Research ArticleMATERIALS SCIENCE

Carbon-boron clathrates as a new class of sp3-bonded framework materials

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Science Advances  10 Jan 2020:
Vol. 6, no. 2, eaay8361
DOI: 10.1126/sciadv.aay8361
  • Fig. 1 Stable compounds in the Sr-B-C system.

    (A) Ternary phase diagram at 50 GPa. Green circles represent thermodynamically stable compounds, while orange squares represent metastable compositions used in the search. (B) Ternary convex hull for the Sr-B-C system at 50 GPa based on formation enthalpies. Compounds with enthalpy data represented by red points are on the convex hull and thermodynamically stable against decomposition. Black points show the formation enthalpies of metastable structures found in the structure searches.

  • Fig. 2 Structure of SrB3C3 clathrate.

    The cubic structure (Pm3¯n) is composed of face-sharing boron-carbon cages that encapsulate Sr2+ cations. Each cage contains 24 atoms with six four-sided faces and eight six-sided faces (4668). Different color cages are used to emphasize the stacking of cages that tile 3D space.

  • Fig. 3 XRD and equation of state of SrB3C3.

    (A) Experimental XRD data (black points) collected at 57(3) GPa with Rietveld refinement (blue line) of the SrB3C3 phase. Green ticks indicate contributions from Ne with Le Bail refinement. The 2D diffraction (“cake”) aligned with the integrated pattern shows nearly complete powder averaging with sharp peaks for the SrB3C3 phase. Black regions on the detector image indicate nonintegrated (“masked”) regions due to diamond anvil reflections and features of the detector. The inset shows a magnified view at high angle with sharp SrB3C3 peaks to a limiting resolution of 0.75 Å. (B) Experimental third-order Birch-Murnaghan equation of state (EoS) (solid blue line) with B0 = 249(3) GPa, B0′ = 4.0 (fixed) and calculated EoS (dashed lines) with B0 (DFT-LDA) = 257 GPa, B0′ = 4.0 (fixed); B0 (DFT-GGA) = 225 GPa, B0′ = 4.0 (fixed). Different colored symbols represent data points from six independent experimental runs.

  • Fig. 4 Electronic properties of SrB3C3 at 0 GPaAB.

    (A) 2D electron localization function (ELF) for SrB3C3. The ELF indicates the probability of finding electrons in different regions of the crystal. Large ELF values (>0.6) indicate the formation of covalent bonds. (B) Electronic band structure for SrB3C3 projected onto atomic orbitals represented by different colors, where the width of each band is proportional to the weight of the corresponding orbital character. The projected density of states (DOS) in SrB3C3 is shown in the right. The Fermi energy is set to 0 eV (dashed line).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/2/eaay8361/DC1

    Single-crystal diffraction analysis

    Fig. S1. Stability of SrB3C3 and analysis of different possible stoichiometries.

    Fig. S2. SEM and EDS measurements.

    Fig. S3. Raw XRD patterns.

    Fig. S4. Sr-B-C phase identification.

    Fig. S5. Optical images of SrB3C3 during synthesis near 50 GPa.

    Fig. S6. Electronic structures for SrB3C3.

    Fig. S7. Phonon dispersion curves and energetic stabilities as a function of pressure.

    Fig. S8. Fourier difference map (Fobs-Fcalc) from single-crystal analysis.

    Table S1. Comparison of single-crystal diffraction refinement quality indicators for different “colorings” of clathrate framework in crystal structure models of the SrB3C3 clathrate.

    Table S2. Calculated Bader partial charges of the SrB3C3 clathrate at 0 GPa.

    Table S3. Calculated structural parameters of Sr-B-C phases.

    Table S4. SrB3C3 lattice parameters during decompression.

    Data file S1. CIF file of the single-crystal XRD data and the best model of the crystal structure for the SrB3C3 clathrate.

  • Supplementary Materials

    The PDFset includes:

    • Single-crystal diffraction analysis
    • Fig. S1. Stability of SrB3C3 and analysis of different possible stoichiometries.
    • Fig. S2. SEM and EDS measurements.
    • Fig. S3. Raw XRD patterns.
    • Fig. S4. Sr-B-C phase identification.
    • Fig. S5. Optical images of SrB3C3 during synthesis near 50 GPa.
    • Fig. S6. Electronic structures for SrB3C3.
    • Fig. S7. Phonon dispersion curves and energetic stabilities as a function of pressure.
    • Fig. S8. Fourier difference map (Fobs-Fcalc) from single-crystal analysis.
    • Table S1. Comparison of single-crystal diffraction refinement quality indicators for different “colorings” of clathrate framework in crystal structure models of the SrB3C3 clathrate.
    • Table S2. Calculated Bader partial charges of the SrB3C3 clathrate at 0 GPa.
    • Table S3. Calculated structural parameters of Sr-B-C phases.
    • Table S4. SrB3C3 lattice parameters during decompression.

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    Other Supplementary Material for this manuscript includes the following:

    • Data file S1. CIF file of the single-crystal XRD data and the best model of the crystal structure for the SrB3C3 clathrate.

    Files in this Data Supplement:

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