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. 2016 Mar 1;6:21794. doi: 10.1038/srep21794

A new type of vanadium carbide V5C3 and its hardening by tuning Fermi energy

Wandong Xing 1, Fanyan Meng 1,a, Rong Yu 2,b
PMCID: PMC4772090  PMID: 26928719

Abstract

Transition metal compounds usually have various stoichiometries and crystal structures due to the coexistence of metallic, covalent, and ionic bonds in them. This flexibility provides a lot of candidates for materials design. Taking the V-C binary system as an example, here we report the first-principles prediction of a new type of vanadium carbide, V5C3, which has an unprecedented stoichiometry in the V-C system, and is energetically and mechanically stable. The material is abnormally much harder than neighboring compounds in the V-C phase diagram, and can be further hardened by tuning the Fermi energy.

Transition metal carbides have attracted continuing interest due to their excellent physical properties and wide engineering applications1,2,3,4,5,6. Because of the coexistence of the covalent, ionic, and metallic bonding types between the transition metals and carbon, the transition metal carbides usually have various stoichiometries. The flexibility in stoichiometry leads to rich chemical and physical behaviors, and provides a lot of candidates for materials design.

The V-C system is a typical binary system which has many different stoichiometries. V2C, V4C3, V6C5, V8C7, and VC have been synthesized and investigated for many years7,8,9,10,11. T5M3 is a common stoichiometry composed of transition metals T and main-group elements M. There are several structure types for this specific stoichiometry, including D88 (Mn5Si3, hexagonal, P63/mcm, No.193), D8l (Cr5B3, tetragonal, I4/mcm, No.140), and D8m (W5Si3, tetragonal, I4/mcm, No.140), with their prototypes and space groups given in the parentheses. For silicides of group VB transition metals, both Ta5Si3 and Nb5Si3 have the Cr5B3-type structure, and V5Si3 has the Mn5Si3-type structure12,13,14,15,16,17. But carbides with this stoichiometry have never been synthesized nor theoretically studied.

In this work, we take the V-C system as a model system to explore the possibility to design new materials by changing the stoichiometry. The calculations were performed to investigate the crystal structure, phase stability, electronic structure, and mechanical properties of V5C3. The results show that the Cr5B3-type V5C3 is stable mechanically, dynamically, and thermodynamically, and can be synthesized at high pressures. The hardness of the hard material can be enhanced further through tuning the Fermi energy.

Results and Discussion

As mentioned above, three typical structure types for T5M3, i.e., Mn5Si3, Cr5B3, and W5Si3 types are considered in this work, as shown in Fig. 1. For comparison, the known vanadium carbides in the V-C phase diagram, i.e. VC (cubic, Fm-3m), V2C (orthorhombic, Pbcn), V4C3 (hexagonal, R-3m), V6C5 (hexagonal, P31), and V8C7 (cubic, P4332) are also included in the calculations.

Figure 1.

Figure 1

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Structure models of V5C3: (a) Cr5B3-type, (b) W5Si3-type, (c) Mn5Si3-type. The large and small spheres represent V and C, respectively.

The formation enthalpy was calculated using the following equation,

graphic file with name srep21794-m1.jpg

where Etotal(VxCy) was the obtained total energies for the considered vanadium carbide, Etotal(V) and Etotal(C) were the total energy of the pure metal V and the graphite, respectively. The calculated lattice parameters and formation enthalpy ∆H at zero pressure are listed in Table 1. For the known vanadium carbides, the calculated values are in good agreement with previous calculation values.

Table 1. Calculated lattice parameters a, b and c (Å) and formation enthalpy ∆H (eV/atom).

Phase a b c ∆H Ref.
V5C3(Cr5B3) 5.485 – 10.028 −0.371 This study
V5C3(W5Si3) 8.323 – 4.361 −0.188 This study
V5C3(Mn5Si3) 6.238 – 4.532 −0.265 This study
VC 4.156 – – −0.368 This study
VC 4.091 – – −0.405 Ref. 11
VC 4.158 – – −0.216 Ref. 8
V2C 4.540 5.726 5.031 −0.432 This study
V2C 4.495 5.628 4.929 −0.466 Ref. 11
V2C 4.551 5.735 5.032 −0.164 Ref. 8
V4C3 2.918 – 27.907 −0.421 This study
V4C3 2.948 – 27.782 −0.107 Ref. 8
V6C5 5.100 – 14.351 −0.503 This study
V6C5 5.005 – 14.099 −0.541 Ref. 11
V6C5 5.101 – 14.354 −0.052 Ref. 8
V8C7 8.326 – – −0.482 This study
V8C7 8.181 – – −0.522 Ref. 11
V8C7 8.329 – – −0.036 Ref. 8
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The total energies of V5C3 as a function of volume for the three structure types are plotted in Fig. 2(a). The Cr5B3-type V5C3 has the lowest energy at all the volumes. Hereafter, only the Cr5B3-type V5C3 is considered unless stated otherwise. It is worth noting that the formation enthalpies of these vanadium carbides are all negative at zero pressure. The negative formation enthalpies indicate that the carbides are more stable than the mixture of elemental V and C.

Figure 2.

Figure 2

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(a) Energy-volume relationships for the Cr5B3-type, W5Si3-type and Mn5Si3-type V5C3. (b) The relative enthalpy-pressure diagram of the Cr5B3-type V5C3 and its respective competing phases.

For a compound to be synthesized experimentally, it is more reliable to compare its enthalpy with the known compounds of neighboring stoichiometries. In the V-C phase diagram, V5C3 would locate in the two-phase region bounded by V2C and V4C3. Therefore, we need to compare the formation enthalpy of V5C3 with the mixture of V2C and V4C3. The formation enthalpies as a function of pressure have been calculated for both V5C3 and the mixture of V2C and V4C3, as shown in Fig. 2(b). The mixture is more stable than V5C3 under pressures below 9.2 GPa, above which V5C3 becomes more stable. It indicates that V5C3 is thermodynamically more stable than that of the mixture at high pressures.

The elastic properties of a material are very important as they determine the mechanical stability, strength, hardness, and ductile or brittleness behavior. The calculated elastic constants Cij, the minimum elastic eigenvalue λ1 18, bulk modulus B, shear modulus G, Young’s modulus E, Poisson’s ratio ν and hardness Hν of these vanadium carbides are listed in Table 2. The calculated values of V2C, V4C3, V6C5, V8C7, and VC in this work are in good agreement with the previous calculation values.

Table 2. Calculated elastic constants Cij (GPa), the minimum elastic eigenvalue λ1 (GPa), bulk modulus B (GPa), shear modulus G (GPa), Young’s modulus E (GPa),Poisson’s ratio ν, and hardness Hν (GPa).

  C11 C12 C13 C23 C22 C33 C44 C55 C6 B G E ν λ1 Hν Ref.
V5C3 539 179 193 – – 492 193 – 153 278 179 441 0.235 153 21.85 This study
VC 668 130 – – – – 198 – – 309 224 542 0.208 198 29.54 This study
VC 748 139 – – – – 182 – – 342 224 551 0.230 – 25.90 Ref. 11
VC 663 122 – – – – 203 – – 302 228 546 0.198 – 31.48 Ref. 8
VC 578 147 – – – – 176 – – 291c 216c 519c – – 29.75 Ref. 9
V2C 393 181 122 189 381 410 107 125 131 240 118 303 0.290 107 7.73 This study
V2C 452 207 146 205 450 493 122 143 161 279 140 359 0.290 – 13.07 Ref. 11
V2C 400 182 120 189 383 414 110 130 135 242 121 311 0.286 – 11.70 Ref. 8
V4C3 512 124 137 – – 477 99 – 194 253 148 372 0.255 113 16.87 This study
V4C3 537 154 206 – – 480 148 – – 299 162 412 0.271 – 16.15 Ref. 8
V6C5 452 108 130 – – 472 190 – 172 235 176 422 0.200 154 26.36 This study
V6C5 505 126 155 – – 512 229 – 190 266 198 475 0.200 – 28.23 Ref. 11
V6C5 456 114 130 – – 474 189 – – 237 176 423 0.202 – 26.07 Ref. 8
V8C7 528 107 – – – – 162 – – 247 180 432 0.207 162 25.81 This study
V8C7 651 120 – – – – 179 – – 297 210 509 0.210 – 27.44 Ref. 11
V8C7 512 108 – – – – 167 – – 243 180 433 0.203 – 26.37 Ref. 8
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The Cr5B3-type V5C3 is tetragonal. For a tetragonal system, the mechanical stability criteria are given by C11 > 0, C33 > 0, C44 > 0, C66 > 0, C11 − C12 > 0, C11 + C33 − 2 C13 > 0, and 2(C11 + C12) + C33 + 4 C13 > 019. The elastic constants of the Cr5B3-type V5C3 satisfy these stability conditions, indicating that it is mechanically stable.

The phonon dispersions were calculated to verify the dynamical stability of the Cr5B3-type V5C3. A dynamically stable crystal structure requires that all phonon frequencies should be positive20. As shown in Fig. 3 for the Cr5B3-type V5C3 at zero pressure, it is clear that no imaginary phonon frequency can be found in the whole Brillouin zone, indicating that the Cr5B3-type V5C3 is dynamically stable under ambient conditions.

Figure 3. Phonon dispersions of the Cr5B3-type V5C3 at zero pressure along high symmetry directions of the Brillouin zone.

Figure 3

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Because the hardness measurement involves complex deformation processes, including elastic deformations, plastic deformations, and fracture, it is difficult to obtain directly the hardness value of a material from first-principles calculations. Therefore, correlations between elastic moduli and hardness have been suggested as indirect indicators of materials hardness. A hard material should have a high bulk modulus to resist the volume contraction in response to an applied load, and a high shear modulus to resist shear deformation. Recently, the softest elastic mode has been shown to correlate better to the hardness number than the other elastic moduli18, indicating that elastic anisotropy is essential in determining the hardness. The elastic properties (B, G, E, and λ1) of V5C3 and the other previously known vanadium carbides as a function of the V/C ratio are plotted in Fig. 4. For the know vanadium carbides, the general trend is that the elastic moduli decrease with the V/C ratio. An abnormal increase occurs at V5C3, the elastic moduli of which are higher than both the neighboring V2C and V4C3.

Figure 4.

Figure 4

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(a) The minimum elastic eigenvalue λ1, (b) shear modulus G, (c) bulk modulus B and (d) Young’s modulus E of vanadium carbides as a function of the V/C ratio. The lines are guide to the eye.

In order to explain the origin of the stability and the abnormal mechanical properties of the Cr5B3-type V5C3, the electronic structure of V5C3, V2C and V4C3 has been analyzed. Their densities of states (DOS) are plotted in Fig. 5(a). They are metallic with non-zero DOS values at the Fermi level. There are valleys (sometimes called pseudogap) close to the Fermi level for all the three compounds. In general, the electronic states with lower energies than the valley are bonding orbitals, and those with higher energies are antibonding orbitals21. To clarify the nature of the chemical bonding near the Fermi level, we performed the Crystal Orbital Hamilton Population (−COHP) analysis22, which gives an idea about the participating orbital pair. The positive value represents the bonding states and negative value represents the antibonding states. As shown in Fig. 5(c) for V5C3, it is clear that the pseudogap separates the bonding and antibonding states appears. A deeper valley means that the bonding orbitals are more stabilized and the antibonding orbitals are more destabilized, forming strong chemical bonds. Among the three compounds, V5C3 has the deepest valley close to the Fermi level. Therefore, the stability and the abnormal mechanical properties of V5C3 can be attributed to the pseudogap effect23,24.

Figure 5.

Figure 5

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(a) Densities of states of V5C3, V2C and V4C3; (b) Densities of states; and (c) Crystal Orbital Hamilton Population (−COHP) analysis of V5C3. The red vertical dashed lines denote the Fermi level at zero and the black vertical dashed lines correspond to the energy valley.

The electronic structure of V5C3 suggests an interesting method to improve its hardness. The Fermi level of V5C3 has a higher energy than the valley, indicating that some antibonding orbitals are occupied. Since the antibonding orbitals would weaken the chemical bonds, once they are made empty, the material could be further strengthened. We consider alloying V5C3 with Ti, which has one less valence electron than V. Since Ti is neighboring to V in the periodic table, it should be relatively easy to enter the lattice of V5C3. According to the rigid band model, the alloying element normally generates small changes in the nature of chemical bond in the host materials. The Cr5B3-type V5C3 with the alloying contents of 5 at.%, 10 at.%, 20 at.%, 25 at.%, and 30 at.% Ti were investigated. The supercells for the calculations are shown in Fig. 6. In order to minimize the interactions between the alloying atoms, they were placed as far as allowed in the supercells.

Figure 6.

Figure 6

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The supercells of (a) V5C3, (b) (V0.95Ti0.05)5C3, (c) (V0.9Ti0.1)5C3, (d) (V0.8Ti0.2)5C3, (e) (V0.75Ti0.25)5C3 and (f) (V0.7Ti03)5C3.

The DOS curves of V5C3 and its alloys (V1−xTix)5C3 were illustrated in Fig. 5(b). As expected, the Fermi level shifts to lower energies with increasing content of Ti from xTi = 0 to xTi = 0.3. The Fermi level is located at the valley for xTi = 0.2.

The calculated elastic constants are listed in Table 3. All the alloys are mechanically stable because the elastic constants of these alloys satisfy the mechanical stability criteria and there is no negative elastic eigenvalue. For the Cr5B3-type V5C3 and its alloys, the smallest elastic eigenvalue λ1 is C66, which represents the shear deformation in xy planes. The smallest elastic eigenvalue λ1, the hardness Hν, shear modulus G and Young’s modulus E are plotted in Fig. 7. A general trend is that λ1, Hν, G and E increase with the content of Ti from xTi = 0.05 to xTi = 0.2, where they reach their maxima, and then decrease as xTi increases further. The trend is exactly what we expect from the electronic structure analysis. At xTi = 0.2, the Fermi level is located at the valley in DOS. In this case, all of the bonding orbitals are occupied and the antibonding orbitals empty, leading to the strongest chemical bonds.

Table 3. Calculated elastic constants Cij (GPa), the minimum elastic eigenvalue λ 1 (GPa), bulk modulus B (GPa), shear modulus G (GPa), Young’s modulus E (GPa), Poisson’s ratio ν and hardness Hν (GPa) of (V1−xTix)5C3.

x C11 C12 C13 C33 C44 C66 B G E ν Hν λ1
0.00 539 179 193 492 193 153 278 179 441 0.235 21.85 153
0.05 534 66 191 483 196 144 272 177 436 0.233 21.99 144
0.10 541 69 180 504 198 145 271 182 446 0.225 23.36 145
0.20 546 72 170 480 194 167 266 186 452 0.217 24.98 167
0.25 535 72 165 475 186 166 261 182 443 0.217 24.54 166
0.30 506 50 169 456 182 124 248 165 406 0.228 21.62 124
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Figure 7.

Figure 7

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(a) The smallest elastic eigenvalue λ1, (b) hardness Hν, (c) shear modulus G and (d) Young’s modulus E of V5C3 alloys.

Conclusions

In summary, the crystal structure, phase stability, electronic structure, and mechanical properties of V5C3 have been studied. It is demonstrated that the Cr5B3-type V5C3 is thermodynamically, mechanically, and dynamically stable, and can be synthesized under pressures above 9.2 GPa.

The elastic properties and electronic structures of (V1−xTix)5C3 alloys have also been investigated. When 20 at.% V is substituted by Ti, the Fermi level is tuned to the valley in DOS, giving the maximum hardness of V5C3 alloys. While V5C3 itself is not a superhard material, the electronic structure and the hardness optimization based on it suggest an interesting way for searching hard materials. The Fermi energy of a material can be tuned to maximize the occupation of bonding orbitals and minimize the occupation of antibonding orbitals, thus strengthening the material.

Computational Methods

In this work, the density functional theory (DFT) calculations were performed using the projector-augmented wave (PAW) method25,26,27, as implemented in the Vienna Ab-initio Simulation Package (VASP) code28. The generalized gradient approximation (GGA)29 with the Perdew-Burke-Ernzerhof (PBE) scheme was used to describe the exchange-correlation function. Geometry optimization was carried out using the conjugate gradient algorithm. The plane-wave cutoff energy was 500 eV. The k-points were generated using the Monkhorst-Pack mesh30. Lattice parameters and atomic positions were optimized simultaneously. In order to obtain equilibrium volume of the materials, the total-energies were calculated at several fixed volume with the ionic positions and the cell shape allowed to vary. These total energies were then fitted with the Birch-Murnaghan equation of state31,32,33. The elastic constants were calculated using the universal-linear-independent coupling-strains (ULICS) method34, which is computationally efficient and has been widely used in calculations of single-crystal elastic constants35,36,37,38,39. Based on the single-crystal elastic constants, the bulk modulus B and the shear modulus G were calculated according to the Voigt-Reuss-Hill approximation40. Young’s modulus E and Poisson’s ratio ν were obtained by the following equation:

graphic file with name srep21794-m2.jpg
graphic file with name srep21794-m3.jpg

The hardness (Hν) of V5C3 is relative to G and B through the empirical formulabased on the Pugh modulus ratio k = G/B41,42:

graphic file with name srep21794-m4.jpg

Phonon dispersions were calculated using the direct supercell method, as implemented in the PHONOPY code43,44. The Crystal Orbital Hamilton Population (−COHP) analysis have been performed to determine the bonding properties of the electronic states close to the Fermi level. Density functional method with LCAO basis sets, as implemented in the SIESTA code45, has been used to calculate the COHP. The PBE parameterization of GGA was used. The DZP basis sets were employed. The norm-conserving Troullier-Martins pseudopotentials46 were used for the core-valence interactions. The mesh cut-off value was set at 200 Rydberg and the Brillouin zone was sampled using Monkhorst-Packset of k points.

Additional Information

How to cite this article: Xing, W. et al. A new type of vanadium carbide V5C3 and its hardening by tuning Fermi energy. Sci. Rep. 6, 21794; doi: 10.1038/srep21794 (2016).

Acknowledgments

This work was supported by National Basic Research Program of China (2011CB606406), the Fundamental Research Funds for the Central Universities (TP-A3:06108170), and NSFC (51371102, 51390475). This work used the resources of Shanghai Supercomputer Center and National Center for Electron Microscopy in Beijing.

Footnotes

Author Contributions F.M. and R.Y. proposed and supervised the project. W.X. performed the first principles calculations and prepared the figures. All authors discussed the results wrote the manuscript.

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