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First-principles study of Ca5N4 at high pressure

Shi Xu-Han Li Hai-Yan Yao Zhen Liu Bing-Bing

First-principles study of Ca5N4 at high pressure

Shi Xu-Han, Li Hai-Yan, Yao Zhen, Liu Bing-Bing
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  • Recent studies have shown that introducing metal elements into nitrogen matrix can induce more stable poly-nitrogen structures than the pure nitrogen phase due to the ionic interaction between metal elements and nitrogen matrix. Many types of poly-nitrogen structures have been reported by using the alkaline earth metal elements (M = Be, Mg, Ca, Sr, Ba) as the coordinate elements. For example, the one-dimensional (1D) infinite armchair poly-nitrogen chain (N) structure and N6 ring structure are obtained for the MN4 and MN3 chemical stoichiometry, respectively. Interestingly, the stabilities of theses MNx structures are enhanced 2–3 times compared with that of the pure nitrogen. Therefore, exploring the novel and stable poly-nitrogen structure by introducing alkaline earth metal elements under high pressure is a great significant job. As an alkaline earth element, Ca is abundant in the earth. Its ionization energy (I1 = 590 kJ/mol) is far lower than that of Be (900 kJ/mol) and Mg (738 kJ/mol), which means that Ca can form calcium nitrides more easily. Zhu et al. (Zhu S, Peng F, Liu H, Majumdar A, Gao T, Yao Y 2016Inorg. Chem. 55  7550) proposed that the Ca-N system can obtain poly-nitrogen structures under high pressure, such as CaN4 structure with armchair nitrogen chain, CaN5 and CaN3 consisting of pentazolate “N5” and benzene-like “N6” anions. These poly-nitrogen structures have potential applications in the field of high energy density materials. Here, we report the prediction of Ca-N system at 100 GPa by using particle swarm optimization algorithm technique for crystal structure prediction. A new thermal stable phase with P 21/c-Ca5N4 space group is found at 100 GPa, which enriches the phase of Ca-N system under high pressure. The dynamic stability and mechanical stability of new phase are confirmed by phono dispersion spectrum and elastic constant calculations. The electron localization function analysis shows that the nitrogen atoms in P 21/c-Ca5N4 are bonded by N—N single bond and electron transfer from Ca atom to N atom enables Ca5N4 to serve as an ionic-bonding interaction structure. Band structure calculation shows that the Ca5N4 has a semiconductor structure with a direct band gap of 1.447 eV. The PDOS calculation shows the valence band near Fermi energy is mainly contributed by N_p electrons, while the conduction band is mainly contributed by Ca_d electrons, indicating that electrons are transferred from Ca atom to N atom. Bader calculation shows that each N atom obtains 1.26e from Ca atom in P 21/c-Ca5N4. The Raman spectrum and X-ray diffraction spectrum are calculated and detailed Raman vibration modes are identified, which provides theoretical guidance for experimental synthesis.
      Corresponding author: Yao Zhen, yaozhen@jlu.edu.cn ; Liu Bing-Bing, liubb@jlu.edu.cn
    [1]

    Pickard C J, Needs R J 2009 Phys. Rev. Lett. 102 125702

    [2]

    Erba A, Maschio L, Pisani C, Casassa S 2011 Phys. Rev. B 84 012101

    [3]

    Hirshberg B, Gerber R B, Krylov A I 2014 Nat. Chem. 6 52

    [4]

    Özçelik V O, Aktürk O Ü, Durgun E, Ciraci S 2015 Phys. Rev. B 92 125420

    [5]

    Plašienka D, Martoňák R 2015 J. Chem. Phys. 142 094505

    [6]

    Yakub L N 2016 Low Temp. Phys. 42 1

    [7]

    Martin R M, Needs R J 1986 Phys. Rev. B 34 5082

    [8]

    Mailhiot C, Yang L H, McMahan A K 1992 Phys. Rev. B 46 14419

    [9]

    Wang X, Wang Y, Miao M, Zhong X, Lv J, Cui T, Li J, Chen L, Pickard C J, Ma Y 2012 Phys. Rev. Lett. 109 175502

    [10]

    Ma Y, Oganov A R, Li Z, Xie Y, Kotakoski J 2009 Phys. Rev. Lett. 102 065501

    [11]

    Bondarchuk S V, Minaev B F 2017 Comput. Mater. Sci. 133 122

    [12]

    Eremets M I, Gavriliuk A G, Trojan I A, Dzivenko D A, Boehler R 2004 Nat. Mater. 3 558

    [13]

    Tomasino D, Kim M, Smith J, Yoo C S 2014 Phys. Rev. Lett. 113 205502

    [14]

    Zhao J F, Li N, Li Q S 2003 Theor. Chem. Acc. 110 10

    [15]

    Steele B A, Oleynik I I 2016 Chem. Phys.Lett. 643 21

    [16]

    Zhang M, Yin K, Zhang X, Wang H, Li Q, Wu Z 2013 Solid State Commun. 161 13

    [17]

    Peng F, Yao Y, Liu H, Ma Y 2015 J. Phys. Chem. Lett. 6 2363

    [18]

    Zhang J, Zeng Z, Lin H Q, Li Y L 2015 Sci. Rep. 4 4358

    [19]

    Wang X, Li J, Zhu H, Chen L, Lin H 2014 J. Chem. Phys. 141 044717

    [20]

    Williams A S, Steele B A, Oleynik I I 2017 J. Chem. Phys. 147 234701

    [21]

    Wei S, Li D, Liu Z, Wang W, Tian F, Bao K, Duan D, Liu B, Cui T 2017 J. Phys. Chem. C 121 9766

    [22]

    Yu S, Huang B, Zeng Q, Oganov A R, Zhang L, Frapper G 2017 J. Phys. Chem. C 121 11037

    [23]

    Wei S, Li D, Liu Z, Li X, Tian F, Duan D, Liu B, Cui T 2017 Phys. Chem. Chem. Phys. 19 9246

    [24]

    Hou P, Lian L, Cai Y, Liu B, Wang B, Wei S, Li D 2018 RSC Adv. 8 4314

    [25]

    Braun C, Börger S L, Boyko T D, Miehe G, Ehrenberg H, Höhn P, Moewes A, Schnick W 2011 J. Am. Chem. Soc. 133 4307

    [26]

    Hao J, Li Y, Wang J, Ma C, Huang L, Liu R, Cui Q, Zou G, Liu J, Li X 2010 J. Phys. Chem. C 114 16750

    [27]

    Römer S R, Schnick W, Kroll P 2009 J. Phys. Chem. C 113 2943

    [28]

    Gregory D H, Bowman A, Baker C F, Weston D P 2000 J. Mater. Chem. 10 1635

    [29]

    Zhu S, Peng F, Liu H, Majumdar A, Gao T, Yao Y 2016 Inorg. Chem. 55 7550

    [30]

    Dong X, Oganov A R, Goncharov A F, Stavrou E, Lobanov S, Saleh G, Qian G R, Zhu Q, Gatti C, Deringer V L, Dronskowski R, Zhou X F, Prakapenka V B, Konôpková Z, Popov I A, Boldyrev A I, Wang H T 2017 Nat. Chem. 9 440

    [31]

    Ma Y, Eremets M, Oganov A R, Xie Y, Trojan I, Medvedev S, Lyakhov A O, Valle M, Prakapenka V 2009 Nature 458 182

    [32]

    Einaga M, Sakata M, Ishikawa T, Shimizu K, Eremets M I, Drozdov A P, Troyan I A, Hirao N, Ohishi Y 2016 Nat. Phys. 12 835

    [33]

    Wang Y, Lv J, Zhu L, Ma Y 2012 Comput. Phys. Commun. 183 2063

    [34]

    Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169

    [35]

    Chaput L, Togo A, Tanaka I, Hug G 2011 Phys. Rev. B 84 094302

    [36]

    Henkelman G, Arnaldsson A, Jónsson H 2006 Comput. Mater. Sci. 36 354

    [37]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865

    [38]

    Hammer B, Hansen L B, Nørskov J K 1999 Phys. Rev. B 59 7413

  • 图 1  100 GPa下Ca-N体系落在凸包图上热力学稳定的各比例

    Figure 1.  Stable phases on the convex hulls of Ca-N system at 100 GPa.

    图 2  100 GPa下预测得到的Ca5N4晶体结构图((a))及多面体单元结构((b), (c))

    Figure 2.  Crystalline structure of the predicted stable Ca5N4: (a) P 21/c phase at 100 GPa; (b), (c) he polyhedron units of Ca5N4.

    图 3  P 21/c相在100 GPa下的声子色散曲线图

    Figure 3.  Phonon dispersion curves of P 21/c phase at 100 GPa

    图 4  P 21/c-Ca5N4结构在100 GPa下的二维ELF图

    Figure 4.  Cross-sections of electron local function of P 21/c-Ca5N4 at 100 GPa.

    图 5  P 21/c-Ca5N4在100 GPa下的电子能带结构图和PDOS

    Figure 5.  Band structure and projected density of states of P 21/c-Ca5N4 at 100 GPa, respectively.

    图 6  P 21/c-Ca5N4在100 GPa下的拉曼光谱

    Figure 6.  Raman spectrum of P 21/c-Ca5N4 at 100 GPa.

    图 7  P 21/c-Ca5N4在100 GPa下的XRD图谱

    Figure 7.  The X-ray diffraction spectrum of P 21/c-Ca5N4 at 100 GPa.

  • [1]

    Pickard C J, Needs R J 2009 Phys. Rev. Lett. 102 125702

    [2]

    Erba A, Maschio L, Pisani C, Casassa S 2011 Phys. Rev. B 84 012101

    [3]

    Hirshberg B, Gerber R B, Krylov A I 2014 Nat. Chem. 6 52

    [4]

    Özçelik V O, Aktürk O Ü, Durgun E, Ciraci S 2015 Phys. Rev. B 92 125420

    [5]

    Plašienka D, Martoňák R 2015 J. Chem. Phys. 142 094505

    [6]

    Yakub L N 2016 Low Temp. Phys. 42 1

    [7]

    Martin R M, Needs R J 1986 Phys. Rev. B 34 5082

    [8]

    Mailhiot C, Yang L H, McMahan A K 1992 Phys. Rev. B 46 14419

    [9]

    Wang X, Wang Y, Miao M, Zhong X, Lv J, Cui T, Li J, Chen L, Pickard C J, Ma Y 2012 Phys. Rev. Lett. 109 175502

    [10]

    Ma Y, Oganov A R, Li Z, Xie Y, Kotakoski J 2009 Phys. Rev. Lett. 102 065501

    [11]

    Bondarchuk S V, Minaev B F 2017 Comput. Mater. Sci. 133 122

    [12]

    Eremets M I, Gavriliuk A G, Trojan I A, Dzivenko D A, Boehler R 2004 Nat. Mater. 3 558

    [13]

    Tomasino D, Kim M, Smith J, Yoo C S 2014 Phys. Rev. Lett. 113 205502

    [14]

    Zhao J F, Li N, Li Q S 2003 Theor. Chem. Acc. 110 10

    [15]

    Steele B A, Oleynik I I 2016 Chem. Phys.Lett. 643 21

    [16]

    Zhang M, Yin K, Zhang X, Wang H, Li Q, Wu Z 2013 Solid State Commun. 161 13

    [17]

    Peng F, Yao Y, Liu H, Ma Y 2015 J. Phys. Chem. Lett. 6 2363

    [18]

    Zhang J, Zeng Z, Lin H Q, Li Y L 2015 Sci. Rep. 4 4358

    [19]

    Wang X, Li J, Zhu H, Chen L, Lin H 2014 J. Chem. Phys. 141 044717

    [20]

    Williams A S, Steele B A, Oleynik I I 2017 J. Chem. Phys. 147 234701

    [21]

    Wei S, Li D, Liu Z, Wang W, Tian F, Bao K, Duan D, Liu B, Cui T 2017 J. Phys. Chem. C 121 9766

    [22]

    Yu S, Huang B, Zeng Q, Oganov A R, Zhang L, Frapper G 2017 J. Phys. Chem. C 121 11037

    [23]

    Wei S, Li D, Liu Z, Li X, Tian F, Duan D, Liu B, Cui T 2017 Phys. Chem. Chem. Phys. 19 9246

    [24]

    Hou P, Lian L, Cai Y, Liu B, Wang B, Wei S, Li D 2018 RSC Adv. 8 4314

    [25]

    Braun C, Börger S L, Boyko T D, Miehe G, Ehrenberg H, Höhn P, Moewes A, Schnick W 2011 J. Am. Chem. Soc. 133 4307

    [26]

    Hao J, Li Y, Wang J, Ma C, Huang L, Liu R, Cui Q, Zou G, Liu J, Li X 2010 J. Phys. Chem. C 114 16750

    [27]

    Römer S R, Schnick W, Kroll P 2009 J. Phys. Chem. C 113 2943

    [28]

    Gregory D H, Bowman A, Baker C F, Weston D P 2000 J. Mater. Chem. 10 1635

    [29]

    Zhu S, Peng F, Liu H, Majumdar A, Gao T, Yao Y 2016 Inorg. Chem. 55 7550

    [30]

    Dong X, Oganov A R, Goncharov A F, Stavrou E, Lobanov S, Saleh G, Qian G R, Zhu Q, Gatti C, Deringer V L, Dronskowski R, Zhou X F, Prakapenka V B, Konôpková Z, Popov I A, Boldyrev A I, Wang H T 2017 Nat. Chem. 9 440

    [31]

    Ma Y, Eremets M, Oganov A R, Xie Y, Trojan I, Medvedev S, Lyakhov A O, Valle M, Prakapenka V 2009 Nature 458 182

    [32]

    Einaga M, Sakata M, Ishikawa T, Shimizu K, Eremets M I, Drozdov A P, Troyan I A, Hirao N, Ohishi Y 2016 Nat. Phys. 12 835

    [33]

    Wang Y, Lv J, Zhu L, Ma Y 2012 Comput. Phys. Commun. 183 2063

    [34]

    Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169

    [35]

    Chaput L, Togo A, Tanaka I, Hug G 2011 Phys. Rev. B 84 094302

    [36]

    Henkelman G, Arnaldsson A, Jónsson H 2006 Comput. Mater. Sci. 36 354

    [37]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865

    [38]

    Hammer B, Hansen L B, Nørskov J K 1999 Phys. Rev. B 59 7413

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  • Received Date:  28 November 2019
  • Accepted Date:  31 December 2019
  • Published Online:  20 March 2019

First-principles study of Ca5N4 at high pressure

    Corresponding author: Yao Zhen, yaozhen@jlu.edu.cn
    Corresponding author: Liu Bing-Bing, liubb@jlu.edu.cn
  • State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun 130012, China

Abstract: Recent studies have shown that introducing metal elements into nitrogen matrix can induce more stable poly-nitrogen structures than the pure nitrogen phase due to the ionic interaction between metal elements and nitrogen matrix. Many types of poly-nitrogen structures have been reported by using the alkaline earth metal elements (M = Be, Mg, Ca, Sr, Ba) as the coordinate elements. For example, the one-dimensional (1D) infinite armchair poly-nitrogen chain (N) structure and N6 ring structure are obtained for the MN4 and MN3 chemical stoichiometry, respectively. Interestingly, the stabilities of theses MNx structures are enhanced 2–3 times compared with that of the pure nitrogen. Therefore, exploring the novel and stable poly-nitrogen structure by introducing alkaline earth metal elements under high pressure is a great significant job. As an alkaline earth element, Ca is abundant in the earth. Its ionization energy (I1 = 590 kJ/mol) is far lower than that of Be (900 kJ/mol) and Mg (738 kJ/mol), which means that Ca can form calcium nitrides more easily. Zhu et al. (Zhu S, Peng F, Liu H, Majumdar A, Gao T, Yao Y 2016Inorg. Chem. 55  7550) proposed that the Ca-N system can obtain poly-nitrogen structures under high pressure, such as CaN4 structure with armchair nitrogen chain, CaN5 and CaN3 consisting of pentazolate “N5” and benzene-like “N6” anions. These poly-nitrogen structures have potential applications in the field of high energy density materials. Here, we report the prediction of Ca-N system at 100 GPa by using particle swarm optimization algorithm technique for crystal structure prediction. A new thermal stable phase with P 21/c-Ca5N4 space group is found at 100 GPa, which enriches the phase of Ca-N system under high pressure. The dynamic stability and mechanical stability of new phase are confirmed by phono dispersion spectrum and elastic constant calculations. The electron localization function analysis shows that the nitrogen atoms in P 21/c-Ca5N4 are bonded by N—N single bond and electron transfer from Ca atom to N atom enables Ca5N4 to serve as an ionic-bonding interaction structure. Band structure calculation shows that the Ca5N4 has a semiconductor structure with a direct band gap of 1.447 eV. The PDOS calculation shows the valence band near Fermi energy is mainly contributed by N_p electrons, while the conduction band is mainly contributed by Ca_d electrons, indicating that electrons are transferred from Ca atom to N atom. Bader calculation shows that each N atom obtains 1.26e from Ca atom in P 21/c-Ca5N4. The Raman spectrum and X-ray diffraction spectrum are calculated and detailed Raman vibration modes are identified, which provides theoretical guidance for experimental synthesis.

    • 氮原子有五个价电子(2s22p3), 具有丰富的成键方式[1]. 氮在大气中含量最丰富, 常压下, 氮气(N2)分子之间存在弱的范德瓦耳斯作用力. 高压下, N2分子之间的距离逐渐减小, 当N2分子间的范德瓦耳斯作用力接近于分子间的共价键作用力时, 氮分子内的共价三键发生解离, 氮原子间重新键合, 形成非分子相, 称为共价聚合氮结构[2-6]. 聚合氮不需要氧气, 靠自身分解便可释放能量, 其产物是对环境无污染的氮气, 是一种潜在的高能量密度清洁材料, 在能量存储、火箭推进剂和炸药方面有着广泛的应用前景. 理论和实验对聚合氮的研究工作均取得了一定的进展. 如理论报道的聚合氮结构: 网络状cg-N[7,8]、笼状N10[9]、层状LP-N[10]以及之字链状A7-N[11]等. 实验上, Eremets等[12]和Tomasino等[13]分别通过激光加热金刚石对顶砧实验技术成功合成出了cg-N (110 GPa, 2000 K)和LP-N (150 GPa, 3000 K)聚合氮结构, 验证了理论研究工作. 然而, 聚合氮只能在高温、高压的极端条件下才能合成, 并且只能稳定在高压的条件下, 这种苛刻的合成条件和稳定条件限制了聚合氮的应用. 近年来的研究表明, 引入配位元素, 利用配位元素和氮元素之间形成的离子键相互作用, 可以获得稳定性更高的多氮聚合结构. 相关研究也取得了很大的进展, 如引入碱金属元素(M = Li, Na, K, Rb, Cs), 可以获得具有氮六环结构的MN3多氮聚合结构以及具有氮五环结构的MN5多氮聚合结构[14-20]. 当引入碱土金属元素(M = Be, Mg, Ca, Sr), 可以获得具有扶手椅链结构的MN4多氮聚合结构[21-24]. 理论计算表明, 引入配位元素获得的多氮聚合结构比纯氮聚合结构的稳定性提高了2—3倍以上. 因此, 利用配位元素与氮元素之间复杂的电子结构相互作用, 开展多氮聚合结构的高压研究, 很可能获得结构更新奇、稳定性更高的多氮聚合结构, 是一项非常有意义的工作.

      Ca元素在地球中含量丰富, 其电离能(I1 = 590 kJ/mol)远低于同主族的Be (900 kJ/mol)和Mg (738 kJ/mol), 更易和氮原子形成具有离子键相互作用的钙氮化物. 钙氮化物在工业生产领域有着广泛的应用, 如Ca3N2是合成其他多元氮化物理想的前驱体, 同时因其催化特性, 在立方氮化硼工业生产过程中被广泛应用[25-27]. 室温下Ca2N是一种顺磁、二维层状带电体结构, 在光电方面应用广泛. 同时, 由于其阴离子[N2]2–结构含有氮-氮双键, 又是潜在的能源材料[28]. 理论上, 对不同配比的Ca-N二元化合物给出了详细的报道, 前人通过结构预测方法, 给出了钙氮体系八个配比CaxNy (xy = 2∶1, 3∶2, 1∶1, 2∶3, 1∶2, 1∶3, 1∶4, 1∶5)的常压/高压结构[29]. 如常压下四种稳定配比的CaN, CaN2, Ca3N2, Ca2N钙氮化合物. 随着压力的升高, 更多配比的稳定钙氮化合物陆续被发现, 如氮-氮双键结构的Ca2N3, 扶手椅型氮链结构的CaN4、氮五环结构的CaN5和氮六环结构的CaN3. 其中, 富氮结构CaN3, CaN4, CaN5在高能量密度材料领域有着潜在的应用前景. 此外, 压力作为独立于组分和温度的力学参量, 可以有效减小分子、原子之间的间距, 改变价电子轨道间的杂化模式, 降低化学势垒, 是生成新物质结构非常有效的手段[30-32]. 因此, 利用高压方法, 通过改变配比的方式, 寻找具有新奇特性的钙氮高压结构, 是一项非常有意义的工作.

      本文在密度泛函理论框架下, 采用基于粒子群算法的结构搜索方法, 结合VASP结构计算软件包, 搜索配比为5∶4和2∶5的钙氮体系在100 GPa下的能量最优结构. 通过热力学稳定性、动力学和机械稳定性的分析, 寻找区别于以往的钙氮结构、且具有优异性能的稳定高压结构, 进一步丰富Ca-N体系高压结构. 结果表明, Ca2N5在100 GPa下热力学不稳定, 而Ca5N4在100 GPa下同时满足热力学稳定性、机械稳定性和动力学稳定性. 能带结构计算表明具有P 21/c对称性的Ca5N4是直接带隙为1.447 eV的半导体结构. 群论分析表明该结构共有51种振动模式, 其中24种拉曼振动模式, 并详细指认了所有的拉曼振动模式. 该研究不仅从理论上提出了一种新配比的钙氮高压稳定结构, 丰富了钙氮高压相图, 而且给出了该结构的Raman振动模式, 为实验合成该高压相提供了理论指导.

    2.   理论计算方法
    • 钙氮体系的高压结构搜索是采用基于粒子群优化算法的CALYPSO结构预测软件完成的[33]. 结构优化和性质计算采用VASP软件完成[34], 声子谱计算采用PHONOPY软件包完成[35], Raman光谱是用Quantum Espresso软件计算完成, 电子转移是采用Bader软件完成[36]. 计算采用广义梯度近似方法[37], 选用基于Perdew-Burke-Ernzerhof泛函的投影缀加平面波(PAW)赝势[38]. Ca和N原子的价电子分别是3s23p64s2和2s22p3. 结构弛豫和性质计算的截断能分别是520 和600 eV, 能量收敛标准为1 × 10–5 eV/atom, 力收敛标准为–5 × 10–3 eV/Å. 布里渊K点取样是以Gamma为中心, 密度为2π × 0.03 Å–1网格. 结构的形成焓计算公式为ΔHf(CaxNy) = [H(CaxNy)–xH(Ca)–yH(N)]/(x+y),xy 分别为2∶1, 3∶2, 5∶4, 1∶1, 2∶3, 1∶2, 2∶5, 1∶3, 1∶4, 1∶5. 在对结构的拉曼计算过程中采取模守恒赝势, 应用平面波基组和赝势方法, 交换关联能为Perdew-Wang 局域密度近似, 截断能分别为80 Ry和320 Ry.

    3.   结果与讨论
    • 分别选取1 → 4倍胞, 在100 GPa下开展结构预测, 每代产生50个结构, 共计30代. 该预测工作顺利地找到了前人已经报道的稳定结构相, 如CaN的Pbam相、CaN2Pbam相以及Ca2N的I4/mmm相, 证明了本文理论预测的可靠性. 通过对Ca2N5和Ca5N4两种配比的钙氮化物高压结构搜索, 分别获得了两个配比的最优结构. 为了确定新获得的最优结构的热力学稳定性, 借助于已经报道的配比为2∶1, 3∶2, 1∶1, 2∶3, 1∶2, 1∶3, 1∶4, 1∶5的CaxNy钙氮化合物, 绘制了体系在100 GPa下的凸包图. 如图1所示, 位于凸包图上的用红实线相连的是热力学稳定的结构, 用黑实线相连的没有位于凸包图上的则是一些不稳定或者亚稳定结构. 可以看出, Ca2N5不具有热力学稳定性, 而Ca5N4具有热力学稳定性. 图2给出了Ca5N4单胞结构图及多面体单元结构图. Ca5N4是空间群为P 21/c单斜晶体结构. 晶格常数为a = 8.701 Å, b = 5.847 Å, c = 5.573 Å, 晶格夹角为α = γ = 90°, β = 143.63°. P 21/c-Ca5N4的原子占位为Ca1 (0.6833, 0.66271, 0.74828), Ca2 (0.24663, 0.66164, 0.44596), Ca3 (0.0, 0.0, 1.0), N1 (0.02894, 0.1585, 0.69206), N2 (0.431, 0.53487, 0.01961). Ca5N4中的Ca原子有两种配位形式, 一种是每个钙原子被6个氮原子包围形成六配位的八面体结构(图2(b)), 另一种是每个钙原子被7个氮原子包围形成七配位的十面体结构(图2(c)), 与经典的八面体结构不同的是, 十面体结构中5个氮原子位于同一平面, 这其中就存在一个N2单元, 其余的2个氮原子分居面的两侧, 并且八面体和十面体之间是彼此共面链接的. 结构中的氮原子类型有两种, 分别是独立的氮原子和双氮键合结构. 其中, 双氮键合结构形成的共价键键长是1.442 Å, 大于氮氮双键(1.20 Å)和三键(1.10 Å)的键长, 属于N—N单键(> 1.3 Å).

      Figure 1.  Stable phases on the convex hulls of Ca-N system at 100 GPa.

      Figure 2.  Crystalline structure of the predicted stable Ca5N4: (a) P 21/c phase at 100 GPa; (b), (c) he polyhedron units of Ca5N4.

      为了确定Ca5N4结构的动力学稳定性和机械稳定性, 计算了该结构的声子谱和弹性常数. 如图3所示, Ca5N4P 21/c相结构在100 GPa下的声子谱中没有虚频, 说明该结构具有动力学稳定性. 弹性常数计算结果表明, 该结构弹性模量矩阵具有13个独立的刚度矩阵元, 分别为C11 = 491.812 GPa, C12 = 254.816 GPa, C13 = 194.381 GPa, C15 = 6.354 GPa, C22 = 486.404 GPa, C23 = 204.206 GPa, C25 = –21.519 GPa, C33 = 469.087 GPa, C35 = 15.203 GPa, C44 = 167.03 GPa, C46 = –11.832 GPa, C55 = 134.979 GPa, C66 = 190.363 GPa. 满足单斜结构相机械稳定性的力学判据标准[24]:

      因此, 该结构也具有机械稳定性. 通过以上讨论可知, 在100 GPa条件下, 获得了同时满足热力学稳定、动力学稳定以及机械稳定的新高压P 21/c相Ca5N4结构.

      Figure 3.  Phonon dispersion curves of P 21/c phase at 100 GPa

      为了研究Ca5N4结构的成键方式和电子结构性质, 分别计算了该结构的电子局域函数(ELF)、能带结构和投影态密度(PDOS). 图4为Ca5N4的二维ELF图, 橘红色区域局域性函数值为1, 对应代表电子高度局域, 成键方式为较强的共价键, 蓝色则对应局域函数值为0, 代表高度离域的电子分布. 可看出, 双氮键合结构的外侧形成高度局域的孤对电子, 氮原子间电子局域性很强, 属于共价sigma键, 该结果与我们通过键长判定其为N—N单键的结论一致. 同时, 钙原子附近电子离域性较强, 说明钙原子和氮原子间形成了离子键相互作用. 如图5所示, 能带结构和PDOS的研究结果表明, P 21/c相能带展宽较为平稳, 具有较强的电子局域性. 没有能带贯穿费米能级, 是直接带隙为1.447 eV的半导体结构. 从PDOS可以看出P 21/c-Ca5N4的费米能级附近的价带区域主要是由氮原子的N_p电子贡献, 而导带区域则是主要由钙原子的Ca_d电子贡献, 这也说明了钙原子与氮原子之间存在电子转移现象, 与前面ELF分析结果相一致. 通过Bader软件定量计算表明, P 21/c-Ca5N4结构中每个氮原子从钙原子获得约1.26个电子, 这与前面的ELF和PDOS的分析结果相一致.

      Figure 4.  Cross-sections of electron local function of P 21/c-Ca5N4 at 100 GPa.

      Figure 5.  Band structure and projected density of states of P 21/c-Ca5N4 at 100 GPa, respectively.

      Ca5N4空间群为P 21/c, 对应的点群为C2h(2/m), 群论分析表明结构共有51种振动模式, 其中24种为拉曼振动模式, 结构振动模式遵循下面的不可约表示:

      其中A模式和B模式表示表非简并态. 如图6所示, 通过Raman振动的分析, 给出了振动模式和对应峰的指认. 其中168.1, 227.4, 268.2, 284.8, 359.9, 460.7, 567.2, 652.3, 749.8, 828.2, 851.2和1125.0 cm–1归属于Ag拉曼振动模式; 206.3, 270.9, 298.3, 338.7, 386.4, 441.6, 584.6, 662.6, 751.9, 872.4, 902.1和1124.1 cm–1归属于Bg拉曼振动模式. 该Raman振动模式的指认为实验合成该高压相提供了理论性指导. 同时, 对P 21/c-Ca5N4结构进行了X射线衍射(XRD)理论计算, 并绘制得到XRD图谱, 如图7所示, 为实验合成提供更全面的理论指导.

      Figure 6.  Raman spectrum of P 21/c-Ca5N4 at 100 GPa.

      Figure 7.  The X-ray diffraction spectrum of P 21/c-Ca5N4 at 100 GPa.

    4.   结 论
    • 利用第一性原理结合结构搜索技术, 在100 GPa条件下预测出一个新的空间群为P 21/c的Ca5N4相, 丰富了钙氮体系高压相. 通过形成焓计算、声子谱、弹性常数的计算表明, 该结构同时具有热力学稳定性、动力学稳定性和机械稳定性. 通过成键分析表明, 该结构内部氮原子之间以N—N单键键合, 氮原子和钙原子之间是离子键相互作用. 通过电子结构性质的计算发现, P 21/c-Ca5N4是一个直接带隙为1.447 eV的半导体结构, 费米能级附近的价带主要是由氮原子的N_p电子贡献, 而导带则主要由钙原子的Ca_d电子贡献, 说明钙原子与氮原子之间存在电子转移现象. Bader计算表明P 21/c-Ca5N4结构中平均每个氮原子从钙原子获得的电子数约为1.26e. 最后计算了P 21/c-Ca5N4结构的拉曼振动光谱及XRD光谱, 指认了拉曼振动模式, 为实验合成该结构提供了理论指导.

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