High-Pressure Transformation of ${\mathrm{SiO}}_{2}$ Glass from a Tetrahedral to an Octahedral Network: A Joint Approach Using Neutron Diffraction and Molecular Dynamics

High-Pressure Transformation of ${SiO}_{2}$ Glass from a Tetrahedral to an Octahedral Network: A Joint Approach Using Neutron Diffraction and Molecular Dynamics

Anita Zeidler, Kamil Wezka, Ruth F. Rowlands, Dean A. J. Whittaker, Philip S. Salmon, Annalisa Polidori, James W. E. Drewitt, Stefan Klotz, Henry E. Fischer, Martin C. Wilding, Craig L. Bull, Matthew G. Tucker, and Mark Wilson

Phys. Rev. Lett. 113, 135501 – Published 23 September 2014

Abstract

A combination of in situ high-pressure neutron diffraction at pressures up to 17.5(5) GPa and molecular dynamics simulations employing a many-body interatomic potential model is used to investigate the structure of cold-compressed silica glass. The simulations give a good account of the neutron diffraction results and of existing x-ray diffraction results at pressures up to $\sim 60 GPa$ . On the basis of the molecular dynamics results, an atomistic model for densification is proposed in which rings are “zipped” by a pairing of five- and/or sixfold coordinated Si sites. The model gives an accurate description for the dependence of the mean primitive ring size $⟨ n ⟩$ on the mean Si-O coordination number, thereby linking a parameter that is sensitive to ordering on multiple length scales to a readily measurable parameter that describes the local coordination environment.

Received 8 November 2013

DOI:https://doi.org/10.1103/PhysRevLett.113.135501

Authors & Affiliations

Anita Zeidler¹, Kamil Wezka¹, Ruth F. Rowlands¹, Dean A. J. Whittaker¹, Philip S. Salmon^1,*, Annalisa Polidori¹, James W. E. Drewitt², Stefan Klotz³, Henry E. Fischer⁴, Martin C. Wilding⁵, Craig L. Bull⁶, Matthew G. Tucker⁶, and Mark Wilson^7,†

¹Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
²Centre for Science at Extreme Conditions, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
³IMPMC, CNRS UMR 7590, Université Pierre et Marie Curie, 75252 Paris, France
⁴Institut Laue Langevin, 6 rue Jules Horowitz, BP 156, 38042 Grenoble, France
⁵IMPS, Aberystwyth University, Aberystwyth SY23 3BZ, United Kingdom
⁶ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
⁷Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom

^*Corresponding author. p.s.salmon@bath.ac.uk
^†Corresponding author. mark.wilson@chem.ox.ac.uk

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Vol. 113, Iss. 13 — 26 September 2014

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Figure 1
The pressure dependence of the (a) neutron and (b) x-ray $S (k)$ functions. In (a), the broken (blue) curve ( $p = 8.5 GPa$ ) and solid (black) curves (all other pressures) give spline fits to the measured data represented by the points with vertical error bars. For the experiments in the pressure range 8.5–17.5 GPa, the region $k \leq 1.55 Å^{- 1}$ was not accessible and the curves in this region are fitted Lorentzian functions [25]. In (b), the XRD results are from Refs. [6] [solid light (green) curves at ambient, 8.0 and 20.0 GPa], [29] [solid (black) curve at ambient], [10] [solid (black) curves at high $p$ ] and [11] [broken (blue) curves]. In (a) and (b), the solid light (red) curves show the TS MD results for the same or comparable pressures.
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Figure 2
The pressure dependence of the (a) neutron and (b) x-ray $G (r)$ functions. In (a), the broken (blue) curve ( $p = 8.5 GPa$ ) and solid (black) curves (all other pressures) are the Fourier transforms of the spline fitted measured $S (k)$ functions shown in Fig. 1, and the broken light (green) curves show the unphysical small- $r$ oscillations. In (b), the solid (black) curves are the Fourier transforms of the measured $S (k)$ functions shown in Fig. 1 from Refs. [10, 29] with a cutoff $k_{\max} = 15 Å^{- 1}$ (and also with a Lorch [47] modification function for the Ref. [10] data), and the chained (green) curves show the unphysical small- $r$ oscillations. The broken (blue) curves are the measured $G (r)$ functions from Ref. [11]. In (a) and (b), the solid light (red) curves are the Fourier transforms of the TS MD results given in Fig. 1, where the same modification functions were used as in experiment.
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Figure 3
The pressure dependence of the mean Si-O (a) bond distance ${\bar{r}}_{SiO}$ and (b) coordination number ${\bar{n}}_{Si}^{O}$ as measured by ND (present work) [(black) filled circle] or by XRD in the work from Refs. [5] [(magenta) filled downward triangle], [10] [(green) filled upward triangle] and [11] [(blue) open diamond]. The results are compared to MD simulations using the TS [present work, broken (red) curves] or BKS [49] [solid (cyan) curve] potentials, and to first-principles MD simulations [50] [chained (green) curves]. (c) The pressure dependence of the fractions of Si4 [(blue) filled upward triangle], Si5 [(magenta) filled backward triangle], Si6 [(black) filled downward triangle] and Si7 [(orange) filled circle] sites and of O2 [(red) open square], O3 [(green) open diamond] and O4 [(blue) open upward triangle] sites from the TS MD simulations (present work). (d) The pressure dependence of the preference factors $f_{Si 5}^{Si 5}$ [(red) filled circle], $f_{Si 5}^{Si 6}$ [(green) $\times$ ] and $f_{Si 6}^{Si 6}$ [(blue) filled square] from the TS MD model (present work).
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Figure 4
(a) The pressure dependence of the probability $P (α, p_{i} and β, p_{j})$ from cold-compression TS MD simulations. The $α \to β$ labels indicate a change (broken curves) or not (solid curves) in the number $α$ of O atoms bound to a Si atom as the pressure is increased from $p_{i}$ to the next-highest value $p_{j}$ . (b) The pressure dependence of the mean primitive ring size $⟨ n ⟩$ from cold-compression [(red) open square] and quench-from-the-melt [(green) open triangle] TS MD simulations. The inset shows the same information but as a function of ${\bar{n}}_{Si}^{O}$ . In each panel the solid (black) curve gives the prediction of the ring closure model.
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Physical Review Letters

High-Pressure Transformation of SiO2 Glass from a Tetrahedral to an Octahedral Network: A Joint Approach Using Neutron Diffraction and Molecular Dynamics

Anita Zeidler, Kamil Wezka, Ruth F. Rowlands, Dean A. J. Whittaker, Philip S. Salmon, Annalisa Polidori, James W. E. Drewitt, Stefan Klotz, Henry E. Fischer, Martin C. Wilding, Craig L. Bull, Matthew G. Tucker, and Mark Wilson

Phys. Rev. Lett. 113, 135501 – Published 23 September 2014

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High-Pressure Transformation of ${SiO}_{2}$ Glass from a Tetrahedral to an Octahedral Network: A Joint Approach Using Neutron Diffraction and Molecular Dynamics