A lot of physical properties of Th2S3-type Ti2O3 have investigated experimentally, hence, we calculated electronic structure and thermoelectric transport properties by the first-principles calculation under pressure. The increase of the band gaps is very fast from 30GP to 35GP, which is mainly because of the rapid change of the lattice constants. The total density of states becomes smaller with increasing pressure, which shows that Seebeck coefficient gradually decreases. Two main peaks of Seebeck coefficients always decrease and shift to the high doping area with increasing temperature under pressure. The electrical conductivities always decrease with increasing temperature under pressure. The electrical conductivity can be improved by increasing pressure. Electronic thermal conductivity increases with increasing pressure. It is noted that the thermoelectric properties is reduced with increasing temperature.

The electronic structure of bulk titanium sesquioxide (Ti2O3) has been the object of much experimental and theoretical investigation in the past few decades. The importance of transition-metal oxides in technological applications has motivated several experimental and theoretical studies. Titanium oxides are particularly well studied because they share the same transition metal but with different structures and properties.1–8 An oxide with trivalent titanium, i.e. Ti2O3, has a dual importance. This is a system with an intermediate between TiO and TiO2 ratio of O/Ti = 1.5, and hence intermediate titanium valence; for this reason an investigation of its properties is critically important for an understanding of the Ti–O system. Sesquioxides are also an important class of materials for condensed matter physics, since their fundamental properties partly predetermine those of the more complex ‘mixed sesquioxides’ with exciting physical behaviour.

Very recently, a new polymorph of Ti2O3 can be indexed on a Pnma orthorhombic cell, and the unit-cell parameters are a = 7.6965 Å, b = 2.8009 Å, c = 7.9300 Å, V = 170.95 Å3 at 19 GPa, and a = 7.8240 Å, b = 2.8502 Å, c = 8.1209 Å, V = 181.10 Å3 at ambient conditions.9 Thermoelectric-power measurements in these alloys have been carried out. For T > 350 K the Seebeck coefficient S for pure Ti2O3 diminished rapidly with increasing T, which reflects the semiconductor-to-metal transition. Thermoelectric power was also measured for rhombohedral Ti2O3.10 The negative value of thermo-power within the whole temperature range indicates that the electrons are the majority carriers over the investigated range of temperature for rhombohedral Ti2O3. The samples of the Th2S3-type Ti2O3 were examined by Raman, absorption, and reflectance spectroscopy as well as by measurements of electrical resistivity, Hall effect, thermoelectric power, and magnetoresistance. In addition, electronic band-structure calculations were performed.11 The high-pressure electronic transport studies confirmed that the Th2S3-type Ti2O3 remains semiconducting up to 21 GPa at ambient and low temperatures down to 4.2 K.12 

However, thermoelectric transport properties have not been explored. In the present work, we performed carefully the theoretic investigations of electronic structure and thermoelectric transport properties of high pressures up to 60 GPa at the different temperature.

Our calculations were performed by using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code.13 The exchange-correlation energy is in the form of Perdew–Burke–Ernzerhof14 with generalized gradient approximations (GGA). We take RmtKmax equal to 8.5 and make the expansion up to l=10 in the muffin tins spheres (MT). Nonoverlapping MT sphere radii of 1.99 and 1.77 a.u. were used for Ti and O, respectively. We have used 15 × 42 × 15 meshes for this material, which represents 10000 k-points in the first Brillouin zone. Self-consistency is considered to be achieved when the total energy difference between succeeding iterations is less than 10−5 Ry per formula unit.

The method for the calculation of transport properties of a crystalline solid is based on the semiclassical Boltzmann theory15 and the rigid band approach. This ab initio approach has succeeded in rationalizing and predicting the optimal doping level of known compounds.16–21 Our transport calculations are performed from the electronic structure using the semiclassical Boltzmann theory as implemented in the BOLTZTRAP code.22 The relaxation time τ is inserted as a constant, and doping is treated within the rigid band approximation.23 

The atomic position and the lattice constants of Ti2O3 are determined theoretically by minimizing the total energy using the first-principles electronic structure calculation within the Pnma symmetry. After geometry optimization, we find that the calculated lattice constants are a = 7.8764 Å, b = 2.8517 Å, c = 8.1957 Å, which are very close to those found experimentally.11,12 To compare with the available experimental data under different pressures, the calculated equilibrium lattice constants and the band gaps are listed in Table I. It is noted that the lattice constants decrease with increasing pressure, whereas band gaps increase. It is clear that the calculated lattice parameters are in good agreement with the experiments, which shows that our method is reliable. These calculated lattice constants are slightly larger than the experimental values because the GGA often overestimates the lattice constants.24 

TABLE I.

Lattice parameters and band gaps. (experimental results 11, 12 in parenthesis).

GP a (Å) b (Å) c (Å) band gap (eV)
7.8764 (7.8248)  2.8517 (2.8507)  8.1959 (8.0967)  0.3007 (∼0.1–0.2 eV) 
7.8260  2.8343  8.1299  0.3070 
10  7.7804  2.8184  8.0697  0.3110 
15  7.7393  2.8036  8.0150  0.3145 
20  7.7015  2.7900  7.9635  0.3174 
25  7.6667  2.7771  7.9154  0.3209 
30  7.6346  2.7650  7.8701  0.3239 
35  7.5389  2.7286  7.7758  0.3349 
40  7.5131  2.7183  7.7368  0.3365 
45  7.4890  2.7086  7.7016  0.3381 
50  7.4654  2.6994  7.6688  0.3407 
55  7.4433  2.6906  7.6370  0.3428 
60  7.4223  2.6821  7.6067  0.3439 
GP a (Å) b (Å) c (Å) band gap (eV)
7.8764 (7.8248)  2.8517 (2.8507)  8.1959 (8.0967)  0.3007 (∼0.1–0.2 eV) 
7.8260  2.8343  8.1299  0.3070 
10  7.7804  2.8184  8.0697  0.3110 
15  7.7393  2.8036  8.0150  0.3145 
20  7.7015  2.7900  7.9635  0.3174 
25  7.6667  2.7771  7.9154  0.3209 
30  7.6346  2.7650  7.8701  0.3239 
35  7.5389  2.7286  7.7758  0.3349 
40  7.5131  2.7183  7.7368  0.3365 
45  7.4890  2.7086  7.7016  0.3381 
50  7.4654  2.6994  7.6688  0.3407 
55  7.4433  2.6906  7.6370  0.3428 
60  7.4223  2.6821  7.6067  0.3439 

Figure 1 presents the results of band structures along the high symmetry directions at different pressures. It is clearly seen that the band structures of Ti2O3 are significantly modified near the Fermi level with increasing pressure. These calculated band gaps are higher than the experimental values12 because the experimental band gap was measured from the golden polymorph of Ti2O3. It is noted that the conduction band (CB) and the valence band (VB) move away from the Fermi level, which is mainly caused by the increase of band gaps. It is interesting that the increase of the band gaps is very fast from 30GP to 35GP, which is mainly because of the rapid changing of the lattice constants.

FIG. 1.

Band structures of Ti2O3 under the different presures.

FIG. 1.

Band structures of Ti2O3 under the different presures.

Close modal

To see clearly the states of the valence bands (VB) and the conduction bands (CB) near the Fermi level, the total density of states (DOS) of Ti2O3 and the projected density of states (PDOS) of atoms are calculated and shown in Fig. 2 and Fig. 3 at different pressures. The total DOS becomes smaller with increasing pressure. It is seen that the electrons of CB move up and tend to lessen with increasing pressure; moreover, the electrons of VB rapidly move down and tend to lessen with increasing pressure. It is seen that the growth of band gap is mainly due to p states of O atoms. The above density of states shows that Seebeck coefficient gradually decreases with increasing pressure.

FIG. 2.

Total density of states of Ti2O3 is presented at different pressures.

FIG. 2.

Total density of states of Ti2O3 is presented at different pressures.

Close modal
FIG. 3.

Partial density of states of Ti2O3 at different pressures.

FIG. 3.

Partial density of states of Ti2O3 at different pressures.

Close modal

As seen from Fig. 3, the top of the VB is mainly derives from O p states, and the bottom of the CB is primarily dominated by Ti d states. O p states of the top of the VC change a lot with increasing pressure; however, Ti d states of bottom of the CB change very little. Therefore, its thermoelectric properties are mainly determined by O p states. It is seen that the varieties of the density of states near the Fermi level are mainly caused by Ti d states and O p under the different pressures. Therefore the growth of band gap is mainly due to O p states and Ti d states.

It should be noted that our conclusions are correct only when the chemical potential is near the Fermi level. Thus, we only give calculated transport coefficient within the carrier concentration ranging from −0.2 e/uc to 0.2 e/uc, without considering the specific dopant elements. Seebeck coefficient under pressure as a function of carrier concentration is shown in Fig. 4 with different temperatures for Ti2O3. It can be seen that two main peaks of the Seebeck coefficients always decrease and shift to the high doping area with increasing temperature under different pressures. With increasing pressure, the Seebeck coefficient changed little at 300K; however, the Seebeck coefficient increases at 900K. For p-type doping, the peaks of Seebeck coefficient almost changes little at 300K with increasing pressure, and furthermore, the change of the peaks of Seebeck coefficient is also small for n-type doping. The peaks of Seebeck coefficient begins to change at 500K and 700K with increasing pressure, but the change is very small. The peaks of Seebeck coefficient increase at 900K with increasing pressure, regardless of the doping type.

FIG. 4.

Seebeck coefficient under different pressure with different temperatures as a function of carrier concentration for Ti2O3.

FIG. 4.

Seebeck coefficient under different pressure with different temperatures as a function of carrier concentration for Ti2O3.

Close modal

Electrical conductivity relative to relaxation time under pressure as a function of carrier concentration is shown in Fig. 5 with different temperatures for Ti2O3. Regardless of n-type or p-type doping, electrical conductivities increase with increasing carrier concentration, which is in agreement with electrical conductivity proportional to the carrier concentration. However, the electrical conductivities for n-type doping increase much faster than that for p-type doping. Electrical conductivities increase with increasing pressure at 300K, which is in agreement with the experimental values.12 The calculated results show that electrical conductivity can not be improved by improving temperature. However, electrical conductivity can be improved by increasing pressure.

FIG. 5.

Electrical conductivity relative to relaxation time under different pressure with different temperatures as a function of carrier concentration for Ti2O3.

FIG. 5.

Electrical conductivity relative to relaxation time under different pressure with different temperatures as a function of carrier concentration for Ti2O3.

Close modal

Electronic thermal conductivity κ0 under different pressures as a function of carrier concentration is shown in Fig. 6 with different temperatures for Ti2O3. The electrical conductivity increases rapidly with increasing temperature. Regardless of n-type or p-type doping, electronic thermal conductivity increases with increasing carrier concentration. Electronic thermal conductivity increases with increasing pressure. The above results show that electronic thermal conductivity can not be reduced by increasing carrier concentration and improving temperature.

FIG. 6.

Electronic thermal conductivity κ0 under different pressure with different temperatures as a function of carrier concentration for Ti2O3.

FIG. 6.

Electronic thermal conductivity κ0 under different pressure with different temperatures as a function of carrier concentration for Ti2O3.

Close modal

ZeT as a function of carrier concentration is shown in Fig. 7 with different temperatures for Ti2O3. The main peaks of ZeT decrease and shift to the high doping area with increasing temperature for Ti2O3. The above results are mainly because the electronic thermal conductivity rapidly increases with increasing temperature and the main peaks of the Seebeck coefficient shift to high doping area. It is seen that ZeT of p-type doping decreases faster than that of n-type doping, which is mainly because electrical conductivity of p-type doping decreases faster than that of n-type doping. The main peaks of ZeT decrease with increasing pressure at 300K, 500K and 700K for n-type doping, however, the main peaks of ZeT increase with increasing pressure at 900K for n-type doping. In general, the thermoelectric properties are reduced with increasing temperature, which is mainly because of the increase of the electronic thermal conductivity rapidly, and the decrease of Seebeck coefficient and electrical conductivity.

FIG. 7.

ZeT under different pressure with different temperatures as a function of carrier concentration for Ti2O3.

FIG. 7.

ZeT under different pressure with different temperatures as a function of carrier concentration for Ti2O3.

Close modal

In summary, the electronic structure and transport properties of Ti2O3 are studied using the first-principles calculations. It is noted that the lattice constants decrease, whereas band gaps increase with increasing pressure. The total density of states becomes smaller with increasing pressure, which shows that Seebeck coefficient gradually decreases with increasing pressure. There is high DOS near the Fermi level, so Ti2O3 is one of the good thermoelectric materials. Two main peaks of Seebeck coefficients always decrease and shift to the high doping area with increasing temperature. The electrical conductivities always decrease with increasing temperature. Electronic thermal conductivity rapidly increases with increasing temperature. ZeT first increases, and then decreases as the carrier concentration increase.

This research was sponsored by the National Natural Science Foundation under Grant No. U1404108, The research projects of science and technology of the Education Department of Henan province (12A140008), Funding scheme for young teachers in Colleges and universities in Henan Province (2012GGJS-104), Henan International Cooperation projects (134300510010 )

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