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Pressure-dependent structures of amorphous red phosphorus and the origin of the first sharp diffraction peaks

Nature Materials volume 7, pages 890–899 (2008)Cite this article

Abstract

Characterizing the nature of medium-range order (MRO) in liquids and disordered solids is important for understanding their structure and transport properties. However, accurately portraying MRO, as manifested by the first sharp diffraction peak (FSDP) in neutron and X-ray scattering measurements, has remained elusive for more than 80 years. Here, using X-ray diffraction of amorphous red phosphorus compressed to 6.30 GPa, supplemented with micro-Raman scattering studies, we build three-dimensional structural models consistent with the diffraction data. We discover that the pressure dependence of the FSDP intensity and line position can be quantitatively accounted for by a characteristic void distribution function, defined in terms of average void size, void spacing and void density. This work provides a template to unambiguously interpret atomic and void-space MRO across a broad range of technologically promising network-forming materials.

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Figure 1: Atomic number densities are computed from total scattering function results and these parameters constrain structurally refined models that compare extremely well to X-ray diffraction results.
Figure 2: Experimentally constrained structural refinement models provide a means to plausibly discern 3D MRO atomic structures.
Figure 3: When pressure is applied, winding phosphorus chains contract up to 3.61 GPa, where connected subunit structures then separate from each other and buckle into surrounding space.
Figure 4: Calculated void-pixel pair distribution functions and a model for g(r)void quantitatively tie FSDP attributes to average void size, void spacing and void density.

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Acknowledgements

J.M.Z. thanks J. Molitoris for sparking an interest to study a-rP, M. Bastea for providing a-rP sample material and C. Thompson of www.mathengineering.com for Matlab consulting and code acceleration tips. We thank J. Eggert for his guidance to properly determine density from high-pressure diffraction data. This work was carried out under the auspices of the US Department of Energy jointly by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under Contract DE-AC03-76SF00098.

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Authors and Affiliations

  1. Chemistry Materials Energy and Life Sciences, Lawrence Livermore National Laboratory, 7000 E. Avenue, L-350, Livermore, California 94551, USA

    Joseph M. Zaug

  2. ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Didcot, OX11 0QX, UK

    Alan K. Soper

  3. Advanced Light Source, Lawrence Berkeley Laboratory, Berkeley, California 20015, USA

    Simon M. Clark

  4. Department of Earth and Planetary Sciences, University of California, Berkeley, California 94720, USA

    Simon M. Clark

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Contributions

J.M.Z. devised the project and design engineered the ultrawide-aperture DAC. J.M.Z. and S.M.C. conducted X-ray experiments and subsequent data reductions. J.M.Z. conducted micro-Raman scattering experiments and corresponding data analysis. A.K.S. carried out EPSR analysis of diffraction data. J.M.Z. and A.K.S. wrote the manuscript.

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Correspondence to Joseph M. Zaug.

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Zaug, J., Soper, A. & Clark, S. Pressure-dependent structures of amorphous red phosphorus and the origin of the first sharp diffraction peaks. Nature Mater 7, 890–899 (2008). https://doi.org/10.1038/nmat2290

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