Forbidden Reflections and Interference Effects in X-ray Reflectivity from Si(111)7x7

POSTER

Abstract

In diffraction, X-ray reflections from diamond crystal structures with Miller indices that satisfy h$+$k$+$l $=$ 4n$+$2, where n is an integer, are considered to be forbidden by crystal symmetry. However, these ``forbidden reflections'' have been observed experimentally, starting with W.H. Bragg over 90 years ago. Asymmetric charge distributions and anharmonic vibrations break the crystal symmetry and result in weak, but non-zero, intensities for these reflections. In the present work, we investigate the forbidden reflections in x-ray reflectivity and crystal truncation rods where we have discovered that the interference between bulk and surface waves can distinguish between the charge and vibrational origins of the reflections. Synchrotron x-ray scattering results, as well as a model, are presented. Understanding the properties of the forbidden reflections in diamond crystal structures not only provides greater insight into the crystal bonding and vibrations, but will also lead to better models for surface structures.

Authors

  • J.W. Kremenak

    University of Missouri

  • Mark Neubauer

    University of Missouri-Columbia, Southern Illinois University Carbondale, Indiana University, Purdue University, Argonne National Laboratory, University of Missouri, College of Physics Science, Qingda University, Qingdao, 266071, China, Indian Institute of Science, Bangalore, India, University of Massachusetts Amherst, Iowa State University, Technical University of Denmark, University of Missouri - Columbia, University of California - San Diego, La Jolla, CA 92093, Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211, Department of Physics and Astronomy, University of Missouri-Columbia, University of Missouri, Columbia, MO, Department of Physics and Department of Biochemistry, University of Missouri, Columbia, MO 65211, Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, Univ of Missouri - Columbia, Duke University, Shanghai Jiaotong University, Ames Laboratory, U.S. DOE, Texas Center of Superconductivity and the Department of Physics, University of Houston, Institute of Physics, Siberian Division, Russian Academy of Sciences, Krasnoyarsk, 66036, Russia, Oak Ridge National Laboratory, NIST Center for Neutron Research, MU Research Reactor, Ames Laboratory and Dep. of Physics and Astronomy, Iowa State University, AmesAmes Laboratory and Dep. of Physics and Astronomy, Iowa State University, HFIR, Oak Ridge National Laboratory, University of Illinois at Urbana-Champaign

  • Mark Neubauer

    University of Missouri-Columbia, Southern Illinois University Carbondale, Indiana University, Purdue University, Argonne National Laboratory, University of Missouri, College of Physics Science, Qingda University, Qingdao, 266071, China, Indian Institute of Science, Bangalore, India, University of Massachusetts Amherst, Iowa State University, Technical University of Denmark, University of Missouri - Columbia, University of California - San Diego, La Jolla, CA 92093, Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211, Department of Physics and Astronomy, University of Missouri-Columbia, University of Missouri, Columbia, MO, Department of Physics and Department of Biochemistry, University of Missouri, Columbia, MO 65211, Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, Univ of Missouri - Columbia, Duke University, Shanghai Jiaotong University, Ames Laboratory, U.S. DOE, Texas Center of Superconductivity and the Department of Physics, University of Houston, Institute of Physics, Siberian Division, Russian Academy of Sciences, Krasnoyarsk, 66036, Russia, Oak Ridge National Laboratory, NIST Center for Neutron Research, MU Research Reactor, Ames Laboratory and Dep. of Physics and Astronomy, Iowa State University, AmesAmes Laboratory and Dep. of Physics and Astronomy, Iowa State University, HFIR, Oak Ridge National Laboratory, University of Illinois at Urbana-Champaign

  • Mark Neubauer

    University of Missouri-Columbia, Southern Illinois University Carbondale, Indiana University, Purdue University, Argonne National Laboratory, University of Missouri, College of Physics Science, Qingda University, Qingdao, 266071, China, Indian Institute of Science, Bangalore, India, University of Massachusetts Amherst, Iowa State University, Technical University of Denmark, University of Missouri - Columbia, University of California - San Diego, La Jolla, CA 92093, Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211, Department of Physics and Astronomy, University of Missouri-Columbia, University of Missouri, Columbia, MO, Department of Physics and Department of Biochemistry, University of Missouri, Columbia, MO 65211, Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, Univ of Missouri - Columbia, Duke University, Shanghai Jiaotong University, Ames Laboratory, U.S. DOE, Texas Center of Superconductivity and the Department of Physics, University of Houston, Institute of Physics, Siberian Division, Russian Academy of Sciences, Krasnoyarsk, 66036, Russia, Oak Ridge National Laboratory, NIST Center for Neutron Research, MU Research Reactor, Ames Laboratory and Dep. of Physics and Astronomy, Iowa State University, AmesAmes Laboratory and Dep. of Physics and Astronomy, Iowa State University, HFIR, Oak Ridge National Laboratory, University of Illinois at Urbana-Champaign

  • Mark Neubauer

    University of Missouri-Columbia, Southern Illinois University Carbondale, Indiana University, Purdue University, Argonne National Laboratory, University of Missouri, College of Physics Science, Qingda University, Qingdao, 266071, China, Indian Institute of Science, Bangalore, India, University of Massachusetts Amherst, Iowa State University, Technical University of Denmark, University of Missouri - Columbia, University of California - San Diego, La Jolla, CA 92093, Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211, Department of Physics and Astronomy, University of Missouri-Columbia, University of Missouri, Columbia, MO, Department of Physics and Department of Biochemistry, University of Missouri, Columbia, MO 65211, Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, Univ of Missouri - Columbia, Duke University, Shanghai Jiaotong University, Ames Laboratory, U.S. DOE, Texas Center of Superconductivity and the Department of Physics, University of Houston, Institute of Physics, Siberian Division, Russian Academy of Sciences, Krasnoyarsk, 66036, Russia, Oak Ridge National Laboratory, NIST Center for Neutron Research, MU Research Reactor, Ames Laboratory and Dep. of Physics and Astronomy, Iowa State University, AmesAmes Laboratory and Dep. of Physics and Astronomy, Iowa State University, HFIR, Oak Ridge National Laboratory, University of Illinois at Urbana-Champaign