DOI: 10.1021/cg100659g
Bulk Re2C: Crystal Structure, Hardness, and Ultra-incompressibility Zhisheng Zhao,† Lin Cui,† Li-Min Wang,† Bo Xu,† Zhongyuan Liu,† Dongli Yu,† Julong He,† Xiang-Feng Zhou,‡ Hui-Tian Wang,‡ and Yongjun Tian*,†
2010, Vol. 10 5024–5026
†
State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China, and ‡School of Physics and Key Laboratory of Weak-Light Nonlinear Photonics, Ministry of Education, Nankai University, Tianjin 300071, China Received May 21, 2010; Revised Manuscript Received September 19, 2010
ABSTRACT: A hard ultra-incompressible bulk Re2C material is first synthesized under moderate pressure (2-6 GPa) and high temperature (873-1873 K). The phase composition of Re2C was determined by a chemical analysis method, and its structure is finally determined to be a ReB2-type structure by means of X-ray diffraction, Raman technology, and ab initio calculations. The hardness measurements show that it is a hard material which can rival ReB2. More impressively, its volume incompressibility is comparable with that of diamond, and its c axis incompressibility even exceeds that of diamond. In the end, the P-T phase diagram of the Re-C system has also been determined in the regions of P=1-6 GPa and T=873-1873 K. The moderate synthesis conditions show that this hard ultra-incompressible bulk material will obtain the further applications. Searching for intrinsic hard or superhard materials is of great practical significance. At present, these explorations primarily focus on two classes of materials. One is the compounds composed of light elements (B, C, N, and O), such as BC5, B6O, and BC2N.1-4 Another is the light-element compounds of transition metals, for example, ReB2, OsB2, IrN2, OsN2, PtN2, PtN, PtC, and TiO2.5-13 Transition metals are known to be soft because of their nondirectional metallic bonding. However, localized covalent bonds can be generated, which give rise to a high degree of hardness, when light atoms (B, C, N, and O) are inserted into the interstitial sites among the transition metal atoms. The binary equilibrium phase diagram of the Re-C system shows that there is no stable Re-C compound formed under ambient pressure.14 Therefore, only a few reports concerning rhenium carbides exist in the literature.15-18 Early in the 1970s, Popova et al.15 synthesized a new metastable rhenium carbide under high pressure (g6 GPa) and high temperature (g1073 K), which they suggested was γ0 -MoC structured ReC. Later, Popova et al.16 claimed the NaCl-type ReC was also synthesized under high pressure (16-18 GPa) and high temperature (1273 K). Recently, Juarez-Arellano et al.17,18 also investigated the reaction of rhenium and carbon under high pressure and high temperature (P = ∼67 GPa, T = ∼3800 K). A hexagonal rhenium carbide ReCx was obtained, and a structural model was proposed. The composition of ReC0.5 was determined by density functional theory (DFT) calculations. However, no NaCl-type ReC or any other phase was found. From the P-T diagram given by JuarezArellano et al.,18 no Re-C compound was obtained in the lower pressure region ( 2:1, no peaks of *Corresponding author. Fax: þ86-335-8074545. Telephone: þ86-3358387888. E-mail:
[email protected]. pubs.acs.org/crystal
Published on Web 10/29/2010
graphite or diamond were found and the intensities of the Re* (Re saturated with C) peaks gradually increased with increases in rhenium content. On the other hand, when Re/C < 2:1, graphite peaks were found and the intensities were gradually weakened with decreasing carbon content. Only when Re/C = 2:1, purephase bulk Re-C sintered compact was obtained. The corresponding X-ray diffraction (XRD) pattern is shown in Figure 1. Comparing the XRD data (Table S1 in the Supporting Information) with that of rhenium carbide (ReC) reported by Popova et al.,15 the rhenium carbide synthesized in the present study appears to be the same material. However, the composition and crystal structure of the rhenium carbide presented previously are doubtful. When Re/C = 1:1, Popova et al.15 observed one weak line of graphite appeared in their X-ray powder photographs. The same situation was also found in our experiment when Re/C = 1:1. Because of the large mass difference between carbon and rhenium, the light element carbon is less sensitive in XRD measurements than the heavy rhenium. For this reason, we consider that there was excessive carbon in Popova’s product. Juarez-Arellano et al.17 believed that the composition of the synthesized ReCx was probably Re4C2, based on direct comparison of the lattice parameters by Le Bail fit and those obtained by DFT calculations. However, the Rietveld refinement presented in the paper was carried out considering only the rhenium position without the carbon position, and the previously proposed structure of Re2C is not the most stable phase at the ground state by our calculations. To determine the exact ratio Re/C in the rhenium carbide, carbon content analysis was detected with a high-frequency infrared carbon and sulfur analyzer. The mass percent of carbon in the pure Re-C compound is 2.88788%; namely, its atomic ratio is Re/C = 2:0.924. The synthesized Re-C phase in our experiment is Re2C0.924. To identify the crystal structure of Re2C, the hexagonal crystal system and the approximate lattice parameters were first confirmed by the TREOR90 program.19 Accurate lattice parameters, with a = 2.845(1) A˚ and c = 9.877(3) A˚ (RWP = 8.68%, RP = 5.42%; Rp and Rwp are the profile factor and weighted profile factor used in the refinement, respectively), were then obtained by Pawley refinement.20 The lattice parameters agreed well with those given by Popova et al.15 and Juarez-Arellano et al.17 (Table S2 in the Supporting Information), which indicates this was the same product as that described previously. Next, we performed two-step optimizations to find a stable structure with the least energy. Structures with different starting r 2010 American Chemical Society
Communication
Crystal Growth & Design, Vol. 10, No. 12, 2010
Figure 1. Experimental X-ray diffraction (XRD) pattern of the pure-phase bulk Re2C sintered compact (black crosses): blue line, Rietveld refinement fit; vertical dashes, calculated positions of observed reflections of ReB2-type Re2C. The difference curve between the data and fit is shown. The insets are (a) the structure of Re2C proposed by Juarez-Arellano et al.17,18 and (b) the ReB2-type Re2C determined in the present study. Re atoms and C atoms are represented by green and red spheres, respectively.
positions of the atoms were first relaxed at the ground state by fixing the lattice parameters. Full geometry optimizations were then performed to check the structural stability after the first optimizations. When Re/C was 4:2, we found several different Re2C structures that had lower total energy than that previously proposed by Juarez-Arellano et al.17 Among these structures, ReB2-type Re2C had the lowest total energy at the ground state, at 0.208 eV/atom lower than that of the Re2C structure proposed by Juarez-Arellano et al.17 The calculated lattice parameters [a= 2.859(1) A˚, c=9.907(5) A˚] of the ReB2-type Re2C are consistent with our experimental data. Furthermore, we calculated the ground-state phonon dispersion curves of ReB2-type Re2C. No imaginary phonon frequency was found throughout the whole Brillouin zone, indicating its dynamical stability. The phonon dispersion curves are presented in Figure S2 (see Supporting Information). Using ReB2-type Re2C as a starting model, a full-profile Rietveld refinement21 was carried out for the XRD spectrum of the Re2C phase, over the angular range from 10° to 130°, using Materials Studio software22 (Figure 1). The Rietveld refinement gave a satisfactory result with RWP = 10.71% and RP = 7.68%, and modified lattice parameters of a=2.846(7) A˚, c=9.873(3) A˚. The crystal structure of the ReB2-type Re2C belongs to the P63/ mmc (194) space group, with Re atoms occupying a 4f position (1/3, 2/3, 0.6085) and C atoms occupying a 2c position (1/3, 2/3, 0.25), as shown in the inset of Figure 1. The Raman spectrum of Re2C provides indirect evidence for its phase characterization. There are four peaks in the measured Raman spectrum, located at 124, 178, 281, and 589 (cm-1), respectively (see Figure 2). The calculated corresponding positions of the Raman-active modes of ReB2-type Re2C are 123 (E2g), 174 (E1g), 275 (A1g), and 581 (E2g) (cm-1), which are in good agreement with the experimental results. Up to now, the synthesized rhenium carbide is finally identified to be ReB2-type Re2C. To measure the Vickers hardness (HV) of bulk Re2C, microindentation experiments were performed on the polished compacts using a pyramidal diamond indenter. The loading force of the microhardness tester could be adjusted from 0.098 to 9.8 N (0.098, 0.245, 0.49, 0.98, 1.96, 2.94, 4.9, and 9.8 N loads). The dwell time was fixed at 10 s. Under each load, 15 indentations were made. HV is defined as the applied load P (N) divided by the surface area of the indentation: HV ¼ 1854:4P=d 2
ð1Þ
where d is the arithmetic mean of the two diagonals of the indent in micrometers (μm). The averaged HV values were 27.3 ( 2.2, 24.4 ( 2, 21.8 ( 1.6, 20.7 ( 1.8, 19.1 ( 1.3, 18.5 ( 1.1, 17.9 ( 0.7, and 17.5 ( 0.6 GPa under loads of 0.098, 0.245, 0.49, 0.98, 1.96,
5025
Figure 2. Experimentally obtained Raman spectrum of Re2C measured under ambient conditions. Red vertical dashes: the calculated positions of Raman-active modes of ReB2-type Re2C.
Figure 3. HV as a function of applied loads measured under ambient conditions. The inset is the sintered sample with about height 6 mm and diameter 8 mm.
Figure 4. Normalized lattice parameters and unit cell volumes of Re2C as a function of pressure compared with diamond. The black lines were the experimental values from ref 18.
2.94, 4.9, and 9.8 N, respectively. In the asymptotic-hardness region (see Figure 3), the hardness of Re2C reaches 17.5 GPa, which is comparable to that of ReB2 (18 GPa),7 indicating it is a hard material. In addition, we estimated the theoretical hardness of Re2C by our hardness model.23-25 The calculated bond properties, lattice parameters, and Vickers hardness of ReB2-type Re2C are listed in Tables S4 and S5 (see the Supporting Information). Seen from them, the Re-C bonds with a small metallic component have high hardness values; however, the Re-Re bonds with a large metallic component have low hardness values. The calculated theoretical hardness of the Re2C crystal is 19.7 GPa, compared with the experimental asymptotic hardness (17.5 GPa) of the bulk compact. The normalized lattice parameters and unit cell volumes of Re2C as a function of pressure compared with diamond are shown in Figure 4. It can be seen that the volume incompressibility of Re2C can rival that of diamond in the considered pressure range 0-100 GPa. The high bulk modulus B (388.9 GPa) calculated
5026
Crystal Growth & Design, Vol. 10, No. 12, 2010
Zhao et al. (Grant No. IRT0650), NBRPC (Grant Nos. 2005CB724400 and 2011CB808205), and the Natural Science Foundation of Heibei Province of China (Grant No. E2009000453). Supporting Information Available: Experimental X-ray diffraction data and densities of the pure-phase bulk Re2C sintered compact. The calculated formation enthalpy-pressure (ΔH-P) diagram of different structural modifications of rhenium carbide. The calculated cell parameters, phonon dispersion curve, Vickers hardness, elastic constants, bulk modulus B, and shear modulus G of ReB2-type Re2C at ground state. This material is available free of charge via the Internet at http://pubs.acs.org.
Figure 5. Experimentally obtained pressure-temperature (P-T) diagram of Re-C: solid circles, Re2C phase; open circles, Re* þ C; halfsolid circles, Re2C phase þ Re* þ C; Re*, Re saturated with C.
at ground state (Table S3 in the Supporting Information) can take responsibility for its ultra-incompressibility. It was still found that the c axis of Re2C is always less compressible than the a (or b) axes in the pressure range. Despite the anisotropy, it is remarkable that the c axis of Re2C is even less compressible than those of ReB2 (ref 5) and diamond. It is interesting to note that, early in the 1970s, Popova et al.15 reported the synthesis of Re2C at pressure g 6 GPa, but more recently, Juarez-Arellano et al.17,18 found no Re-C compound at pressure lower than 10 GPa. In fact, as shown in the present study, Re2C can be formed under moderate pressure (2-6 GPa). By fixing the stoichiometric ratios of the reactants (Re/C=2:1), the P-T phase diagram was determined in the region (P= 1-6 GPa and T = 873-1873 K), as presented in Figure 5. From the calculated formation enthalpy-pressure (ΔH-P) diagram (Figure S1 in the Supporting Information), it is clearly seen that the synthesis is favorable under high pressure, and ReB2-type Re2C has the only negative formation enthalpy, compared with previous structures proposed. This can explain the moderate synthesis conditions of Re2C compound through the solid-solid reaction. Since this synthesis did not require very rigorous conditions, it is highly likely that hard ultra-incompressible bulk rhenium carbide (Re2C) will find uses in applications that currently employ hard TiC, WC, TiN, etc. In summary, bulk rhenium carbide Re2C has been synthesized under moderate pressure and high temperature. The content of carbon in the pure Re-C phase was obtained by the chemical analysis method, and the composition was determined to be Re2C0.924. By our calculations and refinement of the experimental results, a structure of ReB2-type Re2C is proposed. [Crystal data for Re2C: Re2C, formula weight 384.425, hexagonal, space group P63/mmc, Z=2, a=2.846(7) A˚, c=9.873(3) A˚, R=β=90°, γ= 120°, Re atoms occupying a 4f position (1/3, 2/3, 0.6085), C atoms occupying a 2c position (1/3, 2/3, 0.25), V = 69.293(1) A˚3, F=18.424(8) g 3 cm-3.] The calculated positions of Raman-active modes of ReB2-type Re2C are in satisfactory agreement with the experiment results. The Vickers hardness of the Re2C sintered compact is 17.5 GPa, estimated in the asymptotic-hardness region. More impressively, its volume incompressibility is comparable with that of diamond, and its c axis incompressibility even exceeds that of diamond. In the end, the P-T phase diagram has also been determined in the region (P = 1-6 GPa and T = 873-1873 K). The moderate synthesis conditions indicate that this hard ultra-incompressible bulk material will obtain the further applications. Acknowledgment. This work was supported by NSFC (Grant Nos. 50872118, 50821001, and 91022029), PCSIRT
References (1) Solozhenko, V. L.; Kurakevych, O. O.; Andrault, D.; Godec, Y. L.; Mezouar, M. Phys. Rev. Lett. 2009, 102, 015506. (2) He, D. W.; Zhao, Y. S.; Daemen, L.; Qian, J.; Shen, T. D.; Zerda, T. W. Appl. Phys. Lett. 2002, 81, 643–645. (3) Solozhenko, V. L.; Andrault, D.; Fiquet, G.; Mezouar, M.; Rubie, D. C. Appl. Phys. Lett. 2001, 78, 1385–1387. (4) Zhou, X. F.; Sun, J.; Fan, Y. X.; Chen, J.; Wang, H. T.; Guo, X. J.; He, J. L.; Tian, Y. J. Phys. Rev. B 2007, 76, 100101 (R). (5) Chung, H. Y.; Weinberger, M. B.; Levine, J. B.; Kavner, A.; Yang, J. M.; Tolbert, S. H.; Kaner, R. B. Science 2007, 316, 436–439. (6) Dubrovinskaia, N.; Dubrovinsky, L.; Solozhenko, V. L. Science 2007, 318, 1550c. (7) Qin, J. Q.; He, D. W.; Wang, J. H.; Fang, L. M.; Lei, L.; Li, Y. J.; Hu, J.; Kou, Z. L.; Bi, Y. Adv. Mater. 2008, 20, 1–4. (8) Cumberland, R. W.; Weinberger, M. B.; Gilman, J. J.; Clark, S. M.; Tolbert, S. H.; Kaner, R. B. J. Am. Chem. Soc. 2005, 127, 7264– 7265. (9) Young, A. F.; Sanloup, C.; Gregoryanz, E.; Scandolo, S.; Hemley, R. J.; Mao, H. K. Phys. Rev. Lett. 2006, 96, 155501. (10) Crowhurst, J. C.; Goncharov, A. F.; Sadigh, B.; Evans, C. L.; Morrall, P. G.; Ferreira, J. L.; Nelson, A. J. Science 2006, 311, 1275–1278. (11) Gregoryanz, E.; Sanloup, C.; Somayazulu, M.; Badro, J.; Fiquet, G.; Mao, H. K.; Hemley, R. J. Nat. Mater. 2004, 3, 294–297. (12) Ono, S.; Kikegawa, T.; Ohishi, Y. Solid State Commun. 2005, 133, 55–59. (13) Dubrovinsky, L. S.; Dubrovinskaia, N. A.; Swamy, V.; Muscat, J.; Harrison, N. M.; Ahuja, R.; Holm, B.; Johansson, B. Nature 2001, 410, 653–654. (14) Khar’kova, A. M.; Velikanova, T. Y. Poroshk. Metall. 1987, 12, 52–56. (15) Popova, S. V.; Boiko, L. G. High Temp.-High Pressures 1971, 3, 237–238. (16) Popova, S. V.; Fomicheva, L. N.; Khvostantsev, L. G. Zh. Eksp. Teor. Fiz., Pis’ma Red. 1972, 16, 609–610. (17) Juarez-Arellano, E. A.; Winkler, B.; Friedrich, A.; Wilson, D. J.; Koch-Muller, M.; Knorr, K.; Vogel, S. C.; Wall, J. J.; Reiche, H.; Crichton, W.; Ortega-Aviles, M.; Avalos-Borja, M. Z. Kristallogr. 2008, 223, 492–501. (18) Juarez-Arellano, E. A.; Winkler, B.; Friedrich, A.; Bayarjargal, L.; Milman, V.; Yan, J. Y.; Clark, S. M. J. Alloys Compd. 2009, 481, 577–581. (19) Werner, P. E.; Eriksson, L.; Westdahl, M. J. Appl. Crystallogr. 1985, 18, 367–370. (20) Pawley, G. S. J. Appl. Crystallogr. 1981, 14, 357–361. (21) Rietveld, H. M. J. Appl. Crystallogr. 1969, 2, 65–71. (22) MATERIALS STUDIO, Version 4.1; Accelrys Inc.: San Diego, CA, 2006. (23) Guo, X. J.; Li, L.; Liu, Z. Y.; Yu, D. L.; He, J. L.; Liu, R. P.; Xu, B.; Tian, Y. J.; Wang, H. T. J. Appl. Phys. 2007, 104, 023503. (24) Gao, F. M.; He, J. L.; Wu, E. D.; Liu, S. M.; Yu, D. L.; Li, D. C.; Zhang, S. Y.; Tian, Y. J. Phys. Rev. Lett. 2003, 91, 015502. (25) He, J. L.; Wu, E. D.; Wang, H. T.; Liu, R. P.; Tian, Y. J. Phys. Rev. Lett. 2005, 94, 015504.
