Friedrich, W., Knipping, P., and von Laue, M., “Interferenz-Erscheinungen bei Röntgenstrahlen” (transl.: “Interference Phenomena with X-rays”), Sitzungsberichte der Königlichen Bayerischen Akademie der Wissenschaften Math. Phys. Kl., Band 1912, 14, pp. 303–322, 1912.Google Scholar

Bragg, W. L., “The Diffraction of Short Electromagnetic Waves by a Crystal”, Proc. Cambridge Philos. Soc., vol. 17, pp. 43–57, 1913.Google Scholar

Golovchenko, J. A., Patel, J. R., Kaplan, D. R., Cowan, P. L., and Bedzyk, M. J., “Solution to the Surface Registration Problem Using X-ray Standing Waves”, Phys. Rev. Lett., vol. 49, pp. 560–563, 1982.Google Scholar

Eisenberger, P. and Marra, W. C., “X-ray Diffraction Study of the Ge(001) Reconstructed Surface”, Phys. Rev. Lett., vol. 46, pp. 1081–1084, 1981.Google Scholar

Davisson, C. and Germer, L. H., “The Scattering of Electrons by a Single Crystal of Nickel”, Nature, vol. 119, pp. 558–560, 1927.Google Scholar

Davisson, C. and Germer, L. H., “Diffraction of Electrons by a Crystal of Nickel”, Phys. Rev., vol. 30, pp. 705–740, 1927.Google Scholar

Thomson, G. P. and Reid, A., “Diffraction of Cathode Rays by a Thin Film”, Nature, vol. 119, pp. 890–890, 1927.Google Scholar

Pendry, J. B., Low Energy Electron Diffraction: The Theory and its Application to Determination of Surface Structure, Academic Press, London, 1974, out of print.Google Scholar

Clarke, L. J., Surface Crystallography: An Introduction to Low Energy Electron Diffraction, Wiley, Chichester, 1985, out of print.Google Scholar

Van Hove, M. A., Weinberg, W. H., and Chan, C.-M., Low-Energy Electron Diffraction: Experiment, Theory and Surface Structure Determination, Springer, Berlin, 1986, out of print.Google Scholar

Feidenhans’l, R., “Surface Structure Determination by X-ray Diffraction”, Surf. Sci. Rep., vol. 10, pp. 105–188, 1989.Google Scholar

Robinson, I. K., “Surface Crystallography”, in Handbook on Synchrotron Radiation, eds. Moncton, D. E. and Brown, G. S., Elsevier, Amsterdam, 1991, vol. III, ch. 7, pp. 221–266.Google Scholar

Stierle, A. and Vlieg, E., “Surface‐Sensitive X‐Ray Diffraction Methods”, in Modern Diffraction Methods, eds. Mittemeijer, E. J. and Welzel, U., Wiley-VCH, Weinheim, 2013, ch. 8, pp. 221–257.Google Scholar

Zhou, X.-L. and Chen, S.-H., “Theoretical Foundation of X-ray and Neutron Reflectometry”, Phys. Rep., vol. 257, pp. 223–348, 1995.Google Scholar

“Symmetry Relations between Space Groups”, in International Tables of Crystallography, vol. A1, eds. Wondratschek, H. and Müller, U., Kluwer Academic Publishers, Dordrecht, 2004.Google Scholar

Giacovazzo, C., ed., Fundamentals of Crystallography, Oxford University Press, Oxford, 1992.Google Scholar

Shmueli, U., Theories and Techniques of Crystal Structure Determination, Oxford University Press, Oxford, 2007.Google Scholar

Clegg, W., ed., Crystal Structure Analysis, Principles and Practice, Oxford University Press, Oxford, 2009.Google Scholar

Glusker, J. P. and Trueblood, K. N., Crystal Structure Analysis, Oxford University Press, Oxford, 2010.Google Scholar

Hermann, K., Crystallography and Surface Structure: An Introduction for Surface Scientists and Nanoscientists, 2nd ed., Wiley, Weinheim, 2016.CrossRefGoogle Scholar

Grosse-Kunstleve, R. W., Sauter, N. K., and Adams, P. D., “Numerically Stable Algorithms for the Computation of Reduced Unit Cells”, Acta Cryst., vol. A60, pp. 1–6, 2004.Google Scholar

Wood, E. A., “Vocabulary of Surface Crystallography”, J. Appl. Phys., vol. 35, pp. 1306–1312, 1964.Google Scholar

Moritz, W., Landskron, J., and Deschauer, M., “Perspectives for Surface Structure Analysis with Low Energy Electron Diffraction”, Surf. Sci., vol. 603, pp. 1306–1314, 2009.Google Scholar

Meyerheim, H. L., Gloege, T., and Maltor, H., “Surface X-ray Diffraction on Large Organic Molecules: Thiouracil on Ag(111)”, Surf. Sci. Lett., vol. 442, pp. L1029–L1035, 1999.Google Scholar

Lang, B., Joyner, R. W., and Somorjai, G. A., “Low Energy Electron Diffraction Studies of Chemisorbed Gases on Stepped Surfaces of Platinum”, Surf. Sci., vol. 30, pp. 454–474, 1972.CrossRefGoogle Scholar

Van Hove, M. A. and Somorjai, G. A., “A New Microfacet Notation for High-Miller-Index Surfaces of Cubic Materials with Terrace, Step and Kink Structures”, Surf. Sci., vol. 92, pp. 489–518, 1980.Google Scholar

Sands, D. E., Vectors and Tensors in Crystallography, Addison-Wesley, Boston, 1982.Google Scholar

Balsac program. Available at: www.fhi-berlin.mpg.de/KHsoftware/Balsac/index.html, last accessed 2 April 2022.Google Scholar

CRYSCON program. Available at: www.shapesoftware.com/00_Website_Homepage/, last accessed 2 April 2022.Google Scholar

Seah, M. P. and Dench, W. A., “Quantitative Electron Spectroscopy of Surfaces: A Standard Data Base for Electron Inelastic Mean Free Paths in Solids”, Surf. Interface Anal., vol. 1, pp. 2–11, 1979.Google Scholar

Ibach, H., “Surfaces in Ultrahigh Vacuum”, in Physics of Surfaces and Interfaces, Chapter 2.2, Springer-Verlag, Berlin, 2006.Google Scholar

Pentcheva, R., Moritz, W., Rundgren, J., Frank, S., Schrupp, D., and Scheffler, M., “A Combined DFT/LEED-Approach for Complex Oxide Surface Structure Determination: Fe₃O₄(001)”, Surf. Sci., vol. 602, pp. 1299–1305, 2008.CrossRefGoogle Scholar

Heilmann, P., Lang, E., Heinz, K., and Müller, K., “Fast LEED-Intensity Measurements with a Computer Controlled Television System”, Appl. Phys., vol. 9, pp. 247–251, 1976.Google Scholar

Scheithauer, U., Meyer, G., and Henzler, M., “A New LEED Instrument for Quantitative Spot Profile Analysis”, Surf. Sci., vol. 178, pp. 441–451, 1986.Google Scholar

Telieps, W. and Bauer, E., “An analytical reflection and emission UHV surface electron microscope”, Ultramicroscopy, vol. 17, pp. 57–66, 1985.Google Scholar

Yu, D., Math, Ch., Meier, M., Escher, M., Rangelov, G., and Donath, M., “Characterisation and application of a SPLEED–based spin polarisation analyser”, Surf. Sci., vol. 601, pp. 5803–5808, 2007.Google Scholar

Dake, L. S., King, D. E., Pitts, J. R., and Czanderna, A. W., “Beam Effects, Surface Topography, and Depth Profiling in Surface Analysis”, in Methods in Surface Characterisation, Czanderna, A. W., Madey, T. E. and Powell, C. J., eds., Kluwer Academic Publishers, New York, 2002, vol. 5, ch. 3, pp. 97–273.Google Scholar

Becker, C., “UHV Surface Preparation Methods”, in Encyclopedia of Interfacial Chemistry: Surface Science, Wandelt, K., ed., Elsevier, Amsterdam, 2015, vol. 1.1, pp. 580–590.Google Scholar

Crotti, C., Farnetti, E., Celestino, T., and Fontana, S., “Preparation of Solid-State Samples of a Transition Metal Coordination Compound for Synchrotron Radiation Photoemission Studies”, J. Electr. Spectr. Rel. Phen., vol. 128, pp. 141–157, 2003.Google Scholar

Sterrer, M. and Freund, H.-J., “Surface Science Approach to Catalyst Preparation Using Thin Oxide Films as Substrates”, in Encyclopedia of Interfacial Chemistry: Surface Science, Wandelt, K., ed., Elsevier, Amsterdam, 2018, pp. 632–642.Google Scholar

Lübbe, M. and Moritz, W., “A LEED Analysis of the Clean Surfaces of α-Fe₂O₃(0001) and α-Cr₂O₃(0001) Bulk Single Crystals”, J. Phys.: Condens. Matter, vol. 21, p. 134010, 2009.Google Scholar

Cunningham, S. L. and Weinberg, W. H., “Determining the Angles of Incidence in a LEED Experiment”, Rev. Sci. Instrum., vol. 49, pp. 752–755, 1978.Google Scholar

Hove, M. A. Van, Weinberg, W. H., and Chan, C.-M., Low-Energy Electron Diffraction: Experiment, Theory and Surface Structure Determination, Berlin, Springer, 1986, ch. 2.6.Google Scholar

Price, G. P., “Techniques for Very Low Energy Electron Diffraction”, Rev. Sci. Instrum., vol. 51, pp. 605–609, 1980.Google Scholar

Sobrero, A. C. and Weinberg, W. H., “Unified Approach to Photographic Methods for Obtaining the Angles of Incidence in Low-Energy Electron Diffraction”, Rev. Sci. Instrum., vol. 53, pp. 1566–1572, 1982.Google Scholar

Sojka, F., Meissner, M., Zwick, Ch., Forker, R., and Fritz, T., “Determination and Correction of Distortions and Systematic Errors in Low-Energy Electron Diffraction”, Rev. Sci. Instrum., vol. 84, p. 015111, 2013.Google Scholar

Sojka, F., Meissner, M., Zwick, Ch., Forker, R., Vyshnepolsky, M., Klein, C., Horn-von Hoegen, M., and Fritz, T., “To Tilt or Not to Tilt: Correction of the Distortion Caused by Inclined Sample Surfaces in Low-Energy Electron Diffraction”, Ultramicroscopy, vol. 133, pp. 35–40, 2013.Google Scholar

Klein, C., Nabbefeld, T., Hattab, H., Meyer, D., Jnawali, G., Kammler, M., Meyer zu Heringdorf, F.-J., Golla-Franz, A., Müller, B. H., Schmidt, Th., Henzler, M., and Horn-von Hoegen, M., “Lost in Reciprocal Space? Determination of the Scattering Condition in Spot Profile Analysis Low-Energy Electron Diffraction”, Rev. Sci. Instrum., vol. 82, p. 035111, 2011.Google Scholar

Henzler, M., “LEED-Investigation of Step Arrays on Cleaved Germanium (111) Surfaces”, Surf. Sci., vol. 19, pp. 159–171, 1970.Google Scholar

Schindler, K. M., Huth, M., and Widdra, W., “Improved Extraction of I–V Curves from Low-Energy Electron Diffraction Images”, Chem. Phys. Lett., vol. 532, pp. 116–118, 2012.Google Scholar

Moritz, W., Landskron, J., and Deschauer, M., “Perspectives for Surface Structure Analysis with Low Energy Electron Diffraction”, Surf. Sci., vol. 603, pp. 1306–1314, 2009.CrossRefGoogle Scholar

Deschauer, M., “LEED-Strukturanalyse organischer Molekülschichten: 2-Thiouracil auf Ag(111)”, Dissertation, University of Munich, Dept. of Earth and Environmental Sciences, Germany, 2000.Google Scholar

Park, R. L., Houston, J. E., and Schreiner, D. G., “The LEED Instrument Response Function”, Rev. Sci. Instrum., vol. 42, pp. 60–65, 1971.Google Scholar

Wang, G.-C. and Lagally, M. G., “Quantitative Island Size Determination in the Chemisorbed Layer: W(110)p(2 × 1)-O”, Surf. Sci., vol. 81, pp. 69–89, 1979.CrossRefGoogle Scholar

Lu, T.-M. and Lagally, M.G., “The Resolving Power of a Low-Energy Electron Diffractometer and the Analysis of Surface Defects”, Surf. Sci., vol. 99, pp. 695–713, 1980.Google Scholar

Welkie, D. G. and Lagally, M. G., “Investigation of the Instrumental Response of a Vidicon based Low Energy Electron Diffraction System”, Appl. Surf. Sci., vol. 3, pp. 272–292, 1979.Google Scholar

Comsa, G., “Coherence Length and/or Transfer Width”, Surf. Sci., vol. 81, pp. 57–68, 1979.Google Scholar

Henzler, M., “Atomic Steps on Single Crystals: Experimental Methods and Properties”, Appl. Phys., vol. 9, pp. 11–17, 1976.Google Scholar

Henzler, M., “LEED Studies of Defects at Surfaces and Interfaces”, Surf. Sci., vol. 168, pp. 744–750, 1986.Google Scholar

Specs GmbH, Berlin, Germany, ErLEED 100/150, Reverse View LEED Optics, https://www.specs-group.com/, last accessed 5 April 2022.Google Scholar

Scienta Omicron, Uppsala, Sweden and Taunusstein, Germany, Femto-LEED with Integral Shutter Model DLD-L800, www.scientaomicron.com/en/Components/LEED-RHEED/LEED-800-MCP, last accessed 2 April 2022.Google Scholar

OCI Vacuum Microengineering, Inc., Ontario, Canada. Femto-LEED with Integral Shutter Model DLD-L800, http://ocivm.com/leed_aes_spectrometers.html#Femto-LEED-ISH, last accessed 2 April 2022.Google Scholar

Seidel, C., Poppensieker, J., and Fuchs, H., “Real-Time Monitoring of Phase Transitions of Vacuum Deposited Organic Films by Molecular Beam Deposition LEED”, Surf. Sci., vol. 408, pp. 223–231, 1998.Google Scholar

Horn-von Hoegen, M., “Growth of Semiconductor Layers Studied by Spot Profile Analysing Low Energy Electron Diffraction”, Z. Krist., vol. 214, pp. 591–629 and 684–721, 1999.Google Scholar

Dr. Kury, Peter, out-of-the-box systems GmbH, Nierenhofer Strasse 68a, 45257 Essen, Germany, www.spa-leed.com, last accessed 2 April 2022.Google Scholar

Kirschbaum, P., Brendel, L., Roos, K. R., Horn-von Hoegen, M., and Meyer zu Heringdorf, F.-J., “Decay of Isolated Hills and Saddles on Si(001)”, Mater. Res. Express, vol. 3, p. 085011, 2016.Google Scholar

Held, G., Uremovic, S., Stellwag, C., and Menzel, D., “A Low-Energy Electron Diffraction Data Acquisition System for Very Low Electron Doses Based upon a Slow Scan Charge Coupled Device Camera”, Rev. Sci. Instr., vol. 67, pp. 378–383, 1996.Google Scholar

Kubsky, S., Borucki, L., Gorris, F., Becker, H. W., Rolfs, C., Schulte, W. H., Baumvol, I. J. R., and Stedile, F. C., “Interconnected UHV Facilities for Materials Preparation and Analysis”, Nuclear Instr. Methods Phys. Res. A, vol. 435, pp. 514–522, 1999.Google Scholar

Kakefuda, Y., Yamashita, Y., Mukai, K., and Yoshinobu, J., “Compact UHV System for Fabrication and In Situ Analysis of Electron Beam Deposited Structures Using a Focused Low Energy Electron Beam”, Rev. Sci. Instrum., vol. 77, p. 053702, 2006.Google Scholar

Pesty, F. and Garoche, P., “Improving the Coherence of a Low-Energy Electron Beam by Modulation”, Appl. Phys., vol. 94, pp. 7910–7913, 2003.Google Scholar

Mizuno, S., Rahman, F., and Iwanaga, M., “Low-Energy Electron Diffraction Patterns Using Field-Emitted Electrons from Tungsten Tips”, Jpn. J. Appl. Phys., vol. 45, pp. L178–L209, 2006.Google Scholar

Janzen, A., Krenzer, B., Zhou, P., von der Linde, D., and Horn-von Hoegen, M., “Ultrafast Electron Diffraction at Surfaces after Laser Excitation”, Surf. Sci., vol. 600, pp. 4094–4098, 2006.Google Scholar

Wall, S., Krenzer, B., Wippermann, S., Sanna, S., Klasing, F., Hanisch-Blicharski, A., Kammler, M., Schmidt, W. G., and Horn-von Hoegen, M., “An Atomistic Picture of Charge Density Wave Formation at Surfaces”, Phys. Rev. Lett., vol. 109, p. 186101, 2012.Google Scholar

Hanisch-Blicharski, A., Janzen, A., Krenzer, B., Wall, S., Klasing, F., Kalus, A., Frigge, T., Kammler, M., and Horn-von Hoegen, M., “Ultra-fast Electron Diffraction at Surfaces: From Nanoscale Heat Transport to Driven Phase Transitions”, Ultramicroscopy, vol. 127, pp. 2–8, 2013.Google Scholar

Hafke, B., Witte, T., Brand, C., Duden, Th., and Horn-von Hoegen, M., “Pulsed Electron Gun for Electron Diffraction at Surfaces with Femtosecond Temporal Resolution and High Coherence Length”, Rev. Sci. Instr., vol. 90, p. 045119, 2019.Google Scholar

Gulde, M., Schweda, S., Storeck, G., Maiti, M., Yu, H. K., Wodtke, A. M., Schäfer, S., and Ropers, C., “Ultrafast Low-Energy Electron Diffraction in Transmission Resolves Polymer/Graphene Superstructure Dynamics”, Science, vol. 345, pp. 200–204, 2014.Google Scholar

Nibbering, E. T. J., “Low-Energy Electron Diffraction at Ultrafast Speeds”, Science, vol. 345, pp. 137–138, 2014.Google Scholar

Storeck, G., Vogelgesang, S., Sivis, M., Schäfer, S., and Ropersa, C., “Nanotip-based Photoelectron Microgun for Ultrafast LEED”, Struct. Dyn., vol. 4, p. 044024, 2017.Google Scholar

Mas-Ballesté, R., Gómez-Navarro, C., Gómez-Herrero, J., and Zamora, F., “2D Materials: To Graphene and Beyond”, Nanoscale, vol. 3, pp. 20–30, 2011.Google Scholar

Stahl, U., Gador, D., Soukopp, A., Fink, R., and Umbach, E., “Coverage-Dependent Superstructures in Chemisorbed NTCDA Monolayers: A Combined LEED and STM Study”, Sur. Sci., vol. 414, pp. 423–434, 1998.Google Scholar

LEEDpat, graphical LEED pattern simulator, PC-based software tool to visualize and analyze LEED spot patterns of well-ordered substrates and overlayers, available for download at www.fhi-berlin.mpg.de/KHsoftware/LEEDpat/ where more information is available (executable for Windows; by Hermann, K. and Van Hove, M. A.), last accessed 2 April 2022.Google Scholar

Sojka, F., Meissner, M., Zwick, Ch., Forker, R., and Fritz, T., “Determination and Correction of Distortions and Systematic Errors in Low-Energy Electron Diffraction”, Rev. Sci. Instr., vol. 84, p. 015111, 2013.Google Scholar

Sojka, F., Meissner, M., Zwick, Ch., Forker, R., Vyshnepolsky, M., Klein, C., Horn-von Hoegen, M., and Fritz, T., “To Tilt or Not to Tilt: Correction of the Distortion Caused by Inclined Sample Surfaces in Low-Energy Electron Diffraction”, Ultramicroscopy, vol. 133, pp. 35–40, 2013.Google Scholar

Glöckler, K., Seidel, C., Soukopp, A., Sokolowski, M., Umbach, E., Böhringer, M., Berndt, R., and Schneider, W.-D., “Highly Ordered Structures and Submolecular Scanning Tunnelling Microscopy Contrast of PTCDA and DM-PBDCI Monolayers on Ag (111) and Ag (110)”, Surf. Sci., vol. 405, pp. 1–20, 1998.Google Scholar

Horn-von Hoegen, M., “Growth of Semiconductor Layers Studied by Spot Profile Analysing Low Energy Electron Diffraction”, Z. Krist., vol. 214, pp. 591–629 and 684–721, 1999.Google Scholar

Chen, Q. and Richardson, N. V., “Surface Facetting Induced by Adsorbates”, Progr. Surf. Sci., vol. 73, pp. 59–77, 2003.Google Scholar

Tegenkamp, C., “Vicinal Surfaces for Functional Nanostructures”, J. Phys.: Condens. Matter, vol. 21, p. 013002, 2009.Google ScholarPubMed

Madey, T. E., Nien, C.-H., Pelhos, K., Kolodziej, J. J., Abdelrehim, I. M., and Tao, H.-S., “Faceting Induced by Ultrathin Metal Films: Structure, Electronic Properties and Reactivity”, Surf. Sci., vol. 438, pp. 191–206, 1999.Google Scholar

Hermann, K., Crystallography and Surface Structure: An Introduction for Surface Scientists and Nanoscientists, 2nd ed., Wiley, Weinheim, 2016, ch. 4.2, p. 205.Google Scholar

Reinecke, N. and Taglauer, E., “The Kinetics of Oxygen-Induced Faceting of Cu(115) and Cu(119) Surfaces”, Surf. Sci., vol. 454–456, pp. 94–100, 2000.Google Scholar

Zeppenfeld, P., Kern, K., David, R., and Comsa, G., “Diffraction from Domain-Wall Systems”, Phys. Rev. B, vol. 38, pp. 3918–3924, 1988.Google Scholar

Timmer, F. and Wollschläger, J., “Effects of Domain Boundaries on the Diffraction Patterns of One-Dimensional Structures”, Condens. Matter, vol. 2, p. 7, 2017.Google Scholar

Hämäläinen, S. K., Boneschanscher, M. P., Jacobse, P. H., Swart, I., Pussi, K., Moritz, W., Lahtinen, J., Liljeroth, P., and Sainio, J.: “Structure and Local Variations of the Graphene Moiré on Ir(111)”, Phys. Rev. B, vol. 88, p. 201406(R), 2013.Google Scholar

Zhu, X., Guo, J., Zhang, J., and Plummer, E. W., “Misconceptions Associated with the Origin of Charge Density Waves”, Adv. Phys.: X, vol. 2, pp. 622–640, 2017.Google Scholar

He, R., Okamoto, J., Ye, Z., Ye, G., Anderson, H., Dai, X., Wu, X., Hu, J., Liu, Y., Lu, W., Sun, Y., Pasupathy, A. N., and Tsen, A. W., “Distinct Surface and Bulk Charge Density Waves in Ultrathin 1T−TaS2”, Phys. Rev. B, vol. 94, p. 201108(R), 2016.Google Scholar

Pendry, J. B., Low Energy Electron Diffraction, Academic, London, 1974.Google Scholar

Tong, S. Y., “Theory of Low Energy Electron Diffraction”, Progr. Surf. Sci., vol. 7, pp. 1–48, 1975.Google Scholar

Van Hove, M. A., Weinberg, W. H., and Chan, C.-M., Low-Energy Electron Diffraction: Experiment, Theory and Structural Determination, Springer, Berlin, 1986.Google Scholar

Tuan, D. F.-T. and Loar, G. W., “Corrections of Overlapping Spheres in the Self-consistent Field X_α Scattered-Wave Method”, J. Mol. Struct., vol. 223, pp. 123–148, 1990.Google Scholar

Rundgren, J., “Optimized Surface-Slab Excited-State Muffin-Tin Potential and Surface Core Level Shifts”, Phys. Rev. B, vol. 68, p. 125405, 2003.Google Scholar

Nagano, S. and Tong, S. Y., “Multiple-Scattering Theory of Low-Energy Electron Diffraction for a Nonspherical Scattering Potential”, Phys. Rev. B, vol. 32, pp. 6562–6570, 1985.Google Scholar

Peetz, J.-V. and Schattke, W., “Non-Muffin-Tin Atomic Scattering-Matrices for Semiconductor LEED-Calculations”, J. Electr. Spectr. Rel. Phen., vol. 68, pp. 167–173, 1994.Google Scholar

Rubner, O., Kottcke, M., and Heinz, K., “Tensor LEED for the Approximation of Non-spherical Atomic Scattering”, Surf. Sci., vol. 340, pp. 172–178, 1995.Google Scholar

Joly, Y., “Finite-Difference Method for the Calculation of Low Energy Electron Diffraction”, Phys. Rev. Lett., vol. 68, pp. 950–953, 1992.Google Scholar

Gavaza, G. M., Yu, Z. X., Tsang, L., Chan, C. H., Tong, S. Y., and Van Hove, M. A., “Theory of Low-Energy Electron Diffraction for Detailed Structural Determination of Nanomaterials: Finite-Size and Disordered Structures”, Phys. Rev. B, vol. 75, p. 235403, 2007.CrossRefGoogle Scholar

Gavaza, G. M., Yu, Z. X., Tsang, L., Chan, C. H., Tong, S. Y., and Van Hove, M. A., “Efficient Calculation of Electron Diffraction for the Structural Determination of Nanomaterials”, Phys. Rev. Lett., vol. 97, p. 055505, 2006.Google Scholar

Gavaza, G. M., Yu, Z. X., Tsang, L., Chan, C. H., Tong, S. Y., and Van Hove, M. A., “Theory of Low-Energy Electron Diffraction for Detailed Structural Determination of Nanomaterials: Ordered Structures”, Phys. Rev. B, vol. 75, p. 014114, 2007.Google Scholar

Gavaza, G. M., Yu, Z. X., Van Hove, M. A., and Tong, S. Y., “Theory of Low-Energy Electron Diffraction for Nanomaterials: Subclusters, Automated Searches”, J. Phys. Condens. Matter, vol. 20, p. 304202, 2008.Google Scholar

Spence, J. C., Poon, H. C., and Saldin, D. K., “Convergent-Beam Low Energy Electron Diffraction (CBLEED) and the Measurement of Surface Dipole Layers”, Microsc. Microanal., vol. 10, pp. 128–133, 2004.Google Scholar

Steinwand, E., Longchamp, J.-N., and Fink, H.-W., “Coherent Low-Energy Electron Diffraction on Individual Nanometer Sized Objects”, Ultramicroscopy, vol. 111, pp. 282–284, 2011.Google Scholar

Telieps, W. and Bauer, E., “An Analytical Reflection and Emission UHV Surface Electron Microscope”, Ultramicroscopy, vol. 17, pp. 57–66, 1985. See https://elmitec.de/Users_List for installed instruments and applications, last accessed 2 April 2022.Google Scholar

Kakefuda, Y., Yamashita, Y., Mukai, K., and Yoshinobu, J., “Compact UHV System for Fabrication and In Situ Analysis of Electron Beam Deposited Structures Using a Focused Low Energy Electron Beam”, Rev. Sci. Instrum., vol. 77, p. 053702, 2006.Google Scholar

Mizuno, S., Rahman, F., and Iwanaga, M., “Low-Energy Electron Diffraction Patterns Using Field-Emitted Electrons from Tungsten Tips”, Jpn. J. Appl. Phys., part 2, vol. 45, p. L178, 2006.Google Scholar

Barret, R., Berry, M., Chan, T. F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., and Van der Vorst, H., Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd ed., SIAM, Philadelphia, PA, 1994, vol. 1, ch. 2.3.1, p. 14.Google Scholar

Tsang, L. and Li, Q., “Wave Scattering with UV Multilevel Partitioning Method for Volume Scattering by Discrete Scatterers”, Microwave Opt. Technol. Lett., vol. 41, pp. 354–360, 2004.Google Scholar

Saldin, D. K. and Pendry, J. B., “The Cluster Approach to LEED Calculations”, Surf. Sci., vol. 162, pp. 941–944, 1985.Google Scholar

Van Hove, M. A., Moritz, W., Over, H., Rous, P. J., Wander, A., Barbieri, A., Materer, N., Starke, U., and Somorjai, G. A., “Automated Determination of Complex Surface Structures by LEED”, Surf. Sci. Rep., vol. 19, pp. 191–229, 1993.Google Scholar

Kambe, K., “Theory of Low-Energy Electron Diffraction I. Application of the Cellular Method to Monatomic Layers”, Z. Naturforsch., vol. 22a, pp. 322–330, 1967.Google Scholar

Kambe, K., “Theory of Electron Diffraction by Crystals I. Green’s Function and Integral Equation”, Z. Naturforsch., vol. 22a, pp. 422–431, 1967.Google Scholar

Kambe, K., “Theory of Low-Energy Electron Diffraction II. Cellular Method for Complex Monolayers and Multilayer”, Z. Naturforsch., vol. 23a, pp. 1280–1294, 1968.Google Scholar

Rous, P. J. and Pendry, J. B., “Diffuse LEED from Simple Stepped Surfaces”, Surf. Sci., vol. 173, pp. 1–19, 1986.Google Scholar

Jepsen, D. W., “New Transfer-Matrix Method for Low-Energy-Electron Diffraction and Other Surface Electronic-Structure Problems”, Phys. Rev. B, vol. 22, pp. 5701–5715, 1980.Google Scholar

Pinkava, P. and Crampin, S., “On the Calculation of LEED Spectra from Stepped Surfaces”, Surf. Sci., vol. 233, pp. 27–34, 1990.Google Scholar

Zhang, X.-G. and Gonis, A., “New, Real-Space, Multiple-Scattering-Theory Method for the Determination of Electronic Structure”, Phys. Rev. Lett., vol. 62, 1161–1164, 1989.Google Scholar

MacLaren, J. M., Zhang, X.-G., and Gonis, A., “Multiple-Scattering Solutions to the Schrödinger Equation for Semi-infinite Layered Materials”, Phys. Rev. B, vol. 40, pp. 9955–9958, 1989.Google Scholar

Zhang, X.-G., Van Hove, M. A., Somorjai, G. A., Rous, P. J., Tobin, D., Gonis, A., MacLaren, J. M., Heinz, K., Michl, M., Lindner, H., Müller, K., Ehsasi, M., and Block, J. H., “Efficient Determination of Multilayer Relaxation in the Pt(210) Stepped and Densely Kinked Surface”, Phys. Rev. Lett., vol. 67, pp. 1298–1301, 1991.Google Scholar

Zhang, X.-G., Rous, P. J., MacLaren, J. M., Gonis, A., Van Hove, M. A., and Somorjai, G. A., “A Real-Space Multiple Scattering Theory of Low-Energy Electron Diffraction: A New Approach for the Structure Determination of Stepped Surfaces”, Surf. Sci., vol. 239, pp. 103–118, 1990.Google Scholar

Moritz, W., “Effective Calculation of LEED Iintensities Using Symmetry Adapted Functions”, J. Phys. C, vol. 17, pp. 353–362, 1984.Google Scholar

Bradley, C. J. and Cracknell, A. P., The Mathematical Theory of Symmetry in Solids, Clarendon, Oxford, 1972.Google Scholar

Heinz, K., Kottcke, M., Löffler, U., and Döll, R., “Recent Advances in LEED Surface Crystallography”, Surf. Sci., vol. 357–358, pp. 1–9, 1996.Google Scholar

Rous, P. J. and Pendry, J. B., “Tensor LEED I: A Technique for High Speed Surface Structure Determination by Low Energy Electron Diffraction. TLEED l”, Comp. Phys. Comm., vol. 54, pp. 137–156, 1989.Google Scholar

Rous, P. J. and Pendry, J. B., “Tensor LEED II: A Technique for High Speed Surface Structure Determination by Low Energy Electron Diffraction. TLEED 2”, Comp. Phys. Comm., vol. 54, pp. 157–166, 1989.Google Scholar

Yu, Z. X. and Tong, S. Y., “Surface Structure Determination by a One-Stop Search Method for the Deepest Minimum”, Phys. Rev. B, vol. 71, p. 161404(R), 2005.CrossRefGoogle Scholar

Pendry, J. B. and Saldin, D. K., “SEXAFS without X-rays”, Surf. Sci., vol. 145, pp. 33–47, 1984.Google Scholar

Van Hove, M. A., “Solving Complex and Disordered Surface Structures with Electron Diffraction”, in Chemistry and Physics of Solid Surfaces VII, eds. Howe, R. F. and Vanselow, R., Springer-Verlag, Berlin, 1988, Springer Series in Surface Sciences, vol. 10, pp. 513–546.Google Scholar

Starke, U., Pendry, J. B., and Heinz, K., “Diffuse Low-Energy Electron Diffraction”, Progr. Surf. Sci., vol. 52, pp. 53–124, 1996.Google Scholar

Barnes, C. J., AlShamaileh, E., Pitkänen, T., and Lindroos, M., “Early Stages of Surface Alloy Formation: A Diffuse LEED I(V) Study”, Surf. Sci., vol. 482, pp. 1425–1430, 2001.Google Scholar

Poon, H. C., Weinert, M., Saldin, D. K., Stacchiola, D., Zheng, T., and Tysoe, W. T., “Structure Determination of Disordered Organic Molecules on Surfaces from the Bragg Spots of Low-Energy Electron Diffraction and Total Energy Calculations”, Phys. Rev. B, vol. 69, p. 035401, 2004.Google Scholar

Heinz, K., Starke, U., Van Hove, M. A., and Somorjai, G. A., “The Angular Dependence of Diffuse LEED Intensities and Its Structural Information Content”, Surf. Sci., vol. 261, pp. 57–63, 1992.Google Scholar

Ogletree, D. F., Blackman, G. S., Hwang, R. Q., Starke, U., Somorjai, G. A., and Katz, J. E., “A New Pulse Counting Low‐Energy Electron Diffraction System Based on a Position Sensitive Detector”, Rev. Sci. Instrum., vol. 63, pp. 104–113, 1992.Google Scholar

Ibach, H. and Lehwald, S., “Elastic Diffuse and Inelastic Electron Scattering from Surfaces with Disordered Overlayers”, Surf. Sci., vol. 176, pp. 629–634, 1986.Google Scholar

Saldin, D. K., Pendry, J. B., Van Hove, M. A., and Somorjai, G. A., “Interpretation of Diffuse Low-Energy Electron Diffraction Intensities”, Phys. Rev. B, vol. 31, pp. 1216–1218, 1985.Google Scholar

Van Hove, M. A., Lin, R. F., and Somorjai, G. A., “Efficient Scheme for LEED Calculations in the Presence of Large Superlattices, with Application to the Structural Analysis of Benzene Adsorbed on Rh(111)”, Phys. Rev. Lett., vol. 51, pp. 778–781, 1983.Google Scholar

Wei, C. M. and Tong, S. Y., “Direct Atomic Structure by Holographic Diffuse LEED”, Surf. Sci., vol. 274, pp. L577–L582, 1992.Google Scholar

Heinz, K., “LEED and DLEED As Modern Tools for Quantitative Surface Structure Determination”, Rep. Prog. Phys., vol. 58, pp. 637–704, 1995.Google Scholar

Hu, P. J. and King, D. A., “A Direct Inversion Method for Surface Structure Determination from LEED Intensities”, Nature, vol. 360, pp. 655–658, 1992.Google Scholar

Mendez, M. A., Gluck, C., and Heinz, K., “Holography with Conventional LEED”, J. Phys.: Cond. Matt., vol. 4, pp. 999–1006, 1992.Google Scholar

Saldin, D. K. and Chen, X., “Three-Dimensional Reconstruction by Holographic LEED: Proper Identification of the Reference Wave”, Phys. Rev. B, vol. 52, pp. 2941–2948, 1995.Google Scholar

Saldin, D. K., Reuter, K., de Andres, P. L., Wedler, H., Chen, X., Pendry, J. B., and Heinz, K., “Direct Reconstruction of Three-Dimensional Atomic Adsorption Sites by Holographic LEED”, Phys. Rev., vol. B, 54, pp. 8172–8176, 1996.Google Scholar

Tong, S. Y., Huang, H., and Guo, X. Q., “Low-Energy Electron and Low-Energy Positron Holography”, Phys. Rev. Lett., vol. 69, pp. 3654–3657, 1992.Google Scholar

Heinz, K., Saldin, D. K., and Pendry, J. B., “Diffuse LEED and Surface Crystallography”, Phys. Rev. Lett., vol. 55, pp. 2312–2315, 1985.Google Scholar

Rous, P. J., Pendry, J. B., Saldin, D. K., Heinz, K., Müller, K., and Bickel, N., “Tensor LEED: A Technique for High-Speed Surface-Structure Determination”, Phys. Rev. Lett., vol. 57, pp. 2951–2954, 1986.Google Scholar

Oed, W., Starke, U., Heinz, K., Müller, K., and Pendry, J. B., “Ordered and Disordered Oxygen and Sulfur on Ni(100)”, Surf. Sci., vol. 251, pp. 488–492, 1991.Google Scholar

Ri, C. S. and Watson, P. R., “Surface Structure of the Disordered Cl/Ti(0001) System Determined by Diffuse Low‐Energy Electron Diffraction”, J. Vac. Sci. Technol., vol. A10, pp. 2535–2539, 1992.Google Scholar

Ri, C.-S. and Watson, P. R., “Identification of the Bonding Site of Chlorine on the Ti(0001) Surface”, Solid St. Comm., vol. 81, pp. 541–543, 1992.Google Scholar

Hu, P., Barnes, C. J., and King, D. A., “Dominance of Short-Range-Order Effects in Low-Energy Electron-Diffraction Intensity Spectra”, Phys. Rev. B, vol. 45, pp. 13595–13598, 1992.Google Scholar

Wedler, H., Mendez, M. A., Bayer, P., Löffler, U., Heinz, K., Fritzsche, V., and Pendry, J. B., “Coverage-Dependent DLEED Analysis of the Adsorption Structure of K on Ni(100)”, Surf. Sci., vol. 293, pp. 47–56, 1993.Google Scholar

Mapledoram, L. D., Wander, A., and King, D. A., “Islanding or Random Growth? The Low Coverage Growth Modes and Structure of NO on Ni{111} Studied by Diffuse ATLEED”, Surf. Sci., vol. 312, pp. 54–61, 1994.Google Scholar

Barnes, C. J., Wander, A., and King, D. A., “A Tensor LEED Structural Study of the Coverage-Dependent Bonding of Iodine Adsorbed on Rh{111}”, Surf. Sci., vol. 281, pp. 33–41, 1993.Google Scholar

Sporn, M., Platzgummer, E., Forsthuber, S., Schmid, M., Hofer, W., and Varga, P., “The Accuracy of Quantitative LEED in Determining Chemical Composition Profiles of Substitutionally Disordered Alloys: A Case Study”, Surf. Sci., vol. 416, pp. 423–429, 1998.Google Scholar

Zasada, I., “On the Disordered Adsorption of CO on Pt(111) by Diffuse SPLEED”, Surf. Sci., vol. 498, pp. 293–306, 2002.Google Scholar

Zasada, I. and Rychtelska, T., “Theoretical Studies of Spin-Polarized DLEED Rotation Curves: Disordered CO Overlayer on Pt(111)”, Solid St. Comm., vol. 123, pp. 267–272, 2002.Google Scholar

Zasada, I. and Rychtelska, T., “Coverage-Dependent Diffuse Spin-Polarized Electron Diffraction Analysis of CO on Pt(111)”, Surf. Sci., vol. 507, pp. 362–367, 2002.Google Scholar

Wander, A., Held, G., Hwang, R. Q., Blackman, G. S., Xu, M. L., de Andres, P., Van Hove, M. A., and Somorjai, G. A., “A Diffuse LEED Study of the Adsorption Structure of Disordered Benzene on Pt(111)”, Surf. Sci., vol. 249, pp. 21–34, 1991.Google Scholar

Döll, R., Gerken, C. A., Van Hove, M. A., and Somorjai, G. A., “Structure of Disordered Ethylene Adsorbed on Pt(111) Analyzed by Diffuse LEED: Asymmetrical di-σ Bonding Favored”, Surf. Sci., vol. 374, pp. 151–161, 1997.Google Scholar

Starke, U., Heinz, K., Materer, N., Wander, A., Michl, M., Döll, R., Van Hove, M. A., and Somorjai, G. A., “Low-Energy Electron Diffraction Study of a Disordered Monolayer of H₂O on Pt(111) and an Ordered Thin Film of Ice Grown on Pt(111)”, J. Vac. Sci. Technol., vol. A10, pp. 2521–2528, 1992.Google Scholar

Starke, U., Materer, N., Barbieri, A., Döll, R., Heinz, K., Van Hove, M. A., and Somorjai, G. A., “A Low-Energy Electron Diffraction Study of Oxygen, Water and Ice Adsorption on Pt(111)”, Surf. Sci., vol. 287/288, pp. 432–437, 1993.Google Scholar

Desjonquères, M. C. and Spanjaard, D., Concepts in Surface Physics, Springer, Berlin, 1993.Google Scholar

Kuhs, F. W., “Generalized Atomic Displacements in Crystallographic Structure Analysis”, Acta Cryst., vol. A48, pp. 80–98, 1992.Google Scholar

Ibach, H. and Mills, D. L., Electron Energy Loss Spectroscopy and Surface Vibrations, Academic Press, New York, 1982.Google Scholar

Landskron, J., Moritz, W., Narloch, B., Held, G., and Menzel, D., “Analysis of Thermal Vibrations by Temperature-Dependent Low Energy Electron Diffraction: Comparison of Soft Modes of Pure and O-Coadsorbed CO on Ru(0001)”, Surf. Sci., vol. 441, pp. 91–106, 1999.Google Scholar

Meyerheim, H. L., Moritz, W., Schulz, H., Eng, P. J., and Robinson, I. K., “Anharmonic Thermal Vibrations Observed by Surface X-ray Diffraction for Cs/Cu(001)”, Surf. Sci., vol. 331–333, pp. 1422–1429, 1995.Google Scholar

Willis, B. T. M. and Pryor, A. W., Thermal Vibrations in Crystallography, Cambridge University Press, London, 1975.Google Scholar

Trueblood, K. N., Bürgi, H.-B., Burzlaff, H., Dunitz, J. D., Gramaccioli, C. M., Schulz, H. H., Shmueli, U., and Abrahams, S. C., “Atomic Displacement Parameter Nomenclature”, Acta Cryst., vol. A52, pp. 770–781, 1996.Google Scholar

Krivoglaz, M. A., The Theory of X-ray and Thermal Neutron Diffraction by Real Crystals, Plenum Press, London, 1969.Google Scholar

McKinney, J. T., Jones, E. R., and Webb, M. B., “Surface Lattice Dynamics of Silver. II. Low-Energy Electron Thermal Diffuse Scattering”, Phys. Rev., vol. 160, pp. 523–530, 1967.Google Scholar

Zielasek, V., Büssenschütt, A., and Henzler, M., “Low-Energy Electron Thermal Diffuse Scattering from Al(111) Individually Resolved in Energy and Momentum”, Phys. Rev. B, vol. 55, pp. 5398–5403, 1997.Google Scholar

Piccini, G. M. and Sauer, J., “Effect of Anharmonicity on Adsorption Thermodynamics”, J. Chem. Theory Comput., vol. 10, pp. 2479−2487, 2014.Google Scholar

Brune, H., “Thermal Dynamics at Surfaces”, Ann. Phys., vol. 18, pp. 675–698, 2009.Google Scholar

Prince, E., Mathematical Techniques in Crystallography and Materials Science, Springer-Verlag, New York, 1982.Google Scholar

Schmueli, U., Theories and Techniques of Crystal Structure Determination, Oxford University Press, Oxford, 2007.Google Scholar

Gierer, M., Bludau, H., Over, H., and Ertl, G., “The Bending Mode Vibration of CO on Ru(0001) Studied with Low-Energy Electron-Diffraction”, Surf. Sci., vol. 346, pp. 64–72, 1996.Google Scholar

Duke, C. B. and Laramore, G. E., “Effect of Lattice Vibrations in a Multiple-Scattering Description of Low-Energy Electron Diffraction. I. Formal Perturbation Theory”, Phys. Rev. B, vol. 2, pp. 4765–4782, 1970. Laramore, G. E. and Duke, C. B., “Effect of Lattice Vibrations in a Multiple-Scattering Description of Low-Energy Electron Diffraction. II. Double-Diffraction Analysis of the Elastic Scattering Cross Section”, Phys. Rev. B, vol. 2, pp. 4783–4795, 1970.CrossRefGoogle Scholar

Landskron, J., “Analyse thermischer Schwingungen an Oberflächen mittels Beugung langsamer Elektronen”, Dissertation, University of Munich, Dept. of Earth and Environmental Sciences, Germany, 1996.Google Scholar

Moritz, W. and Landskron, J., “Anisotropic Temperature Factors in the Calculation of Low-Energy Electron Diffraction Intensities”, Surf. Sci., vol. 337, pp. 278–284, 1995.Google Scholar

Moritz, W. and Landskron, J., “Thermal Vibrations at Surfaces Analysed with LEED”, in Solid-State Photoemission and Related Methods, eds. Schattke, W. and Van Hove, M. A., Wiley-VCH, Weinheim, 2003, pp. 433–459.Google Scholar

de Andres, P. L. and King, D. A., “Anisotropic and Anharmonic Effects through the t-Matrix for Low-Energy Electron Diffraction (TMAT V1.1)”, Comp.Phys. Commun., vol. 138, pp. 281–301, 2001.Google Scholar

Messiah, A., Quantum Mechanics, Dover, Mineola, NY, vols. I & II, 2014.Google Scholar

Blanco-Rey, M., de Andres, P. L., Held, G., and King, D. A., “A Molecular T-Matrix Approach to Calculating Low-Energy Electron Diffraction Intensities for Ordered Molecular Adsorbates”, Surf. Sci., vol. 579, p. 89–99, 2005.Google Scholar

Blanco-Rey, M., de Andres, P., Held, G., and King, D. A., “Molecular t-Matrices for Low-Energy Electron Diffraction (TMOL v1.1)”, Comp. Phys. Commun., vol. 161, pp. 166–178, 2004.Google Scholar

Riedl, W. and Menzel, D., “ESDIAD Beam Widths”, Surf. Sci., vol. 207, pp. 494–451, 1989.Google Scholar

Watson, P. R., Van Hove, M. A., and Hermann, K., NIST Surface Structure Database Ver. 5.0, NIST Standard Reference Data Program, Gaithersburg, MD, USA, 2004.Google Scholar

Van Hove, M. A., Watson, P. R., and Hermann, K., “Adsorbate-Induced Changes in Surface Structure on Metals and Semiconductors”, in Landolt-Börnstein, Group III: Condensed Matter, Vol. 42: Physics of Covered Solid Surfaces, Springer, Berlin, 2002, subvol. A, part 2, ch. 4.1, pp. 4.1-43–4.1-164.Google Scholar

Moritz, W., “Elastic Scattering and Diffraction of Electrons and Positrons”, in Landolt-Börnstein, Group III: Condensed Matter, Vol. 45: Physics of Solid Surfaces, Springer, Berlin, 2015, subvol. A, ch. 5, pp. 5.1-134–5.8-243.Google Scholar

Giacovazzo, C., Direct Phasing in Crystallography, Fundamentals and Applications, Oxford University Press, Oxford, 1998.Google Scholar

Clegg, W., Blake, A. J., Gould, R. O., and Main, P., Crystal Structure Analysis, Principles and Practice, Oxford University Press, Oxford, 2001.Google Scholar

Oszlányi, G. and Sütő, A., “Ab Initio Structure Solution by Charge Flipping”, Acta Cryst. A, vol. 60, pp. 134–141, 2004.Google Scholar

Van Hove, M. A., Cerdá, J., Sautet, P., Bocquet, M.-L., and Salmeron, M., “Surface Structure Determination by STM vs. LEED”, Progr. Surf. Sci., vol. 54, pp. 315–329, 1997.Google Scholar

Heinz, K., Hammer, L., and Müller, S., “The Power of Joint Application of LEED and DFT in Quantitative Surface Structure Determination”, J. Phys.: Condens. Matter, vol. 20, p. 304204, 2008.Google Scholar

Soares, E. A., de Castilho, C. M. C., and de Carvalho, V. E., “Advances on Surface Structural Determination by LEED”, J. Phys.: Condens. Matter, vol. 23, p. 303001, 2011.Google Scholar

Lagally, M. G., Ngoc, T. C., and Webb, M. B., “Kinematic Low-Energy Electron-Diffraction Intensities from Averaged Data: A Method for Surface Crystallography”, Phys. Rev. Lett., vol. 26, pp. 1557–1559, 1971.Google Scholar

Adams, D. L. and Landman, U., “Further Evaluation of the Transform-Deconvolution Method for Surface-Structure Determination by Analysis of Low-Energy Electron-Diffraction Intensities”, Phys. Rev. B, vol. 15, pp. 3775–3787, 1977.Google Scholar

Wu, H. and Tong, S. Y., “Surface Patterson Function by Inversion of Low-Energy Electron Diffraction I–V Spectra at Multiple Incident Angles”, Phys. Rev. Lett., vol. 87, p. 036101, 2001.Google Scholar

Tong, S. Y. and Wu, H., “Direct Inversion of Low-Energy Electron Diffraction (LEED) IV Spectra: The Surface Patterson Function”, J. Phys.: Condens. Matter, vol. 14, pp. 1231–1236, 2002.Google Scholar

Wang, J., Wu, H. S., So, R., Liu, Y., Xie, M. H., and Tong, S. Y., “Structure Determination of Indium-Induced Si(111)-In-4×1 Surface by LEED Patterson Inversion”, Phys. Rev. B, vol. 72, p. 245324, 2005.Google Scholar

Abukawa, T., Yamazaki, T., and Kono, S., “Fully Performed Constant-Momentum-Transfer-Averaging in Low-Energy Electron Diffraction Demonstrated for a Single-Domain Si(111)4×1-In Surface”, e-J. Surf. Sci. Nanotechn., vol. 4, pp. 661–668, 2006.Google Scholar

Rogero, C., Martin-Gago, J.-A., and de Andres, P. L., “Patterson Function from Low-Energy Electron Diffraction Measured Intensities and Structural Discrimination”, Phys. Rev. B, vol. 67, p. 073402, 2003.Google Scholar

Kuzushita, T., Murata, A., Yamamoto, A., and Urano, A., “Surface Structure Analysis of Metal Adsorbed Si(111) Surfaces by Patterson Function with LEED I–V Curves”, Appl. Surf. Sci., vol. 254, pp. 7824–7826, 2008.Google Scholar

Chang, C. Y., Lin, Z. C., Chou, Y. C., and Wei, C. M., “Direct Three-Dimensional Patterson Inversion of Low-Energy Electron Diffraction I(E) Curves”, Phys. Rev. Lett., vol. 83, pp. 2580–2583, 1999.Google Scholar

Wang, J., So, R., Liu, Y., Wu, H., Xie, M. H., and Tong, S. Y., “Observation of a (√3×√3)-R30° Reconstruction on GaN(0001) by RHEED and LEED”, Surf. Sci., vol. 600, pp. L169–L174, 2006.Google Scholar

Xu, S. H., Wu, H. S., Dai, X. Q., Lau, W. P., Zheng, L. X., Xie, M. H., and Tong, S. Y., “Direct Observation of a Ga Adlayer on a GaN(0001) Surface by LEED Patterson Inversion”, Phys. Rev. B, vol. 67, p. 125409, 2003.Google Scholar

Gabor, D., “A New Microscopic Principle”, Nature, vol. 161, pp. 777–778, 1948.Google Scholar

Tong, S. Y., “Inversion of Low-Energy Electron Diffraction Data with No Pre-knowledge Factor beyond Optical Holography”, Adv. Phys., vol. 48, pp. 135–165, 1999.Google Scholar

Heinz, K., Starke, U., and Bernhardt, J., “Surface Holography with LEED Electrons”, Progr. Surf. Sci., vol. 64, pp. 163–178, 2000.Google Scholar

Barton, J. J., “Photoelectron Holography”, Phys. Rev. Lett., vol. 61, pp. 1356–1359, 1988.Google Scholar

Fadley, C. S., Van Hove, M. A., Kaduwela, A., Omori, S., Zhao, L., and Marchesini, S., “Photoelectron and X-ray Holography by Contrast: Enhancing Image Quality and Dimensionality”, J. Phys.: Condens. Matter, vol. 13, pp. 10517–10532, 2001.Google Scholar

Daimon, H., “Overview of Three-Dimensional Atomic-Resolution Holography and Imaging Techniques: Recent Advances in Local-Structure Science”, J. Phys. Soc. Jpn., vol. 87, p. 061001, 2018.Google Scholar

Omori, S., Nihei, Y., Rotenberg, E., Denlinger, J. D., Kevan, S. D., Tonner, B. P., Van Hove, M. A., and Fadley, C. S., “Differential Photoelectron Holography: A New Approach for Three-Dimensional Atomic Imaging”, Phys. Rev. Lett., vol. 88, p. 055504, 2002.Google Scholar

Suzuki, A., Hashimoto, A., Nojima, M., Owari, M., and Nihei, Y., “Holographic Imaging of TiO₂ (110) Surface Structure by Differential Photoelectron Holography”, Surf. Interface Anal., vol. 40, pp. 1627–1630, 2008.Google Scholar

Saldin, D. K. and de Andres, P. L., “Holographic LEED”, Phys. Rev. Lett., vol. 64, pp. 1270–1273, 1990.Google Scholar

Saldin, D. K., Harp, G. R., Chen, B. L., and Tonner, B. P., “Theoretical Principles of Holographic Crystallography”, Phys. Rev. B, vol. 44, pp. 2480–2494, 1991.Google Scholar

Mendez, M. A., Gluck, C., and Heinz, K., “Holography with Conventional LEED”, J. Phys.: Condens. Matter, vol. 4, pp. 999–1006, 1992.Google Scholar

Hu, P. J. and King, D. A., “A Direct Inversion Method for Surface Structure Determination from LEED Intensities”, Nature, vol. 360, pp. 655–658, 1992.Google Scholar

Wei, C. M. and Tong, S. Y., “Direct Atomic Structure by Holographic Diffuse LEED”, Surf. Sci., vol. 274, pp. L577–L582, 1992.Google Scholar

Saldin, D. K. and Chen, X., “Three-Dimensional Reconstruction by Holographic LEED: Proper Identification of the Reference Wave”, Phys. Rev. B, vol. 52, pp. 2941–2948, 1995.Google Scholar

Saldin, D. K., Reuter, K., de Andres, P. L., Wedler, H., Chen, X., Pendry, J. B., and Heinz, K., “Direct Reconstruction of Three-Dimensional Atomic Adsorption Sites by Holographic LEED”, Phys. Rev. B, vol. 54, pp. 8172–8176, 1996.Google Scholar

Reuter, K., Schardt, J., Bernhardt, J., Wedler, K., Starke, U., and Heinz, K., “LEED Holography Applied to a Complex Superstructure: A Direct View of the Adatom Cluster on SiC(111)-(3×3)”, Phys. Rev. B, vol. 58, pp. 10806–10814, 1998.Google Scholar

Schardt, J., Bernhardt, J., Starke, U., and Heinz, K., “Crystallography of the (3×3) Surface Reconstruction of 3C-SiC(111), 4H-SiC(0001), and 6H-SiC(0001) Surfaces Retrieved by Low-Energy Electron Diffraction”, Phys. Rev. B, vol. 62, pp. 10335–10344, 2000.Google Scholar

Starke, U., Pendry, J. B., and Heinz, K., “Diffuse Low-Energy Electron Diffraction”, Progr. Surf. Sci., vol. 52, pp. 53–123, 1996.Google Scholar

Seubert, A. and Heinz, K., “Iterative Image Recovery in Holographic LEED”, Surf. Rev. Lett., vol. 9, pp. 1413–1423, 2002.Google Scholar

Seubert, A., Heinz, K., and Saldin, D. K., “Direct Determination by Low-Energy Electron Diffraction of the Atomic Structure of Surface Layers on a Known Substrate”, Phys. Rev. B, vol. 67, p. 125417, 2003.Google Scholar

Kolthoff, D., Schwennicke, C., and Pfnür, H., “Holographic Diffuse LEED Image Reconstruction for Simultaneous Occupation of Different Oxygen Adsorption Sites on Ni(111)”, Surf. Sci., vol. 529, pp. 443–454, 2003.Google Scholar

Wu, H., Xu, S., Ma, S., Lau, W. P., Xie, M. H., and Tong, S. Y., “Surface Atomic Arrangement Visualization via Reference-Atom-Specific Holography”, Phys. Rev. Lett., vol. 89, p. 216101, 2002.Google Scholar

Abukawa, T. and Kono, S., “Semi-direct Method for Surface Structure Analysis Using Correlated Thermal Diffuse Scattering”, Progr. Surf. Sci., vol. 72, pp. 19–51, 2003.Google Scholar

Kleinle, G., Moritz, W., and Ertl, G., “An Efficient Method for Surface Crystallography”, Surf. Sci., vol. 238, pp. 119–131, 1990.Google Scholar

Pendry, J. B., “Reliability Factors for LEED Calculations”, J. Phys. C: Solid State Phys., vol. 13, pp. 937–944, 1980.Google Scholar

Sirtl, Th., Jelic, J., Meyer, J., Das, K., Heckl, W. M., Moritz, W., Rundgren, J., Schmittel, M., Reuter, K., and Lackinger, M., “Adsorption Structure Determination of a Large Polyaromatic Trithiolate on Cu(111): Combination of LEED-I(V) and DFT-vdW”, Phys. Chem. Chem. Phys., vol. 15, pp. 11054–11060, 2013,Google Scholar

Pussi, K., Li, H. I., Shin, H., Serkovic Loli, L. N., Shukla, A. K., Ledieu, J., Fournée, V., Wang, L. L., Su, S. Y., Marino, K. E., Snyder, M. V., and Diehl, R. D., “Elucidating the Dynamical Equilibrium of C₆₀ Molecules on Ag(111)”, Phys. Rev. B, vol. 86, p. 205406, 2012.Google Scholar

Primorac, E., Kuhlenbeck, H., and Freund, H.-J., “LEED I/V Determination of the Structure of a MoO₃ Monolayer on Au(111): Testing the Performance of the CMA-ES Evolutionary Strategy Algorithm, Differential Evolution, a Genetic Algorithm and Tensor LEED Based Structural Optimization”, Surf. Sci., vol. 649, pp. 90–100, 2016.Google Scholar

Zanazzi, E. and Jona, F., “A Reliability Factor for Surface Structure Determination by Low Energy Electron Diffraction”, Surf. Sci., vol. 62, pp. 61–80, 1977.Google Scholar

Philip, J. and Rundgren, J., “Metric Distance between LEED Spectra”, in Determination of Surface Structure by LEED, eds. Marcus, P. M. and Jona, F., Plenum, New York, 1984, pp. 409–437.Google Scholar

Rundgren, J., “Electron Inelastic Mean Free Path, Electron Attenuation Length, and Low-Energy Electron-Diffraction Theory”, Phys. Rev. B, vol. 59, pp. 5106–5114, 1999.Google Scholar

Tanuma, S., Powell, C. J., and Penn, D. R., “Calculations of Electron Inelastic Mean Free Paths. IX. Data for 41 Elemental Solids over the 0 eV to 30 keV Range”, Surf. Interface Anal., vol. 43, pp. 689–713, 2011.Google Scholar

Adams, D. L., “A Simple and Effective Procedure for the Refinement of Surface Structure in LEED”, Surf. Sci., vol. 519, pp. 157–172, 2002.Google Scholar

Duke, C. B., Lazarides, A., Paton, A., and Wang, Y. R., “Statistical Error Analysis of Surface-Structure Parameters Determined by Low-Energy Electron and Positron Diffraction: Data Errors”, Phys. Rev. B, vol. 52, pp. 14878–14894, 1995.Google Scholar

Mulakaluri, N., Pentcheva, R., Wieland, M., Moritz, W., and Scheffler, M., “Partial Dissociation of Water on Fe₃O₄(001): Adsorbate Induced Charge and Orbital Order”, Phys. Rev. Lett., vol. 103, p. 176102, 2009.Google Scholar

Hofmann, J. P., Rohrlack, S. F., Heß, F., Goritzka, J. C., Krause, P. P. T., Seitsonen, A. P., Moritz, W., and Over, H., “Adsorption of Chlorine on Ru(0001): A Combined Density Functional Theory and Quantitative Low Energy Electron Diffraction Study”, Surf. Sci., vol. 606, pp. 297–304, 2012.Google Scholar

Li, H. I., Pussi, K., Hanna, K. J., Wang, L.-L., Johnson, D. D., Cheng, H.-P., Shin, H., Curtarolo, S., Moritz, W., Smerdon, J. A., McGrath, R., and Diehl, R. D., “Surface Geometry of C₆₀ on Ag(111)”, Phys. Rev. Lett., vol. 103, p. 056101, 2009.Google Scholar

Wyrwich, R., Jones, T. E., Günther, S., Moritz, W., Ehrensperger, M., Böcklein, S., Zeller, P., Lünser, A., Locatelli, A., Menteş, T. O., Niño, M. Á., Knop-Gericke, A., Schlögl, R., Piccinin, S., and Wintterlin, J., “LEED‑I(V) Structure Analysis of the (7×√3)rect SO₄ Phase on Ag(111): Precursor to the Active Species of the Ag-Catalyzed Ethylene Epoxidation”, J. Phys. Chem. C, vol. 122, pp. 26998−27004, 2018.Google Scholar

Over, H., Ketterl, U., Moritz, W., and Ertl, G., “Optimisation Methods and Their Use in Low-Energy Electron-Diffraction Calculations”, Phys. Rev. B, vol. 46, pp. 15438–15446, 1992.Google Scholar

Marquardt, D. W., “An Algorithm for Least-Squares Estimation of Nonlinear Parameters”, J. Soc. Indust. Appl. Math., vol. 11, pp. 431–441, 1963.Google Scholar

Reichelt, R., Günther, S., Wintterlin, J., Moritz, W., Aballe, L., and Mentes, T. O., “Low Energy Electron Diffraction and Low Energy Electron Microscopy Microspot I/V Analysis of the (4×4) O Structure on Ag(111): Surface Oxide or Reconstruction”, J. Chem. Phys., vol. 127, p. 134706, 2007.Google Scholar

Lübbe, M. and Moritz, W., “A LEED Analysis of the Clean Surfaces of α-Fe₂O₃(0001) and α-Cr₂O₃(0001) Bulk Single Crystals”, J. Phys.: Condens. Matter, vol. 21, p. 134010, 2009.Google Scholar

Rous, P. J., “The Tensor LEED Approximation and Surface Crystallography by Low-Energy Electron Diffraction”, Progr. Surf. Sci., vol. 39, pp. 3–63, 1992.Google Scholar

Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., Numerical Recipes, Cambridge University Press, Cambridge, 1986.Google Scholar

Brent, R. P., Algorithms for Minimization without Derivatives, Prentice-Hall, Englewood Cliffs, NJ, 1973.Google Scholar

Rosenbrook, H. H., “An Automatic Method for Finding the Greatest or Least Value of a Function”, Comput. J., vol. 3, pp. 175–184, 1960.Google Scholar

Stout, G. H. and Jensen, L. H., X-ray Structure Determination, MacMillan, New York, 1968.Google Scholar

Cowell, P. G. and de Carvalho, V. E., “Unconstrained Optimisation in Surface Crystallography by LEED: Preliminary Results of its Application to CdTe(110)”, Surf. Sci., vol. 187, pp. 175–193, 1987.Google Scholar

Powell, M. J. D., “The BOBYQA Algorithm for Bound Constrained Optimization without Derivatives” (Report), Department of Applied Mathematics and Theoretical Physics, Cambridge University, DAMTP 2009/NA06, www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf, last accessed 2 April 2022.Google Scholar

Rous, P. J., “A Global Approach to the Search Problem in Surface Crystallography by Low-Energy Electron Diffraction”, Surf. Sci., vol. 296, pp. 358–373, 1993.Google Scholar

Szu, H. and Hartley, R., “Fast Simulated Annealing”, Phys. Lett. A, vol. 122, pp. 157–162, 1987.Google Scholar

Tsallis, C., “Possible Generalization of Boltzmann-Gibbs Statistics”, J. Stat. Phys., vol. 52, pp. 479–487, 1988.Google Scholar

Nascimento, V. B., de Carvalho, V. E., de Castilho, C. M. C., Costa, B. V., and Soares, E. A., “The Fast Simulated Annealing Algorithm Applied to the Search Problem in LEED”, Surf. Sci., vol. 487, pp. 15–27, 2001.Google Scholar

Correia, E. dos R., Nascimento, V. B., de Castilho, C. M. C., Soares, E. A., and de Carvalho, V. E., “The Generalized Simulated Annealing Algorithm in the Low Energy Electron Diffraction Search Problem”, J. Phys.: Condens. Matter, vol. 17, pp. 1–16, 2005.Google Scholar

Kottcke, M. and Heinz, K., “A New Approach to Automated Structure Optimization in LEED Intensity Analysis”, Surf. Sci., vol. 376, pp. 352–366, 1997.Google Scholar

Viana, M. L., dos Reis, D. D., Soares, E. A., Van Hove, M. A., Moritz, W., and de Carvalho, V. E., “Novel Genetic Algorithm Searching Procedure for LEED Surface Structure Determination”, J. Phys.: Condens. Matter, vol. 26, p. 225005, 2014.Google Scholar

Döll, R. and Van Hove, M. A., “Global Optimization in LEED Structure Determination Using Genetic Algorithms”, Surf. Sci., vol. 355, pp. L393–L398, 1996.Google Scholar

Viana, M. L., Diez Muiño, R., Soares, E. A., Van Hove, M. A., and de Carvalho, V. E., “Global Search in Photoelectron Diffraction Structure Determination Using Genetic Algorithms”, J. Phys.: Condens. Matter, vol. 19, p. 446002, 2007.Google Scholar

Viana, M. L., Simões e Silva, W., Soares, E. A., de Carvalho, V. E., de Castilho, C. M. C., and Van Hove, M. A., “Scaling Behavior of Genetic Algorithms Applied to Surface Structural Determination by LEED”, Surf. Sci., vol. 602, pp. 3395–3402, 2008.Google Scholar

Storn, R. and Price, K., “Differential Evolution: A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces”, J. Global Optimization, vol. 11, pp. 341–359, 1997.Google Scholar

Hansen, N., “The CMA Evolution Strategy: A Comparing Review”, in Towards a New Evolutionary Computation. Advances on Estimation of Distribution Algorithms, eds. Lozano, J. A., Larranaga, P., Inza, I., and Bengoetxea, E., Springer, Berlin, 2006, pp. 75–102.Google Scholar

Nascimento, V. B. and Plummer, E. W., “Differential Evolution: Global Search Problem in LEED-IV Surface Structural Analysis”, Mater. Charact., vol. 100, pp. 143–151, 2015.Google Scholar

Zhao, Z. J., Meza, J. C., and Van Hove, M., “Using Pattern Search Methods for Surface Structure Determination of Nanomaterials”, J. Phys.: Condens. Matter, vol. 18, pp. 8693–8706, 2006.Google Scholar

Audet, C. and Dennis, J. E. Jr., “Pattern Search Algorithms for Mixed Variable Programming”, SIAM J. Optim., vol. 11, pp. 573–594, 1999.Google Scholar

Kolda, T. G., Lewis, R. M., and Torczon, V., “Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods”, SIAM Rev., vol. 45, pp. 385–482, 2003.Google Scholar

Abramson, M. A., Audet, C., Chrissis, J. W., and Walston, J. G., “Mesh Adaptive Direct Search Algorithms for Mixed Variable Optimization”, Optim. Lett., vol. 3, pp. 35–47, 2009.Google Scholar

Jiang, H., Mizuno, S., and Tochihara, H., “Adsorption Mode Change from Adlayer- to Restructuring-Type with Increasing Coverage, Evidenced by Structural Determination of c(2×2)→(4×4)→(5×5) Sequence Formed on Ni(001) by Li Deposition”, Surf. Sci., vol. 380, pp. L506–L512, 1997.Google Scholar

Schwarz, K., “DFT Calculations of Solids with LAPW and WIEN2k”, J. Solid State Chem., vol. 176, pp. 319–328, 2003.Google Scholar

Loucks, T. L., Augmented Plane Wave Method, Benjamin, New York, 1967.Google Scholar

Mattheiss, L. F., “Energy Bands for Solid Argon”, Phys. Rev. A, vol. 133, pp. A1399–A1403, 1964.Google Scholar

Pendry, J. B., Titterington, D. J., Gurman, S. J., and Aers, G., MUFPOT code, Daresbury, 1970. No longer available.Google Scholar

Barbieri, A. and Van Hove, M. A., phase shift code, https://www.icts.hkbu.edu.hk/VanHove_files/leed/phshift2007.zip, last accessed 2 April 2022.Google Scholar

Kinniburgh, C. G., “A LEED Study of MgO(100). II. Theory at Normal Incidence”, J. Phys. C: Solid State Phys., vol. 8, pp. 2382–2394, 1975.Google Scholar

Kinniburgh, C. G. and Walker, J. A., “LEED Calculations for the NiO(100) Surface”, Surf. Sci., vol. 63, pp. 274–282, 1977.Google Scholar

Lindsay, R., Wander, A., Ernst, A., Montanari, B., Thornton, G., and Harrison, N. M., “Revisiting the Surface Structure of TiO₂(110): A Quantitative Low-Energy Electron Diffraction Study”, Phys. Rev. Lett., vol. 94, p. 246102, 2005.Google Scholar

Chamberlin, S. E., Hirschmugl, C. J., Poon, H. C., and Saldin, D. K., “Geometric Structure of TiO₂(011)(2×1) Surface by Low Energy Electron Diffraction (LEED)”, Surf. Sci., vol. 603, pp. 3367–3373, 2009.Google Scholar

Rundgren, J., “Optimized Surface-Slab Excited-State Muffin-Tin Potential and Surface Core Level Shifts”, Phys. Rev. B, vol. 68, p. 125405, 2003.Google Scholar

Rundgren, J., “Elastic Electron-Atom Scattering in Amplitude-Phase Representation with Application to Electron Diffraction and Spectroscopy”, Phys. Rev. B, vol. 76, p. 195441, 2007.Google Scholar

Hedin, L. and Lundqvist, B. I., “Explicit Local Exchange-Correlation Potentials”, J. Phys. C, vol. 4, pp. 2064–2083, 1971.Google Scholar

Mahan, G. D. and Sernelius, B. E., “Electron–Electron Interactions and the Band Width of Metals”, Phys. Rev. Lett., vol. 62, pp. 2718–2721, 1989.Google Scholar

Nascimento, V. B., Moore, R. G., Rundgren, J., Zhang, J., Cai, L., Jin, R., Mandrus, D. G., and Plummer, E. W., “Procedure for LEED I–V Structural Analysis of Metal Oxide Surfaces: Ca_1.5Sr_0.5RuO₄(001)”, Phys. Rev. B, vol. 75, p. 035408, 2007.Google Scholar

NIST Electron Inelastic-Mean-Free-Path Database 71, Version 1.1: https://www.nist.gov/srd/nist-standard-reference-database-71, last accessed 5 April 2022.Google Scholar

Ruf, J. P., King, P. D. C., Nascimento, V. B., Schlom, D. G., and Shen, K. M., “Surface Atomic Structure of Epitaxial LaNiO₃ Thin Films Studied by in situ LEED-I(V)”, Phys. Rev. B, vol. 95, p. 115418, 2017.Google Scholar

Rundgren, J., Sernelius, B. E., and Moritz, W., “Low-Energy Electron Diffraction with Signal Electron Carrier-Wave Wavenumber Modulated by Signal Exchange–Correlation Interaction”, J. Phys. Commun., vol. 5, p. 105012, 2021.Google Scholar

Saldin, D. K. and Spence, J. C. H., “On the Mean Inner Potential in High- and Low-Energy Electron Diffraction”, Ultramicroscopy, vol. 55, pp. 397–406, 1994.Google Scholar

Tuan, D. F.-T. and Loar, G. W., “Corrections of Overlapping Spheres in the Self-Consistent Field Xα Scattered-Wave Method”, J. Mol. Struct., vol. 223, pp. 123–148, 1990.Google Scholar

Tuan, D. F.-T. and Loar, G. W., “Corrections of Overlapping Spheres in the Self-Consistent Field Xα Scattered-Wave Method”, J. Mol. Struct., vol. 228, pp. 167–180, 1991.Google Scholar

Vitos, L., Skriver, H. L., Johansson, B., and Kollár, J., “Application of the Exact Muffin-Tin Orbitals Theory: The Spherical Cell Approximation”, Comp. Mat. Sci., vol. 18, pp. 24–38, 2000.Google Scholar

Watson, R. E., Herbst, J. F., Hodges, L., Lundqvist, B. I., and Wilkins, J. W., “Effect of Ground-State and Excitation Potentials on Energy Levels of Ni Metal”, Phys. Rev. B, vol. 13, pp. 1463–1467, 1976.Google Scholar

Moritz, W., unpublished.Google Scholar

Walter, S., Blum, V., Hammer, L., Müller, S., Heinz, K., and Giesen, M., “The Role of an Energy-Dependent Inner Potential in Quantitative Low-Energy Electron Diffraction”, Surf. Sci., vol. 458, pp. 155–161, 2000.Google Scholar

Vuorinen, J., Pussi, K., Diehl, R. D., and Lindroos, M., “Correlation of Electron Self-Energy with Geometric Structure in Low-Energy Electron Diffraction”, J. Phys.: Condens. Matter, vol. 24, p. 015003, 2012.Google Scholar

Seah, M. P. and Dench, W. A., “Quantitative Electron Spectroscopy of Surfaces: A Standard Data Base for Electron Inelastic Mean Free Paths in Solids”, Surf. Interface Anal., vol. 1, pp. 2–11, 1979.Google Scholar

Jablonski, A. and Powell, C. J., “The Electron Attenuation Length Revisited”, Surf. Sci. Rep., vol. 47, pp. 33–91, 2002.Google Scholar

Powell, C. J. and Jablonski, A., “Evaluation of Calculated and Measured Electron Inelastic Mean Free Paths Near Solid Surfaces”, J. Phys. Chem. Ref. Data, vol. 28, pp. 19–62, 1999.Google Scholar

de Vera, P. and Garcia-Molina, R., “Electron Inelastic Mean Free Paths in Condensed Matter Down to a Few Electronvolts”, J. Phys. Chem. C, vol. 123, pp. 2075−2083, 2019.Google Scholar

Tanuma, S., Powell, C. J., and Penn, D. R., “Calculations of Electron Inelastic Mean Free Paths. IX. Data for 41 Elemental Solids over the 50 eV to 30 keV Range”, Surf. Interface Anal., vol. 43, pp. 689–713, 2011.Google Scholar

Yu. Ridzel, O., Astašauskas, V., and Werner, W. S. M., “Low Energy (1–100 eV) Electron Inelastic Mean Free Path (IMFP) Values Determined from Analysis of Secondary Electron Yields (SEY) in the Incident Energy Range of 0.1–10 keV”, J. Electr. Spectr. Rel. Phen., vol. 241, p. 146824, 2020.Google Scholar

Zielasek, V., Büssenschütt, A., and Henzler, M., “Low-Energy Electron Thermal Diffuse Scattering from Al(111) Individually Resolved in Energy and Momentum”, Phys. Rev. B, vol. 55, pp. 5398–5403, 1997.Google Scholar

van Smaalen, S., “Incommensurate Crystal Structures”, Cryst. Rev., vol. 4, pp. 19–202, 1995.Google Scholar

Steurer, W. and Haibach, T., “Reciprocal-Space Images of Aperiodic Crystals”, in International Tables for Crystallography, Kluwer Academic Publishers, Dordrecht, vol. B, ch. 4.6, pp. 486–532, 2006.Google Scholar

Shechtman, D., Blech, I., Gratias, D., and Cahn, J. W., “Metallic Phase with Long-Range Orientational Order and No Translational Symmetry”, Phys. Rev. Lett., vol. 53, pp. 1951–1954, 1984.Google Scholar

Janot, C., Quasicrystals: A Primer, Clarendon Press, Oxford, 1994.Google Scholar

Steurer, W., “Twenty Years of Structure Research on Quasicrystals. Part I. Pentagonal, Octagonal, Decagonal and Dodecagonal Quasicrystals”, Z. Kristallogr., vol. 219, pp. 391–446, 2004.Google Scholar

Trebin, H.-R., ed., Quasicrystals, Structure and Physical Properties, Wiley-VCH, Weinheim, 2003.Google Scholar

Suck, B., Schreiber, M., and Haussler, P., eds., Quasicrystals: An Introduction to Structure, Physical Properties and Applications, Springer, Berlin, 2002.Google Scholar

Dubois, J. M., Useful Quasicrystals, World Scientific Press, Singapore, 2005.Google Scholar

Steurer, W. and Deloudi, S., Crystallography of Quasicrystals: Concepts, Methods and Structures, Springer, Berlin, 2009.Google Scholar

Boettinger, W. J., Biancaniello, F. S., Kalonji, G. M., and Cahn, J. W., “Eutectic Solidification and the Formation of Metallic Glasses”, in Proceedings of the Second International Conference on Rapid Solidification Processing: Principles and Technologies, II, ed. Mehrabian, R., Kear, B. H. and Cohen, M., Claitor’s Publishing Division, Baton Rouge, 1980, pp. 50–55.Google Scholar

Gille, P., Dreier, P., Gräber, M., and Scholpp, T., “Large Single-Grain AlCoNi Quasicrystals Grown by the Czochralski Method”, J. Cryst. Growth, vol. 207, pp. 95–101, 1999.Google Scholar

McGrath, R., Ledieu, J., Cox, E. J., and Diehl, R. D., “Quasicrystal Surfaces: Structure and Potential as Templates”, J. Phys.: Condens. Matter, vol. 14, pp. R119–R144, 2002.Google Scholar

Diehl, R. D., Ledieu, J., Ferralis, N., Szmodis, A. W., and McGrath, R., “Low-Energy Electron Diffraction from Quasicrystal Surfaces”, J. Phys.: Condens. Matter, vol. 15, pp. R63–R81, 2003.Google Scholar

Penrose, R., “The Role of Aesthetics in Pure and Applied Mathematical Research”, Bull. Inst. Math. & Appl., vol. 10, pp. 266–271, 1974.Google Scholar

Hermann, K., Crystallography and Surface Structure: An Introduction for Surface Scientists and Nanoscientists, 2nd ed., Wiley, Weinheim, 2016.Google Scholar

Cai, T., Shi, F., Shen, Z., Gierer, M., Goldman, A. I., Kramer, M. J., Jenks, C. J., Lograsso, T. A., Delaney, D. W., Thiel, P. A., and Van Hove, M. A., “Structural Aspects of the Fivefold Quasicrystalline Al-Cu-Fe Surface from STM and Dynamical LEED Studies”, Surf. Sci., vol. 495, pp. 19–34, 2001.Google Scholar

MacKay, A. L., “Crystallography and the Penrose Pattern”, Physica, vol. 114A, pp. 609–613, 1982.Google Scholar

Steurer, W., Haibach, T., Zhang, B., Kek, S., and Lück, R., “The Structure of Decagonal Al₇₀Ni₁₅Co₁₅”, Acta Cryst. B, vol. 49, pp. 661–675, 1993.Google Scholar

Gierer, M., Van Hove, M. A., Goldman, A. I., Shen, Z., Chang, S.-L., Jenks, C. J., Zhang, C.-M., and Thiel, P. A., “Structural Analysis of the Fivefold Symmetric Surface of the Al₇₀Pd₂₁Mn₉ Quasicrystal by Low Energy Electron Diffraction”, Phys. Rev. Lett., vol. 78, pp. 467–470, 1997.Google Scholar

Gierer, M., Van Hove, M. A., Goldman, A. I., Shen, Z., Chang, S.-L., Pinhero, P. J., Jenks, C. J., Anderegg, J. W., Zhang, C.-M., and Thiel, P. A., “Fivefold Surface of Quasicrystalline AlPdMn: Structure Determination Using Low-Energy-Electron Diffraction”, Phys. Rev. B, vol. 57, pp. 7628–7641, 1998.Google Scholar

Gierer, M., “Struktur und Fehlordnung an periodischen und aperiodischen Kristalloberflächen”, Habilitation, Faculty of Geosciences, University of Munich, 2000.Google Scholar

Gierer, M., Mikkelsen, A., Gräber, M., Gille, P., and Moritz, W., “Quasicrystalline Surface Order on Decagonal Al_72.1Ni_11.5Co_16.4: An Investigation with Spot Profile Analysis LEED”, Surf. Sci. Lett., vol. 463, pp. L654–L660, 2000.Google Scholar

Schaub, T. M., Bürgler, D. E., Güntherodt, H. J., and Suck, J. B., “Quasicrystalline Structure of Icosahedral Al₆₈Pd₂₃Mn₉ Resolved by Scanning Tunneling Microscopy”, Phys. Rev. Lett., vol. 73, pp. 1255–1258, 1994.Google Scholar

Ledieu, J., Munz, A., Parker, T., McGrath, R., Diehl, R. D., Delaney, D. W., and Lograsso, T. A., “Structural Study of the Five-fold Surface of the Al₇₀Pd₂₁Mn₉ Quasicrystal”, Surf. Sci., vol. 433–435, pp. 666–671, 1999.Google Scholar

Ledieu, J., McGrath, R., Diehl, R. D., Lograsso, T. A., Delaney, D. W., Papadopolos, Z., and Kasner, G., “Tiling of the Surface of Al₇₀Pd₂₁Mn₉”, Surf. Sci., vol. 492, pp. L729–L734, 2001.Google Scholar

Wu, X., Kycia, S. W., Olson, C. G., Benning, P. J., Goldman, A. I., and Lynch, D. W., “Electronic Band Dispersion and Pseudogap in Quasicrystals: Angular-Resolved Photoemission Studies on Icosahedral Al₇₀Pd_21.5Mn_8.5”, Phys. Rev. Lett., vol. 75, pp. 4540–4543, 1995.Google Scholar

Shen, Z., Raberg, W., Heinzig, M., Jenks, C. J., Fournée, V., Van Hove, M. A., Lograsso, T. A., Delaney, D., Cai, T., Canfield, P. C., Fisher, I. R., Goldman, A. I., Kramer, M. J., and Thiel, P. A., “A LEED Comparison of Structural Stabilities of the Three High-Symmetry Surfaces of Al-Pd-Mn Bulk Quasicrystals”, Surf. Sci., vol. 450, pp. 1–11, 2000.Google Scholar

Kortan, A. R., Becker, R. S., Thiel, F. A., and Chen, H. S., “Real-Space Atomic Structure of a Two-Dimensional Decagonal Quasicrystal”, Phys. Rev. Lett., vol. 64. pp. 200–203, 1990.Google Scholar

Erbudak, M., Nissen, H.-U., Wetli, E., Hochstrasser, M., and Ritsch, S., “Real-Space Imaging of Pentagonal Symmetry Elements by 2-keV Electrons in the Icosahedral Quasicrystal Al₇₀Mn₉Pd₂₁”, Phys. Rev. Lett., vol. 72, pp. 3037–3040, 1994.Google Scholar

Thiel, P. A., “Quasicrystal Surfaces”, Annu. Rev. Phys. Chem., vol. 59, pp. 129–152, 2008.Google Scholar

Ferralis, N., Pussi, K., Cox, E. J., Gierer, M., Ledieu, J., Fisher, I. R., Jenks, C. J., Lindroos, M., McGrath, R., and Diehl, R. D., “Structure of the Tenfold d-Al-Ni-Co Quasicrystal Surface”, Phys. Rev. B, vol. 69, p. 153404, 2004.Google Scholar

Pussi, K., Ferralis, N., Mihalkovic, M., Widom, M., Curtarolo, S., Gierer, M., Jenks, C. J., Canfield, P., Fisher, I. R., and Diehl, R. D., “Use of Periodic Approximants in a Dynamical LEED Study of the Quasicrystalline Tenfold Surface of Decagonal Al-Ni-Co”, Phys. Rev. B, vol. 73, p. 184203, 2006.Google Scholar

Chang, S.-L., Chin, W. B., Zhang, C.-M., Jenks, C. J., and Thiel, P. A., “Oxygen Adsorption on a Single-Grain, Quasicrystal Surface”, Surf. Sci., vol. 337, pp. 135–146, 1995.Google Scholar

Gierer, M. and Over, H., “Complex Surface Structures Studied by Low-Energy Electron Diffraction”, Z. Kristallogr., vol. 214, pp. 14–56, 1999.Google Scholar

Steurer, W., “Reflections on Symmetry and Formation of Axial Quasicrystals”, Z. Kristallogr., vol. 221, pp. 402–411, 2006.Google Scholar

Steurer, W., “Quasicrystals: What Do We Know? What Do We Want to Know? What Can We Know?” Acta Cryst. A, vol. 74, pp. 1–11, 2018.Google Scholar

Moritz, W., Günther, S., and Pussi, K., “Quantitative LEED Studies on Graphene”, in Encyclopedia of Interfacial Chemistry: Surface Science and Electrochemistry, ed. Wandelt, K., Elsevier, Amsterdam, 2018, vol. 4, pp. 370–377.Google Scholar

Hagstrom, S., Lyon, H. B., and Somorjai, G. A., “Surface Structures of the Clean Platinum (100) Surface”, Phys. Rev. Lett., vol. 15, pp. 491–493, 1965.Google Scholar

Fedak, D. G. and Gjostein, N. A., “Structure and Stability of the (100) Surface of Gold”, Phys. Rev. Lett., vol. 16, pp. 171–174, 1966.Google Scholar

Heilmann, P., Heinz, K., and Müller, K., “The Superstructures of the Clean Pt(100) and Ir(100) Surfaces”, Surf. Sci., vol. 83, pp. 487–497, 1979.Google Scholar

Heinz, K., Lang, E., Strauss, K., and Müller, K., “Metastable 1×5 Structure of Pt(100)”, Surf. Sci., vol. 120, pp. L401–L404, 1982.Google Scholar

Gibbs, D., Grübel, G., Zehner, D. M., Abernathy, D. L., and Mochrie, S. G. J., “Orientational Epitaxy of the Hexagonally Reconstructed Pt(001) Surface”, Phys. Rev. Lett., vol. 67, pp. 3117–3120, 1991.Google Scholar

Kuhnke, K., Kern, K., Comsa, G., and Moritz, W., “Top-Layer Superstructures of the Reconstructed Pt(100) Surface”, Phys. Rev. B, vol. 45, pp. 14388–14392, 1992.Google Scholar

Ritz, G., Schmid, M., Varga, P., Borg, A., and Rønning, M., “Pt(100) Quasihexagonal Reconstruction: A Comparison between Scanning Tunneling Microscopy Data and Effective Medium Theory Simulation Calculations”, Phys. Rev. B, vol. 56, pp. 10518–10526, 1997.Google Scholar

Hammer, R., Meinel, K., Krahn, O., and Widdra, W., “Surface Reconstruction of Pt(001) Quantitatively Revisited”, Phys. Rev. B, vol. 94, p. 195406, 2016.Google Scholar

Van Hove, M. A., Koestner, R. J., Stair, P. C., Bibérian, J. P., Kesmodel, L. L., Bartoš, I., and Somorjai, G. A., “The Surface Reconstructions of the (100) Crystal Faces of Iridium, Platinum and Gold: I. Experimental Observations and Possible Structural Models”, Surf. Sci., vol. 103, pp. 189–217, 1981.Google Scholar