Structural softening of solid nitrogen under pressure by first-principles calculations

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Highlights

  • First-principles calculated phonons of tetragonal solid nitrogen under pressure.

  • Negative group velocity is considered to be the structural phase transition velocity.

  • The phase transition starts at a,b-axis along [001] direction.

Abstract

Solid nitrogen has received widespread attention. In this paper, the calculated structural, electronic, phonon and mechanical properties are used to investigate the phase transition of solid nitrogen (space group P42/mnm). Acoustic phonons can be divided into two parts. One acoustic phonon shows that tetragonal solid nitrogen is dynamically stable at c-axis, while the remaining two acoustic phonons have virtual frequencies at a,b-axis. The virtual frequency of phonon indicates that tetragonal solid nitrogen has a structural softening process. We point out that the softening process of acoustic phonon is considered to be related to the phase transition. Based on the results in our calculation, the phase transition of tetragonal solid nitrogen starts at a,b-axis along [001] direction (from k-point Z to Γ). The negative group velocity of phonon is considered as the speed of phase transition. The phase transition velocity is increasing under pressure, and the low pressure corresponds to low velocity.

Introduction

The study of nitrogen phase diagram has always been an important work and has attracted a large number of researchers [[1], [2], [3], [4], [5], [6]]. Crystal structures [[1], [2], [3],5], enthalpies [4,[6], [7], [8], [9]], phonons [[10], [11], [12], [13], [14], [15], [16]] and Raman spectra [4,8,[17], [18], [19], [20], [21], [22]] are all relating to the phase stability of solid nitrogen. In details, the crystal structure of solid nitrogen includes lattice parameters, crystal faces, bond angles, bond lengths and space group [[1], [2], [3], [4], [5],7]. The phonons of nitrogen and polymeric nitrogen are mainly relating to the dynamical stability of their equilibrium crystals [[10], [11], [12], [13], [14]]. Moreover, the dynamical stability of nitrogen compounds [14,15] has been discussed too. Experimental Raman spectra are associating with the internal vibration [21], activity of vibration [20], transition of vibration [18] and structural transformation [17], and the spectra are used to discuss the phase transition of solid nitrogen under pressure. Furthermore, the calculated Raman spectra have been used to study the stability [4] and sensitivity of crystal structure under pressure and temperature [22]. By contrast, the experiments including the Raman scattering [19,20], inelastic scattering [23], X-scattering [3,24] and NQR (Nuclear Quadrupole Resonance) [25] are used to study the phonon stability and solid nitrogen structure in early time relatively, and the calculations have developed in the last two decades.

It can be seen that researchers pay high attention to the phase transition process [[26], [27], [28]]. The phase transition process is significant in the nitrogen-rich high energy density materials [29,30]. Hence, the transition of crystal structure [8,[10], [11], [12], [13], [14],16,31,32], structural transition path [9], magnetic transition [33] and polarization symmetry [34] of nitrogen have been taken into consideration. Recently, the transitions form N-N single bonds from solid nitrogen to layered nitrogen [17,35], solid nitrogen to polymeric nitrogen [14,16,29], and polymeric nitrogen to cage-like nitrogen [10,14,16,36] under high pressure have made a major breakthrough. However, the discussion of the phase transition path is relatively lacking.

In this paper, we try to use the softened acoustic phonons to find the structural transition path using density functional perturbation theory. Taking tetragonal P42/mnm nitrogen as an example, the structural, electronic, mechanical properties and softened acoustic phonons are investigated and discussed.

Section snippets

Computational methods

The CASTEP code [37] based on density functional theory (DFT) and density functional perturbation theory (DFPT) was adopted. The exchange-correlation functional was set to the generalized gradient approximation (GGA) with PW91 [38], PBESOL [39] and PBE + TS [40]. Norm-conserving pseudopotentials were chosen and the valence electrons of N were set to 2s22p3. The k-point of Brillouin zone was set to 3×3×2. The maximum force, maximum stress and maximum displacement were set to 0.01 eV/Å, 0.02 GPa

Results and discussion

The solid nitrogen (N2) with space group P42/mnm is built as computational model, which is shown in Fig. 1. The optimized lattice parameters are listed in Table 1 along with the experimental values [3]. It can be seen that the results based on the GGA-PBE + TS are in great agreement with experimental data. As we all known, the PBE-TS theory was proved to be reliable in nitrogen-based system [41]. Therefore, the calculated results using the GGA-PBE + TS are chosen for discussion.

The lattice

Conclusions

First-principles calculations are used to investigate the softening process of tetragonal solid nitrogen. The calculated bandgap and PDOS have no breaking point revealing that the electrons are stable under pressure. The acoustic phonons of tetragonal solid nitrogen have softening process at a,b-axis, while it is dynamic stability at c-axis under pressure. In details, the softening process is regarded as the beginning of phase transition. The negative group velocity, positive group velocity and

Ethical statement

On behalf of, and having obtained permission from all the authors, I declare that: a. the material has not been published in whole or in part elsewhere; b. the paper is not currently being considered for publication elsewhere; c. all authors have been personally and actively involved in substantive work leading to the report, and will hold themselves jointly and individually responsible for its content; d. all relevant ethical safeguards have been met in relation to patient or subject

Declaration of competing interest

We declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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