Structural Ordering in Liquid Gallium under Extreme Conditions

Open Access

Structural Ordering in Liquid Gallium under Extreme Conditions

James W. E. Drewitt, Francesco Turci, Benedict J. Heinen, Simon G. Macleod, Fei Qin, Annette K. Kleppe, and Oliver T. Lord

Phys. Rev. Lett. 124, 145501 – Published 9 April 2020

Abstract

The atomic-scale structure, melting curve, and equation of state of liquid gallium has been measured to high pressure ( $p$ ) and high temperature ( $T$ ) up to 26 GPa and 900 K by in situ synchrotron x-ray diffraction. Ab initio molecular dynamics simulations up to 33.4 GPa and 1000 K are in excellent agreement with the experimental measurements, providing detailed insight at the level of pair distribution functions. The results reveal an absence of dimeric bonding in the liquid state and a continuous increase in average coordination number ${\bar{n}}_{Ga}^{Ga}$ from 10.4(2) at 0.1 GPa approaching $\sim 12$ by 25 GPa. Topological cluster analysis of the simulation trajectories finds increasing fractions of fivefold symmetric and crystalline motifs at high $p − T$ . Although the liquid progressively resembles a hard-sphere structure towards the melting curve, the deviation from this simple description remains large ( $\geq 40 %$ ) across all $p − T$ space, with specific motifs of different geometries strongly correlating with low local two-body excess entropy at high $p − T$ .

Received 7 January 2020
Accepted 20 March 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.145501

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Atomic & molecular structure Equations of state Liquid-liquid phase transition

Disordered systems Liquid metals

Ab initio calculations Molecular dynamics Pressure techniques X-ray diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

James W. E. Drewitt ^1,*, Francesco Turci², Benedict J. Heinen ¹, Simon G. Macleod^3,4, Fei Qin¹, Annette K. Kleppe ⁵, and Oliver T. Lord¹

¹School of Earth Sciences, University of Bristol, Wills Memorial Building, Queens Road, Bristol BS8 1RJ, United Kingdom
²H H Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
³Atomic Weapons Establishment, Aldermaston, Reading RG7 4PR, United Kingdom
⁴SUPA, School of Physics and Astronomy, and Centre for Science at Extreme Conditions, The University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom
⁵Diamond Light Source Ltd, Diamond House, Harwell Science and Innovation Campus, Chilton OX11 0DE, United Kingdom

^*james.drewitt@bristol.ac.uk; james.drewitt@gmail.com

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Issue

Vol. 124, Iss. 14 — 10 April 2020

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Images

Figure 1
Melting curve for gallium. SXRD acquisitions are denoted by open (liquid) or closed (solid) circles (run 1) or squares (run 2). Enlarged symbols represent locations of longer acquisitions for liquid structure determination. The diamonds are the midpoints of melting brackets fitted to the Simon Glatzel equation (solid line). The blue field represents 95% confidence bands. The $+$ symbols denote the $p − T$ conditions in the ab initio MD simulations. The previously reported low- $p$ liquid ( $L$ ) and crystalline (I, II, III) phase boundaries are also shown (black lines) [22]. The inset shows an example diffraction image in the liquid field.
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Figure 2
(a) Structure factors $S_{GaGa} (Q)$ measured in the DAC by SXRD, and (b) corresponding pair distribution functions $g_{GaGa} (r)$ obtained by Fourier transformation (black curves). Previously reported ambient- $p$ measurements [63] are represented by the open red circles. A selection of the $S_{GaGa}$ and $g_{GaGa} (r)$ functions computed from the ab initio MD trajectories are also shown at comparable conditions just above the melting curve at (i) 303 K, (ii) 3.4 GPa, 400 K, (iii) 10.9 GPa, 600 K, (iv) 18.3 GPa, 800 K, and (v) 33.4 GPa, 1000 K (dashed blue curves).
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Figure 3
(a) Mie-Gruniesen-Debye thermal equation of state isotherms from 300 (blue) to 1000 K (red) in 100 K steps. (b) Average coordination number ${\bar{n}}_{Ga}^{Ga}$ . Solid circles with error bars denote SXRD, open symbols denote ab initio MD. The dashed black curve indicates the density approximated to 6 GPa from ultrasonic measurements [34].
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Figure 4
Comparison of structural features between ab initio MD and RMC for a selected state point and two distinct seeds for the RMC fitting: an ordered and a disordered configuration. (a) Voronoi spectrum. (b) TCC spectrum. The structural motifs are illustrated with rings indicated by colored bonds. (c) Pair distribution functions from ab initio MD (green background) and the two RMC fits (overlapping blue dots and red line).
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Figure 5
Fractional population of atoms detected in a given motif in the ab initio MD trajectories close to the melting curve, where 6A: octahedra, 6Z: tetrahedral tripyramids, 7A: pentagonal bipyramids, 10A: twisted double square pyramids, 10B: a partial icosahedron, 11F: a section of a hexagonal closed packed layer, and 12D: a complex combination of four pentagonal rings.
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Figure 6
(a) Deviation from hard-sphere structure $Δ$ : evaluated state points (circles) and interpolated contour map. (b) Distribution (violin-plots) of locally averaged two-body excess entropy for particles in different local environments.
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