailed analsis of AC-STEM images combined with theoretical modelling to extract atomic coordinates. An objective function formed by a linear combination of a fit to the two-dimensional AC-STEM image plus an estimate of the cluster’s energy for adding information about the third dimension is used in a global optimization algorithm to extract the atomic coordinates. The method is illustrated by analyzing model images generated for the Garzón structure of the Au55 cluster, which is a metastable structure for the embedded atom method (EAM) potential function used here to estimate the total energy. As the method does not rely on the alignment of atom rows in the AC-STEM image, the partially disordered chiral structure of the Au55 can successfully be determined even when a significant level of noise is added to the images.

nanoclusterAC-STEMatomic structureglobal optimizationgenetic algorithmnanoclusterAC-STEMatomic structureglobal optimizationgenetic algorithmWe thank Ignacio Garzón for providing us with the atomic coordinates in the optimal Au55 structure deduced from the Gupta potential function. This work was supported by the Icelandic Research Fund and the University of Iceland Doctoral Fund. KS and MVDB gratefully acknowledge computer resources at the University of Iceland Computing Services (Reiknistofnun) and through a SNIC grant at C3SE (Göteborg, Sweden).ReferencesBinning G., Rohrer H., Gerber Ch., Weibel E. Surface studies by scanning tunneling microscopy. Phys. Rev. Letters, 1982, 49(1), P. 57–61.Binning G., Rohrer H., Gerber Ch., Weibel E. Surface studies by scanning tunneling microscopy. Phys. Rev. Letters, 1982, 49(1), P. 57–61.Valden M., Lai X., Goodman D.W. Onset of catalytic activity of gold clusters on titania with the appearance of nonmetallic properties. Science, 1998, 281, P. 1647.Valden M., Lai X., Goodman D.W. Onset of catalytic activity of gold clusters on titania with the appearance of nonmetallic properties. Science, 1998, 281, P. 1647.Yamauchi M., Abe R., Tsukuda T., Kato K., Takata M. Highly selective ammonia synthesis from nitrate with photocatalytically generated hydrogen on CuPd/TiO2. J. Am. Chem. Soc., 2011, 133(5), P. 1150–1152.Yamauchi M., Abe R., Tsukuda T., Kato K., Takata M. Highly selective ammonia synthesis from nitrate with photocatalytically generated hydrogen on CuPd/TiO2. J. Am. Chem. Soc., 2011, 133(5), P. 1150–1152.Li H., Li L., Pedersen A., Gao Y., Khetrapal N., Jónsson H., Zeng X.C. Magic-number gold nanoclusters with diameter 1 to 3.5 nm: Relative stability and catalytic activity for CO oxidation. Nano Letters, 2015, 15, P. 682.Li H., Li L., Pedersen A., Gao Y., Khetrapal N., Jónsson H., Zeng X.C. Magic-number gold nanoclusters with diameter 1 to 3.5 nm: Relative stability and catalytic activity for CO oxidation. Nano Letters, 2015, 15, P. 682.Brown L.M. A Synchrotron in a Microscope. Institute of Physics Conference Series, 1997, 153, P. 22.Brown L.M. A Synchrotron in a Microscope. Institute of Physics Conference Series, 1997, 153, P. 22.Krivanek O.L., Dellby N., Lupini A.R. Towards sub-Å electron beams. Ultramicroscopy, 1999, 78(1-4), P. 1–11.Krivanek O.L., Dellby N., Lupini A.R. Towards sub-Å electron beams. Ultramicroscopy, 1999, 78(1-4), P. 1–11.Li Z.Y. al. Three-dimensional atomic-scale structure of size-selected gold nanoclusters. Nature, 2007, 451(7174), P. 46–48.Li Z.Y. al. Three-dimensional atomic-scale structure of size-selected gold nanoclusters. Nature, 2007, 451(7174), P. 46–48.W Zhou W., Ross-Medgaarden E.I., Knowles W.V., Wong M. S., Wachs I.E., Kiely C.J., Nature Chemistry, 2009, 1, P. 722.W Zhou W., Ross-Medgaarden E.I., Knowles W.V., Wong M. S., Wachs I.E., Kiely C.J., Nature Chemistry, 2009, 1, P. 722.Van Aert S., Batenburg K.J., Rossell M.D., Erni R., Van Tendeloo G. Three-dimensional atomic imaging of crystalline nanoparticles. Nature, 2011, 470, P. 374.Van Aert S., Batenburg K.J., Rossell M.D., Erni R., Van Tendeloo G. Three-dimensional atomic imaging of crystalline nanoparticles. Nature, 2011, 470, P. 374.Bals S., Van Aert S., Romero C.P., Lauwaet K., Van Bael M.J., Schoeters B., Partoens B., Yu¨celen E., Lievens P., Van Tendeloo G., Atomic scale dynamics of ultrasmall germanium clusters. Nature Communications, 2012, 3, P. 897.Bals S., Van Aert S., Romero C.P., Lauwaet K., Van Bael M.J., Schoeters B., Partoens B., Yu¨celen E., Lievens P., Van Tendeloo G., Atomic scale dynamics of ultrasmall germanium clusters. Nature Communications, 2012, 3, P. 897.Liu J., Single atom and cluster catalysis: The era of aberration-corrected scanning transmission electron microscopy. Microscopy and Microanalysis, 2013, 19 (Suppl. 2), P. 1678.Liu J., Single atom and cluster catalysis: The era of aberration-corrected scanning transmission electron microscopy. Microscopy and Microanalysis, 2013, 19 (Suppl. 2), P. 1678.Corma A. et al., Exceptional oxidation activity with size-controlled supported gold clusters of low atomicity. Nature Chemistry, 2013, 5, P. 775.Corma A. et al., Exceptional oxidation activity with size-controlled supported gold clusters of low atomicity. Nature Chemistry, 2013, 5, P. 775.Garzón I.L., Posada-Amarillas A. Structural and vibrational analysis of amorphous Au55 clusters. Phys. Rev. B, 1996, 54, P. 11796–11802.Garzón I.L., Posada-Amarillas A. Structural and vibrational analysis of amorphous Au55 clusters. Phys. Rev. B, 1996, 54, P. 11796–11802.Garzón I.L. et al. Lowest Energy Structures of Gold Nanoclusters. Phys. Rev. Letters, 1998, 81, P. 1600–1603.Garzón I.L. et al. Lowest Energy Structures of Gold Nanoclusters. Phys. Rev. Letters, 1998, 81, P. 1600–1603.Michaelian K., Rendo´n N., Garzón I.L. Structure and energetics of Ni, Ag, and Au nanoclusters. Phys. Rev. B, 1999, 60(3), P. 2000–2010.Michaelian K., Rendo´n N., Garzón I.L. Structure and energetics of Ni, Ag, and Au nanoclusters. Phys. Rev. B, 1999, 60(3), P. 2000–2010.Wang Z.W., Palmer R.E. Experimental evidence for fluctuating, chiral-type Au55 clusters by direct atomic imaging. Nanoletters, 2012, 12, P. 5510–5514.Wang Z.W., Palmer R.E. Experimental evidence for fluctuating, chiral-type Au55 clusters by direct atomic imaging. Nanoletters, 2012, 12, P. 5510–5514.Yu M., Yankovich A.B., Kaczmarowski A., Morgan D., Voyles P.M. Integrated computational and experimental structure refinement for nanoparticles. ACS Nano, 2016, 10(4), P. 4031–4038.Yu M., Yankovich A.B., Kaczmarowski A., Morgan D., Voyles P.M. Integrated computational and experimental structure refinement for nanoparticles. ACS Nano, 2016, 10(4), P. 4031–4038.Foiles S.M., Baskes M.I., Daw M.S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B, 1986, 33(12), P. 7983–7991.Foiles S.M., Baskes M.I., Daw M.S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B, 1986, 33(12), P. 7983–7991.He D.S., Li Z.Y., Yuan J. Kinematic HAADF-STEM image simulation of small nanoparticles. Micron, 2015, 74(C), P. 47–53.He D.S., Li Z.Y., Yuan J. Kinematic HAADF-STEM image simulation of small nanoparticles. Micron, 2015, 74(C), P. 47–53.Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys., 1995, 117(1), P. 1–19.Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys., 1995, 117(1), P. 1–19.Head J.D., Zerner M.C. A Broyden-Fletcher-Goldfarb-Shanno optimization procedure for molecular geometries. Chem. Phys. Lett., 1985, 122(3), P. 264–270.Head J.D., Zerner M.C. A Broyden-Fletcher-Goldfarb-Shanno optimization procedure for molecular geometries. Chem. Phys. Lett., 1985, 122(3), P. 264–270.Vilhelmsen L.B., Hammer B. Systematic study of Au6 to Au12 gold clusters on MgO(100) F centers using density-functional theory. Phys. Rev. Lett., 2012, 108(12), P. 126101(4 pp.).Vilhelmsen L.B., Hammer B. Systematic study of Au6 to Au12 gold clusters on MgO(100) F centers using density-functional theory. Phys. Rev. Lett., 2012, 108(12), P. 126101(4 pp.).Bahn S.R., Jacobsen K.W. An object-oriented scripting interface to a legacy electronic structure code. Comput. Sci. Eng., 2002, 4(3), P. 56–66.Bahn S.R., Jacobsen K.W. An object-oriented scripting interface to a legacy electronic structure code. Comput. Sci. Eng., 2002, 4(3), P. 56–66.Larsen A.H., et al. The atomic simulation environment a Python library for working with atoms. J. Phys.: Condens. Matter, 2017, 29(27), P. 273002.Larsen A.H., et al. The atomic simulation environment a Python library for working with atoms. J. Phys.: Condens. Matter, 2017, 29(27), P. 273002.Lyakhov A.O., Oganov A.R., Stokes H.T., Zhu Q. New developments in evolutionary structure prediction algorithm USPEX. Comput. Phys. Commun., 2013, 184(4), P. 1172–1182.Lyakhov A.O., Oganov A.R., Stokes H.T., Zhu Q. New developments in evolutionary structure prediction algorithm USPEX. Comput. Phys. Commun., 2013, 184(4), P. 1172–1182.Vilhelmsen L.B., Walton K.S., and Sholl D.S., Structure and mobility of metal clusters in MOFs: Au, Pd, and AuPd clusters in MOF-74. J. Am. Chem. Soc., 2012, 134(30), P. 12807–12816.Vilhelmsen L.B., Walton K.S., and Sholl D.S., Structure and mobility of metal clusters in MOFs: Au, Pd, and AuPd clusters in MOF-74. J. Am. Chem. Soc., 2012, 134(30), P. 12807–12816.Daven D.M., Tit N., Morris J. R., Ho K.M. Structural optimization of Lennard-Jones clusters by a genetic algorithm. Chem. Phys. Lett., 1996, 256(12), P. 195–200.Daven D.M., Tit N., Morris J. R., Ho K.M. Structural optimization of Lennard-Jones clusters by a genetic algorithm. Chem. Phys. Lett., 1996, 256(12), P. 195–200.Kuhn H.W. The Hungarian method for the assignment problem. Naval Research Logistics, 1955, 2(1-2), P. 83–97.Kuhn H.W. The Hungarian method for the assignment problem. Naval Research Logistics, 1955, 2(1-2), P. 83–97.Munkres J. Algorithms for the assignment and transportation problems. J. Soc. Ind. Appl. Math., 1957, 5(1), P. 32–38.Munkres J. Algorithms for the assignment and transportation problems. J. Soc. Ind. Appl. Math., 1957, 5(1), P. 32–38.Kilaas R. Optimal and near-optimal filters in high-resolution electron microscopy. J. Microsc., 1998, 190(1-2), P. 45–51.Kilaas R. Optimal and near-optimal filters in high-resolution electron microscopy. J. Microsc., 1998, 190(1-2), P. 45–51.

The authors declare that there are no conflicts of interest present.