- Email: [email protected]
First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure
Materials Chemistry and Physics xxx (2016) 1e7
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure Qi-Jun Liu a, b, *, Han Qin a, b, Zhen Jiao a, b, Fu-Sheng Liu a, b, Zheng-Tang Liu c a
School of Physical Science and Technology, Southwest Jiaotong University, Key Laboratory of Advanced Technologies of Materials, Ministry of Education of China, Chengdu 610031, People’s Republic of China b Bond and Band Engineering Group, Sichuan Provincial Key Laboratory (for Universities) of High Pressure Science and Technology, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China c State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Physical properties of ilmenite-type ZnSnO3 under pressure have been investigated. Ilmenite-type ZnSnO3 behaves in a ductile manner. Ilmenite-type ZnSnO3 is a direct bandgap compound with 3.977 eV. Bandgap of Ilmenite-type ZnSnO3 increases with the increasing pressure.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 September 2015 Received in revised form 11 May 2016 Accepted 15 May 2016 Available online xxx
First-principles calculations of the structural, elastic, mechanical and electronic properties of ilmenitetype ZnSnO3 under pressure have been investigated in the present paper. Our calculated lattice constants at zero pressure are in agreement with the published theoretical and experimental data. The elastic constants at zero and high pressure have been obtained, which are used to discuss the mechanical stability of ilmenite-type ZnSnO3. The mechanical properties such as bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio under pressure have been studied. Electronic properties show that ilmenite-type ZnSnO3 is shown to be a direct bandgap of 1.063 (GGA-PW91)/3.977 (PBE0) eV. The bandgap increases with the increasing pressure. Moreover, the partial density of states has been analyzed to explain the increased bandgap. © 2016 Elsevier B.V. All rights reserved.
Keywords: Oxides Ab initio calculations Elastic properties Mechanical properties Electronic structure
1. Introduction ZnSnO3 has attracted wide attention due to its interesting physical properties such as polar [1], gas-sensitive [2], piezoelectric
* Corresponding author. School of Physical Science and Technology, Southwest Jiaotong University, Key Laboratory of Advanced Technologies of Materials, Ministry of Education of China, Chengdu 610031, People’s Republic of China. E-mail address: [email protected] (Q.-J. Liu).
[3], ferroelectric [4], pyroelectric [5] and optoelectronic [6] properties. Thus, it is currently under intensive study, including gas sensors [7e16], piezoelectric material for energy conversion [17,18], ferroelectric thin films [4], solar cells [19], etc. Cubic perovskitetype [16,20], LiNbO3-type [1,21], ilmenite-type [22], as well as the hypothetical phases CdSnO3-type, HgSnO3-type, post-perovskitetype [23e26] have been investigated, indicating its technological importance. Many theoretical efforts have been devoted to study the LiNbO3-
http://dx.doi.org/10.1016/j.matchemphys.2016.05.041 0254-0584/© 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
2
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7
type ZnSnO3 after it had been synthesized [1]. Within the accurate full-potential linearized augmented plane-wave method, Wang et al. [27] calculated the structural, electronic and optical properties of LiNbO3-type ZnSnO3. The obtained results showed that ZnSnO3 was a direct bandgap semiconductor of 1.0 eV. Gou et al. [28] found that LN-type ZnSnO3 had a strong covalence and a direct bandgap of 2.42 eV. Another calculated direct bandgap was 1.669 eV [29]. Furthermore, phase transition of LN-type ZnSnO3 has been reported [26,30]. However, the ilmenite-type ZnSnO3 has rarely been addressed theoretically. Using the plane wave pseudopotential density functional theory and the local density approximation, Ge et al. [29] studied the structural properties of ilmenite-type ZnSnO3 under pressure. They found there was no structural phase transition between ilmenite-type and LiNbO3-type ZnSnO3 under pressure up to 100 GPa. Then we want to further study the electronic and elastic properties of ilmenite-type ZnSnO3. Specifically, the bandgap obtained by the traditional DFT is underestimated, which should be accurately calculated. In the paper, we study the structural, elastic, and electronic properties of ilmenite-type ZnSnO3 under pressure. Moreover, we calculate the structural and mechanical properties of cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3 for comparison. This work is organized as follows: Section 2 shows the computational methods, Section 3 gives the obtained results, including structural parameters, elastic constants, mechanical properties, and electronic structures, the main conclusions are shown in Section 4. 2. Methodology All of the first-principles calculations were performed by using the CASTEP code [31]. We used the PW91 functional [32] within the generalized gradient approximation (GGA) for the exchangecorrelation functional. However, the GGA-PW91 functional can’t correctly give the band gap due to imprecise description of exchange-correlation effects. In order to gain precise band gap, we used the hybrid PBE0 functional [33]. The GGA-PW91 plus ultrasoft pseudopotential have been used to calculate structural and physical properties. The PBE0 plus norm-conserving pseudopotential have been used to obtain precise band gap (the PBE0 functional is nonlocal exchange functional, whose calculations are available for norm-conserving pseudopotential). The cut-off energy 380 eV (ultrasoft pseudopotential) and 830 eV (norm-conserving pseudopotential) were carried out. The 3 3 2, 4 4 4, 3 3 2, 3 2 3, 3 3 2, 5 1 2 Monkhorst-Pack k-point grids for ilmenite-type, cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3 were used for integrations within Brillouin zone. The Zn 3d104s2, Sn 5s25p2 and O 2s22p4 electrons were treated as valence electrons. The convergence tolerance parameters of maximum force, maximum displacement and maximum stress were 0.01 eV/Å, 5 104 Å and 0.02 GPa, respectively. 3. Results and discussion 3.1. Structural parameters
The space group of ilmenite-type ZnSnO3 is R3 , where the Zn, Sn and O atoms are located at 6c (0,0,0.3520(3)), 6c (0,0,0.1463(2)), and 18f (0.309(1), 0.002(2), 0.2470(5)) [22], respectively. The calculated lattice constants and atomic positions of ilmenite-type ZnSnO3 are listed in Table 1 along with previous theoretical [26,28,29] and experimental data [22]. It can be seen that our results are in agreement with previous data. Compared with the
experimental data, the calculated data based on the GGA are slightly larger, and the data based on the LDA are slightly smaller. These results show that our computational methods are reliable and can be used to further study the physical properties. In order to compare with other phases of ZnSnO3, we also calculate the structural parameters of cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3, which are shown in Table 1. The optimized structural parameters of five ZnSnO3 are consistent with the theoretical [26e29] and experimental values [1]. The R3c phase is found to have the minimum ground state energy. The order of ground state energy is R3c(3119.473 eV/unit) < R3 (3119.309 eV/ unit) < R3 c(3119.295 eV/unit) < Pnma(3119.202 eV/ unit) < Cmcm(3118.542 eV/unit) < Pm3 m(3115.628 eV/unit). Fig. 1 shows the pressure dependence of lattice parameters for ilmenite-type and LiNbO3-type ZnSnO3. We can see that the lattice parameters decrease with the increasing pressure at zero temperature. 3.2. Elastic and mechanical properties Elastic properties are very important for solids, which are related to various physical properties, e.g. equation of state, phonon spectra, Debye temperature, etc. [34]. The independent components of elastic constants of trigonal (R3 ) phase are seven, namely C11, C12, C13, C14, C15, C33, C44. The calculated elastic constants based on the GGA-PW91 calculations of ilmenite-type ZnSnO3 are shown in Table 2. Our data agree with the previous theoretical results [28]. The C11 and C44 represent the unidirectional compression and the resistance against the basal shear deformation, respectively. The high C11 and low C44 mean the good resistance against strain ε11 and the weak resistance against shear deformation. For trigonal structure, the mechanical stability criteria at zero pressure are as follows [35,36]:
h i 2 > 0; C11 > jC12 j; C11 > 0; C33 > 0; C44 > 0; ðC11 þ C12 ÞC33 2C13 h i 2 >0 ðC11 C12 ÞC44 2C14 (1) The obtained elastic constants of ilmenite-type ZnSnO3 satisfy these criteria, indicating that this compound is mechanical stability. Moreover, our calculated elastic constants of cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3 are shown in Table 2 for comparison. According to the mechanical stability criteria [35,36], we can conclude that R3c, Pm3 m, R3 c and Pnma phases are mechanically stable, and Cmcm phase is unstable under zero pressure. Then, we calculate the elastic constants of ZnSnO3 under pressure. Fig. 2 shows the pressure dependence of elastic constants for ilmenite-type ZnSnO3. The C11, C12 and C13 increase with the increasing pressure. According to the Born’s criteria under pressure [37], the mechanical stability conditions can be expressed as follows:
ðC11 PÞ > 0; ðC33 PÞ > 0; ðC44 PÞ > 0; ðC11 PÞ > jC12 þ Pj; ðC11 þ C12 ÞðC33 PÞ > 2ðC13 þ PÞ2 ;
(2)
2 ðC11 C12 2PÞðC44 PÞ > 2C14
Fig. 3 shows the mechanical stability of ZnSnO3 under pressure. 2 can’t We can see that C44P and ðC11 C12 2PÞðC44 PÞ 2C14 satisfy these criteria at 66.5 and 66.6 GPa, respectively. It is wellknown that a positive determinant for a symmetric matrix can
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7
3
Table 1 Calculated lattice constants (Å) and atomic positions of ilmenite-type, cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3 along with previous theoretical [26e29] and experimental data [1,22]. a
R3
R3c
Pm3 m
c
Atomic positions
Method
Ref.
5.4136
b
14.3225
Zn (0,0,0.3654) Sn (0,0,0.1492) O (0.3044,0.0048,0.2493)
GGA-PW91(CASTEP)
Present
5.419 5.2118 5.2835
14.348 13.900 14.0913
GGA-PBE(CASTEP) LDA (CASTEP) Experiment
[26,28] [29] [22]
5.3771
14.4890
5.387 5.3441
14.344 14.2206
5.2048 5.2622(1)
13.85 14.0026(2)
Zn (0,0,0.2827) O (0.0357,0.3587,0.0689) Zn (0,0,0.2859(1)) Sn (0,0,0) O (0.0405(8),0.350(1),0.0709(6)) Zn (0,0,0) Sn (0.5,0.5,0.5) O (0.5,0.5,0)
4.0785
R3 c
4.086 5.4215
Pnma
5.429 5.4264
7.9908
14.387 5.4272
Cmcm
5.422 3.0815
7.994 9.9284
5.428 7.6599
3.082
9.934
7.653
Zn (0,0,0.3520(3)) Sn (0,0,0.1463(2)) O (0.309(1), 0.002(2), 0.2470(5)) Zn (0,0,0.2859) Sn (0,0,0.0011) O (0.0322,0.3610,0.0695)
14.3835
Zn (0,0,0.25) Sn (0,0,0) O (0.3562,0,0.25) Zn (0.5282,0.25,0.4913) Sn (0,0,0.5) O1 (0.9002,0.25,0.3700) O2 (0.3312,0.0725,0.6652) Zn (0,0.2627,0.25) Sn (0,0,0) O1 (0.5,0.3980,0.25) O2 (0.5,0.1362,0.0692)
guarantee mechanical stability of a crystal. The negative C44P at 66.5 GPa means that the mechanical instability appears. Although the mechanical stability pressure is relatively high, the phonon calculations indicate ilmenite-type ZnSnO3 is unstable under low pressure [26]. Next, we obtain the bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio n by using the VRH approximation for ilmenite-type ZnSnO3 [38e40]:
1 þ BVoigt B 2 Reuss 9 8 > > ½ð2S11 þ S33 Þ þ 2ðS12 þ 2S13 Þ1 = < 1 ¼ 1 2 > 2 : þ ð2C þ C Þ þ ðC þ 2C Þ > ; 11 33 13 9 9 12
BHill ¼
(3)
1 GReuss þGVoigt 2 9 8 > 15½4ð2S11 þS33 Þ4ðS12 þ2S13 Þþ6ðS44 þS11 S12 Þ1 > = 1< ¼ 1 1 C C 12 > 2> ; :þ ð2C11 þC33 C12 2C13 Þþ 2C44 þ 11 15 5 2
GHill ¼
(4)
E¼
9BG G þ 3B
(5)
n¼
1 B ð2=3ÞG 2 B þ ð1=3ÞG
Present
GGA-PBE(CASTEP) GGA (WIEN2k)
[26,28] [27]
LDA (CASTEP) Experiment
[29] [1]
GGA-PW91(CASTEP)
Present
GGA-PBE(CASTEP) GGA-PW91(CASTEP)
[26] Present
GGA-PBE(CASTEP) GGA-PW91(CASTEP)
[26] Present
GGA-PBE(CASTEP) GGA-PW91(CASTEP)
[26] Present
GGA-PBE(CASTEP)
[26]
(6)
where Sij corresponds to the elastic compliance constants. Table 3 shows the calculated bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio n of ilmenite-type ZnSnO3 along with previous theoretical data [28,30]. Our bulk modulus of 140.4 GPa agrees with the data 141 [28] and 145 [30] GPa. As we know, bulk modulus can be used to characterize the average atomic bond strength, which also is related to the resistance to fracture. According to the calculated results, we can conclude that the above properties of ilmenite-type ZnSnO3 are ordinary. Shear modulus represents the resistance to plastic deformation. The low shear modulus of 40.8 GPa indicates this compound has weak resistance to plastic deformation. Pugh [41] suggested the ratio of B/G to predict the brittle/ductile behavior of solids. If B/G > 1.75, this material shows ductile manner, otherwise it shows brittle manner. The ratio of B/G at zero pressure is 3.438, showing its good ductileness. Next, we obtain the mechanical properties of cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3, which are shown in Table 3. It can be seen that the order the resistance to fracture is of R3c > Pnma > R3 c > Pm3 m > R3 and the order of the resistance to plastic deformation is R3 c > Pnma > R3c > Pm3 m > R3 . We can conclude that ilmenite-type ZnSnO3 has worst resistances to fracture and plastic deformation. Fig. 4 shows the mechanical properties of ilmenite-type ZnSnO3 under pressure. We can see that the bulk modulus linearly increase
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
4
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7
Fig. 2. Pressure dependence of elastic constants for ilmenite-type ZnSnO3.
Fig. 1. Pressure dependence of lattice parameters for (a) ilmenite-type and (b) LiNbO3type ZnSnO3. Fig. 3. Mechanical stability of ilmenite-type ZnSnO3 under pressure.
with the increasing pressure, indicating that the resistance to volume change is enhanced. The shear and Young’s modulus increase with the increasing pressure from 0 to 40 GPa, then they trend to invariability up to 70 GPa. The n and B/G decrease from 0 to 10 GPa, afterwards they increase with pressure. The results show ilmenitetype ZnSnO3 always behaves in a ductile manner. The compressibilities of ilmenite-type ZnSnO3 are 0.00736, 0.00524, 0.00442, 0.00392, 0.00330, 0.00306, 0.00302, 0.00269, 0.00233 GPa1 from 0 to 80 GPa. Moreover, we investigate the relative stability of three existing phases (ilmenite-type, cubic perovskite-type, and LiNbO3type ZnSnO3) under pressure. According to the calculated results,
we find that there is no structural phase transition from 0 to 80 GPa. 3.3. Electronic properties The calculated band structures of both functionals are shown in Fig. 5. Both functionals show that ilmenite-type ZnSnO3 is a direct bandgap compound with 1.063 (GGA-PW91)/3.977 (PBE0) eV. The GGA value is underestimated. The PBE0 value is close to the experimental value 3.7 eV [42] which is also close to the bandgap of LiNbO3-type ZnSnO3 (3.7e3.9 eV) [43,44]. Fig. 6 shows the total and
Table 2 Calculated elastic constants based on the GGA-PW91 calculations of ilmenite-type, cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3 along with previous theoretical data [28,29].
R3 R3c
Pm3 m
R3 c Pnma Cmcm
C11
C12
C13
C14
C15
268.8 269 286.0 287 360 284.4
132.8 130 130.0 127 167 74.1
78.8 79 107.9 102 137
14.7
14.3
310.4
137.1
100.8
1.4
290.8 316.9
103.8 51.8
116.7 47.8
C22
C23
C33 185.9 191 240.6 227 281
1.7
247.9 210.4
100.4 77.5
C44
C55
C66
23.6 31 66.5 70 86 33.8
175.3
77.3
273.3 223.9
74.7 239.5
Present [28] [28] [29] Present Present 81.3 45.9
55.3 2723.0
Present Present
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7
5
Table 3 Calculated bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio n of ilmenite-type, cubic perovskite-type, LiNbO3-type, CdSnO3-type, and HgSnO3type ZnSnO3 along with previous theoretical data [28e30].
R3
R3c
Pm3 m
R3 c Pnma
B
G
E
n
140.4 141 145 166.1 161 207 164 144.2 170 155.5
40.8
111.6
0.367
73.0
191.0
0.308
91
238
0.3084
54.4
145.0
0.332
77.3
198.9
0.287
Present [28] [30] Present [28] [29] [30] Present [30] Present
74.1
192.7
0.300
Present
160.9
Fig. 5. Calculated band structures of GGA-PW91 and PBE0.
partial density of states (DOS) of ilmenite-type ZnSnO3. The lower part of the valence bands is predominantly made of O-2s states. The valence bands around 6.562 eV consist of Sn-5s and O-2p states. The valence bands around 4.218 eV are mainly composed of Zn-3d states, where the O-2p and Sn-5p states partially contribute. The upper valence bands are primarily composed of O-2p states. The lower conduction bands are mainly dominated by Sn-5s and O-2p states. The Zn-4s and Sn-5p states are dominant in the middle conduction bands. The electronic structures are similar to those of LiNbO3-type ZnSnO3 [27]. Fig. 7 shows the bandgaps of ilmenite-type and LiNbO3-type ZnSnO3 under pressure. The bandgap of ilmenite-type ZnSnO3 increases with the increasing pressure. However, the bandgap of LiNbO3-type ZnSnO3 increases with the increasing pressure from 0 to 50 GPa and then decreases with the increase of pressure. In
order to study the increasing bandgap of ilmenite-type ZnSnO3, we show the PDOS of O-2p, Sn-5s and Sn-5p states under pressure in Fig. 8. In the valence bands, we can see that the height of PDOS decreases with the increasing pressure, but the width increases. The conclusions indicate that the chemical bonds are enhanced with the increasing pressure. In the lower conduction bands, the Sn-5s and O-2p states move to high energy with the increasing pressure, which induces the increase of bandgap. Moreover, the contributions of Sn-5p states in the lower conduction bands increase with the increasing pressure, indicating that the bonds between O and Sn are enhanced.
Fig. 4. Mechanical properties of ilmenite-type ZnSnO3 under pressure.
Fig. 6. Total and partial density of states of ilmenite-type ZnSnO3.
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
6
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7
the first-principles calculations. The calculated structural parameters at zero pressure are in agreement with previous data. The calculated elastic properties show that this phase is mechanical stability until the pressure increases to 66.5 GPa. The bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio have been calculated, showing that this compound behaves in a ductile manner. Electronic properties indicate that this phase is a direct bandgap compound with 3.977 eV. Moreover, the bandgap and PDOS under pressure have been analyzed, indicating that the pressure enhances the intensity of chemical bonds. Acknowledgments
Fig. 7. Bandgap of (a) ilmenite-type and (b) LiNbO3-type ZnSnO3 under pressure.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51402244 and 11547311), the Specialized Research Fund for Doctoral Program of Higher Education of China (Grant No. 20130184120028), the Fundamental Research Fund for the Central Universities, China (Grant Nos. 2682014ZT30 and 2682014ZT31), and the fund of the State Key Laboratory of Solidification Processing in NWPU (Grant No. SKLSP201511), and the Graduate Innovative Experimental Practice Program of SWJTU (Grant No. YC201511101). References
Fig. 8. Partial density of states of (a) O-2p, (b) Sn-5s and Sn-5p states under pressure.
4. Conclusions The structural, elastic, mechanical and electronic properties of ilmenite-type ZnSnO3 under pressure have been investigated using
[1] Y. Inaguma, M. Yoshida, T. Katsumata, J. Am. Chem. Soc. 130 (2008) 6704. [2] Y.J. Chen, L. Yu, Q. Li, Y. Wu, Q.H. Li, T.H. Wang, Nanotechnology 23 (2012) 415501. [3] J.M. Wu, C. Xu, Y. Zhang, Y. Yang, Y.S. Zhou, Z.L. Wang, Adv. Mater 24 (2012) 6094. [4] J.Y. Son, G. Lee, M.H. Jo, H. Kim, H.M. Jang, Y.H. Shin, J. Am. Chem. Soc. 131 (2009) 8386. [5] K.Y. Lee, D. Kim, J.H. Lee, T.Y. Kim, M.K. Gupta, S.W. Kim, Adv. Funct. Mater 24 (2014) 37. [6] X.Y. Xue, T.L. Guo, Z.X. Lin, T.H. Wang, Mater. Lett. 62 (2008) 1356. [7] P. Song, Q. Wang, Z.X. Yang, Mater. Lett. 65 (2011) 430. [8] H.T. Fan, Y. Zeng, X.J. Xu, N. Lv, T. Zhang, Sensors Actuators B 153 (2011) 170. [9] Y. Zeng, T. Zhang, H.T. Fan, W.Y. Fu, G.Y. Lu, Y.M. Sui, H.B. Yang, J. Phys. Chem. C 113 (2009) 19000. [10] Y. Zeng, K. Zhang, X.L. Wang, Y.M. Sui, B. Zou, W.T. Zheng, G.T. Zou, Sensors Actuators B 159 (2011) 245. [11] W. Zeng, T.M. Liu, L.Y. Lin, Mater. Sci. Semicond. Proc. 15 (2012) 319. [12] Z.J. Wang, J. Liu, F.J. Wang, S.Y. Chen, H. Luo, X.B. Yu, J. Phys. Chem. C 114 (2010) 13577. [13] T.G. Zhong, B.F. Quan, X.S. Liang, F.M. Liu, B. Wang, Mater. Sci. Eng. B 151 (2008) 127. [14] D. Bauskar, B.B. Kale, P. Patil, Sensors Actuators B 161 (2012) 396. [15] Y. Zeng, T. Zhang, H.T. Fan, G.Y. Lu, M.H. Kang, Sensors Actuators B 143 (2009) 449. [16] B.Y. Geng, C.H. Fang, F.M. Zhan, N. Yu, Small 4 (2008) 1337. [17] J.M. Wu, C. Xu, Y. Zhang, Z.L. Wang, Acs Nano 6 (2012) 4335. [18] J.M. Wu, C.Y. Chen, Y. Zhang, K.H. Chen, Y. Yang, Y.F. Hu, J.H. He, Z.L. Wang, Acs Nano 6 (2012) 4369. [19] Y.Y. Choi, K.H. Choi, H. Lee, H. Lee, J.W. Kang, H.K. Kim, Sol. Energy Mater. Sol. Cells 95 (2011) 1615. [20] J.Q. Xu, X.H. Jia, X.D. Lou, J.N. Shen, Solid State Electron 50 (2006) 504. [21] Y. Inaguma, D. Sakurai, A. Aimi, M. Yoshida, T. Katsumata, D. Mori, J. Yeon, P.S. Halasyamani, J. Solid State Chem. 195 (2012) 115. [22] D. Kovacheva, K. Petrov, Solid State Ion. 109 (1998) 327. [23] H. Mizoguchi, H.W. Eng, P.M. Woodward, Inorg. Chem. 43 (2004) 1667. [24] M. Yoshida, T. Katsumata, Y. Inaguma, Inorg. Chem. 47 (2008) 6296. [25] Y. Inaguma, K.I. Hasuml, M. Yoshlda, T. Ohba, T. Katsumata, Inorg. Chem. 47 (2008) 1868. [26] H.Y. Gou, J.W. Zhang, Z.P. Li, G.K. Wang, F.M. Gao, R.C. Ewing, J. Lian, Appl. Phys. Lett. 98 (2011) 091914. [27] H. Wang, H.T. Huang, B. Wang, Solid State Commun. 149 (2009) 1849. [28] H.Y. Gou, F.M. Gao, J.W. Zhang, Comput. Mater. Sci. 49 (2010) 552. [29] N.N. Ge, C.M. Liu, Y. Cheng, X.R. Chen, G.F. Ji, Phys. B 406 (2011) 742. [30] M. Nakayama, M. Nogami, M. Yoshida, T. Katsumata, Y. Inaguma, Adv. Mater 22 (2010) 2579. [31] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.J. Probert, K. Refson, M.C. Payne, Z. Krist. 220 (2005) 567. [32] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Phys. Rev. B 46 (1992) 6671. [33] C. Adamo, V. Barone, J. Chem. Phys. 110 (1999) 6158. [34] Q.J. Liu, Z.T. Liu, L.P. Feng, H. Tian, Phys. B 405 (2010) 4032. [35] M. Born, K. Huang, Dynamical Theory and Experiment I, Springer, Berlin, 1982.
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7 [36] [37] [38] [39] [40]
Q.J. Liu, Z.T. Liu, Mater. Sci. Semicond. Proc. 27 (2014) 765. G.V. Sin’ko, N.A. Smirnov, J. Phys. Condens. Matter 14 (2002) 6989. W. Voigt, Lehrbuch der kristallphysik, Teubner, Leipzig, 1928. A. Reuss, Z. Angew, Math. Mech. 9 (1929) 49. R. Hill, Proc. Phys. Soc. Lond. 65 (1952) 349.
[41] [42] [43] [44]
S.F. Pugh, Philos. Mag. 45 (1954) 823. H. Mizoguchi, P.M. Woodward, Chem. Mater 16 (2004) 5233. € rner, P. Gumbsch, C. Els€ W. Ko asser, Phys. Rev. B 86 (2012) 165210. € rner, C. Els€ W. Ko asser, Thin Solid Films 555 (2014) 81.
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
7
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure Qi-Jun Liu a, b, *, Han Qin a, b, Zhen Jiao a, b, Fu-Sheng Liu a, b, Zheng-Tang Liu c a
School of Physical Science and Technology, Southwest Jiaotong University, Key Laboratory of Advanced Technologies of Materials, Ministry of Education of China, Chengdu 610031, People’s Republic of China b Bond and Band Engineering Group, Sichuan Provincial Key Laboratory (for Universities) of High Pressure Science and Technology, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China c State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Physical properties of ilmenite-type ZnSnO3 under pressure have been investigated. Ilmenite-type ZnSnO3 behaves in a ductile manner. Ilmenite-type ZnSnO3 is a direct bandgap compound with 3.977 eV. Bandgap of Ilmenite-type ZnSnO3 increases with the increasing pressure.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 September 2015 Received in revised form 11 May 2016 Accepted 15 May 2016 Available online xxx
First-principles calculations of the structural, elastic, mechanical and electronic properties of ilmenitetype ZnSnO3 under pressure have been investigated in the present paper. Our calculated lattice constants at zero pressure are in agreement with the published theoretical and experimental data. The elastic constants at zero and high pressure have been obtained, which are used to discuss the mechanical stability of ilmenite-type ZnSnO3. The mechanical properties such as bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio under pressure have been studied. Electronic properties show that ilmenite-type ZnSnO3 is shown to be a direct bandgap of 1.063 (GGA-PW91)/3.977 (PBE0) eV. The bandgap increases with the increasing pressure. Moreover, the partial density of states has been analyzed to explain the increased bandgap. © 2016 Elsevier B.V. All rights reserved.
Keywords: Oxides Ab initio calculations Elastic properties Mechanical properties Electronic structure
1. Introduction ZnSnO3 has attracted wide attention due to its interesting physical properties such as polar [1], gas-sensitive [2], piezoelectric
* Corresponding author. School of Physical Science and Technology, Southwest Jiaotong University, Key Laboratory of Advanced Technologies of Materials, Ministry of Education of China, Chengdu 610031, People’s Republic of China. E-mail address: [email protected] (Q.-J. Liu).
[3], ferroelectric [4], pyroelectric [5] and optoelectronic [6] properties. Thus, it is currently under intensive study, including gas sensors [7e16], piezoelectric material for energy conversion [17,18], ferroelectric thin films [4], solar cells [19], etc. Cubic perovskitetype [16,20], LiNbO3-type [1,21], ilmenite-type [22], as well as the hypothetical phases CdSnO3-type, HgSnO3-type, post-perovskitetype [23e26] have been investigated, indicating its technological importance. Many theoretical efforts have been devoted to study the LiNbO3-
http://dx.doi.org/10.1016/j.matchemphys.2016.05.041 0254-0584/© 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
2
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7
type ZnSnO3 after it had been synthesized [1]. Within the accurate full-potential linearized augmented plane-wave method, Wang et al. [27] calculated the structural, electronic and optical properties of LiNbO3-type ZnSnO3. The obtained results showed that ZnSnO3 was a direct bandgap semiconductor of 1.0 eV. Gou et al. [28] found that LN-type ZnSnO3 had a strong covalence and a direct bandgap of 2.42 eV. Another calculated direct bandgap was 1.669 eV [29]. Furthermore, phase transition of LN-type ZnSnO3 has been reported [26,30]. However, the ilmenite-type ZnSnO3 has rarely been addressed theoretically. Using the plane wave pseudopotential density functional theory and the local density approximation, Ge et al. [29] studied the structural properties of ilmenite-type ZnSnO3 under pressure. They found there was no structural phase transition between ilmenite-type and LiNbO3-type ZnSnO3 under pressure up to 100 GPa. Then we want to further study the electronic and elastic properties of ilmenite-type ZnSnO3. Specifically, the bandgap obtained by the traditional DFT is underestimated, which should be accurately calculated. In the paper, we study the structural, elastic, and electronic properties of ilmenite-type ZnSnO3 under pressure. Moreover, we calculate the structural and mechanical properties of cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3 for comparison. This work is organized as follows: Section 2 shows the computational methods, Section 3 gives the obtained results, including structural parameters, elastic constants, mechanical properties, and electronic structures, the main conclusions are shown in Section 4. 2. Methodology All of the first-principles calculations were performed by using the CASTEP code [31]. We used the PW91 functional [32] within the generalized gradient approximation (GGA) for the exchangecorrelation functional. However, the GGA-PW91 functional can’t correctly give the band gap due to imprecise description of exchange-correlation effects. In order to gain precise band gap, we used the hybrid PBE0 functional [33]. The GGA-PW91 plus ultrasoft pseudopotential have been used to calculate structural and physical properties. The PBE0 plus norm-conserving pseudopotential have been used to obtain precise band gap (the PBE0 functional is nonlocal exchange functional, whose calculations are available for norm-conserving pseudopotential). The cut-off energy 380 eV (ultrasoft pseudopotential) and 830 eV (norm-conserving pseudopotential) were carried out. The 3 3 2, 4 4 4, 3 3 2, 3 2 3, 3 3 2, 5 1 2 Monkhorst-Pack k-point grids for ilmenite-type, cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3 were used for integrations within Brillouin zone. The Zn 3d104s2, Sn 5s25p2 and O 2s22p4 electrons were treated as valence electrons. The convergence tolerance parameters of maximum force, maximum displacement and maximum stress were 0.01 eV/Å, 5 104 Å and 0.02 GPa, respectively. 3. Results and discussion 3.1. Structural parameters
The space group of ilmenite-type ZnSnO3 is R3 , where the Zn, Sn and O atoms are located at 6c (0,0,0.3520(3)), 6c (0,0,0.1463(2)), and 18f (0.309(1), 0.002(2), 0.2470(5)) [22], respectively. The calculated lattice constants and atomic positions of ilmenite-type ZnSnO3 are listed in Table 1 along with previous theoretical [26,28,29] and experimental data [22]. It can be seen that our results are in agreement with previous data. Compared with the
experimental data, the calculated data based on the GGA are slightly larger, and the data based on the LDA are slightly smaller. These results show that our computational methods are reliable and can be used to further study the physical properties. In order to compare with other phases of ZnSnO3, we also calculate the structural parameters of cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3, which are shown in Table 1. The optimized structural parameters of five ZnSnO3 are consistent with the theoretical [26e29] and experimental values [1]. The R3c phase is found to have the minimum ground state energy. The order of ground state energy is R3c(3119.473 eV/unit) < R3 (3119.309 eV/ unit) < R3 c(3119.295 eV/unit) < Pnma(3119.202 eV/ unit) < Cmcm(3118.542 eV/unit) < Pm3 m(3115.628 eV/unit). Fig. 1 shows the pressure dependence of lattice parameters for ilmenite-type and LiNbO3-type ZnSnO3. We can see that the lattice parameters decrease with the increasing pressure at zero temperature. 3.2. Elastic and mechanical properties Elastic properties are very important for solids, which are related to various physical properties, e.g. equation of state, phonon spectra, Debye temperature, etc. [34]. The independent components of elastic constants of trigonal (R3 ) phase are seven, namely C11, C12, C13, C14, C15, C33, C44. The calculated elastic constants based on the GGA-PW91 calculations of ilmenite-type ZnSnO3 are shown in Table 2. Our data agree with the previous theoretical results [28]. The C11 and C44 represent the unidirectional compression and the resistance against the basal shear deformation, respectively. The high C11 and low C44 mean the good resistance against strain ε11 and the weak resistance against shear deformation. For trigonal structure, the mechanical stability criteria at zero pressure are as follows [35,36]:
h i 2 > 0; C11 > jC12 j; C11 > 0; C33 > 0; C44 > 0; ðC11 þ C12 ÞC33 2C13 h i 2 >0 ðC11 C12 ÞC44 2C14 (1) The obtained elastic constants of ilmenite-type ZnSnO3 satisfy these criteria, indicating that this compound is mechanical stability. Moreover, our calculated elastic constants of cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3 are shown in Table 2 for comparison. According to the mechanical stability criteria [35,36], we can conclude that R3c, Pm3 m, R3 c and Pnma phases are mechanically stable, and Cmcm phase is unstable under zero pressure. Then, we calculate the elastic constants of ZnSnO3 under pressure. Fig. 2 shows the pressure dependence of elastic constants for ilmenite-type ZnSnO3. The C11, C12 and C13 increase with the increasing pressure. According to the Born’s criteria under pressure [37], the mechanical stability conditions can be expressed as follows:
ðC11 PÞ > 0; ðC33 PÞ > 0; ðC44 PÞ > 0; ðC11 PÞ > jC12 þ Pj; ðC11 þ C12 ÞðC33 PÞ > 2ðC13 þ PÞ2 ;
(2)
2 ðC11 C12 2PÞðC44 PÞ > 2C14
Fig. 3 shows the mechanical stability of ZnSnO3 under pressure. 2 can’t We can see that C44P and ðC11 C12 2PÞðC44 PÞ 2C14 satisfy these criteria at 66.5 and 66.6 GPa, respectively. It is wellknown that a positive determinant for a symmetric matrix can
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7
3
Table 1 Calculated lattice constants (Å) and atomic positions of ilmenite-type, cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3 along with previous theoretical [26e29] and experimental data [1,22]. a
R3
R3c
Pm3 m
c
Atomic positions
Method
Ref.
5.4136
b
14.3225
Zn (0,0,0.3654) Sn (0,0,0.1492) O (0.3044,0.0048,0.2493)
GGA-PW91(CASTEP)
Present
5.419 5.2118 5.2835
14.348 13.900 14.0913
GGA-PBE(CASTEP) LDA (CASTEP) Experiment
[26,28] [29] [22]
5.3771
14.4890
5.387 5.3441
14.344 14.2206
5.2048 5.2622(1)
13.85 14.0026(2)
Zn (0,0,0.2827) O (0.0357,0.3587,0.0689) Zn (0,0,0.2859(1)) Sn (0,0,0) O (0.0405(8),0.350(1),0.0709(6)) Zn (0,0,0) Sn (0.5,0.5,0.5) O (0.5,0.5,0)
4.0785
R3 c
4.086 5.4215
Pnma
5.429 5.4264
7.9908
14.387 5.4272
Cmcm
5.422 3.0815
7.994 9.9284
5.428 7.6599
3.082
9.934
7.653
Zn (0,0,0.3520(3)) Sn (0,0,0.1463(2)) O (0.309(1), 0.002(2), 0.2470(5)) Zn (0,0,0.2859) Sn (0,0,0.0011) O (0.0322,0.3610,0.0695)
14.3835
Zn (0,0,0.25) Sn (0,0,0) O (0.3562,0,0.25) Zn (0.5282,0.25,0.4913) Sn (0,0,0.5) O1 (0.9002,0.25,0.3700) O2 (0.3312,0.0725,0.6652) Zn (0,0.2627,0.25) Sn (0,0,0) O1 (0.5,0.3980,0.25) O2 (0.5,0.1362,0.0692)
guarantee mechanical stability of a crystal. The negative C44P at 66.5 GPa means that the mechanical instability appears. Although the mechanical stability pressure is relatively high, the phonon calculations indicate ilmenite-type ZnSnO3 is unstable under low pressure [26]. Next, we obtain the bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio n by using the VRH approximation for ilmenite-type ZnSnO3 [38e40]:
1 þ BVoigt B 2 Reuss 9 8 > > ½ð2S11 þ S33 Þ þ 2ðS12 þ 2S13 Þ1 = < 1 ¼ 1 2 > 2 : þ ð2C þ C Þ þ ðC þ 2C Þ > ; 11 33 13 9 9 12
BHill ¼
(3)
1 GReuss þGVoigt 2 9 8 > 15½4ð2S11 þS33 Þ4ðS12 þ2S13 Þþ6ðS44 þS11 S12 Þ1 > = 1< ¼ 1 1 C C 12 > 2> ; :þ ð2C11 þC33 C12 2C13 Þþ 2C44 þ 11 15 5 2
GHill ¼
(4)
E¼
9BG G þ 3B
(5)
n¼
1 B ð2=3ÞG 2 B þ ð1=3ÞG
Present
GGA-PBE(CASTEP) GGA (WIEN2k)
[26,28] [27]
LDA (CASTEP) Experiment
[29] [1]
GGA-PW91(CASTEP)
Present
GGA-PBE(CASTEP) GGA-PW91(CASTEP)
[26] Present
GGA-PBE(CASTEP) GGA-PW91(CASTEP)
[26] Present
GGA-PBE(CASTEP) GGA-PW91(CASTEP)
[26] Present
GGA-PBE(CASTEP)
[26]
(6)
where Sij corresponds to the elastic compliance constants. Table 3 shows the calculated bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio n of ilmenite-type ZnSnO3 along with previous theoretical data [28,30]. Our bulk modulus of 140.4 GPa agrees with the data 141 [28] and 145 [30] GPa. As we know, bulk modulus can be used to characterize the average atomic bond strength, which also is related to the resistance to fracture. According to the calculated results, we can conclude that the above properties of ilmenite-type ZnSnO3 are ordinary. Shear modulus represents the resistance to plastic deformation. The low shear modulus of 40.8 GPa indicates this compound has weak resistance to plastic deformation. Pugh [41] suggested the ratio of B/G to predict the brittle/ductile behavior of solids. If B/G > 1.75, this material shows ductile manner, otherwise it shows brittle manner. The ratio of B/G at zero pressure is 3.438, showing its good ductileness. Next, we obtain the mechanical properties of cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3, which are shown in Table 3. It can be seen that the order the resistance to fracture is of R3c > Pnma > R3 c > Pm3 m > R3 and the order of the resistance to plastic deformation is R3 c > Pnma > R3c > Pm3 m > R3 . We can conclude that ilmenite-type ZnSnO3 has worst resistances to fracture and plastic deformation. Fig. 4 shows the mechanical properties of ilmenite-type ZnSnO3 under pressure. We can see that the bulk modulus linearly increase
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
4
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7
Fig. 2. Pressure dependence of elastic constants for ilmenite-type ZnSnO3.
Fig. 1. Pressure dependence of lattice parameters for (a) ilmenite-type and (b) LiNbO3type ZnSnO3. Fig. 3. Mechanical stability of ilmenite-type ZnSnO3 under pressure.
with the increasing pressure, indicating that the resistance to volume change is enhanced. The shear and Young’s modulus increase with the increasing pressure from 0 to 40 GPa, then they trend to invariability up to 70 GPa. The n and B/G decrease from 0 to 10 GPa, afterwards they increase with pressure. The results show ilmenitetype ZnSnO3 always behaves in a ductile manner. The compressibilities of ilmenite-type ZnSnO3 are 0.00736, 0.00524, 0.00442, 0.00392, 0.00330, 0.00306, 0.00302, 0.00269, 0.00233 GPa1 from 0 to 80 GPa. Moreover, we investigate the relative stability of three existing phases (ilmenite-type, cubic perovskite-type, and LiNbO3type ZnSnO3) under pressure. According to the calculated results,
we find that there is no structural phase transition from 0 to 80 GPa. 3.3. Electronic properties The calculated band structures of both functionals are shown in Fig. 5. Both functionals show that ilmenite-type ZnSnO3 is a direct bandgap compound with 1.063 (GGA-PW91)/3.977 (PBE0) eV. The GGA value is underestimated. The PBE0 value is close to the experimental value 3.7 eV [42] which is also close to the bandgap of LiNbO3-type ZnSnO3 (3.7e3.9 eV) [43,44]. Fig. 6 shows the total and
Table 2 Calculated elastic constants based on the GGA-PW91 calculations of ilmenite-type, cubic perovskite-type, LiNbO3-type, CdSnO3-type, HgSnO3-type and post-perovskite-type ZnSnO3 along with previous theoretical data [28,29].
R3 R3c
Pm3 m
R3 c Pnma Cmcm
C11
C12
C13
C14
C15
268.8 269 286.0 287 360 284.4
132.8 130 130.0 127 167 74.1
78.8 79 107.9 102 137
14.7
14.3
310.4
137.1
100.8
1.4
290.8 316.9
103.8 51.8
116.7 47.8
C22
C23
C33 185.9 191 240.6 227 281
1.7
247.9 210.4
100.4 77.5
C44
C55
C66
23.6 31 66.5 70 86 33.8
175.3
77.3
273.3 223.9
74.7 239.5
Present [28] [28] [29] Present Present 81.3 45.9
55.3 2723.0
Present Present
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7
5
Table 3 Calculated bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio n of ilmenite-type, cubic perovskite-type, LiNbO3-type, CdSnO3-type, and HgSnO3type ZnSnO3 along with previous theoretical data [28e30].
R3
R3c
Pm3 m
R3 c Pnma
B
G
E
n
140.4 141 145 166.1 161 207 164 144.2 170 155.5
40.8
111.6
0.367
73.0
191.0
0.308
91
238
0.3084
54.4
145.0
0.332
77.3
198.9
0.287
Present [28] [30] Present [28] [29] [30] Present [30] Present
74.1
192.7
0.300
Present
160.9
Fig. 5. Calculated band structures of GGA-PW91 and PBE0.
partial density of states (DOS) of ilmenite-type ZnSnO3. The lower part of the valence bands is predominantly made of O-2s states. The valence bands around 6.562 eV consist of Sn-5s and O-2p states. The valence bands around 4.218 eV are mainly composed of Zn-3d states, where the O-2p and Sn-5p states partially contribute. The upper valence bands are primarily composed of O-2p states. The lower conduction bands are mainly dominated by Sn-5s and O-2p states. The Zn-4s and Sn-5p states are dominant in the middle conduction bands. The electronic structures are similar to those of LiNbO3-type ZnSnO3 [27]. Fig. 7 shows the bandgaps of ilmenite-type and LiNbO3-type ZnSnO3 under pressure. The bandgap of ilmenite-type ZnSnO3 increases with the increasing pressure. However, the bandgap of LiNbO3-type ZnSnO3 increases with the increasing pressure from 0 to 50 GPa and then decreases with the increase of pressure. In
order to study the increasing bandgap of ilmenite-type ZnSnO3, we show the PDOS of O-2p, Sn-5s and Sn-5p states under pressure in Fig. 8. In the valence bands, we can see that the height of PDOS decreases with the increasing pressure, but the width increases. The conclusions indicate that the chemical bonds are enhanced with the increasing pressure. In the lower conduction bands, the Sn-5s and O-2p states move to high energy with the increasing pressure, which induces the increase of bandgap. Moreover, the contributions of Sn-5p states in the lower conduction bands increase with the increasing pressure, indicating that the bonds between O and Sn are enhanced.
Fig. 4. Mechanical properties of ilmenite-type ZnSnO3 under pressure.
Fig. 6. Total and partial density of states of ilmenite-type ZnSnO3.
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
6
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7
the first-principles calculations. The calculated structural parameters at zero pressure are in agreement with previous data. The calculated elastic properties show that this phase is mechanical stability until the pressure increases to 66.5 GPa. The bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio have been calculated, showing that this compound behaves in a ductile manner. Electronic properties indicate that this phase is a direct bandgap compound with 3.977 eV. Moreover, the bandgap and PDOS under pressure have been analyzed, indicating that the pressure enhances the intensity of chemical bonds. Acknowledgments
Fig. 7. Bandgap of (a) ilmenite-type and (b) LiNbO3-type ZnSnO3 under pressure.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51402244 and 11547311), the Specialized Research Fund for Doctoral Program of Higher Education of China (Grant No. 20130184120028), the Fundamental Research Fund for the Central Universities, China (Grant Nos. 2682014ZT30 and 2682014ZT31), and the fund of the State Key Laboratory of Solidification Processing in NWPU (Grant No. SKLSP201511), and the Graduate Innovative Experimental Practice Program of SWJTU (Grant No. YC201511101). References
Fig. 8. Partial density of states of (a) O-2p, (b) Sn-5s and Sn-5p states under pressure.
4. Conclusions The structural, elastic, mechanical and electronic properties of ilmenite-type ZnSnO3 under pressure have been investigated using
[1] Y. Inaguma, M. Yoshida, T. Katsumata, J. Am. Chem. Soc. 130 (2008) 6704. [2] Y.J. Chen, L. Yu, Q. Li, Y. Wu, Q.H. Li, T.H. Wang, Nanotechnology 23 (2012) 415501. [3] J.M. Wu, C. Xu, Y. Zhang, Y. Yang, Y.S. Zhou, Z.L. Wang, Adv. Mater 24 (2012) 6094. [4] J.Y. Son, G. Lee, M.H. Jo, H. Kim, H.M. Jang, Y.H. Shin, J. Am. Chem. Soc. 131 (2009) 8386. [5] K.Y. Lee, D. Kim, J.H. Lee, T.Y. Kim, M.K. Gupta, S.W. Kim, Adv. Funct. Mater 24 (2014) 37. [6] X.Y. Xue, T.L. Guo, Z.X. Lin, T.H. Wang, Mater. Lett. 62 (2008) 1356. [7] P. Song, Q. Wang, Z.X. Yang, Mater. Lett. 65 (2011) 430. [8] H.T. Fan, Y. Zeng, X.J. Xu, N. Lv, T. Zhang, Sensors Actuators B 153 (2011) 170. [9] Y. Zeng, T. Zhang, H.T. Fan, W.Y. Fu, G.Y. Lu, Y.M. Sui, H.B. Yang, J. Phys. Chem. C 113 (2009) 19000. [10] Y. Zeng, K. Zhang, X.L. Wang, Y.M. Sui, B. Zou, W.T. Zheng, G.T. Zou, Sensors Actuators B 159 (2011) 245. [11] W. Zeng, T.M. Liu, L.Y. Lin, Mater. Sci. Semicond. Proc. 15 (2012) 319. [12] Z.J. Wang, J. Liu, F.J. Wang, S.Y. Chen, H. Luo, X.B. Yu, J. Phys. Chem. C 114 (2010) 13577. [13] T.G. Zhong, B.F. Quan, X.S. Liang, F.M. Liu, B. Wang, Mater. Sci. Eng. B 151 (2008) 127. [14] D. Bauskar, B.B. Kale, P. Patil, Sensors Actuators B 161 (2012) 396. [15] Y. Zeng, T. Zhang, H.T. Fan, G.Y. Lu, M.H. Kang, Sensors Actuators B 143 (2009) 449. [16] B.Y. Geng, C.H. Fang, F.M. Zhan, N. Yu, Small 4 (2008) 1337. [17] J.M. Wu, C. Xu, Y. Zhang, Z.L. Wang, Acs Nano 6 (2012) 4335. [18] J.M. Wu, C.Y. Chen, Y. Zhang, K.H. Chen, Y. Yang, Y.F. Hu, J.H. He, Z.L. Wang, Acs Nano 6 (2012) 4369. [19] Y.Y. Choi, K.H. Choi, H. Lee, H. Lee, J.W. Kang, H.K. Kim, Sol. Energy Mater. Sol. Cells 95 (2011) 1615. [20] J.Q. Xu, X.H. Jia, X.D. Lou, J.N. Shen, Solid State Electron 50 (2006) 504. [21] Y. Inaguma, D. Sakurai, A. Aimi, M. Yoshida, T. Katsumata, D. Mori, J. Yeon, P.S. Halasyamani, J. Solid State Chem. 195 (2012) 115. [22] D. Kovacheva, K. Petrov, Solid State Ion. 109 (1998) 327. [23] H. Mizoguchi, H.W. Eng, P.M. Woodward, Inorg. Chem. 43 (2004) 1667. [24] M. Yoshida, T. Katsumata, Y. Inaguma, Inorg. Chem. 47 (2008) 6296. [25] Y. Inaguma, K.I. Hasuml, M. Yoshlda, T. Ohba, T. Katsumata, Inorg. Chem. 47 (2008) 1868. [26] H.Y. Gou, J.W. Zhang, Z.P. Li, G.K. Wang, F.M. Gao, R.C. Ewing, J. Lian, Appl. Phys. Lett. 98 (2011) 091914. [27] H. Wang, H.T. Huang, B. Wang, Solid State Commun. 149 (2009) 1849. [28] H.Y. Gou, F.M. Gao, J.W. Zhang, Comput. Mater. Sci. 49 (2010) 552. [29] N.N. Ge, C.M. Liu, Y. Cheng, X.R. Chen, G.F. Ji, Phys. B 406 (2011) 742. [30] M. Nakayama, M. Nogami, M. Yoshida, T. Katsumata, Y. Inaguma, Adv. Mater 22 (2010) 2579. [31] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.J. Probert, K. Refson, M.C. Payne, Z. Krist. 220 (2005) 567. [32] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Phys. Rev. B 46 (1992) 6671. [33] C. Adamo, V. Barone, J. Chem. Phys. 110 (1999) 6158. [34] Q.J. Liu, Z.T. Liu, L.P. Feng, H. Tian, Phys. B 405 (2010) 4032. [35] M. Born, K. Huang, Dynamical Theory and Experiment I, Springer, Berlin, 1982.
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
Q.-J. Liu et al. / Materials Chemistry and Physics xxx (2016) 1e7 [36] [37] [38] [39] [40]
Q.J. Liu, Z.T. Liu, Mater. Sci. Semicond. Proc. 27 (2014) 765. G.V. Sin’ko, N.A. Smirnov, J. Phys. Condens. Matter 14 (2002) 6989. W. Voigt, Lehrbuch der kristallphysik, Teubner, Leipzig, 1928. A. Reuss, Z. Angew, Math. Mech. 9 (1929) 49. R. Hill, Proc. Phys. Soc. Lond. 65 (1952) 349.
[41] [42] [43] [44]
S.F. Pugh, Philos. Mag. 45 (1954) 823. H. Mizoguchi, P.M. Woodward, Chem. Mater 16 (2004) 5233. € rner, P. Gumbsch, C. Els€ W. Ko asser, Phys. Rev. B 86 (2012) 165210. € rner, C. Els€ W. Ko asser, Thin Solid Films 555 (2014) 81.
Please cite this article in press as: Q.-J. Liu, et al., First-principles calculations of structural, elastic, and electronic properties of trigonal ZnSnO3 under pressure, Materials Chemistry and Physics (2016), http://dx.doi.org/10.1016/j.matchemphys.2016.05.041
7