Exploring the high pressure behavior of 2D and quasi-3D boron layers in MoB₂

Abstract

The high pressure behavior of α-molybdenum boride (α-MoB₂, P6/mmm) and β-molybdenum boride (β-MoB₂, R3̄m) was studied up to a pressure of 32.1 GPa and 35.5 GPa, respectively. The bulk modulus values for α-MoB₂ and β-MoB₂ were 317 GPa and 299 GPa respectively, which fitted the Birch-Murnaghan equation of state. That the compressibility of MoB₂ mainly depends on electron concentration but is less related to structure difference was reconfirmed in this study. An anomalous second-order transition was found in β-MoB₂ at 26.6 GPa, which resulted in the structure softening and changing the anisotropy of β-MoB₂. The anomalous transition found in β-MoB₂ under high pressure may be attributable to the limitation of the B₂–B₂–B₂ angle in puckered boron layers. These results will promote further understanding of the mechanical properties of transition metal borides (TMBs), and will be helpful in designing hard or superhard materials with TMBs.

---

Introduction

Recently, transition metal borides (TMBs) have aroused much interest in the search for new hard or superhard materials because of their excellent mechanical properties, including low compressibility and high hardness.^1–6 The high electron concentration of the transition metal induces low compressibility in TMBs, such as the high bulk modulus of osmium boride (OsB, 453 GPa) and tungsten boride (WB₂, 372 GPa)⁷ which are comparable with that of single crystalline diamond (443 GPa)⁸ and cubic boron nitride (c-BN, 381 GPa).⁹ The key to restricting the plastic deformation are the strong covalent B–B bonds. One approach suggested to increase the hardness is to form three-dimensional (3D) B–B covalent bonds which may cause super-rigidity in TMBs. Exploring the behaviour of 3D, quasi-3D or even a two-dimensional (2D) framework of boron in TMBs is essential to understand the mechanism of hardness. Recently, the high pressure behaviour of different boron frameworks in TMBs was reported to be of use in understanding the hardness mechanism in OsB,⁷ OsB₂,^7,10 and RuB₂.^7,11 Among these TMBs, the structures of α-molybdenum boride (α-MoB₂, P6/mmm) and β-molybdenum boride (β-MoB₂, R3̄m)¹² are very similar, except for the puckered boron layer in β-MoB₂. The puckered boron layer is a particular attribute of ReB₂,¹³ which has high hardness. Furthermore, the puckered boron layer in the structure increases the hardness of β-MoB₂ by about 7 GPa more than that of α-MoB₂, which has only graphite-like boron layers in its structure.¹² Based on the different hardnesses of the two structures of MoB₂, the high pressure behaviour of the two kinds of MoB₂ may be different. Exploring the high pressure behaviour of these structures is crucial to understand how the quasi-3D and 2D boron layers influence the hardness. Recently Liu et al.¹⁴ reported on the behaviour of β-MoB₂ up to 24.1 GPa, which yielded a bulk modulus of 314 (11) GPa; however, there has rarely been any research on the high pressure behaviour of α-MoB₂. Understanding the high pressure behaviour of α-MoB₂ and β-MoB₂ is essential to understanding further how the puckered boron layer strengthens the resistance to indentation with pressure. This is significant for the design of new hard or super-hard TMBs.

In this work, the compression behaviour of both α-MoB₂ and β-MoB₂ were investigated up to pressures of 32.1 GPa and 35.5 GPa, respectively. According to the Birch-Murnaghan equation of state (BM-EOS),^15,16 high hardness but low bulk modulus was found in β-MoB₂. Furthermore, α-MoB₂ is more isotropic than β-MoB₂. Some anomalous softening was found in β-MoB₂ at a pressure of 26.6 GPa, which was attributed to some sudden strengthening in the X, Y direction, indicative of a second-order transition.

Experimental

Both α-MoB₂ and β-MoB₂ were synthesized at high pressure and high temperature, and the raw materials were powdery molybdenum (200 mesh, 99.95% purity) and amorphous boron powder (99.99%). Powder mixtures which contained Mo : B in atomic ratios of 1 : 2 and 2 : 5 were mixed in an agate mortar for more than 3 hours. The mixed powders were then cold-pressed into cylindrical samples of 6 mm in diameter and 3 mm in height. Finally, the samples were treated in a cubic anvil high pressure-high temperature apparatus (SPD-6 × 600) under a pressure of 5.2 GPa, at a temperature of 2000 K, held for 15 min for α-MoB₂, and at a temperature of 1700 K, held for 60 min for β-MoB₂; the detailed process of preparing MoB₂ is the same as reported before by Tao et al.¹² Scanning electron microscopy (SEM) was carried out on a Jeol JEM-6700F microscope operated at 8 kV. The results for the bulk material of the samples and the SEM results are shown in Fig. S1.† A diamond anvil cell was used to generate high pressure; the gasket was made from T301 stainless steel which was 50 μm thick, and ruby was loaded into the gasket chamber with the powder sample to measure the pressure.^17,18 Silicon oil was used as pressure medium. In situ angle dispersive X-ray diffraction (ADXRD) was carried out using the 4W2 high pressure beam line of the Beijing Synchrotron Radiation Facility (China), with a monochromic wavelength of 0.6199 Å. FIT2D software was used to analyze the 2D diffraction patterns to obtain intensity versus diffraction angle 2θ patterns. Rietveld refinement was performed using GSAS software.^19–21 The bulk modulus was obtained using the BM-EOS:^15,16where P is the pressure, V₀ is the volume under ambient conditions, and V is the volume under pressure. B₀ and B₀′ represent the bulk modulus and pressure derivative, respectively.

Results and discussion

Structures of MoB₂ were confirmed that included the high temperature phase, α-MoB₂ (P6/mmm), and the low temperature phase, β-MoB₂ (R3̄m). The most stable phase is β-MoB₂, and α-MoB₂ is easily transformed to β-MoB₂ with protracted annealing, so that α-MoB₂ is a metastable phase.¹² Under high pressure, both structures exhibit phase stability up to more than 30 GPa (Fig. 1). The diffraction peak shifts to large 2θ angles with increasing pressure, but there is no evidence of peak disappearance, peak appearance or peak splitting. Thus, both the quasi-3D puckered boron layer and the 2D boron layer in the MoB₂ are very stable under a high pressure of more than 30 GPa.

Fig. 1 X-ray diffraction patterns of MoB₂ under high pressure. (a) α-MoB₂ with increasing pressure up to 32.1 GPa. (b) β-MoB₂ with increasing pressure up to 35.5 GPa.

Although both structures are stable under high pressure, the difference of quasi-3D and 2D boron layers in MoB₂ may cause different volume evolution under high pressure. The normalized volume reduction under pressure is shown in Fig. 2. According to the third-order Birch-Murnaghan equation of state (BM3-EOS),^15,16 the bulk modulus of 317 ± 6 GPa with a pressure derivative B′ = 5 GPa is obtained for α-MoB₂, which is comparable with the calculated results of 304 GPa¹² and 302 GPa.²² Even though the hardness of β-MoB₂ is higher than that of α-MoB₂, because of the puckered boron layers in β-MoB₂, the bulk modulus of β-MoB₂ is 299 ± 4 GPa, which indicates that β-MoB₂ is more compressible than α-MoB₂. This bulk modulus value is consistent with the calculation results,^12,23 but somewhat lower than the values reported by Liu et al.¹⁴ The finding of lower incompressibility for β-MoB₂ than for α-MoB₂ is because the bulk modulus depends mainly on the electron concentration but is less related to structural details.⁷ However, β-MoB₂ appears to suddenly soften at 26.6 GPa, and the structure becomes slightly more compressible, with a slightly lower bulk modulus of 281 ± 8 GPa. This softening is anomalous. According to ADXRD results, the structure is not changed at 26.6 GPa. Therefore, this softening in β-MoB₂ is not caused by structural transition.

Fig. 2 Relationship of normalized unit cell volume and pressure. Solid Lines: fitted by third-order Birch-Murnaghan equation of state (BM3-EOS).

To further understand the high pressure behavior and to explore the anisotropy of MoB₂ that is essential for hardness so that the MoB₂ can stand compression in every direction, fractional lattice parameters were plotted as a function of pressure and are shown in Fig. 3. The a-axis is somewhat more compressible than the c-axis in α-MoB₂, but the difference is slight. So the structure of α-MoB₂ is isotropic for compressibility. This is contradicted by the findings of anisotropy in the AlB₂-type structure;^24–26 the contradiction may be attributed to the non-hydrostatic pressure caused by the pressure medium of silicon oil. The c-axis is less compressible than the a-axis at a pressure lower than 26.6 GPa for β-MoB₂, which is consistent with the results of Liu et al. and with calculated results.^12,14 β-MoB₂ is anisotropic, and compared to α-MoB₂, the puckered boron layer in the structure decreases the incompressibility both in the a-axis and the b-axis (Fig. S2†), and the decrement of incompressibility in the a-axis is larger than in the c-axis. The reason for the lower bulk modulus and lower incompressibility of β-MoB₂ than of α-MoB₂ is because the puckered boron layers broaden the spacing of the molybdenum layers (inserted patterns in Fig. 3), which reduces the electron concentration in the unit volume. The lower electron concentration causes lower incompressibility, but β-MoB₂ is harder than α-MoB₂, according to the above-mentioned theoretical results (Table S1†), and the shear modulus of β-MoB₂ is higher than that of α-MoB₂,¹² so the high hardness is mainly attributed to the strong combination of Mo layers and B layers, which enlarges the shear strain to resist collapse under the pressure of indentation.

Fig. 3 MoB₂ fractional lattice parameters plotted as a function of pressure. (a) Normalized lattice parameters decrease under pressure in α-MoB₂. The inserted pattern is the structure of α-MoB₂, and the layer distance of the Mo layer is 3.071 Å. (b) Normalized lattice parameters decrease under pressure in β-MoB₂. The inserted pattern is the structure of β-MoB₂, and the layer distances of the Mo layer are 3.183 Å and 3.797 Å.

In Fig. 3(b), an abrupt change of slope in the a-axis of β-MoB₂ appeared at 26.6 GPa, which is consistent with the softening of structure in Fig. 2. The a-axis becomes less compressible at 26.6 GPa, but the softening of the c-axis is not evident. To further understand the anomalous softening in β-MoB₂, the c/a ratio was examined and is shown in Fig. 4. Up to about 26 GPa, both α-MoB₂ and β-MoB₂ show a linear increase in c/a ratio. Because the a-axis is much more compressible in β-MoB₂ than in α-MoB₂ (Fig. S2†), β-MoB₂ has higher slope of c/a than α-MoB₂. The abrupt change appearing at 26.6 GPa is obvious in β-MoB₂. The change of slope demonstrates that the anisotropy of β-MoB₂ is changed at pressures of 26.6 GPa. The a-axis is more compressible than the c-axis under a pressure which is lower than 26.6 GPa, but the structure is suddenly strengthened in the a-axis at 26.6 GPa. This change is not normal, and no obvious change has happened to the normalized c/a in α-MoB₂. So, the molybdenum layers and graphite-like boron may not be the main reason for the strengthening in the a-axis, but the puckered boron layers may be the key to this abrupt change.

Fig. 4 Normalized c/a ratio plotted as a function of pressure for MoB₂.

Further research on the high pressure behaviours of boron layers is important to understand the abrupt change in β-MoB₂ at 26.6 GPa. The change of the B–B length under pressure is significant for uncovering how the compressibility of the boron layer occurs. The normalized B–B length plotted as a function of pressure is shown in Fig. 5. In α-MoB₂, there is only one kind of B–B bond in the graphite-like boron layer, but there are two kinds of B–B bonds in β-MoB₂; one is in the graphite-like boron layer and the other is in the puckered boron layer. Because of decrement of B-B bonds length is depend on volume decrease, the decrement of the B–B length both in the graphite boron layer and the puckered boron layer are the same (Fig. S3†). So, only the normalized B–B length in the puckered boron of β-MoB₂ is shown in Fig. 5. It is understandable that the decrement in the B–B bond length of the puckered boron layer in β-MoB₂ is larger than the decrement of the B–B length in the graphite-like boron layers of α-MoB₂. Because the B–B length (1.775 Å) in the puckered boron layer is longer than the B–B length (1.755 Å) in the graphite boron layer, this means that the B–B bonds in the puckered boron layer are weaker and more compressible. However, the decrement of the B–B length in the graphite layer is larger in β-MoB₂ than in α-MoB₂. So, this implies that the compressibility of the graphite-like boron layer in the a-axis is associated with electron transfer from the molybdenum layer,²⁷ which may be less than the electron transfer from the molybdenum layer in β-MoB₂, thus causing a lower electron concentration and lower incompressibility of the graphite-like boron layer in the β-MoB₂.

Fig. 5 Normalized B–B length plotted as a function of pressure in α-MoB₂ and β-MoB₂. The B–B length in α-MoB₂ relates to the boron bonds in the graphite-like boron layer, and the B–B length in the β-MoB₂ relates to the boron bonds in the puckered boron layer.

However, the changing of B–B length under pressure cannot confirm that the anomalous structure softening is caused by the puckered boron layer. It is essential to study the changing of the B–B bonds angle under high pressure. The B–B bonds angle in the graphite-like boron layer is B₁–B₁–B₁, both in α-MoB₂ and β-MoB₂. The angle B₁–B₁–B₁ is lying on the X–Y plane, and the angle value is not changed under pressure. The angle B₂–B₂–B₂ represents the B–B bonds angle in the puckered boron layer, which is not lying on the X–Y plane but has an angle with the X–Y plane. To understand the evolution of the B–B bond angle in the puckered boron layer under pressure, the normalized angle B₂–B₂–B₂ is shown in Fig. 6. The angle decreases with increase of pressure up to 26.6 GPa, but the angle increases with pressures higher than 26.6 GPa. The angle decrease before 26.6 GPa is attributed to the fact that the a-axis is more compressible than the c-axis, and the shrinkage of the a-axis is consistent with both length shrinking in B–B bonds and the angle of B₂–B₂–B₂ decreasing in the puckered boron layer. But the shrinkage of the angle of B₂–B₂–B₂ in this puckered boron layer has a limitation of about 116.2° (Fig. S4†) at a pressure of 26.6 GPa, thus decreasing the angle of B₂–B₂–B₂ before it then increases when the pressure is above 26.6 GPa. This means that the a-axis is only decreasing with B–B length, but both the B–B length and angle B₂–B₂–B₂ contribute to the c-axis decrease when the pressure is higher than 26.6 GPa. So the incompressibility of the a-axis is enhanced, but the c-axis is more compressible. That is the reason for the change in the anisotropy, from a situation in which the c-axis is more compressible to one in which the a-axis is more compressible, and it is also the reason for the structure softening observed in β-MoB₂.

Fig. 6 The evolution of a normalized B–B bond angle in the puckered boron layer of β-MoB₂ under pressure.

This anomalous structure softening has rarely been reported before. As the anomaly for β-MoB₂ (26.6 GPa) appears far from the hydrostatic limit of the pressure medium (∼10 GPa),²⁸ it is unlikely to be caused by the deviation of hydrostaticity in this case. The anomaly may better account for the second-order phase transition. This is consistent with the lattice softening that was found to occur in the c direction above 42 GPa in WB₄ (or WB₃) that Xie et al. observed, and they eliminated the cause as electronic topological transitions, but attributed it instead to mechanical reasons.²⁹ The second-order phase transition in β-MoB₂ was also mainly attributed to the limitation of the minimum B–B bonds angle in puckered boron layer.

Conclusions

In conclusion, the high pressure behavior of α-MoB₂ and β-MoB₂ were explored. It was demonstrated that even though β-MoB₂ had a greater hardness than α-MoB₂, β-MoB₂ had a lower bulk modulus and was more anisotropic and thus the greater hardness may be mainly attributed to the higher shear modulus in β-MoB₂. An anomalous second order transition, which caused softening of the structure and changed the anisotropy of the structure, was found in β-MoB₂; this may be attributed to the limitation of the minimum B–B bonds angle in the puckered boron layer. These results will promote the further understanding and development of hard or super-hard materials in transition metal borides.

Acknowledgements

The authors acknowledge funding support from the National Natural Science Foundation of China (under grant nos 10874054, 91022029, 51032001, 51172091 and 11025418), from the Program for New Century Excellent Talents in University (NCET-12-0240), and from the Jilin Province Science and Technology Development Program, China (20130101023JC). Part of this experimental work was performed using 4W2 beamline at the Beijing Synchrotron Radiation Facility which is supported by Chinese Academy of Sciences (no. KJCX2-SW-N20, KJCX2-SWN03).

References

1. R. B. Kaner, J. J. Gilman and S. H. Tolbert, Science, 2005, 308, 1268.
2. A. Latini, J. V. Rau, D. Ferro, R. Teghil, V. R. Albertini and S. M. Barinov, Chem. Mater., 2008, 20, 4507.
3. M. B. Weinberger, J. B. Levine, H. Y. Chung, R. W. Cumberland, H. I. Rasool, J. M. Yang, R. B. Kaner and S. H. Tolbert, Chem. Mater., 2009, 21, 1915.
4. H. Y. Gou, Z. P. Li, H. Niu, F. M. Gao, J. W. Zhang, R. C. Ewing and J. Lian, Appl. Phys. Lett., 2012, 100, 111907.
5. B. Wang, X. Li, Y. X. Wang and Y. F. Tu, J. Phys. Chem. C, 2011, 115, 21429.
6. P. Vajeeston, P. Ravindran and H. Fjellvåg, RSC Adv., 2012, 2, 11687.
7. Q. F. Gu, G. Krauss and W. Steurer, Adv. Mater., 2008, 20, 3620.
8. F. Occelli, P. Loubeyre and R. Letoullec, Nat. Mater., 2003, 2, 151.
9. I. V. Aleksandrov, A. P. Goncharov, I. N. Makarenko, A. N. Zisman, E. V. Jakovenko and S. M. Stishov, High Pressure Res., 1989, 1, 333.
10. R. W. Cumberland, M. B. Weinberger, J. J. Gilman, S. M. Clark, S. H. Tolbert and R. B. Kaner, J. Am. Chem. Soc., 2005, 127, 7264.
11. Y. Pan, W. T. Zheng, K. Xu, X. M. Luo, W. Li and Y. C. Yang, RSC Adv., 2014, 4, 25093.
12. Q. Tao, X. P. Zhao, Y. L. Chen, J. Li, Q. Li, Y. M. Ma, J. J. Li, T. Cui, P. W. Zhu and X. Wang, RSC Adv., 2013, 3, 18317.
13. H. Y. Chung, M. B. Weinberger, J. B. Levine, A. Kavner, J. M. Yang, S. H. Tolbert and R. B. Kaner, Science, 2007, 316, 436.
14. P. P. Liu, F. Peng, S. Yin, F. M. Liu, Q. M. Wang, X. H. Zhu, P. Wang, J. Liu and D. W. He, J. Appl. Phys., 2014, 115, 163502.
15. F. Birch, Phys. Rev., 1947, 71, 809.
16. F. Birch, J. Geophys. Res., 1978, 83, 1257.
17. H. K. Mao, J. Xu and P. M. Bell, J. Geophys. Res., 1986, 91, 4673.
18. H. K. Mao, P. M. Bell, J. W. Shaner and D. J. Steinberg, J. Appl. Phys., 1978, 49, 3276.
19. H. M. Rietveld, J. Appl. Crystallogr., 1969, 2, 65.
20. B. H. Toby, J. Appl. Crystallogr., 2001, 34, 210.
21. A. C. Larson and R. B. Von Dreele, GSAS., LAUR 86–748, Vers. 2000, LANSCE, Los Alamos National Laboratory, MS-H805, Los Alamos, NM 87545.
22. Y. H. Duan, Y. Sun, Z. Z. Guo, M. J. Peng, P. X. Zhu and J. H. He, Comput. Mater. Sci., 2012, 51, 112.
23. M. G. Zhang, H. Wang, H. B. Wang, T. Cui and Y. M. Ma, J. Phys. Chem. C, 2010, 114, 6722.
24. I. R. Shein and A. L. Ivanovskii, J. Phys.: Condens. Matter, 2008, 20, 415218.
25. V. Milman and M. C. Warren, J. Phys.: Condens. Matter, 2001, 13, 5585.
26. H. Li, L. T. Zhang, Q. F. Zeng, J. J. Wang, L. F. Cheng, H. T. Ren and K. Guan, Comput. Mater. Sci., 2010, 49, 814.
27. P. Vajeeston, P. Ravindran, C. Ravi and R. Asokamani, Phys. Rev. B: Condens. Matter Mater. Phys., 2001, 63, 045115.
28. S. J. You, L. C. Chen and C. Q. Jin, Chin. Phys. Lett., 2009, 26, 096202.
29. M. Xie, R. Mohammadi, Z. Mao, M. M. Armentrout, A. Kavner, R. B. Kaner and S. H. Tolbert, Phys. Rev. B: Condens. Matter Mater. Phys., 2012, 85, 064118.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra09527h

---