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High Pressure ResearchVol. 00, No. 0, Month 2011, 1–8

Low-compressibility of tungsten tetraboride: a high pressureX-ray diffraction study

Chenji Liua, Fang Penga*, Ning Tana, Jing Liub, Fengjiao Lia, Jiaqian Qina,c, Jianghua Wanga,Qiming Wanga and Duanwei Hea

aInstitute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, People’s Republic ofChina; bInstitute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, People’sRepublic of China; cGeodynamics Research Center, Ehime University, Matsuyama 7908577, Japan

(Received 28 March 2011; final version received 18 April 2011 )

Diamond anvil cell synchrotron X-ray diffraction (XRD) experiments have been carried out on thesubmicron-sized tungsten tetraboride (WB4) at room temperature up to 50.8 GPa with silicon-oil pres-sure medium. The crystal structure of WB4 remains unchanged up to the highest pressure. The isothermalbulk modulus K0 and its pressure derivatives, K !

0 have been determined from the present compression byfitting the third-order Birch–Murnaghan equation of state: K0 = 325 ± 9 GPa and K !

0 = 5.1 ± 0.6. Thehigh value of bulk modulus shows that WB4 has a high stiffness and/or low-compressibility. Moreover,we also found that the compression behavior of the unit cell axes (a- and c-axes) of WB4 demonstrates ananisotropic nature of compressibility.

Keywords: tungsten tetraboride; equation of state; low-compressibility; synchrotron X-ray diffraction

1. Introduction

Superhard and incompressible materials are of great importance in science and technology, with

Q1

applications not only in coatings and abrasives, but also in cutting and polishing tools. Thus, in thepast few decades, great efforts involving theoretical and experimental studies were universallyfocussed on the possibility of new low-compressible materials with bulk moduli and hardnessexceeding or closing that of the diamond [1–7], the most incompressible and hardest single-phasematerial known so far. In last couple of years, some researchers proposed that some compoundsconsisted of heavy transition metal (TM) and light elements (LEs) are potential superhard materials[8–11]. Several heavy TM and LE compounds have been synthesized (PtN [12], RuB2 [13], OsB2

[11,13,14], ReB2 [7,15,16], etc.); however, they are not superhard.Recently, Gu et al. [13] synthesized tungsten tetraboride (WB4) and investigated its compression

behavior up to 23 GPa. They reported that the isothermal bulk modulus K0 and the averagehardness of WB4 are 200 ± 40 and 46.2 ± 1.2 GPa, respectively. The hardness value indicates

*Corresponding author. Email: pengfang8888@yahoo.com.cn

ISSN 0895-7959 print/ISSN 1477-2299 online© 2011 Taylor & FrancisDOI: 10.1080/08957959.2011.582871http://www.informaworld.com

Techset Composition Ltd, Salisbury GHPR582871.TeX Page#: 8 Printed: 3/5/2011

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2 C. Liu et al.

that WB4 is a superhard material, but, as can be seen, their experimental results suggested that therelative error on bulk modulus K0 is 40 GPa. Moreover, the highest pressure to be loaded in theirexperiments was limited. Thus, more accurate experimental data as well as the behavior underrelative higher pressure, e.g. having phase transition or not, are needful. In theoretical researchaspect, first-principles calculations were carried out by Wang et al. [17] and yet they focussed onunderstanding the origin of hardness in WB4.

In this study, we will investigate the equation of state (EOS) and the compression behavior ofWB4 under high pressures at ambient temperature using angular dispersive synchrotron X-raydiffraction (XRD) in a diamond anvil cell (DAC).

2. Experiments

The phase-pure WB4 was synthesized by the hot-pressed method starting with a mixture of Wand B by collaborator J. Qin in our research team. From the scanning electron microscopy (SEM)microstructural test result shown in Figure 1, they have the grain size of 0.5–1.5 µm. At ambientconditions, the synthesized WB4 has a hexagonal structure (space group P 63/mmc) determinedby XRD. A symmetric diamond anvil cell (DAC) with a culet size of 300 µm was used to exertcompression in our experiment. The starting powder was pre-compressed with a separate pair ofdiamond anvil and loaded into a 120 µm diameter hole of a stainless steel (T301) gasket. A pieceof Pt foil was placed on the top of the sample center and it served as a pressure standard [18,19].To minimize deviatoric stress, we used silicon oil as the pressure-transmitting medium. Angle-Q1dispersive XRD experiments were performed at the 4W2 beam line of the Beijing SynchrotronRadiation Facility (BSRF, China) at room temperature. The incident X-ray beam of wavelength0.6199Å was focussed to approximately 31 " 8 µm2. The integration of the 2D powder patterns,which were collected on a Mar3450 image plate, was realized by means of the program fit2d.Peak positions were obtained by fitting background-subtracted Voigt line shapes to the spectra.

Figure 1. A typical SEM image of WB4.

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High Pressure Research 3

Pressures were determined from the lattice parameter obtained from the diffraction lines (111)of Pt with a precision of 0.1 GPa. The lattice parameters of WB4 were generally derived fromdiffraction lines of (101), (002) and (110). In some cases, the diffraction lines (112) was overlappedby Pt (200), and the diffraction lines (201) and (103) of WB4 were not used due to their very lowintensity and the bad shape.

3. Results and discussion

Selected diffraction patterns for WB4 up to 50.8 GPa are shown in Figure 2. It indicates that thehexagonal structure remains unchanged up to the highest pressure. It also can be seen that alldiffraction peaks markedly shift to larger diffraction angle as pressure increased. The measuredlattice constants at ambient conditions are a = 5.199(0.2)Å and c = 6.347(0.2)Å, which yieldsa unit-cell volume of 148.573Å3.

The pressure-dependent volume measurements are shown in Figure 3. The P –V data ofWB4 arefitted using second- (K !

0 fixed to 4) and third-order Birch–Murnaghan EOS to obtain the ambientpressure bulk modulus K0 and its pressure derivative K !

0. The third-order Birch–Murnaghan EOSis shown as follows:

P(V ) = 1.5K0

!"V0

V

#7/3

#"

V0

V

#5/3$

·%

1 +"

34

#· (K !

0 # 4)

!"V0

V

#2/3

# 1

$&

. (1)

The least-squares fit up to 50.8 GPa yields an ambient bulk modulus K0 = 325 ± 9 GPa and itspressure derivative K !

0 = 5.1 ± 0.6. With K !0 fixed at 4.0, the least-squares fitting turns out a

slightly higher K0 of 342 ± 3 GPa. The high value of bulk modulus K0 of WB4 illustrates that

Figure 2. Typical powder XRD patterns of WB4 at high pressures. The X-ray wavelength was 0.6199 Å.

151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200

4 C. Liu et al.

Figure 3. Normalized unit cell volumes of WB4 as a function of pressure. The solid line represent best fits of third-orderBirch–Murnaghan EOS (BM3), while the dashed line represents a second-order Birch–Murnaghan EOS (BM2) with K !

0fixed to 4.0. The open circles are the data obtained by Gu et al. [13].

this material has low compressibility and are stiffer than other commonly used hard materials[20–31] like, for example, SiC or Al2O3 shown in Table 1. In addition, the P#V data of WB4 arealso fitted using the Vinet universal EOS:

P(V ) = {3K0[1 # (V/V0)1/3]/(V/V0)

2/3} · exp{1.5(K !0 # 1)[1 # (V/V0)

1/3]}, (2)

giving an ambient bulk modulus of K0 = 324 ± 9 GPa and K !0 = 5.2 ± 0.6.

The comparison between our research results and the previously reported data on bulk modulusof WB4 is shown in Table 2. As can be seen from the table, our experimental results show relativesmall errors in contrast with the results in [13]. We have also extended the static pressure range upto 50.8 GPa. But there are still some differences about the compression behavior and/or the bulkmodulus compared with the results reported by Gu et al. [13] shown in Figure 3 and Table 2.In the study by Gu et al. [13], the compressibility seems higher than our research results. Wethink that the reasons are complex. For one thing, the WB4 powders used in their research weresynthesized by arc melting and subsequent annealing method and the grain size was not given. Foranother, the transmission medium used in their experiments was 4:1 methanol:ethanol mixture.Silicone oil used in our experiments is better than the mixture at higher pressures reported by Shenet al. [32]. Thus, some discrepancies are inevitable. When compared with the calculated resultsreported by Wang et al. [17] shown in Table 2, the bulk modulus determined from our experimentsis similar with the result obtained by LDA calculation. In addition, we further make the least-squares fitting only at the pressure range of 0–23.9 GPa, because some researchers have reportedthat the hydrostaticity of silicon oil is excellent only at lower than about 20.0 GPa [32–34]. TheQ1fitting results are also shown in Table 2.

A closer look at the compression behavior of the unit cell axes in accordance with the resultsreported by Gu et al. [13] is shown in Figure 4. It shows a high stiffness and/or low compressibility,as is illustrated in comparison with diamond literature data [20]. From this figure, we can see thatthe compression behavior of the unit cell axes is quite different from the results reported by

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High Pressure Research 5

Table 1. Bulk modulus K0 of the studied TM borides and some common hard materials for comparison.

Material K0 (BM2) (GPa) K0 (BM3) (GPa) K !0 Method

WB4 342(3) 325(9) 5.1(6) XRD in Si oil

Single crystalline diamond [20]a 446(1) 3.0(1) XRD in nitrogen

Diamond [21]b 433–442 –

c-BN [21,22]b 367–382 –

B6O [4] 270(12) 1.8(3) Radial XRD with notransmitting medium

B6O [22]b 200–208 –

B4C [22,23]b 224/200 –

OsB2 [10,24] 307–342 Theoretical calculations

OsB2 [11] 365 395 1.4 XRD inethylcyclohexane

OsB2 [13] 348(7) 343(30) 4.4(2.5) XRD inmethanol:ethanol

OsB2 [14] 297(25) Nanoindentationexperiments

Al2O3 [21,23]b 246–252 –

Al2O3 [25] 219 Theoretical calculations

Al2O3 [26] 249(20) XRD with notransmitting medium

SiC [21–23]b 210–248 –

Si3N4 [21,22]b 249/220 –

W [21]b 299–310 –

W [27] 312(36) 4.32(fixed) Radial XRD with notransmitting medium

Ru [21]b 285 –

!-B [28] 185(7) Neutron diffractionexperiments

!-B [29] 205(16) 4.3(1.6) XRD inmethanol:ethanol

!-B [30,31] 203.5–210 Theoretical calculations

Notes: BM2 denotes a second order Birch–Murnaghan EOS with K !0 fixed to 4.0. BM3 denotes a third-order Birch–Murnaghan EOS.

aVinet EOS fitting.bReferences [21–23] are some review articles, and the measurement methods were not given in their articles.

Table 2. Bulk modulus and its pressure derivative of WB4.

K0 (GPa) K !0 Equation Pmax (GPa) Pressure medium Method References

325(9) 5.1(6) BM3 50.8 Si-oil X-ray Present work342(3) 4 BM2324(9) 5.2(6) Vinet256(19) 14.6(3.7) BM3 23.9324(5) 4 BM2259(16) 13.1(2.4) Vinet200(40) 15.3(5.7) BM3 23 MEa X-ray [13]304(10) 4 BM2292.7 BM3 GGA [17]324.3 BM3 LDA

Note: The pressure range used in the analysis, pressure medium and methods of investigation are indicated.aMethanol–ethanol mixture in the volume ratio of 4:1.

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6 C. Liu et al.

Figure 4. Compressibility of the normalized lattice parameters ofWB4 compared with the data obtained by Gu et al. [13].The dashed line represents the EOS for diamond according to [20].

Gu et al. [13] at a pressure range of 0–25 GPa. At higher pressures, after about 25 GPa, thecompression behavior of a- and c-axes is likely to be in accordance. This can be explained byQ2the gradual solidification of the silicon oil medium at a higher pressure and a concomitant increaseQ1in the uniaxial stress component. Thus, the least-squares fitting of the pressure-dependent latticeconstants was only carried out at defined pressure range framed in Figure 4. The fitting resultyields

a

a0= 1 # 10.7 " 10#4

"P

P0

#+ 10.7 " 10#6

"P

P0

#2

(3)

and

c

c0= 1 # 13.0 " 10#4

"P

P0

#+ 17.3 " 10#6

"P

P0

#2

. (4)

Clearly, the compression behavior of the unit cell axes is anisotropic. Likewise, the unit cell axesincompressibility reported by Gu et al. [13] also seem a little lower than our research results.

We reason that the anisotropic compressional behavior of the unit cell axes of WB4 maybecaused by its inherent crystal structure. Usually, there are some differences in the length ofthe crystallographic a- and c-axes in the hexagonal structure. Materials that have hexagonalcrystal structure such as ReB2 [7,8], Os2B3 [13], WB2 [13] and WC [35] all show an anisotropiccompressional behavior of the unit cell axes. Thus, we propose the physical hypothesis that theinherent hexagonal crystal structures of WB4 maybe the original reason that caused the anisotropiccompressional behavior of the unit cell axes.

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High Pressure Research 7

4. Conclusion

In summary, phase stability and compressibility of WB4 were investigated at high pressures up to50.8 GPa using in situ synchrotron XRD in a DAC. The WB4 is found to be stable throughout thewhole pressure range. The bulk modulus of the WB4 derived from the P#V measurement is 325 ±9 GPa, which is, to date, the most accurate experimental data. The high value of bulk modulusindicates that WB4 has low compressibility and/or high stiffness. Moreover, the compressionbehavior of the unit cell axes obtained from our experimental data demonstrates an anisotropicnature of compressibility.

Acknowledgements

The authors thank Chuanlong Lin, Yanchun Li and Lingyun Tang for experimental assistance. This work was supportedby National Natural Science Foundation of China (Grant No. 11027405), National Natural Science Foundation of China– NSAF (Grant No. 10976018) and the China 973 Program (Grant No. 2011CB808200).

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