Abstract
We report on the prediction of the zincblende structure BP into a novel C2/m phase from 113 to 208 GPa which possesses zigzag phosphorus chain structure, followed by another P4_{2}/mnm structure above 208 GPa above using the particleswarm search method. Strong electronphonon coupling λ in compressed BP is found, in particular for C2/m phase with the zigzag phosphorus chain, which has the highest λ (0.56–0.61) value among them, leading to its high superconducting critical temperature T_{c} (9.4 K–11.5 K), which is comparable with the 4.5 K to 13 K value of black phosphorus phase I (orthorhombic, Cmca). This is the first system in the boron phosphides which shows superconductivity from the present theoretical calculations. Our results show that pressureinduced zigzag phosphorus chain in BP exhibit higher superconducting temperature T_{C}, opening a new route to search and design new superconductor materials with zigzag phosphorus chains.
Introduction
The crucial thermodynamic parameterhigh pressure has been emerging as a powerful tool to investigate physical and chemical behaviours of materials, especially to synthesize or design materials with excellent properties such as superhardness and superconductivity^{1,2,3,4,5,6}. Recently, B and P have been studied extensively in physical, chemical and material science fields due to their interesting structural properties when pressure is applied^{4,5,7,8,9}. Boron has always been recognized as a complex element, both structurally and electronically: its crystalline phases are numerous and inevitably complicated, which is related to its electron deficiency and thus the tendency to form multicenter bonds^{5,7}. Phosphorus, on the other hand, has six known phases at room temperature under high pressure^{10,11,12,13,14,15}. Black phosphorus phase I (orthorhombic, Cmca) is known to be most stable under ambient temperature and pressure^{15}. The experiment at low temperature and high pressure showed that the superconducting temperature of phase I increased from 4.5 K to 13 K under pressure^{14}. These peculiar physical properties of compressed B and P solids have motivated our attention on highpressure study of BP. The binary semiconductor boron phosphide (BP) is the zincblende crystal structure (space group F43m) with lattice parameter a = 4.537 Å^{16}, which has extraordinary properties, such as high hardness, high temperature stability, resistance to chemical corrosion, high thermoelectric powers for direct energy conversion and is regarded as an important candidate for electronic, optical and other engineering applications^{17,18,19,20,21}. In order to understand in detail the pressureinduced structural behaviour, including mainly the phase transitions of BP, further highpressure studies are essential.
Here, on the basis of comprehensive density functional theory (DFT) computations, we report the design of two new high pressure structures of BP. We performed variablecell structure prediction simulations using CALYPSO^{22,23} approach for BP at 0, 50, 100, 150, 200, 250 and 300 GPa, respectively. For comparison, the structures reported in boron nitride (P3m1, P6_{3}mc, P6_{3}/mmc) experimentally and theoretically, are also considered in our calculations. Our calculations demonstrate that, F43m is the most stable phase at ambient conditions, two new high pressure phases C2/m and P4_{2}/mnm can be predicted during compression up to 300 GPa. We further elucidate the energetic, mechanical, electronic and superconducting properties of the obtained novel phases, confirming that F43m is semiconductor and discovering two highpressure superconducting phases C2/m and P4_{2}/mnm.
Results
The analysis of the predicted structures gives us a list of candidate structures with space groups F43m, C2/m, P4_{2}/mnm, P6_{3}mc, Cmmm, Immm, P63/mmcI, P63/mmcII and the previously reported high pressure rock salt structure Fm3m^{20} are depicted in Figure S1 (Supporting Information). The relative enthalpies per chemical formula unit vs. pressure curves of selected structures are plotted in Figure 1(a). Considering that F43m and P6_{3}mc structures hold very close enthalpy, the enthalpy difference vs. pressure curves for the two phases are specially inserted in Figure 1(a) and it indicates that F43m has lower enthalpy, which is consistent with the experimental results. In order to investigate the phase transition pressures clearly, the enthalpies vs. pressure curves for F43m, Immm, P4_{2}/mnm, C2/m, and P3m1 are given in Figure 1(b). From Figure 1, one can see that, for compressed BP, the zincblende crystal structure F43m is the most stable structure below 113 GPa, a C2/m phase takes over the pressure range from 113 to 208 GPa, followed by another P4_{2}/mnm structure above 208 GPa. The pressure evolution of the unit cell volume of BP in the structures F43m, C2/m and P4_{2}/mnm is inserted in Figure 1(b). The experimental equation of state data^{24} for singlecrystal BP with F43m structure up to 55 GPa were listed for comparison. It can be seen that our calculated data are in good agreement with the experimental results. The zincblende crystal structure F43m is stable on compression to 113 GPa and then complete change to C2/m is observed. Comparisons with the F43m cell at 113 GPa shows a 14.5% reduction in volume. Upon further compression into the region of P4_{2}/mnm above 208 GPa, the volume difference peaks at only 1.2%.
The optimized structural parameters of zincblende crystal structure F43m are listed in Table S1. For this phase, the equilibrium lattice constants are 4.547 Å and 4.492 Å, for PBE and LDA calculation, respectively. The present results are in good agreement with the previous results^{21,25,26,27}. In this structure, four boron atoms lie in the Wyckoff 4a site and four phosphorus atoms occupy the 4c site, in which threedimensional (3D) boron and phosphorus network in this structure is formed, as shown in Figure S1. The optimized structural parameters of another two phases C2/m and P4_{2}/mnm at high pressure are presented in Table 1. For monoclinic C2/m phase, the equilibrium lattice constants at 120 GPa are a = 4.275 Å, b = 3.681 Å, c = 8.357 Å and β = 122.627 degree. The structure of C2/m is shown in Figure 2(a) and Figure 2(b), it can be seen that the 1Dzigzag phosphorus chain is formed, which is connected by boron atoms. For hexagonal P4_{2}/mnm phase (Figure 2(c)), the equilibrium lattice constants at 210 GPa are a = 3.631 Å, c = 3.640 Å. The BP, BB and PP bonds are formed in this structure, but PP bonds are not continuous (Figure 2(d)).
The calculated elastic constants for three BP phases with low enthalpy are presented in Table 2. From Table 2, the elastic constants reveal that all BP phases satisfy the mechanical stable criterion at the corresponding pressures. Furthermore, the hexagonal phase P4_{2}/mnm can remain stable at ambient pressure, but monoclinic C2/m does not match the mechanical stable criterion at ambient pressure, which only keeps stable at the high pressure range. Also, the calculated negative formation enthalpies of C2/m and P4_{2}/mnm phases at the pressure ranges indicate the stability against decomposition of BP into the elements boron and phosphorus^{7}. Phonon calculations show that BP phases (F43m, C2/m and P4_{2}/mnm) are dynamically stable at their thermodynamically stable pressure regions. Phonon dispersions and partial phonon density of states (PPHDOS) of BP phases at their stable pressure ranges are shown in Figure 3. The maximum optical branch frequencies are 803.5 cm^{−1} for F43m phase at atmospheric pressure, 983.7 cm^{−1} for C2/m phase at 120 GPa and 1175.2 cm^{−1} for P4_{2}/mnm phase at 210 GPa. One can see that the maximum optical branch frequencies increase with increasing pressure due to an obvious structural difference. From PPHDOS, the lower frequency region is associated with phosphorus atoms, whereas boron atom contributes to the highfrequency region for highpressure phases (C2/m and P4_{2}/mnm) at their corresponding pressure regions. But in the F43m phase, the boron atom dominates the highfrequency region, whereas phosphorus atom contributes almost equally to the high and low frequency region.
To investigate the possibility of pressure induced metallization and superconducting transition, band structures for F43m, C2/m and P4_{2}/mnm phases have been calculated to examine the electronic properties of these polymorphs of BP at their pressure ranges as shown in Figure 3. Electronic structure calculations indicate that F43m phase is a semiconductor, whereas C2/m and P4_{2}/mnm phases are metallic. From projected density of states (PDOS) plotted in Figure 3, it can be observed that all phases of BP have consistent electronic distributions. B2p and P3p electrons dominate in the wide energy range and form the strong covalent bonds as suggested by the matching B2p and P3p curve shapes. The contour plots of charge density on the chosen planes are also shown in Figure 4. The strong covalent BP bonding within in the 3D BP network is evidenced (Figures 4(a), 4(b) and 4(c)). Moreover, according to Mulliken population analysis, PP bonding does not exist in F43m phase, but it exists in C2/m and P4_{2}/mnm phases. Interestingly, PP zigzag chains in phase C2/m transfer to discontinuous bonding in phase P4_{2}/mnm. This conclusion is further substantiated by the electron localization function (ELF) shown in Figures 4(d), 4(e) and 4(f), where the calculated ELF patterns have isosurface values of 0.8, 0.65 and 0.7 for F43m, C2/m and P4_{2}/mnm, respectively.
The highpressure C2/m phase of BP exhibits interesting features in its electronic band structure. As shown in Figure 3(e), the electronic bands of the C2/m phase crossing the Fermi level along the Γ VL and AΓZV are quite flat and this section of band within a narrow energy window centered at the Fermi level gives rise to large electronic density of states near the Fermi energy. The corresponding confined conduction electrons near the band gap possess large effective mass with their group velocities approaching zero. In contrast, the bands along the LMA direction steeply cross the Fermi level, providing itinerant electrons with high conduction electron velocity. Such flat bands with highly mobile and localized electrons have been shown to enhance superconductivity^{28,29,30}. Similar electronic structures have previously been found in niobium that has the highest transition temperature T_{C} of 9.3 K^{31} in all element superconductors at ambient pressure, 9.8 K in CaC_{2}^{28} and 220–235 K in CaH_{6} at high pressure of 150 GPa^{32}. This motivates us to further investigate the superconductivity of BP at high pressures. The calculated spectral function α^{2}F(ω) of BP phases C2/m and P4_{2}/mnm at 120 GPa and 210 GPa were plotted in Figures 3(b) and 3(c). At 120 GPa (Figure 3(b)), the coupling parameter λ is 0.61 with the average phonon frequency ω_{ln} of 593 K. Using the strong coupling AllenDynes equation, an extension of the McMillan theory, with a nominal Coulomb pseudopotential parameter (μ*) of 0.12 the estimated superconducting critical temperature T_{C} is 11.5 K. With increasing pressure, the calculated T_{C} become slightly lower as 11.1 K at 150 GPa and 9.4 K at 200 GPa due to slightly smaller λ of 0.59 at 150 GPa and 0.56 at 200 GPa, respectively. Here the T_{C} of two highpressure phases for BP and T_{C}'s dependence on pressure is shown in Figure 5. Calculated coupling parameter λ values and logarithmic phonon momentum ω_{log} vs. pressure curves are also presented in Figure 5. It can be seen that logarithmic phonon momentum ω_{log} increases with pressure and coupling parameter λ decreases with pressure. Among these two high pressure phases, C2/m phase has the strongest electronphonon coupling and so has the highest T_{C}. Apparently, the fairly high T_{C} is due to the large electron phonon coupling (λ). The origin can be traced from comparing the calculated Eliashberg spectral function (α^{2}F(ω)/ω) with the projected phonon DOS. As shown in Figure 3(b), nearly 80% of the electron phonon coupling is contributed by the lowfrequency vibrations in the frequency region from 100 to 600 cm^{−1}. The lowfrequency vibrations in the frequency region from 100 to 600 cm^{−1}, which are mostly attributed to the P atom. At wide range of pressure, C2/m phase has comparative superconducting critical temperatures (from 11.5 K at 120 GPa to 9.3 K at 200 GPa) with 11.5 K value of CaC_{6}^{33,34}. However, T_{C} of BP is close to zero above 210 GPa due to the smaller electronphonon coupling parameter (λ < 0.4). We thus further analyze the coupling parameter in each qpoint (Figures 3(b) and 3(c)). It is clearly seen that the coupling parameters in ΓZ and XΓ are very strong. This superconducting feature is typical anisotropy, leading a low superconductivity value.
To summarize, using the PSO technique on crystal structure prediction, we designed two new highpressure phases of BP, C2/m and P4_{2}/mnm, which are stable in the pressure ranges of 113–208 GPa and 208–300 GPa, respectively. Elastic constants and phonon calculations have shown their mechanical and dynamical stability at the dominating pressure ranges. Our calculations reveal that the phosphorus atomic arrangement form from single atoms to 1D zigzag chains to discontinuous bonding. The high superconducting transition temperature of the C2/m phase benefits from the simultaneous presence of the steep bands (highly mobile electrons) and extremely flat bands (highly confined electrons), which is known to favor the electron paring and superconducting behavior.
Computational Methods
The search of highpressure structures was performed with variablecell PSO^{35} structure prediction simulations using CALYPSO approach^{22,23} in combined with Vienna ab initio simulation package (VASP)^{36}. CALYPSO was designed to predict stable or metastable crystal structures requiring only chemical compositions of a given compound at specified external conditions. All structures were locally optimized using the DFT method. The 60% structures of each generation with lower enthalpies were selected to generate the structures for the next generation by PSO operation and the other structures in new generation were randomly generated to increase the structural diversity. The underlying ab initio calculations were performed using density functional theory within the generalized gradient approximation (GGA)^{37}, as implemented in the Vienna ab initio simulation package (VASP). The total energy calculations were carried out with the VASP code. The allelectron projector augmented wave (PAW) method^{38} was employed with a planewave cutoff energy of 600 eV for all phases. The kpoint samplings in the Brillouin zone were performed using the MonkhorstPack scheme^{39}. The total energy convergence tests showed that convergence to within 1 meV/atom was achieved with the above calculation parameters. Single crystal elastic constants were calculated via a strainstress approach. i.e., by applying a small strain to the equilibrium lattice of the unit cell and fitting the dependence of the resulting stress on the strain. The bulk modulus, shear modulus, Young's modulus and Poisson's ratio were determined by using the VoigtReussHill approximation^{40}. The latticedynamical and superconducting properties are calculated using the density functional perturbation theory (DFPT)^{41} as implemented in the Quantum Espresso package^{42} using with the TroullierMartins pseudopotentials with cutoff energies of 50 and 500 Ry for the wave functions and the charge density, respectively. Fine kpoints mesh of MP was used and the estimated energy error in selfconsistency was less than 10^{−4} a.u. The electron–phonon coupling was convergent with a finer grid and a Gaussian smearing of 0.02 Ry. In order to check the results, the phonon calculations were also carried out by using a supercell approach as implemented in the PHONOPY code^{43}.
References
McMillan, P. F. Chemistry at high pressure. Chem. Soc. Rev. 35, 855–857 (2006).
Haines, J., Léger, J. & Bocquillon, G. Synthesis and design of superhard materials. Ann. Rev. Mater. Res. 31, 1–23 (2001).
Qin, J. et al. Is Rhenium Diboride a Superhard Material? Adv. Mater. 20, 4780–4783 (2008).
Qin, J. et al. Polycrystalline γboron: As hard as polycrystalline cubic boron nitride. Scripta Mater. 67, 257–260 (2012).
Qin, J. et al. Phase relations in boron at pressures up to 18 GPa and temperatures up to 2200°C. Phys. Rev. B 85, 014107 (2012).
Raza, Z., Errea, I., Oganov, A. R. & Saitta, A. M. Novel superconducting skutteruditetype phosphorus nitride at high pressure from firstprinciples calculations. Sci. Rep. 4, 5889; 10.1038/srep05889 (2014).
Oganov, A. R. et al. Ionic highpressure form of elemental boron. Nature 457, 863–867 (2009).
Ma, Y., Prewitt, C. T., Zou, G., Mao, H.k. & Hemley, R. J. Highpressure hightemperature xray diffraction of βboron to 30 GPa. Phys. Rev. B 67, 174116 (2003).
Ma, Y., Tse, J. S., Klug, D. D. & Ahuja, R. Electronphonon coupling of αGa boron. Phys. Rev. B 70, 214107 (2004).
Kikegawa, T. & Iwasaki, H. An Xray diffraction study of lattice compression and phase transition of crystalline phosphorus. Acta Crystallogr. B 39, 158–164 (1983).
Akahama, Y., Kobayashi, M. & Kawamura, H. Simplecubic–simplehexagonal transition in phosphorus under pressure. Phys. Rev. B 59, 8520–8525 (1999).
Akahama, Y., Kawamura, H., Carlson, S., Le Bihan, T. & Häusermann, D. Structural stability and equation of state of simplehexagonal phosphorus to 280 GPa: Phase transition at 262 GPa. Phys. Rev. B 61, 3139–3142 (2000).
Akahama, Y., Endo, S. & Narita, S. Electrical properties of singlecrystal black phosphorus under pressure. Physica B + C 139–140, 397–400 (1986).
Kawamura, H., Shirotani, I. & Tachikawa, K. Anomalous superconductivity in black phosphorus under high pressures. Solid State Commun. 49, 879–881 (1984).
Brown, A. & Rundqvist, S. Refinement of the crystal structure of black phosphorus. Acta Crystallographica 19, 684–685 (1965).
Peret, J. L. Preparation and Properties of the Boron Phosphides. J. Am. Ceram. Soc. 47, 44–46 (1964).
Archer, R. J., Koyama, R. Y., Loebner, E. E. & Lucas, R. C. Optical Absorption, Electroluminescence and the Band Gap of BP. Phys. Rev. Lett. 12, 538–540 (1964).
Motojima, S., Ohtsuka, Y., Kawajiri, S., Takahashi, Y. & Sugiyama, K. Boron phosphide coatings on molybdenum by chemical vapour deposition and their composition and microhardness. J. Mater. Sci. 14, 496–498 (1979).
Schroten, E., Goossens, A. & Schoonman, J. Photo and electroreflectance of cubic boron phosphide. J. Appl. Phys. 83, 1660–1663 (1998).
Wentzcovitch, R. M., Cohen, M. L. & Lam, P. K. Theoretical study of BN, BP and BAs at high pressures. Phys. Rev. B 36, 6058–6068 (1987).
Wentzcovitch, R. M., Chang, K. J. & Cohen, M. L. Electronic and structural properties of BN and BP. Phys. Rev. B 34, 1071–1079 (1986).
Wang, Y., Lv, J., Zhu, L. & Ma, Y. Crystal structure prediction via particleswarm optimization. Phys. Rev. B 82, 094116–094123 (2010).
Wang, Y., Lv, J., Zhu, L. & Ma, Y. CALYPSO: A method for crystal structure prediction. Comput. Phys. Commun. 183, 2063–2070 (2012).
Godec, Y. et al. Equation of state of singlecrystal cubic boron phosphide. J. Superhard Mat. 36, 61–64 (2014).
Meradji, H. et al. Firstprinciples elastic constants and electronic structure of BP, BAs and BSb. Phys. Status. Solidi. B 241, 2881–2885 (2004).
Lambrecht, W. R. L. & Segall, B. Electronic structure and bonding at SiC/AlN and SiC/BP interfaces. Phys. Rev. B 43, 7070–7085 (1991).
Zaoui, A. & Hassan, F. E. H. Full potential linearized augmented plane wave calculations of structural and electronic properties of BN, BP, BAs and BSb. J. Phys.: Condens. Matter 13, 253–262 (2001).
Li, Y.L. et al. Pressureinduced superconductivity in CaC2 . Proc. Natl. Acad. Sci. USA 110, 9289–9294 (2013).
Ranninger, J., Robin, J. M. & Eschrig, M. Superfluid Precursor Effects in a Model of Hybridized Bosons and Fermions. Phys. Rev. Lett. 74, 4027–4030 (1995).
Simon, A. Superconductivity and chemistry. Angew. Chem. Int. Ed. 36, 1788–1806 (1997).
Broom, R. F., Raider, S. I., Oosenbrug, A., Drake, R. E. & Walter, W. Niobium oxidebarrier tunnel junction. Ieee. T. Electron Dev. 27, 1998–2008 (1980).
Wang, H., Tse, J. S., Tanaka, K., Iitaka, T. & Ma, Y. Superconductive sodalitelike clathrate calcium hydride at high pressures. Proc. Natl. Acad. Sci. USA 109, 6463–6466 (2012).
Emery, N. et al. Superconductivity of Bulk CaC6 . Phys. Rev. Lett. 95, 087003 (2005).
Weller, T. E., Ellerby, M., Saxena, S. S., Smith, R. P. & Skipper, N. T. Superconductivity in the intercalated graphite compounds C6Yb and C6Ca. Nat. Phy. 1, 39–41 (2005).
Call, S. T., Zubarev, D. Y. & Boldyrev, A. I. Global minimum structure searches via particle swarm optimization. J. Comput. Chem. 28, 1177–1186 (2007).
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio totalenergy calculations using a planewave basis set. Phys. Rev. B 54, 11169–11186 (1996).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmentedwave method. Phys. Rev. B 59, 1758–1775 (1999).
Monkhorst, H. J. & Pack, J. D. Special points for Brillouinzone integrations. Phys. Rev. B 13, 5188–5192 (1976).
Hill, R. The Elastic Behaviour of a Crystalline Aggregate. Proc. Phys. Soc. A 65, 349–355 (1952).
Baroni, S., de Gironcoli, S. & Dal Corso, A., Giannozzi P. Phonons and related crystal properties from densityfunctional perturbation theory. Rev. Mod. Phys. 73, 515–562 (2001).
Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and opensource software project for quantum simulations of materials. J. Phys.: Condens. Matter 21, 395502–395530 (2009).
Togo, A., Oba, F. & Tanaka, I. Firstprinciples calculations of the ferroelastic transition between rutiletype and CaCl2type SiO2 at high pressures. Phys. Rev. B 78, 134106–134114 (2008).
Acknowledgements
The authors acknowledge funding from NBRPC (grant 2013CB733000), NSFC (grants 51171160/51171163), J.Q. thanks the support from Ratchadaphisek sompoch Endowment Fund (2013), Chulalongkorn University (CU56805FC), Ratchadapisek Sompoch Endowment Fund, Chulalongkorn University, granted to the Surface Coatings Technology for Metals and Materials Research Unit (GRU 5700562001). This research was supported by Swedish Foundation for Strategic Research, Sweden and the Leading Foreign Research Institute Recruitment Program through theNational Research Foundation of Korea funded by Ministry of Education, Science and Technology Grant 2014039452.
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X.Z., J.Q., R.L. and R.A. designed and coordinated the research. X.Z., J.Q., H.L. and S.Z. did the calculations. X.Z., J.Q., H.L., S.Z., M.M., R.L., W.L. and R.A. analyzed all data. X.Z., J.Q., H.L., R.L. and R.A. wrote the manuscript.
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Zhang, X., Qin, J., Liu, H. et al. Pressureinduced zigzag phosphorus chain and superconductivity in boron monophosphide. Sci Rep 5, 8761 (2015). https://doi.org/10.1038/srep08761
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DOI: https://doi.org/10.1038/srep08761
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