⇦Chinese Physics Letters, 2020, Vol. 37, No. 4, Article code 047101 Pressure-Stabilized New Phase of CaN$_{4}$ * Xu-Han Shi (时旭含), Bo Liu (刘波), Zhen Yao (姚震)**, Bing-Bing Liu (刘冰冰)** Affiliations State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012 Received 23 December 2019, online 24 March 2020 *Supported by the National Key Technology Research and Development Program of China under Grant No. 2018YFA0305900, the National Natural Science Foundation of China under Grant Nos. 11634004, 51320105007, 11604116 and 51602124, and the Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China under Grant No. IRT1132.
**Corresponding author. Email: liubb@jlu.edu.cn; yaozhen@jlu.edu.cn Citation Text: Shi X H, Liu B, Yao Z and Liu B B 2020 Chin. Phys. Lett. 37 047101    Abstract We propose a new CaN$_{4}$ high pressure structure with the $P2_{1}/m$ space group. The $P2_{1}/m$-CaN$_{4}$ structure is constituted by the infinite armchair N-chain. The dynamical stability and mechanical stability are verified by the calculations of phonon dispersion curves and elastic constants. The enthalpy difference calculation shows that the $P2_{1}/m$ phase is more stable than the reported P4$_{1}2_{1}$2 phase. The advantaged properties of $P2_{1}/m$-CaN$_{4}$, such as high nitrogen content (58.3%) and low polymerization pressure (18.3 GPa), allow it to be a potential high energy material. Band structure calculation shows that the $P2_{1}/m$-CaN$_{4}$ structure is a metallic phase. The nonpolar covalent single N–N bond is a sigma bond. The charge transfer between the Ca and N atoms results in an ionic bond interaction. DOI:10.1088/0256-307X/37/4/047101 PACS:71.15.Mb, 71.15.Dx, 71.20.Dg © 2020 Chinese Physics Society Article Text Nitrogen constitutes about 78% of the earth's atmosphere in its elemental form of diatomic gas (N$_{2}$).[1,2] Nitrogen exhibits abundant crystal structures on account of its multi-valence electrons (2$s^{2}2p^{3}$) structures.[3–5] Due to the remarkable differences of bond energy among the single N–N bond (160 kJ$\cdot$mol$^{-1}$), the double N=N bond (418 kJ$\cdot$mol$^{-1}$) and the triple N$\equiv$N bond (954 kJ$\cdot$mol$^{-1}$), polymeric nitrogen solid has received much attention for the purpose of designing high energy density materials (HEDMs).[3,6,7] Moreover, the decomposition product (N$_{2}$) of polymeric nitrogen solid is environmentally friendly to the atmosphere. Hence, polymeric nitrogen has a wide application in energy storage, rocket propellant and explosives. Plenty of studies have been performed in theories and experiments.[8,9] Based on the structural prediction method, the polymeric nitrogen with the one-dimensional (1-D) chainlike structures ($Cmcm$ phase, cis-trans),[10,11] the two-dimensional (2-D) layered structures (arsenic-A7, $Pba2$ and $BP$ phases),[12–15] and the three-dimensional (3-D) polymeric network structures (cg-N and N$_{10}$)[16,17] have been reported at different pressures. In terms of experiments, the cg-N ($P=110$ GPa, $T=2000$ K),[18] LP-N ($P=150$ GPa, $T=3000$ K),[19] and HLP-N ($P=244$ GPa, $T=3300$ K)[20] have been synthesized using the high-temperature and high-pressure (HTHP) technique. Clearly, the harsh condition (HPHT) is necessary for the synthesis of polymeric nitrogen solids. Moreover, the polymeric nitrogen solids only stabilize at high pressure conditions. These two disadvantages limit the applications of polymeric nitrogen solids. An ever-increasing energy demand stimulates researchers to explore suitable high energy materials that possess both the high nitrogen content and the high stability. Recent studies suggest that the poly-nitrogen structures (MN$_{x}$: $x=1,2,3,4,5$) exhibit a higher stability than the pure nitrogen structures by introducing metal ions as coordinate element (M = Li, Na, K, Rb, Cs, Be, Mg, Ca, etc).[21–28] Among these MN$_{x}$ poly-nitrogen structures, alkaline-earth metal nitrides have attracted considerable attention to the applications as nitriding agents for forming other nitrides, as catalysts in synthesizing the superhard materials etc.[29,30] Ca is abundant in the earth and has low ionization energy ($I_{1}=590$ kJ$\cdot$mol$^{-1}$) as alkaline-earth metal, which means that Ca can form calcium nitrides easily. The calcium nitride is unique in the alkaline nitride family due to the alternative ionic (Ca$_{3}$N$_{2}$) or subnitride (Ca$_{2}$N) forms.[31–33] Recently, the high-pressure structures of the Ca–N system with different stoichiometries are reported, including the N$_{6}$ ring structure of CaN$_{3}$, the armchair chain structure of CaN$_{4}$, and the N$_{5}$ ring structure of CaN$_{5}$.[34] Regarding the CaN$_{4}$, two high pressure structures with the P4/mbm and $P4_{1}2_{1}2$ phases were reported in Ref. [34]. The P4/mbm structure with the dinitrogen unit will transform to the $P4_{1}2_{1}2$ structure at 19 GPa. However, we note that the $P4_{1}2_{1}2$ phase of CaN$_{4}$ is unstable for the pressure larger than about 67 GPa.[34] As the pressure further increases, whether the CaN$_{4}$ has the stable high pressure phase is unknown. Thus, further study of the high pressure phase of CaN$_{4}$ is necessary and should be a meaningful work for enriching its high pressure diagram. Here, we propose a new CaN$_{4}$ structure with the $P2_{1}/m$ space group through the theoretical prediction method. The $P2_{1}/m$-CaN$_{4}$ is composed of infinite polymeric armchair N-chains. Compared with the reported $P4_{1}2_{1}2$ phase, the $P2_{1}/m$ phase possesses the lower enthalpy value and exhibits an excellent dynamic stability. The enthalpy difference analysis suggests that the P4/mbm structure of CaN$_{4}$ will transform to the $P2_{1}/m$ phase at 18.3 GPa rather than the reported $P4_{1}2_{1}2$ phase at 19 GPa. The electric structure calculation shows that the $P2_{1}/m$ structure is a metallic phase. The nonpolar covalent single N–N bond is a sigma bond. The charge transfer occurs between the Ca and N atoms, which results in an ionic bond interaction. Thus, we modify the high pressure phase diagram of CaN$_{4}$ by proposing a new $P2_{1}/m$ structure, which may lead to the applications as a high energy material due to its high nitrogen content and polymeric N-chain configuration. The prediction of candidate structure (CaN$_{4}$) is accomplished using the CALYPSO code based on the particle swarm optimization algorithm.[35,36] Structure relaxations, enthalpy and electronic structures are calculated by the Vienna ab initio Simulation Package (VASP) code.[37] The phonon frequencies are calculated using a supercell approach with the finite displacement method implemented in the PHONOPY package.[38] Charge transfer calculation is performed through the Bader code.[39] The structure predictions of CaN$_{4}$ stoichiometry from 1 to 4 formula units (f.u.) in the simulation cell are implemented at 50 and 100 GPa, respectively. The exchange and correlation of the electrons are described by the Perdew–Burke–Ernzerhof (PBE) functional in the generalized gradient approximation and the electron-ion interactions are applied by the projector augmented plane-wave (PAW) method.[40,41] The $3s^{2}3p^{6}4s^{2}$ and $2s^{2}2p^{3}$ are treated as valence electrons for Ca and N atoms, respectively. A plane-wave basis set with a cutoff energy of 600 eV is used for the structure relaxation and electronic structure calculations. Monkhorst-Pack $k$-point mesh sampling in the Brillion zone is set as $2\pi$ $\times$ 0.03 Å$^{-1}$.[42] The convergence criterion of energy and force are $1 \times 10^{-5}$ eV/atom and 0.005 eV/Å, respectively.
cpl-37-4-047101-fig1.png
Fig. 1. View of infinite polymeric nitrogen chains in CaN$_{4}$ phase with $P2_{1}/m$ symmetry along the $c$-axis (left) and $a$-axis (right) directions, respectively. The blue sphere is the nitrogen atom and the green one is the calcium atom.
For the structural prediction, we obtain a monoclinic CaN$_{4}$ structure at 50 GPa. Figure 1 presents the structural configuration of CaN$_{4}$ in [001] and [100] crystal orientations. At 50 GPa, the lattice constants $oa$, $ob$ and $oc$ are 2.9478 Å, 7.5262 Å and 3.6955 Å, respectively. The lattice angles $\alpha$, $\beta$, $\gamma$ are 90$^{\circ}$, 95.59$^{\circ}$ and 90$^{\circ}$, respectively. Two inequivalent crystallographic sites of N atoms are (0.12273, 0.56687, 0.58333) and (0.91727, 0.42584, 0.06532), and one inequivalent crystallographic site of the Ca atom is (0.41724, 0.25, 0.72083). It can be seen that the adjacent nitrogen atoms bond with each other along the [001] crystal orientation. The armchair N-chain contains three different single N–N bonds, for which the lengths are 1.33 Å, 1.32 Å and 1.35 Å, respectively. These lengths are similar to those of N–N bonds in BeN$_{4}$ (1.32 Å and 1.35 Å)[43] and cg-N (1.35 Å) structures.[16] The polymeric single bond N-chain and the high nitrogen content of CaN$_{4}$ allow it to be a potential high energy material.
cpl-37-4-047101-fig2.png
Fig. 2. Phonon dispersion curves of $P2_{1}/m$-CaN$_{4}$ phase at 50 GPa.
To examine the stability of the $P2_{1}/m$ phase of CaN$_{4}$, the phonon dispersion curves are calculated, as shown in Fig. 2. No imaginary vibrational frequency is exhibited in the Brillouin zone, suggesting that the $P2_{1}/m$-CaN$_{4}$ crystal is dynamically stable.[44] The elastic constants ($C_{ij}$) of $P2_{1}/m$-CaN$_{4}$ at 50 GPa are presented as follows: $C_{11}=273.107$ GPa, $C_{12}=208.381$ GPa, $C_{13}=137.998$ GPa, $C_{22}=289.264$ GPa, $C_{23}=122.632$ GPa, $C_{25}=20.593$ GPa, $C_{33}=734.409$ GPa, $C_{35}=-76.495$ GPa, $C_{44}=107.246$ GPa, $C_{55}=37.209$ GPa, $C_{66}=144.947$ GPa. The criteria for mechanical stability of monoclinic phase are given by $C_{11} > 0$, $C_{22} > 0$, $C_{33} > 0$, $C_{44} > 0$, $C_{55 }> 0$, $C_{66} > 0$, [$C_{11} + C_{22} + C_{33} +$ 2($C_{12 }+ C_{13 }+ C_{23}$)] $> 0$, ($C_{11} + C_{22} - 2C_{12}) > 0$, ($C_{11} + C_{33} - 2C_{13}) > 0$, ($C_{22} + C_{33} - 2C_{23}) > 0$, [$C_{22}(C_{33}C_{55}-C_{35}^{2}) + 2C_{23}C_{25}C_{35}- C_{23}^{2}C_{55} - C_{23}^{2}C_{33}$] $> 0$. It can be seen that the elastic constants can satisfy the mechanical stability criteria of monoclinic phase, indicating that the $P2_{1}/m$-CaN$_{4}$ structure is mechanically stable at 50 GPa. According to the above analysis, we know that the $P2_{1}/m$-CaN$_{4}$ possesses both the dynamical stability and the mechanical stability at 50 GPa. In Ref. [34], the authors reported that the $P4_{1}2_{1}2$-CaN$_{4}$ is stable at 50 GPa. A question arises: which of the $P4_{1}2_{1}2$ and $P2_{1}/m$ phases is more stable? To answer this question, we calculate the structural enthalpy values. In Figs. 3(a) and 3(b), the relative enthalpy difference curves of $P2_{1}/m$ with respect to the $P4_{1}2_{1}2$ and P4/mbm phases are presented. It can be seen that the enthalpy of CaN$_{4}$ with the $P2_{1}/m$ phase is lower than its $P4_{1}2_{1}2$ phase in the pressure range 0–100 GPa. Thus, the $P2_{1}/m$ phase is more stable than the $P4_{1}2_{1}2$ phase. As shown in Fig. 3(b), we find that the P4/mbm phase will change into the $P2_{1}/m$ phase at 18.3 GPa, rather than the $P4_{1}2_{1}2$ phase at 19 GPa reported in Ref. [34]. Thus, we suggest a more stable $P2_{1}/m$ phase of CaN$_{4}$ and modify its high pressure phase diagram.
cpl-37-4-047101-fig3.png
Fig. 3. The relative enthalpy difference curves of $P2_{1}/m$ with respect to $P4_{1}2_{1}2$ (a) and P4/mbm (b) phases, respectively.
cpl-37-4-047101-fig4.png
Fig. 4. The two-dimensional electron function localization (ELF) map on the cross section of N$_\infty$ chain in the $P2_{1}/m$-CaN$_{4}$ structure.
The electron localization function (ELF) is calculated for analyzing the internal bonding properties of $P2_{1}/m$-CaN$_{4}$ phase. Figure 4 shows the two-dimensional ELF map on the cross section of armchair N-chain. The red region with the ELF value close to 1 means the distribution of high localization electrons. The high localization electrons between the nitrogen atoms show the typical covalent bond characteristics. Thus, the formed nonpolar covalent single N–N bond is a sigma bond. The presented lone electron pairs at the corner of armchair nitrogen chain indicate that the N atom is in an $sp^{2}$ hybridization state. The blue region with the ELF value close to 0 means a high delocalization electron distribution. The exhibited electron delocalization phenomenon around the Ca atom indicates the ionic bond interactions between the Ca and N atoms. The electronic band structure and projected density of states (PDOS) of $P2_{1}/m$-CaN$_{4}$ at 50 GPa are calculated and presented in Fig. 5. We can see that the $P2_{1}/m$-CaN$_{4}$ is a metallic phase due to the conduction band cross the Fermi level. As shown in PDOS, the total DOS at the Fermi level is mainly contributed by the N $2p$ electrons. The depleted valence electron DOS of the Ca atom near the Fermi level means the charge transfer from Ca to N, leading to an ionic bond interaction between the Ca and N atoms. The charge analysis using the bader code confirms that each N atom obtains about 0.36 electrons from the Ca atom, which is the mechanism of the stable structure.
cpl-37-4-047101-fig5.png
Fig. 5. Electronic band structure and projected density of states (PDOS) of CaN$_{4}$ at 50 GPa.
In summary, we have proposed a new CaN$_{4}$ structure with a $P2_{1}/m$ space group. The $P2_{1}/m$-CaN$_{4}$ structure is constituted by the infinite armchair N-chain, in which the adjacent nitrogen atoms bond with each other in the form of covalent sigma single bond. The ionic bond interaction between the Ca and N atoms is verified by the ELF analysis and charge transfer calculation. The dynamical stability and mechanical stability are verified by the calculations of phonon dispersion and elastic constants. The enthalpy difference calculation shows that the $P2_{1}/m$ phase is more stable than the $P4_{1}2_{1}2$ phase. The P4/mbm phase will change into the $P2_{1}/m$ phase at 18.3 GPa, rather than the $P4_{1}2_{1}2$ phase at 19 GPa. The electronic structure calculation shows that the obtained $P2_{1}/m$-CaN$_{4}$ structure is a metallic phase. The charge analysis using the bader code confirms that each N atom obtains about 0.36 electrons from the Ca atom, which is just the mechanism of the stable structure. This study not only modifies the high-pressure diagram of CaN$_{4}$ stoichiometry but it also suggests a potential high energy material for the application in the future. References Calculations predict a stable molecular crystal of N8Prediction of Stable Iron Nitrides at Ambient and High Pressures with Progressive Formation of New Polynitrogen SpeciesLayered single-bonded nonmolecular phase of nitrogen from first-principles simulationTwo-Dimensional C 4 N Global Minima: Unique Structural Topologies and Nanoelectronic PropertiesNovel triadius-like N4 specie of iron nitride compounds under high pressurePolymerization of nitrogen in sodium azidePressure-induced planar N6 rings in potassium azidePressure Dissociation of Solid Nitrogen under 1 MbarStructural stability of polymeric nitrogen: A first-principles investigationPrediction of New Phases of Nitrogen at High Pressure from First-Principles SimulationsDensity-functional study of nonmolecular phases of nitrogen: Metastable phase at low pressureHigh-pressure atomic phases of solid nitrogenFirst-principles calculations on solid nitrogen: A comparative study of high-pressure phasesPrediction of a new layered phase of nitrogen from first-principles simulationsNovel High Pressure Structures of Polymeric NitrogenPolymeric nitrogenCagelike Diamondoid Nitrogen at High PressuresSingle-bonded cubic form of nitrogenPressure-Induced Symmetry-Lowering Transition in Dense Nitrogen to Layered Polymeric Nitrogen (LP-N) with Colossal Raman IntensityHexagonal Layered Polymeric Nitrogen Phase Synthesized near 250 GPaNovel lithium-nitrogen compounds at ambient and high pressuresSodium pentazolate: A nitrogen rich high energy density materialNovel Potassium Polynitrides at High PressuresNovel rubidium poly-nitrogen materials at high pressureExotic stable cesium polynitrides at high pressureAIP Conference ProceedingsPressure-induced stable BeN 4 as a high-energy density materialEmergence of Novel Polynitrogen Molecule-like Species, Covalent Chains, and Layers in Magnesium–Nitrogen Mg x N y Phases under High PressureSolid state metathesis routes to Group IIIa nitrides : comparison of Li3N, NaN3, Ca3N2 and Mg3N2 as nitriding agentsExperimental Determinations of the High-Pressure Crystal Structures of Ca 3 N 2Density Functional Study of Calcium Nitride: Refined Geometries and Prediction of High-Pressure PhasesDicalcium nitride, Ca2N—a 2D "excess electron" compound; synthetic routes and crystal chemistryStable Calcium Nitrides at Ambient and High PressuresCALYPSO: A method for crystal structure predictionCrystal structure prediction via particle-swarm optimizationEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setPhonon-phonon interactions in transition metalsA fast and robust algorithm for Bader decomposition of charge densityGeneralized Gradient Approximation Made SimpleImproved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionalsSpecial points for Brillouin-zone integrationsA Novel Polymerization of Nitrogen in Beryllium Tetranitride at High Pressure
[1] Hirshberg B, Gerber R B and Krylov A I 2014 Nat. Chem. 6 52
[2] Wu L, Tian R, Wan B, Liu H, Gong N, Chen P, Shen T, Yao Y, Gou H and Gao F 2018 Chem. Mater. 30 8476
[3] Zahariev F, Hu A, Hooper J, Zhang F and Woo T 2005 Phys. Rev. B 72 214108
[4] Pu C, Zhou D, Li Y, Liu H, Chen Z, Wang Y and Ma Y 2017 J. Phys. Chem. C 121 2669
[5] Chen Y, Cai X, Wang H, Wang H and Wang H 2018 Sci. Rep. 8 10670
[6] Eremets M I 2004 J. Chem. Phys. 120 10618
[7] Zhang J, Zeng Z, Lin H Q and Li Y L 2014 Sci. Rep. 4 4358
[8] McMahan A K and LeSar R 1985 Phys. Rev. Lett. 54 1929
[9] Wang X, Tian F, Wang L, Cui T, Liu B and Zou G 2010 J. Chem. Phys. 132 024502
[10] Mattson W D, Sanchez-Portal D, Chiesa S and Martin R M 2004 Phys. Rev. Lett. 93 125501
[11] Alemany M M G and Martins J L 2003 Phys. Rev. B 68 024110
[12] Martin R M and Needs R J 1992 Phys. Rev. B 46 11117
[13] Kotakoski J and Albe K 2008 Phys. Rev. B 77 144109
[14] Wang X, He Z, Ma Y, Cui T, Liu Z, Liu B, Li J and Zhou G 2007 J. Phys.: Condens. Matter 19 425226
[15] Ma Y, Oganov A R, Li Z, Xie Y and Kotakoski J 2009 Phys. Rev. Lett. 102 065501
[16] Mailhiot C, Yang L H and McMahan A K 1992 Phys. Rev. B 46 14419
[17] Wang X, Wang Y, Miao M, Zhong X, Lv J, Cui T, Li J, Chen L, Pickard C J and Ma Y 2012 Phys. Rev. Lett. 109 175502
[18] Eremets M I, Gavriliuk A G, Trojan I A, Dzivenko D A and Boehler R 2004 Nat. Mater. 3 558
[19] Tomasino D, Kim M, Smith J and Yoo C S 2014 Phys. Rev. Lett. 113 205502
[20] Laniel D, Geneste G, Weck G, Mezouar M and Loubeyre P 2019 Phys. Rev. Lett. 122 066001
[21] Shen Y, Oganov A R, Qian G, Zhang J, Dong H, Zhu Q and Zhou Z 2015 Sci. Rep. 5 14204
[22] Steele B A and Oleynik I I 2016 Chem. Phys. Lett. 643 21
[23] Steele B A and Oleynik I I 2017 J. Phys. Chem. A 121 8955
[24] Williams A S, Steele B A and Oleynik I I 2017 J. Chem. Phys. 147 234701
[25] Peng F, Han Y, Liu H and Yao Y 2015 Sci. Rep. 5 16902
[26] Steele B A, Stavrous E, Prakapenka V B, Radousky H, Zaug J, Crowhurst J C and Oleynik I I 2017 AIP Conf. Proc. 1793 040016
[27] Zhang S, Zhao Z, Liu L and Yang G 2017 J. Power Sources 365 155
[28] Yu S, Huang B, Zeng Q, Oganov A R, Zhang L and Frapper G 2017 J. Phys. Chem. C 121 11037
[29]Bruls R J, Hintzen H T and Metselaar R 1999 J. Mater. Sci. 34 4519
[30] Parkin I P and Nartowski A M 1998 Polyhedron 17 2617
[31] Hao J, Li Y W, Wang J S, Ma C L, Huang L Y, Liu R, Cui Q L, Zou G T, Liu J and Li X D 2010 J. Phys. Chem. C 114 16750
[32] Römer S R, Schnick W and Kroll P 2009 J. Phys. Chem. C 113 2943
[33] Gregory D H, Bowman A, Baker C F and Weston D P 2000 J. Mater. Chem. 10 1635
[34] Zhu S, Peng F, Liu H, Majumdar A, Gao T and Yao Y 2016 Inorg. Chem. 55 7550
[35] Wang Y, Lv J, Zhu L and Ma Y 2012 Comput. Phys. Commun. 183 2063
[36] Wang Y, Lv J, Zhu L and Ma Y 2010 Phys. Rev. B 82 094116
[37] Kresse G and Furthmüller J 1996 Phys. Rev. B 54 11169
[38] Chaput L, Togo A, Tanaka I and Hug G 2011 Phys. Rev. B 84 094302
[39] Henkelman G, Arnaldsson A and Jónsson H 2006 Comput. Mater. Sci. 36 354
[40] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[41] Hammer B, Hansen L B and Nørskov J K 1999 Phys. Rev. B 59 7413
[42] Monkhorst H J and Pack J D 1976 Phys. Rev. B 13 5188
[43] Wei S, Li D, Liu Z, Wang W, Tian F, Bao K, Duan D, Liu B and Cui T 2017 J. Phys. Chem. C 121 9766
[44]Lv C W, Wang C J and Gu J B 2019 Acta Phys. Sin. 68 077102 (in Chinese)