The stability of B₆ octahedron in BaB₆ under high pressure

Abstract

We have performed in situ synchrotron X-ray diffraction and first-principles calculations to explore the compression behavior of barium hexaboride (BaB₆) under high pressure. No phase transitions in our experiment are observed up to 49.3 GPa at ambient temperature. It is found that the ambient cage structure (Pm3̄m) is still stable with a basic covalent network during the experimental pressure run. The results of our theoretical calculations show that the ambient structure might transform into three dynamically stable structures (Cmmm, Cmcm and I4/mmm) at 78 GPa, 97 GPa and 105 GPa respectively. The energy band calculations indicate that the sample is still a semiconductor with a narrow gap at 50 GPa.

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Introduction

The hexaborides MB₆ (M = Y, La, Ca…) have a typical cage structure (Pm3̄m). Owing to their non-oxide structure, they have some excellent advantages such as high melting points, high chemical stability, high hardness, low density, and low coefficients of thermal expansion.^1–4 In recent decades they have also been shown to have some attractive properties in their various physical phenomena. For example, rare-earth hexaborides exhibit Kondo behavior and valence-fluctuations in CeB₆;⁵ LaB₆ has low volatility and low work functions through enhancing thermionic emission at high temperature;⁶ a high superconducting critical temperature (T_c) of 7 K is found in YB₆ (ref. 7) and narrow-gap semiconducting behavior exists in YbB₆.⁸ Moreover, alkaline-earth metal hexaborides also have fascinating magnetic features. There is a coexistent phenomenon of weak ferromagnetism and antiferroelectricity in boron-deficient MgB₆.⁹ Possibly because of a low-density free-electron gas, CaB₆ exhibits weak ferromagnetism at high temperature¹⁰ and subsequent experiments performed on undoped systems of CaB₆, SrB₆ and La-doped BaB₆ indicate that magnetism might be an intrinsic property of alkaline-earth metal hexaborides,^10–12 whose mechanism might involve excitonic insulation through the condensation of bound electron–hole pairs (excitons). Hexaborides of alkaline-earth metals are simple polar semiconductors or semimetals with a fraction of an eV band gap because the B₆ molecule acquires two electrons from the alkaline-earth metal to form a large divalent B₆ anion and a stable metallic cation. A large number of theoretical calculations and experiments have been extensively undertaken and an accredited conclusion has been established that the electronic structure of CaB₆ is either a semimetal or semiconductor.^{10,11,13–18} Under ambient conditions, MB₆ (M = Ca, Sr, Ba) has a highly symmetrical CsCl-type structure with Pm3̄m space group in which the B₆ molecule has an octahedral structure. Metal atoms and B₆ molecules replace the positions of the Cs and Cl atoms respectively. Recently, Kolmogorov et al. found a new structure (I4/mmm) of CaB₆ under high pressure.¹⁹

Nevertheless, barium hexaboride, an important alkaline-earth metal hexaboride, has only been researched in terms of its preparation and properties under ambient conditions.²⁰ Over the last several years, considerable experimental and theoretical investigations on the electronic band structures and ferromagnetism of alkaline-earth hexaborides have been performed.^21–26 From the results of DC magnetization measurements on single crystalline BaB₆, the saturation magnetization at low temperatures is 8 times, in line with the other weak ferromagnetism of the hexaboride series.²⁷

Up to now, research on barium hexaboride under extreme conditions has not been reported. In this article, in order to explore the properties of BaB₆ under high pressure, we have carried out in situ synchrotron angle dispersive X-ray diffraction (ADXRD) measurements and first-principles calculations.

Experimental and theoretical methods

BaB₆ powder with a purity of 99.5% was purchased from Alfa Aesar. The sample was ground finely before being loaded into the sample chamber. A symmetric diamond anvil cell (DAC) with 300 μm flat culets was used to generate pressure. A tungsten gasket had a 100 μm diameter hole drilled in the center as a chamber, which had been precompressed to a thickness of 70 μm. The pressure inside the chamber was determined using the standard ruby fluorescence method.²⁸ Furthermore, a mixture of methanol–ethanol–water (16 : 3 : 1, MEW) was selected as the pressure transmitting medium (PTM).²⁹ In situ ADXRD measurements were carried out at the 4W2 High-Pressure Station of the Beijing Synchrotron Radiation Facility (BSRF). The beam size was about 32 (H) × 12 (V) μm² and the incident wavelength was 0.6199 Å. A MAR3450 image plate detector was used to collect the diffraction patterns and the two-dimensional XRD images were radially integrated using FIT2D software,³⁰ yielding intensity versus diffraction angle 2θ patterns. Prior to measurement, a CeO₂ standard was used to calibrate the geometric parameters. The average acquisition time for each diffraction pattern to obtain sufficient intensity was 300 s. The fitted XRD patterns were completed by means of the Reflex module in the Material Studio Program.³¹

First-principles calculations were performed with the pseudopotential plane-wave method based on density functional theory (DFT) implemented in CASTEP³² and VASP code.³³ The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional³⁴ was used in the calculation of optimizations. The hybrid functional of Heyd, Scuseria and Ernzerhof (HSE06)^35,36 was also used to verify the results of band structures. A plane-wave cutoff energy of 540 eV was employed for norm-conserving pseudopotentials and Brillouin zone sampling grids of spacing 2π × 0.03 Å⁻¹. The project-augmented wave (PAW)³⁷ method was adopted with valence electrons of 2s²2p¹ and 5s²5p⁶6s² for B and Ba atoms, respectively.

Results and discussion

Like most of the other hexaborides, BaB₆ has a simple cubic crystal structure with the Pm3̄m space group under ambient conditions. In this structure, six boron atoms form an octahedron connected by covalent bonds and each octahedron connects with the six closest octahedrons by covalent bonds that form a three-dimensional network. Due to this strong covalent network, the framework of the Pm3̄m structure is very stable. A schematic representation of the BaB₆ crystal structure is shown in Fig. 1(a) and the electron localization function (ELF) of BaB₆ is plotted in Fig. 1(b) and (c). The B₆ octahedron pillages two electrons from the Ba atom, and forms a stable divalent B₆ anion. The Ba cation inserts into the interstices of eight B₆ octahedrons, which forms a typical cage structure. There are only two parameters to restrain the BaB₆ crystal structure, one is the lattice constant a, and another is the fractional coordinates (Wyckoff site) of the boron atom 6f (0.5, 0.5, z). The synchrotron XRD patterns have been obtained from 0.8 GPa to 49.3 GPa using MEW as the PTM. The refinement of BaB₆ in Fig. 2(a) has been carried out on an XRD pattern obtained at 0.8 GPa. The refined lattice constant is a = 4.2614 Å and the Wyckoff site of the B atom is (0.5, 0.5, 0.2053) with a unit cell volume V = 77.38 ų. Selected XRD diffraction patterns from this experimental run are illustrated in Fig. 3(a). It shows that there was no appearance of new peaks when the sample was compressed smoothly up to the highest pressure. In the process of compression, all Bragg diffraction peaks gradually broadened compared with the initial sharp peaks and shifted toward higher 2θ angles, which indicates that the interplanar distance of the crystal planes decreased. The original XRD peaks existed up to the highest pressure, 49.3 GPa, without the appearance of new peaks, indicating there was no occurrence of a phase transition. It confirms the stability of the Pm3̄m structure up to 49.3 GPa at least. Besides that, the intensities of the diffraction peaks were affected by the preferred crystallite orientation. Compared with the crystallite size, the X-ray beam size was relatively bigger, which could partly reduce the mismatch in intensity caused by the statistics of measurement.

Fig. 1 (a) The Pm3̄m crystal structure of BaB₆ under ambient conditions. A cubic cage formed by eight B₆ octahedrons and a central Ba cation. Octahedral surfaces are shown in gray. ((b) and (c)) Electron localization function (ELF) maps of different plans.

Fig. 2 (a) The Rietveld full-profile refinement of the synchrotron XRD pattern at 0.8 GPa. (b) Micrograph of the BaB₆ sample in DAC at 0.8 GPa just after loading pressure with a PTM of methanol–ethanol–water.

Fig. 3 (a) Typical XRD patterns at selected pressures of BaB₆ as a function of pressure on compression up to 49.3 GPa at room temperature. The peaks marked with diamond symbols (◆) represent the Bragg peaks from the tungsten gasket. The wavelength of the incident X-ray beam was 0.6199 Å. (b) Evolution of the lattice constant a and length of the B–B_intra bond and B–B_inter bond with respect to pressure. The symbols represent experimental results, and the lines represent fitted results.

In order to analyze the evolution of the lattice constants and unit cell volume with pressure, all XRD patterns were refined using the Rietveld full profile structure. Fig. 3(b) shows the lattice constant a, B–B_intra bond and B–B_inter bond length as a function of pressure. The data were linearly fitted without any jumps: k_a = 0.0066 Å GPa⁻¹, k_intra = 0.00274 Å GPa⁻¹ and k_inter = 0.00270 Å GPa⁻¹. The lattice parameter monotonically decreases with increasing pressure indicating the preservation of the basic covalent network. We have presented the volume reduction as a function of pressure in Fig. 4. The experimental pressure–volume data were fitted using the third-order Birch–Murnaghan (BM) equation of state (EOS)³⁸

where V₀ is the volume per formula unit at ambient pressure, V is the volume per formula unit at pressure P given in GPa, B₀ is the isothermal bulk modulus, and B′₀ is the first pressure derivative of the bulk modulus. As a result of enough experimental data, we set up B′₀ as 4. Then, we obtained a bulk modulus of 94 ± 1 GPa. The volume V₀ was fitted as 77.8 ± 0.2 ų. As is shown in Fig. 4(b), it is clearly seen that the volume of the sample at the highest pressure is reduced by 20% compared with the original pressure point.

Fig. 4 (a) Pressure dependence of the unit cell volume of BaB₆. The red line shows fitted results. Inset (b) represents the volume reduction upon compression. The blue line shows the trend.

The present XRD results have confirmed that the structure Pm3̄m is stable up to 49.3 GPa. Nevertheless, the recent theoretical and experimental results on another alkaline-earth metal hexaboride CaB₆ have reported phase transitions of CaB₆ under high pressure. Most strikingly, A. N. Kolmogorov et al. have proposed three dynamically stable structures through a systematic analysis of multiple imaginary-frequency phonon modes when the ambient structure becomes dynamically unstable at around 25 GPa. The novel structure of CaB₆ was successfully quenched down to ambient pressure, which revealed a transition from the ambient structure Pm3̄m to a tetragonal I4/mmm structure after laser-heating in DAC at 31 GPa.¹⁹ M. Li et al. also found a pressure-induced phase transition at ambient temperature by means of resistance measurements and synchrotron XRD.³⁹ Both Ca and Ba are alkaline earth metal elements and they have similar valence electrons, 3s²3p⁶4s² and 5s²5p⁶6s² respectively. So we suppose that CaB₆ and BaB₆ have the same or similar properties under pressure. We obtained three candidate crystal structures (I4/mmm, Cmmm and Cmcm) by replacing the Ca atom with a Ba atom and the cell parameters which are given in ref. 19. Crystal structure predictions were also performed using CALYPSO code⁴⁰ with two BaB₆ formula units at 100 GPa. The most stable structure is Cmmm which is the same structure as the replaced one. Then, we calculated the enthalpy of the four structures mentioned above (Pm3̄m, I4/mmm, Cmmm and Cmcm) using the optimization method. Taking the enthalpy of the Pm3̄m structure as a reference energy, we plotted the relative enthalpy per formula unit of the other three structures as a function of pressure in Fig. 5. The results illustrate that the Pm3̄m structure might not transform into Cmmm or Cmcm until pressures of up to 78 GPa and 97 GPa respectively. The tetragonal structure (I4/mmm) discovered in CaB₆ at 31 GPa would appear in BaB₆ when the pressure reaches 105 GPa. The calculation results show that Cmmm has a lower enthalpy value than the others above 78 GPa, so the Cmmm structure is the most likely of the candidate structures. But when it is only compressed, the ambient structure might not transform into a new structure under the same conditions as CaB₆ does, it must be supplied with some alternative pathway such as laser-heating in DAC to break the energy barrier.

Fig. 5 The relative enthalpy per formula unit of four structures as a function of pressure for BaB₆. The enthalpy of the Pm3̄m structure is taken as a reference energy compared with the others. The inset figure represents the Cmmm structure, the most likely of the candidate structures above 78 GPa.

It has been confirmed that CaB₆ is a semiconductor with a narrow gap by means of transport measurements,¹⁴ angle-resolved photoemission spectroscopy (ARPES) and momentum-resolved inelastic X-ray scattering.¹⁶ Considering that the calculations with GGA-PBE would underestimate the band gap, we calculated the electronic band structures with HSE06. Fig. 6 plots the band structures of BaB₆ around the Fermi level at 0 GPa and 50 GPa, which illustrates that BaB₆ is a semiconductor with a narrow band gap of 0.22 eV under ambient conditions. The band gap is sensitive to the lattice constant a and Wyckoff position of the boron atom (0, 0, z),^4,41 and our experimental results show that the Wyckoff position (z = 0.20534) would change scarcely. It is obvious that the lattice constant decreases through compression in Fig. 3(b) and the band gap also changes, but BaB₆ is still a semiconductor with a band gap of 0.34 eV at 50 GPa.

Fig. 6 Electronic band structures of the Pm3̄m structure (a) at 0 GPa and (b) at 50 GPa.

Conclusion

In this work, we have successfully investigated the structural stability and compression behavior of BaB₆ by means of in situ high pressure synchrotron X-ray diffraction and first-principles calculations. Our experimental results reveal that it is very difficult to break the covalent network under only high pressure conditions. Under the experimental pressures used here, no phase transitions occurred and the lattice constant a decreased linearly with pressure. Our theoretical calculations propose that BaB₆ is still a semiconductor at 50 GPa. Three candidate dynamic stable structures (Cmmm, Cmcm and I4/mmm) might replace the typical cage structure at 78 GPa, 97 GPa, and 105 GPa, respectively. Attempting to accomplish a phase transition, it must be supplied with an alternative pathway to break the energy barrier.

Acknowledgements

The authors are grateful to Xiaodong Li and Yanchun Li for their help during the experimental research. In situ angle dispersive X-ray diffraction (ADXRD) in this work was performed at the 4W2 HP-Station, Beijing Synchrotron Radiation Facility (BSRF), whom we thank for assistance with measurements. This work was supported by the National Basic Research Program of China (No. 2011CB808200), the National Natural Science Foundation of China (No. 51572108, 51032001, 11504127), the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT1132), the National Found for Fostering Talents of basic Science (No. J1103202), and the China Postdoctoral Science Foundation (2015M570265).

References

1. P. I. Loboda, H. P. Kysla, S. M. Dub and O. P. Karasevs’ka, Mater. Sci., 2009, 45, 108–113.
2. M. Takeda, M. Terui, N. Takahashi and N. Ueda, J. Solid State Chem., 2006, 179, 2823–2826.
3. S. Kimura, T. Nanba, M. Tomikawa, S. Kunii and T. Kasuya, Phys. Rev. B: Condens. Matter Mater. Phys., 1992, 46, 12196–12204.
4. B. Lee and L. W. Wang, Appl. Phys. Lett., 2005, 87, 262509.
5. W. Joss, J. M. van Ruitenbeek, G. W. Crabtree, J. L. Tholence, A. P. J. van Deursen and Z. Fisk, Phys. Rev. Lett., 1987, 59, 1609–1612.
6. X. H. Ji, Q. Y. Zhang, J. Q. Xu and Y. M. Zhao, Prog. Solid State Chem., 2011, 39, 51–69.
7. Y. Xu, L. J. Zhang, T. Cui, Y. Li, Y. Xie, W. Yu, Y. M. Ma and G. T. Zou, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 10.
8. J. M. Tarascon, J. Etourneau, P. Dordor, P. Hagenmuller, M. Kasaya and J. M. D. Coey, J. Appl. Phys., 1980, 51, 574.
9. I. Popov, N. Baadji and S. Sanvito, Phys. Rev. Lett., 2012, 108, 107205.
10. D. P. Young, D. Hall, M. E. Torelli, Z. Fisk, J. L. Sarrao, J. D. Thompson, H. R. Ott, S. B. Oseroff, R. G. Goodrich and R. Zysler, Nature, 1999, 397, 412–414.
11. P. Vonlanthen, E. Felder, L. Degiorgi, H. R. Ott, D. P. Young, A. D. Bianchi and Z. Fisk, Phys. Rev. B: Condens. Matter Mater. Phys., 2000, 62, 10076–10082.
12. J. X. Cao, Y. Zhu, Z. Q. Yang and R. Q. Wu, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79, 4.
13. Y. H. Han, C. X. Gao, Y. Z. Ma, H. W. Liu, Y. W. Pan, J. F. Luo, M. Li, C. Y. He, X. W. Huang and G. T. Zou, Appl. Phys. Lett., 2005, 86, 064104.
14. B. K. Cho, J. S. Rhyee, B. H. Oh, M. H. Jung, H. C. Kim, Y. K. Yoon, J. H. Kim and T. Ekino, Phys. Rev. B: Condens. Matter Mater. Phys., 2004, 69, 113202.
15. K. Taniguchi, T. Katsufuji, F. Sakai, H. Ueda, K. Kitazawa and H. Takagi, Phys. Rev. B: Condens. Matter Mater. Phys., 2002, 66, 064407.
16. J. D. Denlinger, J. A. Clack, J. W. Allen, G. H. Gweon, D. M. Poirier, C. G. Olson, J. L. Sarrao, A. D. Bianchi and Z. Fisk, Phys. Rev. Lett., 2002, 89, 157601.
17. H. J. Tromp, P. van Gelderen, P. J. Kelly, G. Brocks and P. A. Bobbert, Phys. Rev. Lett., 2001, 87, 016401.
18. T. Terashima, C. Terakura, Y. Umeda, N. Kimura, H. Aoki and S. Kunii, J. Phys. Soc. Jpn., 2000, 69, 2423–2426.
19. A. N. Kolmogorov, S. Shah, E. R. Margine, A. K. Kleppe and A. P. Jephcoat, Phys. Rev. Lett., 2012, 109, 075501.
20. G. H. Min, S. Q. Zheng, Z. D. Zou, H. S. Yu and H. D. Han, Mater. Lett., 2003, 57, 1330–1333.
21. S. Shang, T. Wang and Z.-K. Liu, CALPHAD: Comput. Coupling Phase Diagrams Thermochem., 2007, 31, 286–291.
22. K. M. Schmidt, A. B. Buettner, O. A. Graeve and V. R. Vasquez, J. Mater. Chem. C, 2015, 3, 8649–8658.
23. M. Gürsoy, M. Takeda and B. Albert, J. Solid State Chem., 2015, 221, 191–195.
24. S. L. Zhou, J. X. Zhang, L. H. Bao, X. G. Yu, Q. L. Hu and D. Q. Hu, J. Alloys Compd., 2014, 611, 130–134.
25. S. Massidda, R. Monnier and E. Stoll, Eur. Phys. J. B, 2000, 17, 645–649.
26. T. P. Jose, L. Sundar, L. J. Berchmans, A. Visuvasam and S. Angappan, J. Min. Metall., Sect. B, 2009, 45, 101–109.
27. S. Mushkolaj, J. L. Gavilano, D. Rau, H. R. Ott, A. Bianchi and Z. Fisk, Acta Phys. Pol., B, 2003, 34, 1537–1540.
28. H. K. Mao, P. M. Bell, J. W. Shaner and D. J. Steinberg, J. Appl. Phys., 1978, 49, 3276.
29. S. Klotz, J. C. Chervin, P. Munsch and G. Le Marchand, J. Phys. D: Appl. Phys., 2009, 42, 075413.
30. A. Hammersley, S. Svensson, M. Hanfland, A. Fitch and D. Hausermann, High Pressure Res., 1996, 14, 235–248.
31. R. Young, The Rietveld method, IUCr monographs on crystallography 5, Oxford Science Publication, 1993.
32. S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. I. Probert, K. Refson and M. C. Payne, Z. Kristallogr. - Cryst. Mater., 2005, 220, 567–570.
33. G. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
34. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
35. A. V. Krukau, O. A. Vydrov, A. F. Izmaylov and G. E. Scuseria, J. Chem. Phys., 2006, 125, 224106.
36. J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem. Phys., 2003, 118, 8207–8215.
37. G. Kresse and D. Joubert, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 1758–1775.
38. F. Birch, J. Appl. Phys., 1938, 9, 279–288.
39. M. Li, W. Yang, L. Li, H. Wang, S. Liang and C. Gao, Phys. B, 2011, 406, 59–62.
40. Y. C. Wang, J. Lv, L. Zhu and Y. M. Ma, Comput. Phys. Commun., 2012, 183, 2063–2070.
41. S. Shah and A. N. Kolmogorov, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 88, 014107.

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