Stability line of liquid molecular nitrogen based on the SCAN meta-$GGA$ density functional

Stability line of liquid molecular nitrogen based on the SCAN meta- $G G A$ density functional

G. Zhao, H. Wang, M. C. Ding, X. G. Zhao, H. Y. Wang, and J. L. Yan

Phys. Rev. B 98, 184205 – Published 20 November 2018

Abstract

It was recently reported in experiments that at temperatures below 2500 K liquid nitrogen (N) remains molecular up to 120 GPa [Phys. Rev. Lett. 119, 235701 (2017)], which contradicts a liquid-liquid transition at 88 GPa and 2000 K predicted by PBE-GGA density functional. To clarify this, we perform extensive first principles molecular dynamics using SCAN meta-GGA density functional, which captures the intermediate-range part of the van der Waals interaction better than PBE-GGA. It is found that SCAN gives more accurate bond energy and length of an isolated $N_{2}$ molecule than PBE. SCAN, as well as PBE, is capable of reproducing the first-order molecular-to-polymeric phase transition, but in contrast to PBE, it predicts a wider stability range for fluid $N_{2}$ . The boundary of this range is 15 GPa higher than the one predicted with PBE, which is in closer agreement with experiments. In addition, SCAN predicts a higher amount of threefold coordinated atoms in the polymeric phase than PBE, which is expected from experiments in amorphous N. These improvements indicate that SCAN is more accurate than PBE in predicting the phase transition from molecular to polymeric fluid N.

Received 6 August 2018
Revised 2 October 2018

DOI:https://doi.org/10.1103/PhysRevB.98.184205

Physics Subject Headings (PhySH)

Phase diagrams Phase transitions

Liquids

Density functional theory First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

G. Zhao^1,*, H. Wang², M. C. Ding¹, X. G. Zhao¹, H. Y. Wang¹, and J. L. Yan¹

¹School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, People's Republic of China
²Department of Electronic Engineering, Yantai Automobile Engineering Professional College, Yantai 265500, People's Republic of China

^*gzhao19800209@126.com

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Vol. 98, Iss. 18 — 1 November 2018

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Images

Figure 1
The $N \equiv N$ bond energy as a function of bond length in an isolated $N_{2}$ molecule based on PBE and SCAN, respectively. PBE gives 1001.35 kJ/mol and 1.114 Å, while SCAN gives 930 kJ/mol and 1.091 Å, which is closer to the experimental data [32], $941 \sim 954 kJ / mol$ and $1.095 \sim 1.10$ Å, and indicates that SCAN is better than PBE in describing the isolated $N_{2}$ molecule. The blue shadow indicates the range of the bond length obtained in experiments [32].
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Figure 2
The calculated compression isotherms at 2000 K based on SCAN meta-GGA (black solid square) and PBE-GGA (red solid circle), together with the results of 500 eV energy cutoff based on PBE-GGA (blue dotted line) in Ref. [16]. For PBE-GGA, the energy cutoff of 500 eV gives lower pressure than that of 700 eV. Compared with PBE-GGA, SCAN meta-GGA gives the lower pressure and a maximum at higher pressure.
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Figure 3
Upper: Pair correlation function g(r) in fluid $N_{2}$ at $V = 7.353 Å^{3} / atom$ and $T = 2000$ K, indicating more stable $N \equiv N$ triple bonds described by SCAN meta-GGA. Lower: Pair correlation function g(r) and the fraction of $n$ -coordinated atoms $F_{n}$ (inset) in polymeric fluid N at $V = 5.695 Å^{3} / atom$ and $T = 2000$ K. The atoms are mainly two-coordinated for PBE-GGA, while for SCAN meta-GGA, three-coordinated atoms are the majority and there remain some one-coordinated atoms.
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Figure 4
The calculated compression isotherms at eight temperatures based on SCAN meta-GGA. From 2000 to 4000 K, a van der Waals loop is presented and the maximum is located as the spinodal point of fluid $N_{2}$ . However, from 5000 to 7000 K the isotherms do not exhibit a drop in pressure, meaning the existence of a critical point at $4000 < T_{c} < 5000 K$ . Inset: Snapshot of the structure of fluid N at $T = 5000$ K and $V = 6.912 Å^{3} / atom$ . It is a mixture of molecular and polymeric N and no liquid atomic N is found.
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Figure 5
The stability line of fluid $N_{2}$ in phase diagram. The spinodal points (solid symbols) below critical point ( $C_{p}$ ) bounds the stability region of fluid $N_{2}$ and the open symbols are the inflection points of the isotherms above $C_{p}$ . Lines joining the symbols are guides to the eye. The melting curves obtained from Raman experiments (red dash line and green short dash line) [18, 19], synchrotron x-ray diffraction (thin magenta line) [20], optical measurements (blue dash dot line) [21], and DFT based on PBE (cyan dash dot dot line) [17] are also shown. Comparing our SCAN-based results with previous PBE-based results [16, 36], we observe that the stability line of fluid $N_{2}$ shifts about 15 GPa towards high pressure, closer to the proposed stability line. The proposed stability line is based on experimental results from ultrahigh-pressure electrical resistance measurements (pentagon) [14], x-ray diffraction (hexagon) [15], synchrotron x-ray diffraction (diamond) [20], and shockwave experiments (triangle) [37].
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Figure 6
Comparison of the compression isotherms for 48-, 64-, and 128-atom supercells at 2200 K. With decreasing the number of atoms, the maximum tends to higher pressure.
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