Pressure-induced evolution of stoichiometries and electronic structures of host–guest Na–B compounds

Guo Zixuan; Li Xing; Bergara Aitor; Ding Shicong; Zhang Xiaohua; Yang Guochun

doi:10.1063/5.0155005

Volume 8 Issue 6

Nov. 2023

Turn off MathJax

Article Contents

Article Navigation > Matter and Radiation at Extremes > 2023 > 8(6): 068401

Guo Zixuan, Li Xing, Bergara Aitor, Ding Shicong, Zhang Xiaohua, Yang Guochun. Pressure-induced evolution of stoichiometries and electronic structures of host–guest Na–B compounds[J]. Matter and Radiation at Extremes, 2023, 8(6): 068401. doi: 10.1063/5.0155005

Citation:

Guo Zixuan, Li Xing, Bergara Aitor, Ding Shicong, Zhang Xiaohua, Yang Guochun. Pressure-induced evolution of stoichiometries and electronic structures of host–guest Na–B compounds[J]. Matter and Radiation at Extremes, 2023, 8(6): 068401. doi: 10.1063/5.0155005

Citation:

Guo Zixuan, Li Xing, Bergara Aitor, Ding Shicong, Zhang Xiaohua, Yang Guochun. Pressure-induced evolution of stoichiometries and electronic structures of host–guest Na–B compounds[J]. Matter and Radiation at Extremes, 2023, 8(6): 068401. doi: 10.1063/5.0155005

PDF( 9996 KB)

Pressure-induced evolution of stoichiometries and electronic structures of host–guest Na–B compounds

doi: 10.1063/5.0155005

Guo Zixuan^{1
,
,},
Li Xing^1
,,
Bergara Aitor^{2, 3, 4
,},
Ding Shicong^1
,,
Zhang Xiaohua^1
,,
Yang Guochun^{1
,
,}

1.
State Key Laboratory of Metastable Materials Science & Technology and Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, China
2.
Departamento de Física and EHU-Quantum Center, Universidad del País Vasco-Euskal Herriko Unibertsitatea, UPV/EHU, 48080 Bilbao, Spain
3.
Donostia International Physics Center (DIPC), 20018 Donostia, Spain
4.
Centro de Física de Materiales CFM, Centro Mixto CSIC-UPV/EHU, 20018 Donostia, Spain

More Information

Corresponding author: a)Author to whom correspondence should be addressed: yanggc468@nenu.edu.cn
Received Date: 2023-04-17
Accepted Date: 2023-08-27

Available Online: 2023-11-01

Publish Date: 2023-11-01

Abstract

Abstract

Superionic and electride behaviors in materials, which induce a variety of exotic physical properties of ions and electrons, are of great importance both in fundamental research and for practical applications. However, their coexistence in hot alkali-metal borides has not been observed. In this work, we apply first-principles structure search calculations to identify eight Na–B compounds with host–guest structures, which exhibit a wide range of building blocks and interesting properties linked to the Na/B composition. Among the known borides, Na-rich Na₉B stands out as the composition with the highest alkali-metal content, featuring vertex- and face-sharing BNa₁₆ polyhedra. Notably, it exhibits electride characteristics and transforms into a superionic electride at 200 GPa and 2000 K, displaying unusual Na atomic diffusion behavior attributed to the modulation of the interstitial anion electrons. It demonstrates semiconductor behavior in the solid state, and metallic properties associated with Na 3p/3s states in the superionic and liquid regions. On the other hand, B-rich NaB₇, consisting of a unique covalent B framework, is predicted to exhibit low-frequency phonon-mediated superconductivity with a T_c of 16.8 K at 55 GPa. Our work advances the understanding of the structures and properties of alkali-metal borides.

Conflict of Interest
The authors have no conflicts to disclose.
Zixuan Guo: Investigation (equal); Visualization (equal); Writing – original draft (equal). Xing Li: Investigation (equal); Visualization (equal); Writing – original draft (equal). Aitor Bergara: Writing – review & editing (supporting). Shicong Ding: Visualization (supporting). Xiaohua Zhang: Writing – review & editing (supporting). Guochun Yang: Resources (lead); Supervision (lead); Writing – review & editing (lead).
Z.G. and X.L. contributed equally to this work.
Author Contributions
The data that support the findings of this study are available from the corresponding author upon reasonable request.

FullText(HTML)

References(74)

References

[1]	E. Wigner and F. Seitz, “On the constitution of metallic sodium,” Phys. Rev. 43, 804 (1933).10.1103/physrev.43.804
[2]	B. Rousseau, Y. Xie, Y. Ma, and A. Bergara, “Exotic high pressure behavior of light alkali metals, lithium and sodium,” Eur. Phys. J. B 81, 1–14 (2011).10.1140/epjb/e2011-10972-9
[3]	R. J. Nelmes, M. I. McMahon, J. S. Loveday, and S. Rekhi, “Structure of Rb-III: Novel modulated stacking structures in alkali metals,” Phys. Rev. Lett. 88, 155503 (2002).10.1103/physrevlett.88.155503
[4]	H. Olijnyk and W. B. Holzapfel, “Phase transitions in K and Rb under pressure,” Phys. Lett. A 99, 381–383 (1983).10.1016/0375-9601(83)90298-0
[5]	Y. Ma, A. R. Oganov, and Y. Xie, “High-pressure structures of lithium, potassium, and rubidium predicted by an ab initio evolutionary algorithm,” Phys. Rev. B 78, 014102 (2008).10.1103/physrevb.78.014102
[6]	G. Fabbris, J. Lim, L. S. I. Veiga, D. Haskel, and J. S. Schilling, “Electronic and structural ground state of heavy alkali metals at high pressure,” Phys. Rev. B 91, 085111 (2015).10.1103/physrevb.91.085111
[7]	Y. Ma, M. Eremets, A. R. Oganov, Y. Xie, I. Trojan, S. Medvedev, A. O. Lyakhov, M. Valle, and V. Prakapenka, “Transparent dense sodium,” Nature 458, 182–185 (2009).10.1038/nature07786
[8]	T. Matsuoka and K. Shimizu, “Direct observation of a pressure-induced metal-to-semiconductor transition in lithium,” Nature 458, 186–189 (2009).10.1038/nature07827
[9]	M. Marqués, M. I. McMahon, E. Gregoryanz, M. Hanfland, C. L. Guillaume, C. J. Pickard, G. J. Ackland, and R. J. Nelmes, “Crystal structures of dense lithium: A metal-semiconductor-metal transition,” Phys. Rev. Lett. 106, 095502 (2011).10.1103/physrevlett.106.095502
[10]	H. Hosono, S.-W. Kim, S. Matsuishi, S. Tanaka, A. Miyake, T. Kagayama, and K. Shimizu, “Superconductivity in room-temperature stable electride and high-pressure phases of alkali metals,” Philos. Trans. R. Soc., A 373, 20140450 (2015).10.1098/rsta.2014.0450
[11]	Y. Sun, L. Zhao, C. J. Pickard, R. J. Hemley, Y. Zheng, and M. Miao, “Chemical interactions that govern the structures of metals,” Proc. Natl. Acad. Sci. U. S. A. 120, e2218405120 (2023).10.1073/pnas.2218405120
[12]	Y. Li, Y. Wang, C. J. Pickard, R. J. Needs, Y. Wang, and Y. Ma, “Metallic icosahedron phase of sodium at terapascal pressures,” Phys. Rev. Lett. 114, 125501 (2015).10.1103/physrevlett.114.125501
[13]	P. S. Krstic, J. P. Allain, F. J. Dominguez-Gutierrez, and F. Bedoya, “Unraveling the surface chemistry processes in lithiated and boronized plasma material interfaces under extreme conditions,” Matter Radiat. Extremes 3, 165–187 (2018).10.1016/j.mre.2018.03.003
[14]	A. Rodriguez-Prieto, A. Bergara, V. M. Silkin, and P. M. Echenique, “Complexity and Fermi surface deformation in compressed lithium,” Phys. Rev. B 74, 172104 (2006).10.1103/physrevb.74.172104
[15]	A. Bergara, J. B. Neaton, and N. W. Ashcroft, “Pairing, π-bonding, and the role of nonlocality in a dense lithium monolayer,” Phys. Rev. B 62, 8494 (2000).10.1103/physrevb.62.8494
[16]	A. Rodriguez-Prieto and A. Bergara, “Pressure induced complexity in a lithium monolayer: Ab initio calculations,” Phys. Rev. B 72, 125406 (2005).10.1103/physrevb.72.125406
[17]	X. Li, X. Zhang, A. Bergara, Y. Liu, and G. Yang, “Structural and electronic properties of Na-B-H compounds at high pressure,” Phys. Rev. B 106, 174104 (2022).10.1103/physrevb.106.174104
[18]	Y. Sun, J. Lv, Y. Xie, H. Liu, and Y. Ma, “Route to a superconducting phase above room temperature in electron-doped hydride compounds under high pressure,” Phys. Rev. Lett. 123, 097001 (2019).10.1103/physrevlett.123.097001
[19]	X. Dong, A. R. Oganov, A. F. Goncharov, E. Stavrou, S. Lobanov, G. Saleh, G.-R. Qian, Q. Zhu, C. Gatti, V. L. Deringer, R. Dronskowski, X. F. Zhou, V. B. Prakapenka, Z. Konôpková, I. A. Popov, A. I. Boldyrev, and H. T. Wang, “A stable compound of helium and sodium at high pressure,” Nat. Chem. 9, 440–445 (2017).10.1038/nchem.2716
[20]	X. Wang, Y. Wang, J. Wang, S. Pan, Q. Lu, H.-T. Wang, D. Xing, and J. Sun, “Pressure stabilized lithium-aluminum compounds with both superconducting and superionic behaviors,” Phys. Rev. Lett. 129, 246403 (2022).10.1103/physrevlett.129.246403
[21]	P. Baettig and E. Zurek, “Pressure-stabilized sodium polyhydrides: NaHn (n > 1),” Phys. Rev. Lett. 106, 237002 (2011).10.1103/physrevlett.106.237002
[22]	H.-K. Mao, B. Chen, J. Chen, K. Li, J.-F. Lin, W. Yang, and H. Zheng, “Recent advances in high-pressure science and technology,” Matter Radiat. Extremes 1, 59–75 (2016).10.1016/j.mre.2016.01.005
[23]	A. Hermann, A. Suarez-Alcubilla, I. G. Gurtubay, L.-M. Yang, A. Bergara, N. W. Ashcroft, and R. Hoffmann, “LiB and its boron-deficient variants under pressure,” Phys. Rev. B 86, 144110 (2012).10.1103/physrevb.86.144110
[24]	S. Zhang, X. Du, J. Lin, A. Bergara, X. Chen, X. Liu, X. Zhang, and G. Yang, “Superconducting boron allotropes,” Phys. Rev. B 101, 174507 (2020).10.1103/physrevb.101.174507
[25]	T. Chen, Q. Gu, Q. Chen, X. Wang, C. J. Pickard, R. J. Needs, D. Xing, and J. Sun, “Prediction of quasi-one-dimensional superconductivity in metastable two-dimensional boron,” Phys. Rev. B 101, 054518 (2020).10.1103/physrevb.101.054518
[26]	P. Zhang, Y. Tian, Y. Yang, H. Liu, and G. Liu, “Stable Rb-B compounds under high pressure,” Phys. Rev. Res. 5, 013130 (2023).10.1103/physrevresearch.5.013130
[27]	X.-L. He, X. Dong, Q. Wu, Z. Zhao, Q. Zhu, A. R. Oganov, Y. Tian, D. Yu, X.-F. Zhou, and H.-T. Wang, “Predicting the ground-state structure of sodium boride,” Phys. Rev. B 97, 100102 (2018).10.1103/physrevb.97.100102
[28]	B. Zhao, X. Wang, L. Yu, Y. Liu, X. Chen, B. Yang, G. Yang, S. Zhang, L. Gu, and X. Liu, “Fabrication of alkali metal boride: Honeycomb-like structured NaB4 with high hardness and excellent electrical conductivity,” Adv. Funct. Mater. 32, 2110872 (2022).10.1002/adfm.202110872
[29]	F. Peng, M. Miao, H. Wang, Q. Li, and Y. Ma, “Predicted lithium-boron compounds under high pressure,” J. Am. Chem. Soc. 134, 18599–18605 (2012).10.1021/ja308490a
[30]	K. Jun, Y. Sun, Y. Xiao, Y. Zeng, R. Kim, H. Kim, L. J. Miara, D. Im, Y. Wang, and G. Ceder, “Lithium superionic conductors with corner-sharing frameworks,” Nat. Mater. 21, 924–931 (2022).10.1038/s41563-022-01222-4
[31]	M. Hara, M. Kitano, and H. Hosono, “Ru-loaded C12A7:(e−) electride as a catalyst for ammonia synthesis,” ACS Catal. 7, 2313–2324 (2017).10.1021/acscatal.6b03357
[32]	Y. Lu, J. Li, T. Tada, Y. Toda, S. Ueda, T. Yokoyama, M. Kitano, and H. Hosono, “Water durable electride Y5Si3: Electronic structure and catalytic activity for ammonia synthesis,” J. Am. Chem. Soc. 138, 3970–3973 (2016).10.1021/jacs.6b00124
[33]	Z. Zhao, S. Zhang, T. Yu, H. Xu, A. Bergara, and G. Yang, “Predicted pressure-induced superconducting transition in electride Li6P,” Phys. Rev. Lett. 122, 097002 (2019).10.1103/physrevlett.122.097002
[34]	Z. Liu, Q. Zhuang, F. Tian, D. Duan, H. Song, Z. Zhang, F. Li, H. Li, D. Li, and T. Cui, “Proposed superconducting electride Li6C by sp-hybridized cage states at moderate pressures,” Phys. Rev. Lett. 127, 157002 (2021).10.1103/physrevlett.127.157002
[35]	Z. Wan, W. Xu, T. Yang, and R. Zhang, “As-Li electrides under high pressure: Superconductivity, plastic, and superionic states,” Phys. Rev. B 106, L060506 (2022).10.1103/physrevb.106.l060506
[36]	Y. Wang, J. Wang, A. Hermann, C. Liu, H. Gao, E. Tosatti, H.-T. Wang, D. Xing, and J. Sun, “Electronically driven 1D cooperative diffusion in a simple cubic crystal,” Phys. Rev. X 11, 011006 (2021).10.1103/physrevx.11.011006
[37]	H.-J. Sung, W. H. Han, I.-H. Lee, and K. J. Chang, “Superconducting open-framework allotrope of silicon at ambient pressure,” Phys. Rev. Lett. 120, 157001 (2018).10.1103/physrevlett.120.157001
[38]	X. Du, H. Lou, J. Wang, and G. Yang, “Pressure-induced Na–Au compounds with novel structural units and unique charge transfer,” Phys. Chem. Chem. Phys. 23, 6455–6461 (2021).10.1039/d0cp06191c
[39]	Y. Wang, J. Lv, L. Zhu, and Y. Ma, “Crystal structure prediction via particle-swarm optimization,” Phys. Rev. B 82, 094116 (2010).10.1103/physrevb.82.094116
[40]	Y. Wang, J. Lv, L. Zhu, and Y. Ma, “CALYPSO: A method for crystal structure prediction,” Comput. Phys. Commun. 183, 2063–2070 (2012).10.1016/j.cpc.2012.05.008
[41]	X. Li, X. Zhang, Y. Liu, and G. Yang, “Bonding-unsaturation-dependent superconductivity in P-rich sulfides,” Matter Radiat. Extremes 7, 048402 (2022).10.1063/5.0098035.
[42]	D. Duan, Y. Liu, F. Tian, D. Li, X. Huang, Z. Zhao, H. Yu, B. Liu, W. Tian, and T. Cui, “Pressure-induced metallization of dense (H2S)2H2 with high-Tc superconductivity,” Sci. Rep. 4, 6968 (2014).10.1038/srep06968
[43]	F. Peng, Y. Sun, C. J. Pickard, R. J. Needs, Q. Wu, and Y. Ma, “Hydrogen clathrate structures in rare earth hydrides at high pressures: Possible route to room-temperature superconductivity,” Phys. Rev. Lett. 119, 107001 (2017).10.1103/physrevlett.119.107001
[44]	H. Liu, I. I. Naumov, R. Hoffmann, N. W. Ashcroft, and R. J. Hemley, “Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure,” Proc. Natl. Acad. Sci. U. S. A. 114, 6990–6995 (2017).10.1073/pnas.1704505114
[45]	A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontov, and S. I. Shylin, “Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system,” Nature 525, 73–76 (2015).10.1038/nature14964
[46]	A. P. Drozdov, P. P. Kong, V. S. Minkov, S. P. Besedin, M. A. Kuzovnikov, S. Mozaffari, L. Balicas, F. F. Balakirev, D. E. Graf, V. B. Prakapenka, E. Greenberg, D. A. Knyazev, M. Tkacz, and M. I. Eremets, “Superconductivity at 250 K in lanthanum hydride under high pressures,” Nature 569, 528–531 (2019).10.1038/s41586-019-1201-8
[47]	M. Somayazulu, M. Ahart, A. K. Mishra, Z. M. Geballe, M. Baldini, Y. Meng, V. V. Struzhkin, and R. J. Hemley, “Evidence for superconductivity above 260 K in lanthanum superhydride at megabar pressures,” Phys. Rev. Lett. 122, 027001 (2019).10.1103/physrevlett.122.027001
[48]	L. Ma, K. Wang, Y. Xie, X. Yang, Y. Wang, M. Zhou, H. Liu, X. Yu, Y. Zhao, H. Wang, G. Liu, and Y. Ma, “High-temperature superconducting phase in clathrate calcium hydride CaH6 up to 215 K at a pressure of 172 GPa,” Phys. Rev. Lett. 128, 167001 (2022).10.1103/physrevlett.128.167001
[49]	Z. Li, X. He, C. Zhang, X. Wang, S. Zhang, Y. Jia, S. Feng, K. Lu, J. Zhao, J. Zhang, B. Min, Y. Long, R. Yu, L. Wang, M. Ye, Z. Zhang, V. Prakapenka, S. Chariton, P. A. Ginsberg, J. Bass, S. Yuan, H. Liu, and C. Jin, “Superconductivity above 200 K discovered in superhydrides of calcium,” Nat. Commun. 13, 2863 (2022).10.1038/s41467-022-30454-w
[50]	G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B 54, 11169 (1996).10.1103/physrevb.54.11169
[51]	P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B 50, 17953 (1994).10.1103/physrevb.50.17953
[52]	J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865 (1996).10.1103/physrevlett.77.3865
[53]	P. Blaha, K. Schwarz, P. Sorantin, and S. B. Trickey, “Full-potential, linearized augmented plane wave programs for crystalline systems,” Comput. Phys. Commun. 59, 399–415 (1990).10.1016/0010-4655(90)90187-6
[54]	H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Phys. Rev. B 13, 5188 (1976).10.1103/physrevb.13.5188
[55]	A. Togo, F. Oba, and I. Tanaka, “First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures,” Phys. Rev. B 78, 134106 (2008).10.1103/physrevb.78.134106
[56]	S. Baroni, S. De Gironcoli, A. Dal Corso, and P. Giannozzi, “Phonons and related crystal properties from density-functional perturbation theory,” Rev. Mod. Phys. 73, 515 (2001).10.1103/revmodphys.73.515
[57]	P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials,” J. Phys.: Condens. Matter 21, 395502 (2009).10.1088/0953-8984/21/39/395502
[58]	D. J. Evans and B. L. Holian, “The Nose–Hoover thermostat,” J. Chem. Phys. 83, 4069–4074 (1985).10.1063/1.449071
[59]	X. Zhong, Y. Sun, T. Iitaka, M. Xu, H. Liu, R. J. Hemley, C. Chen, and Y. Ma, “Prediction of above-room-temperature superconductivity in lanthanide/actinide extreme superhydrides,” J. Am. Chem. Soc. 144, 13394–13400 (2022).10.1021/jacs.2c05834
[60]	A. R. Oganov, J. Chen, C. Gatti, Y. Ma, Y. Ma, C. W. Glass, Z. Liu, T. Yu, O. O. Kurakevych, and V. L. Solozhenko, “Ionic high-pressure form of elemental boron,” Nature 457, 863–867 (2009).10.1038/nature07736
[61]	C. Liu, H. Gao, A. Hermann, Y. Wang, M. Miao, C. J. Pickard, R. J. Needs, H.-T. Wang, D. Xing, and J. Sun, “Plastic and superionic helium ammonia compounds under high pressure and high temperature,” Phys. Rev. X 10, 021007 (2020).10.1103/physrevx.10.021007
[62]	Q. Zhang, C. Zhang, Z. D. Hood, M. Chi, C. Liang, N. H. Jalarvo, M. Yu, and H. Wang, “Abnormally low activation energy in cubic Na3SbS4 superionic conductors,” Chem. Mater. 32, 2264–2271 (2020).10.1021/acs.chemmater.9b03879
[63]	Q. Chen, N. H. Jalarvo, and W. Lai, “Na ion dynamics in P2-Nax[Ni1/3Ti2/3]O2: A combination of quasi-elastic neutron scattering and first-principles molecular dynamics study,” J. Mater. Chem. A 8, 25290–25297 (2020).10.1039/d0ta08400j
[64]	J. Li, Y. Geng, Z. Xu, P. Zhang, G. Garbarino, M. Miao, Q. Hu, and X. Wang, “Mechanochemistry and the evolution of ionic bonds in dense silver iodide,” JACS Au 3, 402–408 (2023).10.1021/jacsau.2c00550
[65]	Y.-H. Yin and L. Zhang, “The structures and properties of (AgCl)n (n = 2–13),” Comput. Theor. Chem. 1097, 70–78 (2016).10.1016/j.comptc.2016.10.013
[66]	R. Paul, S. X. Hu, V. V. Karasiev, S. A. Bonev, and D. N. Polsin, “Thermal effects on the electronic properties of sodium electride under high pressures,” Phys. Rev. B 102, 094103 (2020).10.1103/physrevb.102.094103
[67]	D. N. Polsin, A. Lazicki, X. Gong, S. J. Burns, F. Coppari, L. E. Hansen, B. J. Henderson, M. F. Huff, M. I. McMahon, M. Millot, R. Paul, R. F. Smith, J. H. Eggert, G. W. Collins, and J. R. Rygg, “Structural complexity in ramp-compressed sodium to 480 GPa,” Nat. Commun. 13, 2534 (2022).10.1038/s41467-022-29813-4
[68]	J. Bardeen, L. N. Cooper, and J. R. Schrieffer, “Theory of superconductivity,” Phys. Rev. 108, 1175 (1957).10.1103/physrev.108.1175
[69]	J. Kortus, I. I. Mazin, K. D. Belashchenko, V. P. Antropov, and L. L. Boyer, “Superconductivity of metallic boron in MgB2,” Phys. Rev. Lett. 86, 4656 (2001).10.1103/physrevlett.86.4656
[70]	J. Du, X. Li, and F. Peng, “Pressure-induced evolution of structures and promising superconductivity of ScB6,” Phys. Chem. Chem. Phys. 24, 10079–10084 (2022).10.1039/d2cp00711h
[71]	P. B. Allen and R. C. Dynes, “Transition temperature of strong-coupled superconductors reanalyzed,” Phys. Rev. B 12, 905 (1975).10.1103/physrevb.12.905
[72]	L. Wu, B. Wan, H. Liu, H. Gou, Y. Yao, Z. Li, J. Zhang, F. Gao, and H.-k. Mao, “Coexistence of superconductivity and superhardness in beryllium hexaboride driven by inherent multicenter bonding,” J. Phys. Chem. Lett. 7, 4898–4904 (2016).10.1021/acs.jpclett.6b02444
[73]	M. M. Davari Esfahani, Q. Zhu, H. Dong, A. R. Oganov, S. Wang, M. S. Rakitin, and X.-F. Zhou, “Novel magnesium borides and their superconductivity,” Phys. Chem. Chem. Phys. 19, 14486–14494 (2017).10.1039/c7cp00840f
[74]	Z. Cui, Q. Yang, X. Qu, X. Zhang, Y. Liu, and G. Yang, “A superconducting boron allotrope featuring anticlinal pentapyramids,” J. Mater. Chem. C 10, 672–679 (2022).10.1039/d1tc03908c