Introduction

Transparent conductive materials (TCMs) play important roles in information and energy technologies and are widely used in the fields such as photovoltaic devices, sensors, flat-panel displays and organic light-emitting diodes1. Traditional TCMs are based on metals or semiconductors. Metals, for example Al, Ag and Cu, have good conductivities, but their high electron concentrations2 (> 5 × 1022 cm–3) bring metals' plasmon energies into the deep-ultraviolet spectral range, thus endowing them with a high absorption in the visible spectral range. Of the different semiconductors available, typically SnO2, ZnO and In2O3 gained widespread attention for their potential applications in the visible and near-ultraviolet spectral range. To make them conductive, element doping was adopted and SnO2:X, In2O3:Sn (ITO) and ZnO:X (where ‘X’ is a dopant) become popular transparent conductive oxides (TCOs) today. However, an intrinsic conductor with a good transmittance at the visible region is an ideal target in view of conductive and optical requirements, especially in the field of solar energy.

Although be paid less attentions, the mechanical parameters also have direct implications for the high performance of TCM-based devices or designing stress-free TCM films on both rigid and flexible substrates. The studies on the mechanical properties so far have been mainly on the scratch resistance of TCM films. Not much is known about the design principles on the hard transparent conductors. One guiding suggestion for forming hard materials has been to increase the sp3 concentration in which tetrahedral hybrids contributes to the hardness and extensive experimental and theoretical efforts have been devoted to searching of diamond-like covalent compounds formed by B, C and N3,4,5. However, those sp3-bonded materials are often related to a wide band gap and there is no reason to expect these compounds comparable in hardness to diamond would show conductivity. On the contrary, the conventional TCOs, such as F-doped SnO2 (FTO), Zn-doped In2O3 (IZO) and ITO, have a Vickers hardness lower than 10 GPa6,7, thus the contradictory mechanical and electrical properties seem hardly to coexist in a stable compound.

An inspiration for designing hard transparent conductors can be derived from graphene8,9. This hard carbon film is a zero bandgap semiconductor with a low resistivity comparable to metals (~10−8 Ωm) and low high electron concentrations (< 0.3 × 1021 cm−3) endowing it almost fully transparent at visible region2. At present, the development of graphene as a TCM is largely restricted by the coupling between graphite sheets. Since the outstanding mechanical, electronic and optical properties of graphene are attributed to the hybrids of sp2 bonds formed intra-graphite sheet, it is expected to fabricate a sandwich-like structure in which the sp2 bonded graphite layers is clipped through hybridized bonding by two "buns". The strong hybrids between sheets keep the hardness and the sp2 bonds in the graphite layer promote conductivity. In addition, this structure should be thermodynamically, mechanically and dynamically stable at ambient conditions.

In order to explore a compound meeting those stringent conditions, we need to select an appropriate system in which the desirable performances may be obtained. Many experimental and theoretical studies indicate that TiO2 have a series of high-pressure phases possessing very high hardness. For example, the cotunnite-structured TiO2 was once thought to be the hardest oxide10 and the Fe2P-type TiO2 was proved to be the densest phase in major metal dioxides11. In addition, doped-TiO2 was reported to be a transparent oxide12. Thus the hardness and transparency requirements can be expected in the TiO2-based system. To pursue high conductivity, we should further introduce carbon element and TiC is thus chosen as the other terminal compound which has a comparable bulk moduli (241 GPa)13 to that of the cotunnite-structured TiO2 (246 GPa)11. Therefore, the TiO2-TiC pseudo-binary system is a promising candidate in which our desired mechanical, electrical and optical properties may be achieved through a stable Ti-C-O ternary compound. However, such a ternary compound is not available at ambient conditions according to the present phase diagram and crystal structure database.

The high-pressure behavior of materials now can be experimentally studied at pressures over 300 GPa14, which motivates searching high-pressure phases in various systems by ab-initio simulations15,16. In the present work, thermodynamically stable compounds in TiO2-TiC system are searched at both ambient and selected high pressures using evolutionary algorithm USPEX17,18,19,20. This popular method is reasonable and accurate in the multidimensional-compounds-predicting and can simultaneously search stable stoichiometries and the corresponding structures together in multi-component systems. Furthermore, the properties of observed novel intermediate compounds in the TiO2-TiC system, including mechanical modulus, electronic structure and optical absorption, are investigated to test our tentative ideals. For the first time, we report two Ti-C-O ternary hard and transparent conductors, namely Ti5C2O6 and Ti3C2O2. Both compounds are stable at ambient conditions with wonderful structural, mechanical, electronic and optical properties.

Results and Discussion

The detail convex hull diagram of TiO2-TiC system at selected pressures are shown in Fig. 1 and we will discuss structural, mechanical, electronic and optical properties of stable compounds in the following two sections.

Figure 1
figure 1

Thermodynamical stability of novel Ti-C-O ternary compounds.

Convex hull diagram for the TiO2-TiC system at selected pressures. The blue solid circles represent stable compounds and the open circles represent meta-stable compounds.

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Terminal compounds in TiO2-TiC system

In TiO2 family, many phases11,21 at constant-, low-, or high-pressure conditions have been reported including anatase (AN), rutile (RT), brookite (BR), columbite (CB), baddeleyite (MI), orthorhombic I (OI), pyrite (PI), fluorite (FL), cotunnite (OII) and Fe2P-TiO2.

In most studies, the starting material at ambient pressure is AN or RT. AN is believed to be more stable than RT when the particle size decreases below 14 nm22. CB and MI are low-pressure phases (below 20 GPa) and the transition sequence under pressure are AN or RT or BR→CB→MI21. At 35 GPa, a Pca21-TiO2 is found energetically close to the MI and cotunnite and conceived as a metastable polymorph of TiO223. Above 50 GPa, OI, PI and FL phases were experimentally and theoretically reported to convert to the OII phase10,21, suggesting that the cotunnite becomes more stable after overcoming a energy barrier. Above 150 GPa, as a post-cotunnite phase, the existence of Fe2P-TiO2 has been proved by a recent crucial high-pressure experiment11.

According to Fig. 1, the enthalpy searching algorithm implemented in USPEX yields anatase-TiO2 (space group I41/amd) and cotunnite-TiO2 (space group Pnma) as the final thermodynamically stable phases at ambient and selected high pressure range (50 ~ 150 GPa), respectively. At 50 GPa, we further analyzed the metastable phases relative to the stable cotunnite. The closest structure in energy to the cotunnite is Pca21-TiO2, then baddeleyite-TiO2 (space group P21/c) is found as a next-metastable phase. The calculated energetic order is consistent with the reported pressure-induced phase transition of TiO2 around 50 GPa24. Above 150 GPa, USPEX finds that the Fe2P-TiO2 (space group P-62m) high-pressure phase become more stable. Thus, our present theoretical predictions on the stable phases of TiO2 at different pressures are well consistent with the known experimental observations, further confirming that USPEX predictions are reasonable.

The other terminal, TiC, was found as a NaCl-B1 (space group Fm-3m) structured crystal at ambient conditions25. In Fig. 1, our detailed enthalpy calculations show that B1-structured TiC seems unshakeable until ~100 GPa. Then C2/m-TiC is found more thermodynamically stable between 100 ~ 150 GPa. Finally, Cmcm-structure notably appeared above 150 GPa as the final high-pressure phase for TiC.

Several transition mechanisms have been used to interpret the high pressure phase transition of B1-structured carbides. It was proposed that most B1-structured compounds follow the B1→CsCl-B2 phase transition route under pressure26. Then, it was experimentally reported that a B1→R (rhombohedron), instead of B1→B2, phase transition in TiC occurred at a pressure above 18 GPa27. However, after re-evaluating these experiments, no phase transition in TiC was really found at pressures up to 26 GPa28. Recently, a new B1→C2/m→Cmcm three high-pressure phase transition route for TiC was put foward29. Our predictions on TiC high-pressure phases totally support this latest investigation.

Novel intermediate compounds in TiO2-TiC system

Based on the convincing results above related to TiO2 and TiC terminal compounds, we can further predict Ti-C-O ternary stable phases in the TiO2-TiC system. In Fig. 1, no thermodynamically stable Ti-C-O ternary compound is observed at 0 GPa. This is consistent with the currently known inorganic crystal structure data. Then, as the first stable intermediate compound in the TiO2-TiC system, Ti5C2O6 (TiO2:TiC = 3:2) appears at ~50 GPa with a monoclinic structure (space group Pm). At a higher pressure (~100 GPa), the second intermediate compound Ti3C2O2 (TiO2:TiC = 1:2) with a hexagonal lattice (space group P3m1), is further found thermodynamically stable in the TiO2-TiC system. Detailed enthalpy calculations show that Pm-Ti5C2O6 phase disappears at ~130 GPa, while P3m1-Ti3C2O2 phase can be thermodynamically stable up to 200 GPa in the TiO2-TiC system.

Ti5C2O6 and Ti3C2O2 has respective unique structural feature. In the Ti5C2O6 lattice, the sp1 hybridized zigzag carbon chains are surrounded by Ti-O polyhedral and run through these cages along the b-axis, forming a tube-structure; while in the Ti3C2O2 lattice, double TiO6 polyhedral are separated by the sp2 hybridized non-coplanar hexagon graphite layer along the c-axis, forming a sandwich-like layer structure. The detail top and side views of the two structures are presented in Fig. 2. The full structural parameters (in cif format) of two compounds can be found in the Supplementary Information.

Figure 2
figure 2

Structural feature.

Top- and side- views of Ti5C2O6 (a) and Ti3C2O2 (b) lattices. In Ti5C2O6, the zigzag carbon chains run through Ti-O polyhedral along the b-axis. In Ti3C2O2, TiO6 polyhedral are separated by the non-coplanar hexagon graphite layers along the c-axis. In (a) and (b), cyan atoms represent titanium, brown atoms represent carbon and red atoms represent oxygen.

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To check the dynamical stability at ambient conditions for the two new Ti-C-O ternary compounds, their structures are fully relaxed and phonon dispersion curves at 0 GPa are calculated. In Fig. 3, no imaginary phonon frequency is observed in the whole Brillouin-zone, indicating that Ti5C2O6 and Ti3C2O2 are both dynamically stable at ambient pressure.

Figure 3
figure 3

Dynamical stabilities.

Phonon dispersion curves at 0 GPa for Ti5C2O6 (a) and Ti3C2O2 (b). No Imaginary frequency is observed in the whole Brillouin-zone.

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The mechanical stability of a structure can be assessed by the elastic constants of the crystal which should satisfy Born elastic stability criteria. Using stress-strain relations, the independent elastic constants of Ti5C2O6 and Ti3C2O2 phases at the zero-pressure are calculated and listed in the Supplementary Information (Table Is). For the monoclinic-Ti5C2O6, the mechanical stability30 are indicated by C11 > 0, C22> 0, C33> 0, C44> 0, C55> 0, C66> 0, [C11+ C22+ C33+ 2(C12+ C13+ C23)] > 0, (C33C55− C235) > 0, (C44C66− C246) > 0 and (C22+ C33− 2C23) > 0; while the stability criteria30 for the hexagonal-Ti3C2O2 are given by C44 > 0, C11 > |C12| and (C11 + 2C12)C33 > 2C213. Obviously, the calculated elastic constants of two ternary compounds fulfill their respective stability criteria.

It is believed the hardness of a compound are related to the elastic parameters, namely bulk modulus B, shear modulus G, Young's modulus E and Poisson's ratio ν31. B and G are calculated by means of the single-crystal elastic constants and the Voigt-Reuss-Hill relations32 and E and ν can be subsequently deduced as E = 9BG/(3B + G) and ν = (3B − 2G)/[2(3B + G)], respectively. In Table I, the calculated bulk moduli for Ti5C2O6 and Ti3C2O2 (228 GPa and 259 GPa) are close to that of cotunnite-TiO2 (246 GPa)10. It was believed that materials having lower G/B and higher v will exhibit better intrinsic plasticity33 and we can thus predict that Ti5C2O6 has a more flexible lattice while the structure of Ti3C2O2 is relatively rigid.

Table 1 The bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio ν and G/B ratio of monoclinic-Ti5C2O6 and hexagonal-Ti3C2O2. All elastic parameters except ν and G/B are in GPa
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The hardness of a crystal can be directly rated by Vickers hardness (HV). The macro- and micro-models for the hardness prediction can be found in Tian's report34. In this study, we evaluate HV of two ternary Ti-C-O compounds based on both Chen's macro-fitting formula35,36 and the micro-electronegativity (EN) model37,38. Using Chen's formula:

the hardness of a compound can be directly obtained from its bulk and shear modulus. For a covalent crystal with n-types of bonds, micro-EN hardness is expressed as

where V is the volume of the unit cell (Å3) and Nab is the number of bonds of a-b kind in the unit cell. Coefficients 423.8, 2.7 and −3.4 were obtained in Ref. 37 by fitting to experimental data for hard materials. In the equation (2), fi is an ionicity indicator of the band a-b and Xab is named as the bond-EN between atoms a and b. In the EN model, fi and Xab can be deduced from the element-EN and element coordination number (CN) in the form of

where χaand χbare the EN of elements a and b and CNa and CNb are respective coordination number of atoms a and b. In Ti5C2O6 and Ti3C2O2, three types of bands, i.e. Ti-O, Ti-C and C-C, are formed. The detail parameters are listed in Table II and both macroscopic and microscopic models yields consistent hardness: ~16 GPa and ~22 GPa for Ti5C2O6 and Ti3C2O2, respectively. It was reported that the experimental hardness of ITO and IZO is 6.5 ± 1.6 GPa and 10.6 ± 3.3 GPa39, respectively, thus we surprisingly found that the two new T-C-O compounds are about twice harder than these conventional transparent conducting oxides.

Table 2 The Vickers hardness (in GPa) of monoclinic-Ti5C2O6 and hexagonal-Ti3C2O2. Hmic is the hardness calculated with the micro-electronegativity (EN) model, while Hmac is obtained through the macro-fitting formula
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The PBE40 exchange-correlation functional is used to calculate the band structures and partial density of electronic states (PDOS) of Ti5C2O6 and Ti3C2O2. In Fig. 4, electronic structure calculations clearly show that Ti5C2O6 and Ti3C2O2 are intrinsic conductors. By comparison, the band structures of two new ternary compounds obtained by the HSE41 method are shown in the Supplementary Information and no bandgaps are found, which further proves the metallic properties of two compounds. We compare PDOS of Ti5C2O6 and Ti3C2O2 with that of TiO2. For TiO2 semiconductor, it was known that its upper valence band is essentially of O-2p bonding type with a small presence of Ti-3d states and the edge of conduction band is dominated by Ti-3d orbitals with a small contribution from O-2p levels42. In the Ti5C2O6 and Ti3C2O2 ternary compounds, we found similar bonding feature analogy to the valence bands and conduction bands in TiO2 (see Fig. 4). However, the original band gaps in TiO2 are filled by Ti-C bonds in the Ti-C-O compounds in which Fermi-levels are located at the conduction bands zone. Therefore, Ti5C2O6 and Ti3C2O2 are proposed as electron (n-type) conductors.

Figure 4
figure 4

Electronic properties.

Band structures and partial density of electronic states (PDOSs) at 0 GPa for Ti5C2O6 (a) and Ti3C2O2 (b), which show the metallic properties of two novel ternary compounds. Bonding features that are similar to the valence bands and conduction bands in anatase-TiO2 are circled by the ovals.

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From the PDOS, the contribution of carbon atoms to the density of states at Fermi level is much smaller than the 3d state of Ti atoms. To understand the conductive properties of novel compounds, we further calculated the conductivity components σij/τ (3 × 3 tensor) of Ti3C2O2 based on Boltzmann transport theory43, where τ is the electron relaxation times and is a constant in the compound (See details in the Supplementary Information). The results suggest that the conductivity of Ti3C2O2 is significantly anisotropic and the conductivity components along the a or b axis is about 10 times higher than that along the c axis. In Ti3C2O2, the TiO part is stacked along the c axis while carbon is extended along the ab plane. Then we can deduce that the TiO part contribute little to the conductivity when compared with carbon. A major channel for the carrier transport may be expressed as that the nonlocalized Ti_3d electrons move to carbon through the Ti-C coupling and then flow along ab plane through the graphite layers. The Ti5C2O6 compound may hold similar hypothesis.

The stable, hard and conductive characteristics of these two ternary compounds drive us to further investigate their transparency towards visible light band. The calculated optical absorption coefficients of Ti5C2O6 and Ti3C2O2 are shown in Fig. 5 and compared with that of SnO2, a principal constituent of conventional TCOs. It delights us that Ti3C2O2 has a weaker optical absorption activity than SnO2 in the visible light region, indicating that Ti3C2O2 is more transparent. However, Ti5C2O6 is not as good as Ti3C2O2 at the optical transparency in view of its relative higher optical absorption than SnO2. The optical absorption coefficient is frequency dependant and different optical adsorption behaviors of Ti3C2O2 and Ti5C2O6 are related to their respective electronic transitions between energy levels.

Figure 5
figure 5

Optical absorptions.

The absorbance of Ti5C2O6 and Ti3C2O2 compared with that of SnO2 bulk materials. In the visible region, the lower optical absorption in Ti3C2O2 results in an increased transparency relative to SnO2.

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The primary n-type TCOs have remained virtually unchanged for about 30 years. FTO, ITO and F- or Al-doped ZnO44 have been the principal commercial TCOs45. Recent work has begun to explore ternary compounds, for example Cd2SnO4, Zn2SnO4, MgIn2O4, ZnSnO3, GaInO3, Zn2In2O5 and ZnGa2O4, as new n-type transparent conductive materials46,47,48,49,50. Our novel Ti-C-O ternary compounds in the TiO2-TiC system, Ti5C2O6 and Ti3C2O2, are found to have attractive mechanical, electronic and optical properties and can be more robust, cost-effective and environmentally benign TCOs used in the environments where conventional transparent conducting materials have difficulties. Following the same materials designing route, we propose that Zr(Hf)O2-Zr(Hf)C can also be expected as promising pseudo-binary systems in which wonderful TCOs may exist, because Zr(Hf)O2 and Zr(Hf)C are similar to TiO2 and TiC in the aspects of structure and phase transition characteristics. The ideals and schemes adopted here toward searching and designing multi-components materials is instructive for developing novel functional materials in the near future.

In summary, to develop novel hard transparent conductors, we explore Ti-C-O ternary compounds in the TiO2-TiC system at ambient and selected high-pressure conditions using ab-initio evolutionary algorithm USPEX. Two new compounds, Ti5C2O6 and Ti3C2O2, are reported for the first time and found to be mechanically and dynamically stable at the ambient pressure with respective unique structure. The sp1 hybridized carbon chains and sp2 hybridized hexagon graphite layers enable Ti5C2O6 and Ti3C2O2 to be efficient intrinsic conductors, while the high-coordinated Ti-O polyhedral guarantee their hardness to be twice harder than that of conventional transparent conducting materials. The optical transparencies of two new compounds are comparable to that of SnO2 in the visible light band and Ti3C2O2 is more transparent. These mechanical, electronic and optical properties make Ti5C2O6 and Ti3C2O2 be attractive hard transparent conductors. More significantly, the ideals and methods towards designing and predicting materials in this work can be applied to other compound systems for the searching of novel functional materials.

Methods

USPEX structure prediction

Combining the evolutionary algorithm USPEX17,18,19,20 with the ab-initio total energy program VASP51, we predict thermodynamically stable structures in the TiO2-TiC system. To construct the pseudopotentials (PPs) of Ti, C, O elements, we treat their respective 3s23p64s23d2, 2s22p2 and 2s22p4 orbitals as valence electronic configurations throughout this work. For bulk geometry optimizations, PBE40 exchange-correlation functional with and without the van der Waals correction52 are adopted respectively and two functionals lead to same results. The plane-wave kinetic energy cutoff is set to 600 eV and the Brillouin zone is sampled with a resolution of 2π × 0.05, which show excellent convergence of the energy differences, stress tensors and structural parameters. The maximum total numbers of atoms in the unit cell are limited to 16 and 32, respectively and enthalpy calculations are performed at pressures of 0 GPa, 50 GPa, 100 GPa, 150 GPa, 200 GPa. The first generation of structures is created randomly, then energetically worst structures (40%) are discarded and a new generation is created from the remaining structures through heredity, lattice mutation and permutation of atoms. The most favorable structures are transferred into the next generation. We generally terminate the runs after 50 generations and all runs have found the minimum-enthalpy structures much earlier.

Phonon dispersion curves

All obtained intermediate compounds are fully relax at constant pressure. To ensure sufficient convergence criteria, the total Hellmann-Feynman force with respect to the structural degrees of freedom is set to 0.01 meV/Å. The quasi-harmonic approximation which has been implemented in the PHON code53 is used to calculate phonon dispersion curves.

Electronic and optical properties

The electronic calculations for the stable Ti-C-O conductors are performed based on density functional theory (DFT) within the framework of PBE approximation. The kinetic-energy cutoff for electronic plane waves is set to 600 eV and the Brillouin-zone integrations are performed using 18 × 18 × 18 k-point meshes. The optical absorptions are calculated using HSE41 functional which has been implemented in the VASP code. The frequency dependent dielectric matrix are first determined based on the calculations of electronic ground states, then the absorption coefficients can be derived from the real and imaginary parts of the dielectric function54.

Ideal shear strength

The shear stress is calculated by straining the crystal in a series of incremental simple shears, calculating the stress as a function of the strain55. Here, a series of shear strains perpendicular to the carbon chains and to the normal of graphite planes are applied to Ti5C2O6 and Ti3C2O2 equilibrium cell, respectively. Using a Cartesian coordinate, the x-vector is selected as perpendicular to the slip plane and the z-vector parallel to the slip direction in the plane. Incrementally deformed lattices are relaxed with respect to the basis vectors orthogonal to the applied strain and the atoms inside the cell.