Research ArticlePHYSICS

Distinct signature of local tetrahedral ordering in the scattering function of covalent liquids and glasses

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Science Advances  01 Mar 2019:
Vol. 5, no. 3, eaav3194
DOI: 10.1126/sciadv.aav3194
  • Fig. 1 Structure factor of an isolated LFTS.

    (A) Regular tetrahedron with the nearest interatomic distance r, height H, edge length L, and width D. (B) Structure factor S(k) of the regular tetrahedron in the x, y, and z directions [see (A) for the definitions of the directions] together with that averaged over all orientations (black square, multiplied by a factor of 4). Arrows in (B) indicate the locations of four characteristic peaks. (C) Si–Si partial structure factor of a typical LFTS, SiSi4 (central Si and its four neighboring Si in the first shell). (D) Si–Si partial structure factor of a cluster of typical LFTS, SiSi16 (central Si and its 16 neighboring Si up to the second shell). The structure factors of the cluster at T > 4000 K are not shown, because at these high temperatures there are few LFTSs forming these clusters. Here, a typical LFTS is selected by imposing the following three criteria on a central Si: (i) the structural descriptor 2.4 ≤ z ≤ 2.6 Å, (ii) four Si neighbors in its first shell, and (iii) the tetrahedral order parameter q ≥ 0.8 (see Materials and Methods for the definitions of z and q).

  • Fig. 2 The Si–Si, O–O, and Si–O partial structure factors at 1 bar and 4000 K.

    The FSDP (red arrow) in the structure factor corresponds to the height HSiSi of the silicon tetrahedron, k1 = 2π/HSiSi. The shoulder (blue arrow) near the second peak of the O–O structure factor corresponds to the height HOO of the oxygen tetrahedron, Embedded Image. The inset shows two regular tetrahedra sharing one center Si. Red and blue spheres denote Si and O atoms, respectively.

  • Fig. 3 Experimental structure factors of various tetrahedral materials.

    (A) Structure factors S(k) of corner-sharing tetrahedral materials [monatomic A=C (34), Si (35), and Ge (36) and binary AB2=SiO2 (24), GeO2 (37), and BeF2 (38)] as a function of the wave number k scaled by the average A-A distance rAA. (B) Structure factors S(k) of edge-sharing tetrahedral materials [binary AB2=ZnCl2 (39), SiSe2 (40), GeSe2 (41), and GeS2 (42)] as a function of the wave number k scaled by the average A-B distance rAB. Peak positions predicted by our tetrahedron model (see Fig. 1B) are shown by arrows. Open and filled symbols denote S(k) measured by neutron and x-ray scattering experiments, respectively. Except for molten ZnCl2, all the materials were measured in the glassy (or amorphous) solid state.

  • Fig. 4 Local structural ordering as a function of temperature in liquid silica.

    (A) Si–Si partial structure factors at 1 bar for various temperatures. (B) Tetrahedral order parameter q for SiSi4 unit at 1 bar for the various temperatures. The tetrahedral order parameter q = 1 for a regular tetrahedron and q = 0 for a random configuration (see Eq. 4 for the definition). Arrows in (A) and (B) denote the direction of the temperature increase. (C) Decomposition of the Si–Si partial structure factor at 4000 K by three Lorentzian functions and one Gaussian function. (D) The integrated intensity, A, of FSDP [green area in (C)] is a good measure of the fraction s of LFTS, which controls the density anomaly of liquid silica (25).

  • Table 1 Geometric parameters characterizing a regular tetrahedron and the corresponding characteristic wave numbers.

    See Fig. 1A for the definition of the parameters.

    Geometric parameterRelation with r in real spacePeak position k in reciprocal spaceScaled primary peak position kr/2π
    LEmbedded ImageEmbedded ImageEmbedded Image
    DEmbedded ImageEmbedded ImageEmbedded Image
    H4r/32π/H = 3π/2r3/4

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/3/eaav3194/DC1

    Supplementary Text

    Fig. S1. Si–Si partial structure factors at 5000 K and various pressures.

    Fig. S2. Relationship between the structure factor S(k) and the tetrahedral order parameter q at 1 bar and 4000 K.

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • Fig. S1. Si–Si partial structure factors at 5000 K and various pressures.
    • Fig. S2. Relationship between the structure factor S(k) and the tetrahedral order parameter q at 1 bar and 4000 K.

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