Electronic Structures and Optical Properties of Ilmenite-Type Hexagonal ZnTiO3

ZHANG Xiao-Chao FAN Cai-Mei,* LIANG Zhen-Hai HAN Pei-De

(1Institute of Clean Technique for Chemical Engineering,Taiyuan University of Technology,Taiyuan 030024,P.R.China;2College of Materials Science and Engineering,Taiyuan University of Technology,Taiyuan 030024,P.R.China)

Electronic Structures and Optical Properties of Ilmenite-Type Hexagonal ZnTiO3

ZHANG Xiao-Chao1FAN Cai-Mei1,*LIANG Zhen-Hai1HAN Pei-De2

(1Institute of Clean Technique for Chemical Engineering,Taiyuan University of Technology,Taiyuan 030024,P.R.China;2College of Materials Science and Engineering,Taiyuan University of Technology,Taiyuan 030024,P.R.China)

Abstract：The electronic structures of ilmenite(IL)-type hexagonal ZnTiO3were investigated using the generalized gradient approximation(GGA)and local density approximation(LDA)based on density functional theory(DFT).The optical properties of ZnTiO3were also calculated by the LDA method.The calculated results were compared with experimental data.Results show that the structural parameters obtained by the LDA calculation are rather close to the experimental values.IL-type hexagonal ZnTiO3is a kind of direct bandgap(Eg=3.11 eV)semiconductor material at theZpoint in the Brillouin zone.An analysis of the density of states(DOS)and the Mulliken charge population clearly reveal that the Zn―O bond is a typical ionic bond whereas the Ti―O bond,which is similar to the Ti―O bond in perovskites ATiO3(A=Sr,Pb,Ba),is covalent in character.Furthermore,the dielectric function,absorption spectrum,and refractive index were obtained and analyzed on the basis of electronic band structures and the DOS for radiation up to 50 eV.

Key Words：First-principles;Electronic structure;Optical property;Ilmenite-type hexagonal ZnTiO3

Fundamental studies concerning the phase diagram and characterization of the ZnO/TiO2system have been published by several researchers[1-4].There are three zinc titanate compounds that exist in ZnO/TiO2system:Zn2TiO4(cubic),ZnTiO3(hexag-onal),and Zn2Ti3O8(cubic).Among these compounds,ilmenite(IL)-type hexagonal zinc titanate(ZnTiO3)has attracted great attention due to its potential application,such as microwave dielectrics[5-6],gas sensors[7],ceramics[8-9],photoluminescence materials[10],sorbents for the desulfurization of hot coal gases and paint pigments[11-13].Recent studies[14-15]had also found that the pure hexagonal ZnTiO3prepared by a modified alcoholysis may be a promising photocatalyst in large-scale application of the photocatalysis under solar light irradiation for photodegradation of water contamination and environmental pollution.

Although the ATiO3(A=Sr,Pb,Ba,Zn,Fe,etc.)materials have been investigated at least for half a century,a proper description of their electronic and optical properties is still an active research area from theoretical point of view.Since 1990s,the electronic structures and optical properties of perovskites ATiO3(A=Sr,Pb,Ba)had been calculated successfully using first-principles methods by several research groups[16-22].In the beginning of 1990s,Cohenet al.[16-17]examined successfully the ferroelectric properties of cubic BaTO3and PbTO3perovskite crystals by the full-potential linearized augmented plane wave(FP-LAPW)approach within the local density approximation(LDA).A few years later,Tinte and Stachiotti[18]reported the results of the generalized gradient approximation(GGA)in the scheme of Perdew-Burke-Erzernhof(PBE)calculations for structural and dynamical properties of perovskite oxides.Soon after,bulk properties and electronic structures of cubic SrTiO3,BaTiO3,and PbTiO3perovskites had been published using anab initioHF/DFT study by Piskunovet al.[19].In 2007,the cohesive energy and electronic properties of PbTiO3had been studied using the FP-LAPW method together with the LDA and GGA methods based on DFT by Hosseiniet al.[20].Most recently,Zhanget al.[21]studied the electronic structures and optical properties of cubic and tetragonal BaTiO3perovskite using the LDA,GGA,and pseudo-potential plane wave(PP-PW)methods,respectively.The effect of In and Scp-type doping on the structural stability,electronic structure,and optical properties of SrTiO3perovskite was investigated by first-principles calculations of PP-PW based on DFT by Yun and Zhang[22].Their calculated results are in good agreement with the experimental data in Refs.[16-22].However,there has been little theoretical work on the electronic structures and optical properties for IL-type hexagonal ZnTiO3,thus it is necessary for us to use the first-principles method to explore the electronic structures and optical properties of IL-type hexagonal ZnTiO3,and we hope the calculated results can provide a theoretical basis for the experimental process and practical application of hexagonal ZnTiO3.

In this paper,the lattice constants of IL-type hexagonal Zn-TiO3were firstly optimized using the LDA in the scheme of Ceperley-Aider and Perdew-Zunger(CA-PZ)and GGA in the scheme of PBE based on DFT,and the calculated lattice constants were compared with experimental data.In addition,a systematic study of the electronic structures,density of states,Mulliken charge population,optical properties of IL-type hexagonal ZnTiO3were conducted and analyzed using the LDA(CA-PZ)method.It is found that our calculated results are in good agreement with experimental data.

1 Computational method

All of the calculations were performed using the well tested CASTEP code[23]in Material Studio 4.1 based on DFT.In the present calculation,the exchange and correlation potential were described with LDA in the scheme of CA-PZ[24]and GGA in the scheme of PBE[25].The states of Zn 3d104s2,Ti 3d24s2,and O 2s22p4were treated as valence states.The cutoff energy of a plane-wave was set at 340 eV.The maximum root-meansquare convergent tolerance was less than 2×10-5eV·atom-1.The force imposed on each atom was not greater than 0.1 eV·nm-1and a stress of less than 0.03 GPa.The Brillouin zone integrations were approximated using the specialk-point sampling scheme of Monkhorst-Pack[26],and a 3×3×4k-point grid was used.

2 Results and discussion

2.1 Geometry optimization

In order to describe IL-type hexagonal ZnTiO3crystals,it is necessary to optimize structural parameters,which would be suitable for the electronic structure calculations of crystals.The lattice constants of ZnTiO3were optimized using the GGA(PBE)and LDA(CA-PZ),respectively.The results and a set of experimental data[2]are listed in Table 1 for comparison.X-ray powder diffraction data(PDF:26-1500)(a=b=0.5079 nm,c=1.3927 nm,α=β=90°,γ=120°,c/a=2.7421,Vo=0.3111 nm3,Z=6)[2]were used as a starting point for geometry optimization.The unit cell of hexagonal ZnTiO3contains six molecules as shown in Fig.1.The space group isR3.

Table 1 Comparison between calculated structural data and experimental data

2.2 Band structure,density of states and Mulliken charge population

The electronic band structures along the symmetry lines of the Brillouin zone for IL-type hexagonal ZnTiO3using LDA calculation are shown in Fig.2.The results demonstrate that the IL-type hexagonal ZnTiO3is a direct band gap semiconductor material atZpoint in the Brillouin zone.The calculated band gap(Eg)is about 3.11 eV,which is a little smaller than the experimental value(3.34 eV[29])of hexagonal ZnTiO3.The reason for this disagreement is the well-known shortcoming of the theoretical frame of the LDAcalculation based on DFT[30].

Total density of state(TDOS)and partial density of states(PDOSs)of IL-type hexagonal ZnTiO3are shown in Fig.3.As shown in Figs.(2-3),the valence band(VB)of ZnTiO3can be divided into two main zones:a lower valence band zone(-17.79--15.86 eV)and an upper one(-5.92-0.00 eV).The top of the upper VB is mainly dominated by the contribution of O 2pstates,which is very similar to those of perovskites ATiO3(A=Sr,Pb,Ba)[16,19-22]and IL-type ZnSnO3[28].Moreover,Zn 3dorbital in ZnTiO3not only distinctly contributes to the whole valence band but also has a strong interaction with O 2p,which is also similar to the case of Zn in IL-type ZnSnO3[28].However,Zn 3din ZnTiO3is quite different from the A site atom in perovskites ATiO3(A=Sr,Pb,Ba)[16,19-22].Therefore,IL-type ZnTiO3would have more covalent features than the previous studied perovskites ATiO3(A=Sr,Pb,Ba).An additional valence band between-17.37 and-15.92 eV mainly consists of O 2sstates.In addition,the other two VBs,-32.28--31.90 eV and-55.44--55.37 eV,are not considered,because their interaction with the two main mentioned VBs is very weak.For the conduction band(CB),the bottom of CB mainly originates from the contribution of Ti 3dstates,which also gives the main contribution to CB at about the lowest portion of the spectrum.There are some small contributions from O 2pstates to this part of the spectrum by analyzing TDOS and PDOSs of IL-type ZnTiO3.

In order to understand bonding behavior,the Mulliken charge population for IL-type ZnTiO3was performed and analyzed and the results are listed in Table 2.For IL-type ZnTiO3,the net charge of Zn(+0.99e)is 1.01eless than its+2eformal charges,whereas O atom is with-0.67enegative charges and Ti atom carries+1.02epositive charges,which are much smaller than their-2eand+4eformal charges by 1.33eand 2.98e,respectively.The analysis shows that the Ti—O bond possesses a stronger covalent bonding strength than the Zn—O bond,which agrees well with the DOS analysis for ZnTiO3.Therefore,we have a conclusion that the bond between Zn—O is typically ionic whereas Ti—O bond has covalent character,these results are very similar to those of perovskites ATiO3(A=Sr,Pb,Ba)[16,1922].

From Table 1 it can be clearly seen that the GGA overestimates the lattice parameters while the LDA underestimates them in comparison with the experimental data.These results are consistent with the general trends of these approximations.The lattice parameters from our LDA calculation are about 0.5%smaller than the experimental value,while the GGA results are about 1.1%larger.The LDA approach gives lattice parameters much closer to the experimental data.The volume change value(+0.0129 nm3)by GGA calculation is also larger than the LDA value(-0.0123 nm3).These trends are very similar to those of the calculated findings of perovskite BaLiF3using the GGA and LDA approaches by Amaraet al.[27]and IL-type ZnSnO3using GGA approach by Gouet al.[28].More importantly,the 0.5%error of the lattice parameters using LDA implies that the LDA approach should be a suitable method for calculating a system like IL-type hexagonal ZnTiO3material.

2.3 Optical properties

The optical properties of matter can be described by the complex dielectric functionε(ω),which represents the linear response of the system to an external electromagnetic fi eld with a small wave vector.It can be expressed as[31]:

Calculations ignore excitonic effects but include the local field effect.The interband contribution to the imaginary part ofdielectric function is calculated by taking all possible transitions from occupied to unoccupied states.The imaginary part of the dielectric function ε2(ω)is then given by[32-33]:

Table 2 Mulliken charge population of IL-type ZnTiO3

where M is the dipole matrix,i and j denote the initial and fi nal states,respectively,fiis the Fermi distribution function for the ith state,and Eiis the energy of the electron in the ith state.

The real part ε1(ω)of the dielectric function can be extracted from the imaginary part using the Kramers-Kroning relation[34]:

where P is the principal value of the integral.The knowledge of both the real and imaginary parts of the dielectric function allows the calculation of important optical functions.Expressions for the absorption coefficient I(ω),refractive index n(ω),and extinction coefficient k(ω)are given below[35-36]:

To give an overview of the optical properties of ZnTiO3and in particular to show the different optical interband transitions,Figs.(4-6)show the calculated complex dielectric function ε(ω),absorption coefficient I(ω),refractive index n(ω),and extinction coefficient k(ω)in an energy region of 0 to 50 eV using LDA(CA-PZ)method.

Fig.4 shows the results of calculated dielectric function of ZnTiO3.The imaginary part ε2(ω)of the dielectric function has three prominent peaks of A(4.15 eV),B(19.8 eV),and C(35.8 eV).The peak A mainly corresponds to the transition of O 2p electron VB into Ti 3d CB states.The peak B originates from the transition of O 2s electron VB into Ti 3d CB states.The peak C is assigned to the transition of inner electrons from Ti 3p levels to the CB.Therefore the origin of these peaks includes the indirect and direct transitions of the inner electrons in materials.

The main features of the dispersive part ε1(ω)of the dielectric function are:a maximum peak in the curve at around 3.2 eV and a minimum peak at around 5.0 eV;there is a rather steep decrease from 3.2 to 5.0 eV;after the minimum peak(5.0 eV),ε1(ω)rises slowly up to 34.5 eV,and then ε1(ω)has a little obvious decrease from 34.5 eV to 36.5 eV followed by a slow increase toward the value of 1.0 at high energies.For ε1(ω),the most important quantity is the zero frequency limit ε1(0),which gives the static dielectric constant of 3.50.These features show that IL-type ZnTiO3could be a good transparent conductive film material.

The calculated absorption coefficient I(ω)of IL-type ZnTiO3is displayed in Fig.5.Three peaks are found in the range of 0 to 50 eV,locating at 5.0,20.0 and 35.9 eV,respectively,which are very similar to the peaks of ε2(ω).Besides,based on the analysis of the transitions of the electrons,the origins of the three peaks structure in the absorption coefficient spectra are consistent with the origin of peaks A,B and C in ε2(ω),respectively.As a material of photo-electron transition,IL-type ZnTiO3may have a promising application not only in the transparent conductive film,but also in the photoelectrocatalysis.There are three main reasons[37]for the application of IL-type ZnTiO3in the high transparent conductive film material:the electrons are not easy to transition,the rather weak absorption of IL-type ZnTiO3is in the lowest(0-3.0 eV)and middle energy regions(10.0-33.5 eV),and IL-type ZnTiO3itself is the wide band gap(3.1 eV).In addition,IL-type ZnTiO3owns the rather strong absorption in the lower energy region(3.1-6.2 eV),which is well consistent with the experiment data(200-401 nm).In the experiment of photocatalytic degradation of the azo dye methyl violet,IL-type ZnTiO3sample exhibits the maximum photocatalytic performance in the ultraviolet range(200-401 nm)[14].

The extinction coefficient k(ω)and the refractive index n(ω)have been calculated and showed in Fig.6.The local maxima of k(ω)corresponds to the zero of ε1(ω)(E=4.73 eV).The extinction coefficient and the refractive index of IL-type ZnTiO3have resonance in the two energy regions(from 1.77 to 10.0 eV,from 33.6 to 37.8 eV).For n(ω),the static value n2(0)=1.87 represents the important quantity.The value of n(ω)increases with the energy increasing in the transparency region and reaches a peak in the ultraviolet at about 3.40 eV.Moreover,we note that the obtained refractive index spectra k(ω)and the extinction coefficient n(ω)is similar to the imaginary part ε2(ω)of the dielectric function and the dispersive part ε1(ω)of the dielectric function,respectively.

3 Conclusions

The electronic structures of IL-type hexagonal ZnTiO3were investigated using the LDA and GGA based on the DFT,and the optical properties of ZnTiO3were also calculated by the LDA method.The obtained results are in good agreement with the experimental data.From the above calculations,the following conclusions can be given.

(1)The lattice constants from LDA calculation are about 0.5%smaller than the experimental value,while the GGA results are about 1.1%larger.It is clear that the LDA approximation gives lattice parameters rather close to the experimental values.

(2)The top of the valence band of IL-type hexagonal ZnTiO3is mainly dominated by the contribution of the hybridization Ti 3d and O 2p states.The bottom of the conduction band mainly originates from the contribution of Ti 3d states.The calculated energy band structure shows that the hexagonal ZnTiO3is a direct band gap(Eg=3.11 eV)semiconductor materials.

(3)The analysis of the density of states and Mulliken charge population indicates that the bond Zn—O is typically ionic whereas Ti—O bond has covalent character.

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钛铁矿型六方相ZnTiO3的电子结构和光学性质

张小超1樊彩梅1,*梁镇海1韩培德2

(1太原理工大学洁净化工研究所,太原030024;2太原理工大学材料科学与工程学院,太原030024)

分别采用基于密度泛函理论(DFT)的局域密度近似(LDA)和广义梯度近似(GGA)方法对钛铁矿型六方相ZnTiO3的电子结构进行了第一性原理计算,并在局域密度近似下计算了六方相ZnTiO3的光学性质,并将计算结果与实验数据进行了对比.结果表明,在局域密度近似下计算得到的结构参数更接近实验数据.理论预测六方相ZnTiO3属于直接带隙半导体材料,其禁带宽度(布里渊区Z点)为3.11 eV.电子态密度和Mulliken电荷布居分析表明Zn―O键是典型的离子键而Ti―O键是类似于钙钛矿型ATiO3(A=Sr,Pb,Ba)的Ti―O共价键.在50 eV的能量范围内研究了ZnTiO3的介电函数、吸收光谱和折射率等光学性质,并基于电子能带结构和态密度对光学性质进行了解释.

第一性原理;电子结构;光学性质;钛铁矿型六方相ZnTiO3

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Received:August 2,2010;Revised:October 27,2010;Published on Web:November 17,2010.

∗Corresponding author.Email:fancm@163.com;Tel:+86-351-6018193,+86-13007011210.

The project was supported by the National Natural Science Foundation of China(20876104,20771080)and Science and Technology Foundation of Shanxi Province,China(20090311082).

国家自然科学基金(20876104,20771080)和山西省科技攻关项目(20090311082)资助