Vanadium Diboride (VB2) Synthesized at High ... - ACS Publications

Oct 5, 2017 - High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Las Vegas, Nevada 89154, United States. ‡. Department o...
0 downloads 0 Views 5MB Size
Download PDF
Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

pubs.acs.org/IC

Vanadium Diboride (VB2) Synthesized at High Pressure: Elastic, Mechanical, Electronic, and Magnetic Properties and Thermal Stability Pei Wang,*,† Ravhi Kumar,† Esakki Muthu Sankaran,† Xintong Qi,‡ Xinyu Zhang,§ Dmitry Popov,∥ Andrew L. Cornelius,† Baosheng Li,‡ Yusheng Zhao,† and Liping Wang*,† †

High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Las Vegas, Nevada 89154, United States Department of Geosciences, Stony Brook University, Stony Brook, New York 11794, United States § State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, People’s Republic of China ∥ High Pressure Collaborative Access Team, Geophysical Laboratory, Carnegie Institution of Washington, Argonne, Illinois 60439, United States ‡

S Supporting Information *

ABSTRACT: Vanadium diboride (VB2) with an AlB2-type structure has been synthesized at 8 GPa and 1700 K in a DDIA-type multianvil apparatus. The obtained bulk modulus is B0 = 262(2) GPa with fixed B′ = 4.0 for VB2 via high-pressure X-ray diffraction measurements. Meanwhile, VB2 has also been demonstrated to possess a high Vickers hardness of 27.2 ± 1.5 GPa, a high thermal stability of 1410 K in air, among the highest for transition-metal borides, and an extremely low resistivity value (41 μΩ cm) at room temperature. Results from first-principles calculations regarding the mechanical and electronic properties of VB2 are largely consistent with the experimental observations and further suggest that VB2 possesses simultaneously the properties of a hard and refractory ceramic and those of an excellent electric conductor.

■

INTRODUCTION Transition-metal borides (TMBs) have attracted considerable interest in recent years because of their unique mechanical and electrical properties. As a group TMBs have displayed large bulk modulus, high hardness, ultrahigh melting points, favorable thermal stability, strong resistance to oxidation, and excellent electric transport properties.1−30 They are promising candidates for use under the extreme conditions experienced by scramjet and rocket propulsion, hypersonic flight, atmospheric re-entry, hard coatings of electromechanical systems, armor, and cutting tools.1,2,13,14,16−24,31 Transition-metal borides are generally characterized by strong covalent boron−boron (B− B) bonds and short bonds between boron and the transitionmetal elements with a high density of valence electrons. In the quest of TMBs having better overall performance, researchers have attempted to avoid the presence of weak metallic bonds in borides, such as Os−Os bonds in OsB2,32 by incorporating more boron into the dense structure of transition metals to form three-dimensional (3D) covalent-bonding networks. Subsequently, boron-rich TMBs, such as WB4, CrB4, FeB4, MnB4, and ZrB12, have been successively synthesized using high-pressure and arc-melting methods.8,9,13,19,33 However, it is not evident that added B−B covalent bonding significantly improves the mechanical properties of TMBs. Moreover, some © XXXX American Chemical Society

transition-metal monoborides also exhibit high hardness. For instance, WB and CrB have Vickers hardnesses of 28.2 ± 1.2 and 19.6 ± 0.7 GPa, respectively.23,24 It is generally accepted that the strength of materials, which is limited by the weakest deformation path under shear stress, is empirically related to the strength of chemical bonds. However, no quantitative relationship has been established. On the other hand, the interaction between metal and boron results in mixed ionic and covalent bonds in TMBs that may dominate their mechanical properties. Hence, discovering new TMBs and the determining factors for their physical and chemical properties remain an active area of research. Vanadium diboride (VB2) adopts an AlB2-type layered structure (P6/mmm) under ambient conditions. Each vanadium atom is coordinated by six boron atoms, forming a VB12 hexagonal prism (Figure 1a). Figure 1b shows a honeycomb graphene-like boron layer overlaying a vanadium layer, and Figure 1c shows the alternating boron and vanadium layers. The boron−boron bond length within B6 rings in VB2 is even shorter than that of ReB2.27−30 Previous theoretical calculations have shown that the covalency (67.7%) of V−B bonds in VB2 is Received: October 5, 2017

A

DOI: 10.1021/acs.inorgchem.7b02550 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 1. Crystal structure of AlB2-type VB2: (a) crystal structure of hexagonal VB2 visualized by a polyhedron; (b) honeycomb crystal structures of VB2; (c) vanadium metal layers and boron layers of VB2. temperature prior to pressure release.38,39 The recovered cylindrical bulk VB2 samples sintered at 1700 K with both a diameter and height of ∼3 mm were either polished or ground into powder to be characterized. Characterization Methods. The obtained polycrystalline products were characterized by XRD with Cu Kα as the radiation source. High-P in situ synchrotron XRD experiments using a symmetric diamond anvil cell (DAC) with a culet size of 300 μm were carried out up to 39.2 GPa at 16-BMD of HPCAT, Advanced Photon Source (APS), Argonne National Laboratory (ANL). The synthetic VB2 powders were loaded into a hole (170 μm in diameter) in the preindented rhenium gasket, and neon was then loaded as the pressure-transmitting medium (PTM). Several ruby spheres were also loaded in the sample chamber to act as the internal pressure standard.41 A focused monochromatic X-ray beam with a diameter of 5 μm and a wavelength of 0.3874 Å was used for the diffraction experiments. The crystal structure was analyzed through Rietveld refinements with GSAS (EXPGUI) software.42 Vickers hardness measurements were performed on a well-sintered VB2 chunk at loads of 50, 100, 200, 300, 500, 1000, and 2000 g using a Micromet-2103 hardness tester (Buehler, USA) with a dwelling time of 15 s. Each load was repeated at least five times to obtain statistically improved averages. The density measured using the Archimedes method is 4.906 g/cm3 for the sintered polycrystalline VB2 sample. The low-T magnetic susceptibility and four-probe resistivity measurements were performed with a Quantum Design PPMS EverCool system. The ac susceptibility was obtained with 1 kHz frequency and 10 Oe amplitude. The data were collected in both the cooling and warming modes without an external magnetic field. Since both curves exhibit similar behavior, we have plotted the data from the cooling mode. For the four-probe resistivity measurement, contacts were made on the sample using conducting silver paste with a sample size of 2.4 × 1.6 × 0.8 mm. A dc current of 1 mA was applied to the sample. XPS (Thermo ESCALAB 250XI, Thermo Fisher Scientific, USA) was perfored by use of monochromatic aluminum Kα X-rays. The TGA investigation was carried out in air using a USTA SDT 600 thermoanalyzer operating at a heating rate of 10 K/min in the 293−1700 K temperature range. The morphology and element composition of bulk VB2 sample were represented using field emission scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS). First-Principles Calculations. Ab initio calculations in the framework of density functional theory (DFT) were carried out with the CASTEP code and VASP with a PBE exchange-correlation functional form of the GGA.43,44 The plane-wave basis set with an energy cutoff of 500 eV was used in the calculations. The Brillouinzone integration was done on a uniform Monkhorst−Pack grid of a kpoint sampling of 15 × 15 × 15. We treated 3s23p63d34s2 and 2s22p1 as valence electrons for V and B atoms, respectively. The convergence criterion of relaxation was that the largest residual component of the stress tensor on the lattice unit cell was less than 0.02 GPa and the Hellman−Feynman forces on the ions were less than 0.01 eV/Å. The Broyden−Fletcher−Goldfarb−Shanno (BFGS) scheme served as the minimization algorithm.45 The Voigt−Reuss−Hill approximation was used to estimate the bulk modulus, Young modulus, shear modulus, and Poisson ratio.46 The ideal strength was acquired from the

second only to that of Ti−B bonds in TiB2 (77.2%) and is significantly higher than those of other AlB2-type layered borides, such as ZrB2 (19.1%), CrB2 (17.8%), HfB2 (21.9%), NbB2 (47.9%), TaB2 (49.3%), MnB2 (8.3%), MgB2 (3.2%), etc.34 The distinctive V frameworks and borophene subunits in VB2 enable the electrons to be transferred in all directions over the entire structure, which may make it a highly active electrocatalyst for the hydrogen evolution reaction (HER).35 Recently VB2 has been also used as an air battery electrode material due to its excellent charge and energy capacities.36 Therefore, VB2 potentially possesses not only the mechanical and chemical properties of hard and refractory ceramics but also the electronic properties of conductors. It also has the advantages of lower density and higher covalency of metal− boron bonds in comparison to many other TMBs. However, there are few experimental data on the elastic, deformational, magnetic, and electronic properties of VB2 because it is difficult to synthesize dense bulk VB2 at ambient pressure. Systematic studies on these properties of VB 2 are important to understanding the vanadium borides as a group and finding the potential pathways for their practical applications. In this work, we have successfully synthesized bulk VB2 at high pressure (P) and high temperature (T) and subsequently investigated its elastic, mechanical, electronic, and magnetic properties and oxidation resistance through in situ high-P synchrotron X-ray diffraction (XRD), microhardness indentation, measurements of low-T resistance and magnetic susceptibility, and thermal gravimetric analysis (TGA). On the basis of first-principles calculations, the ideal strengths and correlation between electronic and elastic properties of the titled material are also elucidated.

■

EXPERIMENTAL AND COMPUTATIONAL DETAILS

HPHT Synthesis. Bulk VB2 samples were prepared using a mixture of V powder (purity 99.5%, Alfa Aesar, US) and amorphous B powder (purity 99.999%, SkySpring Nanomaterials, US) at various molar ratios V:B = 1:2 to 1:4 under high-pressure/-temperature conditions. The syntheses were performed in a 2000-ton two-stage (D-DIA + Kawai) multianvil apparatus at the High Pressure Science and Engineering Center (HiPSEC), University of Nevada, Las Vegas. The 14/8 sample assembly, composed of an MgO octahedron with an edge length of 14 mm, a cylindrical Ta heater, and a ZrO2 sleeve as the thermal insulator, was squeezed by eight cubic WC anvils with 8 mm corner truncations.37−39 Pressures were evaluated on the basis of the calibration defined by phase transitions in SiO2 (quartz−coesite and coesite−stishovite) and CaGeO3 (garnet−perovskite) at high T,40 and temperatures were estimated in situ with a W5%Re−W26%Re thermocouple (type C). The prepressed mixed powder pellets were first compressed at room temperature to the desired oil load, and then the temperature was raised at a rate of ∼20 K/min to the target value and held for 1 h. The temperature was gradually reduced to room B

DOI: 10.1021/acs.inorgchem.7b02550 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 2. (a) Dependence of Vickers hardness on loading forces from 0.245 to 19.6 N for a chunky VB2 sample synthesized at 8 GPa/1700 K. (b) Vickers hardness of traditional hard materials WC. The scale of 10 μm applies to all indentation pictures.

Table 1. Elastic Properties and Vickers Hardness of VB2 and Analogous Hard Materials: Elastic Constants, Shear Modulus G, Young Modulus E, Poisson Ratio ν, and Experimental Vickers Hardness HvExp compound VB2

TiB2 CrB2 TaB2 ReB2 WB2 MoB2 WB3 ZrB12

method

B0 (GPa)

B′

DAC DAC GGA DAC GGA ultrasonic GGA DAC GGA DAC GGA DAC GGA ultrasonic GGA ultrasonic GGA DAC GGA DAC GGA

239(5) 262(2) 284 322(7) 282 240 250 228(5) 295 341(7) 360 360 350 349 318 296 303 326(4) 293 221(8) 236

5.5(3) fixed 4.0

G (GPa)

E (GPa)

v

B/G

245

577

0.165

1.16

241 255 260

563 565 581

0.168 0.108 0.110

1.17 0.94 0.96

170 228 218

417 551 547 712 669 504 512 463 572 595

0.260

1.74 1.50 1.65

464

0.171

HvExp (GPa)

ref

25.8

this work this work this work 62 66, 67 75, 76 66, 67 25 ref 66. ref 54. 66 3 30 21 27 21 66 4 7 22 22

fixed 4.0

fixed 4.0 fixed 4.0

22.1

fixed 4.0

fixed 4.0

25.0

283 200 207 186 231 249 245

0.236

25.6 26.6

0.182 0.259 0.234 0.235 0.240

1.24 1.75 1.54 1.56 1.63 1.31

fixed 4.0

26.5 25.1 25.5 27

199

1.19

achieves 27.2 ± 1.5 GPa under a load of 19.6 N. An asymptotic hardness of 25.8 ± 0.8 GPa is obtained through the fitting, which is comparable to that of analogous TMBs including TiB2 (25.5 GPa),49,50 TaB2 (25.6 GPa),49,50 WB2 (25.5 GPa),4,21,26 WB4 (25.5 GPa),20 ReB2 (26.6 GPa),3 and ZrB12 (27 GPa)22 and is also in good agreement with those obtained on single crystals of VB2.51 The experimentally observed inverse dependence of the Vickers hardness on the loading force is due to the additional storage of defects produced by the gradients in plastic strain field. The larger the loading force, the greater the number of storage sites for defects and hence the lower the hardness.3,52 To evaluate the accuracy of hardness test data, the HV value for commercial tungsten carbide anvils was also measured under the same conditions (Figure 2b). A hardness of 39(2) GPa under a load of 0.49 N and an asymptotic value of 20(1) GPa are consistent with previous reports.53

calculated stress−strain relationships. For tensile deformation, the maximum tensile stress was achieved by fixing the applied strain along selected easy deformation paths and relaxing the lattice vectors and atomic positions step by step.31,47 Shear stress responses to structural deformation were calculated by setting the gradually desired target stress component along specific loading paths until the structure instability was reached, and the peak stress before collapse of the structure served as the corresponding ideal strength.48

■

RESULTS AND DISCUSSION Vickers hardness (HV) as an important performance index of VB2 was measured using an indentation method on the polished surface of chunky VB2 samples synthesized at 8 GPa/ 1700 K. Figure 2a shows the Vickers hardness as a function of loading force. A hardness of 45(3) GPa under a loading force of 0.49 N indicates that VB2 is comparable to ReB2 (48(6) GPa),3 WB4 (43(3) GPa),13 TiB2 (40(1) GPa),49 and ZrB12 (40(1) GPa)22 under the same applied load. The hardness of VB2 gradually decreases with an increase in loading force and C

DOI: 10.1021/acs.inorgchem.7b02550 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 3. (a) Vickers hardness of honeycomb metal borides as a function of covalency of metal−boron bonds. Schematic illustrations of strain− stress relationships obtained by the ab initio DFT theory calculations for (b) VB2, (c) TiB2, and (d) ZrB2.

evaluated on the basis of the experimental results of the hardness anisotropy near room temperature.22,47 VB2 has again a higher shear strength of τ(0001)⟨1̅21̅0⟩ 43 GPa, approaching that of TiB2 (τ(0001)⟨1̅21̅0⟩ = 49 GPa), and both are significantly higher than that of ZrB2 (τ(0001)⟨1̅21̅0⟩ = 36 GPa).47 An in situ high-P powder XRD experiment was conducted to evaluate the phase stability and compressibility of hexagonal VB2 in a DAC up to 39.2 GPa at room temperature. The XRD pattern collected under ambient conditions (Figure 4a) was refined to yield the following lattice constants: a = b = 2.998(2) Å and c = 3.060(2) Å, for a volume of 23.82(1) Å3, which are consistent with the single-crystal results reported earlier.51 The typical diffraction patterns as a function of pressure are shown in Figure S2. Magnesium oxide (MgO; used as capsule material) impurity was detected in the diffraction patterns. No phase transition was observed in hexagonal VB2 within the entire pressure range, and all diffraction lines shifted to larger 2θ with increasing pressure. The normalized pressure F as a function of the Eulerian strain f was plotted to examine the quality of the EoS fit. The relationship between F and f is

To shed light on the relationship between the macroscopic mechanical properties and the strength of chemical bonding, the Vickers hardness and the corresponding covalency of metal−boron bonds in honeycomb metal borides are summarized in Figure 3a.31,33,49−59 It is evident that the hardness is strongly and positively dependent on the strength of metal−boron bonds, the forces that hold together the alternating boron and metal layers in these borides. The greater the covalency, i.e., the interlayer force, the stronger the ability to resist the planar shear under stress, which is the weakest deformation path in honeycomb metal borides. The covalency of V−B bonds in VB2 (67.7%) is high and is second only to that of Ti−B bonds in TiB2 (77.2%), hence the relatively high hardness for VB2. Other metal borides, such as MgB2, MnB2, and ZrB2, have a hardness of mostly below 23 GPa due to their low covalency of metal−boron bonds. To further correlate the covalency of metal−boron bonds to the strength of honeycomb metal borides, the ideal tensile and shear strengths of VB2, TiB2, and ZrB2 were obtained by calculating the stress−strain relationships (Figure 3b−3d). Evidently, these borides show anisotropic tensile strengths in the (101̅0), (1̅21̅0), and (0001) planes and shear strengths along the (0001)⟨1̅ 2 1̅ 0 ⟩, (0001)⟨101̅0⟩, and (101̅0)⟨1̅21̅0⟩ deformation paths. The results show that VB2 possesses the highest tensile strength of σ101̅0 = 56.8 GPa in comparison with that of TiB2 (σ101̅0 = 52.6 GPa) and ZrB2 (σ1010̅ = 31.7 GPa) along the weakest ⟨101̅0⟩ direction. The shear stress responses in the main slip system of borides on the (0001) and (1010̅ ) planes were D

F = P[3f (1 + 2f )2 ]−1

(1)

−2/3 ⎡ ⎤ 1 ⎢⎛ V ⎞ f= − 1⎥ ⎜ ⎟ ⎥⎦ 2 ⎢⎣⎝ V0 ⎠

(2) DOI: 10.1021/acs.inorgchem.7b02550 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 4. (a) Rietveld refinement XRD pattern of VB2 powder under room conditions: (black dots) observed results; (red line) calculated curve; (dark line) difference of the observed and calculated curvea; (green vertical lines) peak positions. (b) Normalized pressure (F) as a function of Eulerian strain ( f) fitted to eq 2 yielding the pressure derivative of bulk modulus, B′ ≈ 4 and F = 257(4). (c) P−V data for VB2 fitted to second-order and third-order BM-EoS. (d) Axial compressibilities as a function of pressure for VB2. The normalized lattice parameters, a/a0 and c/c0, were fitted to a truncated Fourier series expansion of the form (4 and 5).

and MoB 2 (314 GPa) (see Table 1), 21 whose low compressibilities are due to rapidly increasing repulsive forces between the heavy-metal atoms and high valence-electron densities. It is worth noting that a higher bulk modulus does not necessarily translate into a higher hardness, as VB2 exhibits similar hardness in comparison to TMBs with higher bulk modulus. Least-squares regressions of normalized lattice parameters, a/a0 and c/c0, as a function of pressure (Figure 4d) yield the relations

where P, V, and V0 are the experimental pressure, the volume at the pressure P, and the volume under ambient conditions, respectively.60 The linear fits of the F−f plot (Figure 4b) suggest that the pressure derivative of bulk modulus, B′ = ∂B/ ∂P, is ∼4 and the fitted constant, F, is 257(4) GPa, which are in good agreement with the result from fitting P−V data to second-order Birch−Murnaghan equations of state (BM-EoS) (Figure 4c) P=

−7/3 ⎡ ⎛ V ⎞−5/3⎤ 3 ⎢⎛ V ⎞ ⎥ B0 ⎜ ⎟ +⎜ ⎟ ⎥⎦ 2 ⎢⎣⎝ V0 ⎠ ⎝ V0 ⎠

⎧ ⎡⎛ ⎞−2/3 ⎤⎫ ⎪ ⎪ V 3 ⎨1 + (B′ − 4) × ⎢⎜ ⎟ − 1⎥⎬ ⎢⎣⎝ V0 ⎠ ⎥⎦⎪ ⎪ 4 ⎩ ⎭

a = 1 − 1.1 × 10−3 × P + 6.5 × 10−6 × P 2 a0 R2 = 0.9997

(4)

c = 1 − 1.7 × 10−3 × P + 11.3 × 10−6 × P 2 c0

(3)

where B0 is the bulk modulus at ambient pressure and temperature and B′ the pressure derivative of B0.61 Fitting data to the second- and third-order BM-EoS as shown in Figure 4c yielded the bulk modulus B0 = 262(2) GPa with B′ = 4 (fixed) and B0 = 239(5) GPa with B′ = 5.5(3), respectively. The higher bulk modulus of 322(7) GPa reported by Pereira et al. is presumably due to the nonhydrostatic condition created by the pressure medium of methanol/ethanol/water and silicon grease.62 Intriguingly, bulk moduli of VB2 determined in this study are comparable to those of TMBs of neighboring metals, such as TiB2 (240 GPa),49 ZrB2 (245 GPa),63 and CrB2 (228 GPa),25 but are significantly lower than those of TMBs of heavier metals, such as ReB2 (360 GPa),3 WB2 (349 GPa),21

R2 = 0.9991

(5)

where P is the pressure in GPa and R2 the correlation coefficient.64 VB2 exhibits anisotropic compressibility, analogous to that of most TMBs such as ReB2, WB34, MoB2, and WB2: i.e., the a axis is more incompressible than the c axis because of the short and strong B−B bonds in the honeycomb boron layers. However, both parameters decrease with increasing pressure. First-principles calculations were carried out to further evaluate bulk modulus, shear modulus, and Poisson ratio for VB2 from the Voigt−Reuss−Hill approximation method yielded B0 = 284 GPa, G = 245 GPa, and υ = 0.165 (see E

DOI: 10.1021/acs.inorgchem.7b02550 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 5. Isosurface of electronic localization functions (ELF) for the corresponding structure: (a) different slices containing vanadium metal layers, boron layers, and the (110) crystal face; (b) ELF along B layers; (c) ELF along V metal layers; (d) ELF of the (110) lattice plane.

Table 1). The corresponding lattice constants a = b = 2.9914 Å and c = 3.0301 Å agree well with the experimental results. Meanwhile, the elastic constants C11 = 685 GPa, C33 = 494 GPa, C44 = 226 GPa, C12 = 113 GPa, and C13 = 123 GPa are in good agreement with previous calculations (Supporting Information).65−68 It is interesting to note that the C11 value of VB2 is even higher than that of WB4 (C11 = 639 GPa, C33 = 470 GPa), indicating that VB2 is highly incompressible along the a and b axis directions, which may originate from it having the shortest B−B bond (1.731 Å) (Supporting Information). The V−B interactions are analogous to those of WB4 along the c axis,7 with planar boron sheets in the structure. The small Poisson ratio of 0.165 approaching those of ReB2 (0.21),3 WB4 (0.16),7 and ZrB12 (0.171)22 suggests a strong anisotropy in compressibility, consistent with the experimental results (Figure 4d). The ratio of bulk to shear modulus (B/G) is a measure of ductile vs brittle character for solids with a dividing value of 1.75.69 The theoretical B/G value of 1.16 indicates that VB2 exhibits a brittle feature. To further examine the bonding mechanism in VB2, electron localization functions (ELF) were calculated to help visualize different types of bonding.70 Figure 5a highlights a honeycomb boron layer, a vanadium layer, and (110) lattice plane that involve all bonding interactions in VB2. The ELF plot of honeycomb B layers of VB2 is illustrated in Figure 5b. The strong electron localization between B−B trimers indicates that the strong B−B covalent bonds form a tough graphene-like boron sheet perpendicular to the c axis. The lack of electron density between V atoms suggests extremely weak interactions between metal atoms (Figure 4c). Quantitative bond population analysis reveals that the B−B bonding is extremely strong and highly covalent. A high value (2.36) of positive population and short B−B bonds of 1.727 Å indicate a high

degree of covalency in the bond. It is worth stressing that the directional covalent bonds are responsible for the high hardness and bulk modulus. As shown in Figure 5d, unlike the strong directional B−B covalent bonding, the polar V−B bonding interactions are relatively weak because the ELF maxima are strongly biased toward the B atoms. The polarization of electron localization density is believed to weaken the shear deformation paths of VB2 under stress. Finally, the short B−B and V−B bonds and vanadium sheets may make VB2 a unique combination of a good conductor and a hard ceramic. To evaluate the magnetic and electrical transport properties of VB2, magnetization and resistivity measurements were performed in the temperature range of 2−300 K. The dependence of magnetization on temperature for VB2 is shown in Figure 6a. The overall magnitude of magnetization throughout the temperature range seems to be very small; however, there exists a multiple peak structure that closely resembles antiferromagnetic transitions around 195, 43, and 27 K. At temperatures below 27 K, the magnetization shows a huge upturn in the present sample. This may be due to the paramagnetic phase present or to the sample not being totally ordered. Even the vanadium atom shows diamagnetic nature at low temperature but on alloying with boron may show different peaks with low moment. This may be due to the hybridization of the 2p state of nonmagnetic boron with vanadium’s 3d and 4s states. The magnetic band structure calculation reported for VB2 shows a substantial diamagnetic contribution.71 A detailed band structure calculation is necessary to identify the magnetic nature of VB2. The temperature dependence of resistivity shows the metallic nature of the sample with the reduction of the magnitude of resistivity at low temperature (Figure 6b). The resistivity below 50 K is fitted with the equation ρ = ρ0 + AT2, where the coefficient A is a measure of electron−electron F

DOI: 10.1021/acs.inorgchem.7b02550 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

To correlate the chemical bonding, electrical transport, and mechanical properties, the band structure, total density of states (DOS), and partial electronic density of states (PDOS) projected onto atomic orbitals were calculated on the basis of the DFT at zero pressure with the GGA method. Finite DOS emerging at the Fermi level indicates that VB2 exhibits metallic behavior (Figure 7), consistent with the current experimental and previous calculation results.65−68 The electronic structure of VB2 close to the Fermi level is dominated by a strong hybridization of B 2p and V 3d orbitals. The pseudogap at the Fermi energy is considered to originate from an ionic bond or from the covalent hybridization. The bonding nature in VB2 is described as a complex ionic−covalent mixture on the basis of Mulliken population calculation results. The nearly full occupation of the bonding states contributes to the high bulk and shear moduli and small Poisson ratio. Interactions between V 3d and B 2p states near the Fermi level also give rise to the high electrical conductivity in VB2. A SEM with energy dispersive spectrometer (EDS) has been used to investigate the morphology and elemental composition of VB2 samples synthesized at 8 GPa and 1700 K. The grain size is 1−3 μm at the surface of the as-synthesized specimen (Figure 8a). VB2 crystals are morphologically analogous to the V−B hexagonal prism (Figure 1a), indicating that the preferred growth is along the [110] crystallographic direction at high pressure. EDS measurements on elemental distributions reveal that the V:B ratio is 44:56, lower than the starting V:B ratio of 1:2, presumably due to low sensitivity of boron to EDS analysis. The thermal stability of VB2 as a performance index for its potential applications has been measured using thermal gravimetric analysis (TGA) in air (Figure 8b). The VB2 sample achieved an onset oxidation temperature of 1410 K as established from the thermal gravimetric curves, higher than those of most borides, such as TiB2 (1373 K), ZrB2 (1373 K), and WB4 + 3 atom % Mo (673 K).72,73 Core-level X-ray photoelectron spectroscopy (XPS) measurement has been performed to further understand the electronic configuration of VB2. Figure 8c shows that the main deconvolution peak of the B 1s spectrum for VB2 is located at 188.3 eV, a value close to the B 1s binding energy of honeycomb boron layers.20,22 The lower binding energies of boron located at 188.0 and 186.7 eV indicate contributions from the bonding configurations of elemental boron. V 2p spectra can be divided into two

Figure 6. (a) dc susceptibility for VB2 versus temperature from 2 to 300 K at 1 T. The inset gives the inverse of the molar susceptibility vs temperature. (b) Electrical resistivity measurement of VB2 from 2 to 300 K.

interaction strength and ρ0 is the residual resistivity due to impurity scattering in the sample. The values of ρ0 and A obtained from the fitted curve are 7.5 μΩ cm and 7.7 × 10−5 μΩ cm/K2, respectively. The obtained A value indicates the electron−electron interaction at low temperature. VB2 has an extremely low resistivity of only 41 μΩ cm at room temperature, rivaling those of some traditional metals and TMBs, such as titanium, OsB2, CrB, and ZrB12.22,24

Figure 7. Band structure of VB2 and partial density of states (PDOS) of VB2; the purple, green, and red solid curves represent V s, p, and d orbitals, respectively, and the dark green and blue dashed curves display B s and p orbitals, respectively. The vertical dashed line is the Fermi level. G

DOI: 10.1021/acs.inorgchem.7b02550 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 8. (a) Typical SEM image of VB2 crystals (the inset shows the EDS measurement). (b) Thermogravimetric curves for VB2 bulk sample synthesized at 8 GPa/1700 K. (c, d) XPS spectra for B 1s and V 2p core levels for the sample synthesized at 8 GPa/1700 K. The observed spectra (open circles) were fitted to a Gaussian and Lorentzian combination.

components, V 2p1/2 and V 2p3/2, owing to strong spin−orbit coupling of 2p states (Figure 8d). Both have a doublet structure, which differ from the singlet peak of metal V. This phenomenon demonstrates that anion−cation hybridization in VB2 gives rise to the split doublet structure of V 2p1/2 and V 2p3/2.74 The high binding energies of 520.5 and 523.7 eV arise from the vanadium 2p state in VB2, and the low binding energies of 513.0 and 516.1 eV are from the defects of vanadium in VB2.20,22,74

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail for P.W.: [email protected]. *E-mail for L.W.: [email protected].

■

ORCID

CONCLUSION In summary, we have successfully synthesized bulk hexagonal VB2 samples at high P and high T. VB2 exhibits a high bulk modulus of B0 = 262(2) GPa, a high thermal stability of 1410 K in air, and a Vickers hardness of 27.2 GPa. The temperaturedependent ac susceptibility has a multiple-peak structure that closely resembles antiferromagnetic transitions around 27, 43, and 195 K. VB2 also possesses an extremely small electrical resistivity (∼41 μΩ cm) at room temperature. Ab initio calculations suggest that the high-covalency V−B chemical bonds and ultrashort honeycomb B−B covalent bonds contribute to the large bulk modulus and high hardness of vanadium diboride, which is a unique combination of a hard ceramic and an excellent electric conductor.

■

diffraction patterns (Figure S2), and three-dimensional electron localization function (ELF) isosurfaces (Figure S3) (PDF)

Pei Wang: 0000-0002-0423-9639 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank Qiang Zhu for useful discussion and comments. This work was supported by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Cooperative Agreement #DE-NA0001982. The use of HPCAT (16BM-B), APS, was supported by the Carnegie Institute of Washington, Carnegie DOE Alliance Center, University of Nevada at Las Vegas, and Lawrence Livermore National Laboratory through funding from the DOE-National Nuclear Security Administration, the DOE-Basic Energy Sciences, and the NSF; the APS is supported by the DOE-BES, under Contract No. DE-AC0206CH11357.

ASSOCIATED CONTENT

S Supporting Information *

■

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02550. Bond lengths and lattice constants for VB2 (Table SI), single-crystal elastic constants (Table SII), formation enthalpy (Figure S1), high-pressure synchrotron X-ray

REFERENCES

(1) Kaner, R. B.; Gilman, J. J.; Tolbert, S. H. Designing superhard materials. Science 2005, 308, 1268−1269. (2) McMillan, P. F. New materials from high-pressure experiments. Nat. Mater. 2002, 1, 19−25.

H

DOI: 10.1021/acs.inorgchem.7b02550 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry (3) Chung, H. Y.; Weinberger, M. B.; Levine, J. B.; Kavner, A.; Yang, J. M.; Tolbert, S. H.; Kaner, R. B. Synthesis of ultra-incompressible superhard rhenium diboride at ambient pressure. Science 2007, 316, 436−439. (4) Gu, Q. F.; Krauss, G.; Steurer, W. Transition Metal Borides: Superhard versus Ultra-incompressible. Adv. Mater. 2008, 20, 3620− 3626. (5) Qin, J.; He, D.; Wang, J.; Fang, L.; Lei, L.; Li, Y.; Hu, J.; Kou, Z.; Bi, Y. Is rhenium diboride a superhard material? Adv. Mater. 2008, 20, 4780−4783. (6) Nagamatsu, J.; Nakagawa, N.; Muranaka, T.; Zenitani, Y.; Akimitsu, J. Superconductivity at 39 K in magnesium diboride. Nature 2001, 410, 63−64. (7) Zhang, R. F.; Legut, D.; Lin, Z. J.; Zhao, Y. S.; Mao, H. K.; Veprek, S. Stability and strength of transition-metal tetraborides and triborides. Phys. Rev. Lett. 2012, 108, 255502. (8) Gou, H.; Dubrovinskaia, N.; Bykova, E.; Tsirlin, A. A.; Kasinathan, D.; Schnelle, W.; Richter, A.; Merlini, M.; Hanfland, M.; Abakumov, A. M.; Batuk, D. Discovery of a superhard iron tetraboride superconductor. Phys. Rev. Lett. 2013, 111, 157002. (9) Niu, H.; Wang, J.; Chen, X. Q.; Li, D.; Li, Y.; Lazar, P.; Podloucky, R.; Kolmogorov, A. N. Structure, bonding, and possible superhardness of CrB4. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 144116. (10) Rau, J. V.; Latini, A. New hard and superhard materials: RhB1.1 and IrB1.35. Chem. Mater. 2009, 21, 1407−1409. (11) Wang, Y.; Zhang, J.; Daemen, L. L.; Lin, Z.; Zhao, Y.; Wang, L. Thermal equation of state of rhenium diboride by high pressuretemperature synchrotron x-ray studies. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 224106. (12) Zhang, M.; Wang, M.; Cui, T.; Ma, Y.; Niu, Y.; Zou, G. J. Electronic structure, phase stability, and hardness of the osmium borides, carbides, nitrides, and oxides: First-principles calculations. J. Phys. Chem. Solids 2008, 69, 2096−2102. (13) Mohammadi, R.; Lech, A. T.; Xie, M.; Weaver, B. E.; Yeung, M. T.; Tolbert, S. H.; Kaner, R. B. Tungsten tetraboride, an inexpensive superhard material. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 10958− 10962. (14) Carenco, S.; Portehault, D.; Boissiere, C.; Mezailles, N.; Sanchez, C. Nanoscaled metal borides and phosphides: recent developments and perspectives. Chem. Rev. 2013, 113, 7981. (15) Liu, C.; Peng, F.; Tan, N.; Liu, J.; Li, F.; Qin, J.; Wang, J.; Wang, Q.; He, D. Low-compressibility of tungsten tetraboride: a high pressure X-ray diffraction study. High Pressure Res. 2011, 31, 275−282. (16) Mohammadi, R.; Xie, M.; Lech, A. T.; Turner, C. L.; Kavner, A.; Tolbert, S. H.; Kaner, R. B. Toward inexpensive superhard materials: tungsten tetraboride-based solid solutions. J. Am. Chem. Soc. 2012, 134, 20660−20668. (17) Mohammadi, R.; Turner, C. L.; Xie, M.; Yeung, M. T.; Lech, A. T.; Tolbert, S. H.; Kaner, R. B. Enhancing the hardness of superhard transition-metal borides: molybdenum-doped tungsten tetraboride. Chem. Mater. 2016, 28, 632−637. (18) Lech, A. T.; Turner, C. L.; Lei, J.; Mohammadi, R.; Tolbert, S. H.; Kaner, R. B. Superhard Rhenium/Tungsten Diboride Solid Solutions. J. Am. Chem. Soc. 2016, 138, 14398−14408. (19) Gou, H.; Tsirlin, A. A.; Bykova, E.; Abakumov, A. M.; Van Tendeloo, G.; Richter, A.; Ovsyannikov, S. V.; Kurnosov, A. V.; Trots, D. M.; Konôpková, Z.; Liermann, H. P. Peierls distortion, magnetism, and high hardness of manganese tetraboride. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 064108. (20) Tao, Q.; Zheng, D.; Zhao, X.; Chen, Y.; Li, Q.; Li, Q.; Wang, C.; Cui, T.; Ma, Y.; Wang, X.; Zhu, P. Exploring Hardness and the Distorted sp2 Hybridization of B−B Bonds in WB3. Chem. Mater. 2014, 26, 5297−5302. (21) Yin, S.; He, D.; Xu, C.; Wang, W.; Wang, H.; Li, L.; Zhang, L.; Liu, F.; Liu, P.; Wang, Z.; Meng, C. Hardness and elastic moduli of high pressure synthesized MoB2 and WB2 compacts. High Pressure Res. 2013, 33, 409−417.

(22) Ma, T.; Li, H.; Zheng, X.; Wang, S.; Wang, X.; Zhao, H.; Han, S.; Liu, J.; Zhang, R.; Zhu, P.; Long, Y. Ultrastrong Boron Frameworks in ZrB12: A Highway for Electron Conducting. Adv. Mater. 2017, 29, 1604003. (23) Chen, Y.; He, D.; Qin, J.; Kou, Z.; Bi, Y. Ultrasonic and hardness measurements for ultrahigh pressure prepared WB ceramics. Int. J. Refract. Hard Met. 2011, 29, 329−331. (24) Han, L.; Wang, S.; Zhu, J.; Han, S.; Li, W.; Chen, B.; Wang, X.; Yu, X.; Liu, B.; Zhang, R.; Long, Y. Hardness, elastic, and electronic properties of chromium monoboride. Appl. Phys. Lett. 2015, 106, 221902. (25) Wang, S.; Yu, X.; Zhang, J.; Zhang, Y.; Wang, L.; Leinenweber, K.; Xu, H.; Popov, D.; Park, C.; Yang, W.; He, D. Crystal structures, elastic properties, and hardness of high-pressure synthesized CrB2 and CrB4. J. Superhard Mater. 2014, 36, 279−287. (26) Wang, C.; Tao, Q.; Ma, S.; Cui, T.; Wang, X.; Dong, S.; Zhu, P. WB 2: not a superhard material for strong polarization character of interlayer W−B bonding. Phys. Chem. Chem. Phys. 2017, 19, 8919− 8924. (27) Hao, X.; Xu, Y.; Wu, Z.; Zhou, D.; Liu, X.; Cao, X.; Meng, J. Low-compressibility and hard materials ReB2 and WB2: Prediction from first-principles study. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 74, 224112. (28) Chen, X. Q.; Fu, C. L.; Krčmar, M.; Painter, G. S. Electronic and Structural Origin of Ultraincompressibility of 5d Transition-Metal Diborides MB2 (M= W, Re, Os). Phys. Rev. Lett. 2008, 100, 196403. (29) Aydin, S.; Simsek, M. First-principles calculations of MnB2, TcB2, and ReB2 within the ReB2-type structure. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 134107. (30) Zhou, W.; Wu, H.; Yildirim, T. Electronic, dynamical, and thermal properties of ultra-incompressible superhard rhenium diboride: A combined first-principles and neutron scattering study. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 76, 184113. (31) Fahrenholtz, W. G.; Hilmas, G. E.; Talmy, I. G.; Zaykoski, J. A. Refractory diborides of zirconium and hafnium. J. Am. Ceram. Soc. 2007, 90, 1347−1364. (32) Yang, H.; Sun, H.; Chen, C. F. Is osmium diboride an ultra-hard material? J. Am. Chem. Soc. 2008, 130, 7200. (33) Lech, A. T.; Turner, C. L.; Mohammadi, R.; Tolbert, S. H.; Kaner, R. B. Structure of superhard tungsten tetraboride: A missing link between MB2 and MB12 higher borides. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 3223−3228. (34) Chen, X. L.; Tu, Q. Y.; He, M.; Dai, L.; Wu, L. The bond ionicity of MB2 (M= Mg, Ti, V, Cr, Mn, Zr, Hf, Ta, Al and Y). J. Phys.: Condens. Matter 2001, 13, L723. (35) Chen, Y.; Yu, G.; Chen, W.; Liu, Y.; Li, G. D.; Zhu, P.; Tao, Q.; Li, Q.; Liu, J.; Shen, X.; Li, H. Highly Active, Nonprecious Electrocatalyst Comprising Borophene Subunits for the Hydrogen Evolution Reaction. J. Am. Chem. Soc. 2017, 139, 12370−12373. (36) Licht, S.; Wu, H.; Yu, X.; Wang, Y. Renewable highest capacity VB2/air energy storage. Chem. Commun. 2008, 28, 3257−3259. (37) Kawai, N.; Endo, S. The generation of ultrahigh hydrostatic pressures by a split sphere apparatus. Rev. Sci. Instrum. 1970, 41, 1178−1181. (38) Wang, P.; He, D.; Wang, L.; Kou, Z.; Li, Y.; Xiong, L.; Hu, Q.; Xu, C.; Lei, L.; Wang, Q.; Liu, J. Diamond-c BN alloy: A universal cutting material. Appl. Phys. Lett. 2015, 107, 101901. (39) Wang, P.; Wang, Y.; Wang, L.; Zhang, X.; Yu, X.; Zhu, J.; Wang, S.; Qin, J.; Leinenweber, K.; Chen, H.; He, D. Elastic, magnetic and electronic properties of iridium phosphide Ir2P. Sci. Rep. 2016, 6, 21787. (40) Zhang, J.; Li, B.; Utsumi, W.; Liebermann, R. C. In situ X-ray observations of the coesite-stishovite transition: reversed phase boundary and kinetics. Phys. Chem. Miner. 1996, 23, 1−10. (41) Mao, H. K.; Xu, J.; Bell, M. Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions. J. Geophys. Res. 1986, 91, 4673−4676. (42) Toby, B. H. EXPGUI, a graphical user interface for GSAS. J. Appl. Crystallogr. 2001, 34, 210−213. I

DOI: 10.1021/acs.inorgchem.7b02550 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry (43) Segall, M. D.; Lindan, P. J.; Probert, M. A.; Pickard, C. J.; Hasnip, P. J.; Clark, S. J.; Payne, M. C. First-principles simulation: ideas, illustrations and the CASTEP code. J. Phys.: Condens. Matter 2002, 14, 2717. (44) Kresse, G.; Furthmuller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (45) Pfrommer, B. G.; Côté, M.; Louie, S. G.; Cohen, M. L. Relaxation of crystals with the quasi-Newton method. J. Comput. Phys. 1997, 131, 233−240. (46) Hill, R. The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc., London, Sect. A 1952, 65, 349−355. (47) Zhang, X.; Luo, X.; Li, J.; Hu, P.; Han, J. The ideal strength of transition metal diborides TMB2 (TM= Ti, Zr, Hf): Plastic anisotropy and the role of prismatic slip. Scr. Mater. 2010, 62, 625−628. (48) Zhou, X. F.; Qian, G. R.; Dong, X.; Zhang, L.; Tian, Y.; Wang, H. T. Ab initio study of the formation of transparent carbon under pressure. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 134126. (49) Munro, R. G. Material properties of titanium diboride. J. Res. Natl. Inst. Stand. Technol. 2000, 105, 709. (50) Sairam, K.; Sonber, J. K.; Murthy, T. C.; Subramanian, C.; Fotedar, R. K.; Hubli, R. C. Reaction spark plasma sintering of niobium diboride. Int. J. Refract. Hard Met. 2014, 43, 259−262. (51) Bulfon, C.; Leithe-Jasper, A.; Sassik, H.; Rogl, P. Microhardness of Czochralski-grown single crystals of VB2. J. Solid State Chem. 1997, 133, 113−116. (52) Gao, H.; Huang, Y.; Nix, W. D. Modeling plasticity at the micrometer scale. Naturwissenschaften 1999, 86, 507−515. (53) Kim, H. C.; Shon, I. J.; Garay, J. E.; Munir, Z. A. Consolidation and properties of binderless sub-micron tungsten carbide by fieldactivated sintering. Int. J. Refract. Hard Met. 2004, 22, 257−264. (54) Winkler, B.; Juarez-Arellano, E. A.; Friedrich, A.; Bayarjargal, L.; Schröder, F.; Biehler, J.; Milman, V.; Clark, S. M.; Yan, J. In situ synchrotron X-ray diffraction study of the formation of TaB2 from the elements in a laser heated diamond anvil cell. Solid State Sci. 2010, 12, 2059−2064. (55) Okada, S.; Kudou, K.; Iizumi, K.; Kudaka, K.; Higashi, I.; Lundström, T. Single-crystal growth and properties of CrB, Cr3B4, Cr2B3 and CrB2 from high-temperature aluminum solutions. J. Cryst. Growth 1996, 166, 429−435. (56) Ivanovskii, A. L. Hardness of hexagonal AlB2-like diborides of s, p and d metals from semi-empirical estimations. Int. J. Refract. Hard Met. 2013, 36, 179−182. (57) Zhang, X.; Hilmas, G. E.; Fahrenholtz, W. G. Synthesis, densification, and mechanical properties of TaB2. Mater. Lett. 2008, 62, 4251−4253. (58) Subramanian, C.; Murthy, T. C.; Suri, A. K. Synthesis and consolidation of titanium diboride. Int. J. Refract. Hard Met. 2007, 25, 345−350. (59) Ma, S.; Bao, K.; Tao, Q.; Xu, C.; Feng, X.; Zhu, P.; Cui, T. Investigating robust honeycomb borophenes sandwiching manganese layers in manganese diboride. Inorg. Chem. 2016, 55, 11140−11146. (60) Meade, C.; Jeanloz, R. Static compression of Ca(OH)2 at room temperature: observations of amorphization and equation of state measurements to 10.7 GPa. Geophys. Res. Lett. 1990, 17, 1157. (61) Birch, F. Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300 K. J. Geophys. Res. 1978, 83, 1257. (62) Pereira, A. S.; Perottoni, C. A.; da Jornada, J. A. H.; Leger, J. M.; Haines, J. Compressibility of AlB2-type transition metal diborides. J. Phys.: Condens. Matter 2002, 14, 10615. (63) Okamoto, N. L.; Kusakari, M.; Tanaka, K.; Inui, H.; Yamaguchi, M.; Otani, S. Temperature dependence of thermal expansion and elastic constants of single crystals of ZrB2 and the suitability of ZrB2 as a substrate for GaN film. J. Appl. Phys. 2003, 93, 88−93. (64) Lin, Z.; Wang, L.; Zhang, J.; Mao, H. K.; Zhao, Y. Nanocrystalline tungsten carbide: As incompressible as diamond. Appl. Phys. Lett. 2009, 95, 211906.

(65) Mahmud, S. T.; Islam, A. K. M. A.; Islam, F. N. VB2 and ZrB2: a density functional study. J. Phys.: Condens. Matter 2004, 16, 2335. (66) Shein, I. R.; Ivanovskii, A. L. Elastic properties of mono-and polycrystalline hexagonal AlB2-like diborides of s, p and d metals from first-principles calculations. J. Phys.: Condens. Matter 2008, 20, 415218. (67) Zhou, X.; Zhang, H.; Cheng, C.; Gao, J.; Xu, G.; Li, Y.; Luo, Y. First-principles study of structural, electronic and elastic properties of diboride of vanadium. Phys. B 2009, 404, 1527−1531. (68) Li, J.; Zhang, H.; Cheng, X.; Li, D. First-principles study of the structural and electronic properties of VB2 under high pressure. Phys. B 2010, 405, 2768−2771. (69) Pugh, S. F. XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Philos. Mag. 1954, 45, 823. (70) Savin, A.; Nesper, R.; Wengert, S.; Fässler, T. ELF: The electron localization function. Angew. Chem., Int. Ed. Engl. 1997, 36, 1808− 1832. (71) Grechnev, G. E.; Fedorchenko, A. V.; Logosha, A. V.; Panfilov, A. S.; Svechkarev, I. V.; Filippov, V. B.; Lyashchenko, A. B.; Evdokimova, A. V. Electronic structure and magnetic properties of transition metal diborides. J. Alloys Compd. 2009, 481, 75−80. (72) Basu, B.; Raju, G. B.; Suri, A. K. Processing and properties of monolithic TiB2 based materials. Int. Mater. Rev. 2006, 51, 352−374. (73) Mohammadi, R.; Turner, C. L.; Xie, M.; Yeung, M. T.; Lech, A. T.; Tolbert, S. H.; Kaner, R. B. Enhancing the hardness of superhard transition-metal borides: molybdenum-doped tungsten tetraboride. Chem. Mater. 2016, 28, 632−637. (74) Wang, S.; Yu, X.; Zhang, J.; Wang, L.; Leinenweber, K.; He, D.; Zhao, Y. Synthesis, hardness, and electronic properties of stoichiometric VN and CrN. Cryst. Growth Des. 2016, 16, 351−358. (75) Spoor, P. S.; Maynard, J. D.; Pan, M. J.; Green, D. J.; Hellmann, J. R.; Tanaka, T. Elastic constants and crystal anisotropy of titanium diboride. Appl. Phys. Lett. 1997, 70, 1959−1961. (76) Duan, Y. H.; Sun, Y.; Guo, Z. Z.; Peng, M. J.; Zhu, P. X.; He, J. H. Elastic constants of AlB2-type compounds from first-principles calculations. Comput. Mater. Sci. 2012, 51, 112−116.

J

DOI: 10.1021/acs.inorgchem.7b02550 Inorg. Chem. XXXX, XXX, XXX−XXX