Keywords:A. Orthorhombic SrZrO3D. Electronic structureD. Optical propertiesE. Density-functional theory
SrZrO3 belongs to the perovskite oxides family with the generalformula ABO3 and has been extensively studied due to its widetechnological applications such as high- dielectric thin films forhigh-voltage and high-reliability capacitors, buffer layers for theepitaxial growth of ferroelectric thin films, electrical ceramics,solid electrolytes, refractories and heterogeneous catalysis, fuelcells, hydrogen sensors, etc., . SrZrO3 undergoes three phasetransitions as follows: orthorhombic (Pnma) orthorhombic(Cmcm) tetragonal (I4/mcm) cubic perovskite (Pm3m) at9701041 K, 11001130 K and 13761443 K, respectively ,which shows that SrZrO3 adopts the orthorhombic Pnma typeperovskite structure under ambient conductions and undergoesstructural transitions to the cubic perovskite structure at elevatedtemperatures.
Many experimental  and theoretical  investi-gations have been devoted to the study of SrZrO3 because of itshigh-temperature electronic properties. Electronic and structuralproperties of the (001) surface of cubic SrZrO3 have been investi-gated using the B3LYP hybrid functional method with the CRYS-TAL03 code , the FLAPW method with the WIEN2K code and the B3PW hybrid functional method with the CRYSTAL03code . Moreover, structural, elastic, electronic and optical
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properties of cubic SrZrO3 have been extensively studied [22,24,27,28,30,31]. It can be seen that a lot of the literature has concentratedon the cubic phase, but the orthorhombic (Pnma) structure in awide range of temperature where its useful applications take placehas been researched rarely. Vali  has reported the electronicband structure, vibrational modes and dielectric properties of or-thorhombic SrZrO3 and Evarestov et al.  has investigated thestructural properties of orthorhombic SrZrO3. However, a numberof basic properties of orthorhombic SrZrO3 are still unknown. Tothe best of our knowledge, there are no theoretical works explor-ing the optical properties of orthorhombic SrZrO3. In order to fullytake advantage of the properties of orthorhombic SrZrO3 in the fab-rication of optical devices, a theoretical investigation of the opticalproperties is necessary. Furthermore, the detailed charge densities,chemical bonding and physical origins of the optical properties oforthorhombic SrZrO3 which have not been presented should be in-vestigated as soon as possible.
Hence, the aimof this paper is to study the structural, electronic,chemical bonding and optical properties of orthorhombic SrZrO3using the plane-wave ultrasoft pseudopotential technique basedon the first-principles density-functional theory. Compared withprevious theoretical calculations of orthorhombic SrZrO3 [19,20],the charge densities and optical properties have first been studied.The paper is organized as follows: in Section 2, we will give thetechnical details of the employed methods. Section 3 is devotedto the results and disscussion, including the structural parameters,electronic band structure, chemical bonding, optical properties andavailable experimental data. We summarize our main findings inSection 4.Solid State Communicatio
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First-principles study of structural, electrorthorhombic SrZrO3Qi-Jun Liu , Zheng-Tang Liu, Yun-Fang Liu, Li-Ping FState Key Lab of Solidification Processing, College of Materials Science and Engineering, No
a r t i c l e i n f o
Article history:Received 13 March 2010Received in revised form30 July 2010Accepted 9 August 2010by S. ScandoloAvailable online 19 August 2010
a b s t r a c t
Wehave investigated the strubic SrZrO3 using the plane-wfunctional theory (DFT). Ourtheoretical and experimentatematically studied. Furthermoptical reflectivity, absorptioshow an optical anisotropy i0038-1098/$ see front matter 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.ssc.2010.08.011s 150 (2010) 20322035
le at ScienceDirect
onic and optical properties of
eng, Hao Tian, Jian-Gang Dingrthwestern Polytechnical University, Xian, Shaanxi 710072, Peoples Republic of China
ctural parameters, electronic structure and optical properties of orthorhom-veultrasoft pseudopotential technique based on the first-principles density-calculated structural parameters are in good agreement with the previousdata. Band structure, density of states and chemical bonding have been sys-ore, the complex dielectric function, refractive index, extinction coefficient,n coefficient, loss function and optical conductivity are calculated, whichthe components of polarization directions (100), (010) and (001).
2010 Elsevier Ltd. All rights reserved.
Q.-J. Liu et al. / Solid State Commu
Table 1Calculated lattice parameters a, b, c (in ) and atomic coordinates x, y, z (infractional units of cell parameters) compared with available theoretical [19,20]and experimental data  for orthorhombic SrZrO3 (the atomic coordinates arepresented below the lattice parameters).
Atom a b c
This work 5.8118 5.8701 8.2426CASTEP Sr 0.0070 0.5319 0.25GGA-PW91 Zr 0 0 0
O1 0.0760 0.0201 0.25O2 0.2142 0.2856 0.0399
Previous  5.652 5.664 7.995ABINIT Sr 0.007 0.534 0.25
Zr 0 0 0O1 0.107 0.036 0.25O2 0.199 0.301 0.056
Previous  5.847 5.911 8.295VASP Sr 0.007 0.533 0.250DFT-PW Zr
O1 0.077 0.021 0.250O2 0.213 0.287 0.041
Expt.  5.7963 5.8171 8.2048Sr 0.0040 0.5242 0.25Zr 0 0 0O1 0.0687 0.0133 0.25O2 0.2154 0.2837 0.0363
2. Computational methodology
Density-functional theory calculations are performed withplane-wave ultrasoft pseudopotentials using the generalized gra-dient approximation (GGA) with the PerdewWang 1991 (PW91)functional  as implemented in the CASTEP code . Theionic cores are represented by ultrasoft pseudopotentials for Sr, Zrand O atoms. The Sr 4s2, 4p6, 5s2 electrons, Zr 4s2, 4p6, 4d2, 5s2electrons and O 2s2, 2p4 electrons are explicitly treated as va-lence electrons. The plane-wave cutoff energy is 450 eV and theBrillouin-zone integration is performed over the 4 4 3 gridsizes using theMonkorstPackmethod for orthorhombic structureoptimization. This set of parameters assures a maximum force of0.01 eV/, amaximumstress of 0.02GPa and amaximumdisplace-ment of 5.0 104 .3. Results and discussion
3.1. Structural parameters
The crystal structure of orthorhombic SrZrO3 belongs to thespace group Pnma and the local symmetry D162h . The energy versusvolume curve is fitted using the BirchMurnaghan equation  tofind the optimized parameters. The calculated equilibrium latticeparameters and atomic coordinates compared with availabletheoretical [19,20] and experimental data  for orthorhombicSrZrO3 are summarized in Table 1. It can be seen that ourresults are better than previous calculated values compared withexperimental data. Moreover, the computed lattice constants a, band c are larger by about 0.27%, 0.91% and 0.46% compared withexperiment, respectively, which show the agreement with theexperiments can be considered to be very good and the GGAcalculations overestimate the lattice constants.
3.2. Band structure and chemical bonding
Table 2 shows the optical transition energies together with thevalence-to-conduction band transitions for orthorhombic SrZrO3.The calculated band structure shows that orthorhombic SrZrO3 has
an indirect band gap because the top valence and the bottom con-duction are found at S point and point, respectively. In addition,nications 150 (2010) 20322035 2033
Table 2Optical transition energies (eV) and symmetry of the valence-to-conduction bandtransitions along with experimental band gap (eV)  of orthorhombic SrZrO3 .
Experimental bandgap 
S Z 3.961S T 5.093S Y 4.732S X 4.712S U 5.205S R 4.831 3.767Z Z 4.017T T 5.307Y Y 4.937S S 4.045X X 4.883U U 5.452R R 5.052
Fig. 1. The total and partial density of states of orthorhombic SrZrO3 .
the indirect gap from S to is calculated to be 3.749 eV and thedirect gap at is 3.767 eV, which are consistent with the priorcalculated results of 3.764 eV (indirect) and 3.799 eV (direct) .Compared with the previous electronic band structure results ofthe cubic phase of SrZrO3 (an indirect band gap of 3.23 eV and adirect band gap of 3.50 eV , an indirect band gap of 3.42 eV anda direct band gap of 3.72 eV ), our results show that the bandgap of orthorhombic SrZrO3 is larger than that of the cubic phase.However, these results are all smaller than the experiment data of5.6 eV  due to the well-known underestimation of conductionband state energies in DFT calculations.
The total and partial densities of states are shown in Fig. 1.The valence bands from 17.434 to 12.593 eV are composedpredominantly of Sr 4p and O 2s. The upper valence bands show astrong hybridization between O 2p and Zr 4d electrons. The lowerconduction bands are composed mostly of Zr 4d which shows thehybridization character with O 2p. Additionally, the total chargedensities of orthorhombic SrZrO3 from (002) and (020) planes arepresented in Fig. 2. Fig. 2 shows that the bonding between Sr andO is mainly ionic and the bonding between Zr and O is mainly
covalent due to Zr 4d and O 2p hybridization, which is in goodagreement with our analysis of densities of states.
2034 Q.-J. Liu et al. / Solid State Commu
(b) (020)Fig. 2. Charge densities in the (a) (002) and (b) (020) planes of orthorhombicSrZrO3 .
3.3. Optical properties
The optical applications of SrZrO3 are important to manytechnological and industrial applications. Among the optical ap-plications are its use as optical wave-guides, violetblue lightemission, laser-host crystals, transparent ceramics and multilayerheterostructured systems for optical applications, etc., [31,36,37].The calculated optical properties at the equilibrium lattice con-stant are presented in Figs. 36, for the energy range up to 35 eV.Because of localization, we have used a scissors operator to dealwith the underestimated band gap and theminimum band gap be-comes 5.6 eV for orthorhombic SrZrO3, which is in agreement withexperiment by a rigid shift of 1.851 eV. The dielectric function andall the related optical properties are obtained by using the scissorsoperator, which displaces the empty and occupied bands relativeto each other. Good agreementwith experiment is obtained for theoptical properties of, e.g., TiO2 , ZrO2  and HfO2  usingthe scissors operator, which indicates that the scissors operator isreasonable and our calculated optical properties are believable.
The optical properties show an optical anisotropy from (100),(010) and (001). Fig. 3 shows the dielectric functions for or-
thorhombic SrZrO3. The calculated imaginary parts exhibit mainlyseven structures labeled A (7.726 eV, 7.814 eV and 7.814 eV fornications 150 (2010) 20322035
Fig. 3. The calculated complex dielectric function for polarization vectors (100),(010) and (001) for orthorhombic SrZrO3 .
Fig. 4. The calculated refractive index and extinction coefficient for polarizationvectors (100), (010) and (001) for orthorhombic SrZrO3 .
(100), (010) and (001) directions), B (9.987 eV, 9.987 eV and10.031 eV), C (11.716 eV, 11.495 eV and 11.583 eV), D (18.102 eV,18.457 eV and 18.324 eV), E (19.654 eV, 19.166 eV and 20.408 eV), F(25.152 eV, 25.019 eV and 25.064 eV) and G (32.469 eV, 32.336 eVand 32.469 eV), respectively. Structure A originates mainly fromO 2p to the conduction bands. Structure B (C) originates mainlyfrom the hybridization ( ) bonding between Zr 4d and O 2pinto the conduction bands. Structures D and E originate mainlyfrom the hybridization bonding between Sr 4p and O 2s into thelower conduction bands. Structure F originates mainly from thehybridization bonding between Sr 4p and O 2s into the upperconduction bands. Structure G orginates mainly from Zr 4p to the
conduction bands. The calculated static dielectric constants are4.032, 3.996 and 3.996 from (100), (010) and (001).
Q.-J. Liu et al. / Solid State Commu
Fig. 5. The calculated optical reflectivity, absorption coefficient and loss functionfor polarization vectors (100), (010) and (001) for orthorhombic SrZrO3 .
Fig. 6. The calculated optical conductivity for polarization vectors (100), (010) and(001) as well as experimental data  for orthorhombic SrZrO3 .
The refractive index and extinction coefficient are displayed inFig. 4which shows that the static refractive indices are 2.008, 1.999and 1.999 from (100), (010) and (001). Fig. 5 shows the calculatedresults on the reflectivity, absorption coefficient and loss functionfrom polarization vectors (100), (010) and (001) for orthorhombicSrZrO3. Moreover, the calculated and experimental  real partsof the optical conductivity of orthorhombic SrZrO3 are shownin Fig. 6. It can be seen that our values are in good agreementwith the experimental data, which indicates that our calculatedresults are believable. We hope the calculated values can help tooffer a theoretical basis for the experiment and applications oforthorhombic SrZrO3.
In summary, we have performed first-principles computationson orthorhombic SrZrO3, including the structural parameters,electronic structure, chemical bonding and optical properties. Thecalculated equilibrium lattice parameters are in good agreementwith the experimental values. The calculated band structure showsthat orthorhombic SrZrO3 has an indirect band gap of about3.749 eV. From the band structure, the charge densities areobtained and the chemical bonding is analyzed. Our results show
that Zr and O is mainly covalent whereas Sr and O is mainly ionic.The optical properties have been calculated and the peak positionnications 150 (2010) 20322035 2035
distribution of imaginary parts of the complex dielectric functionhas been explained, which shows an optical anisotropy from (100),(010) and (001).
This work was financially supported by the National Natu-ral Science Foundation of China (Contract no. 50902110), theNational Aerospace Science Foundation of China (Contract no.2008ZF53058), the Specialized Research Foundation for Doc-toral Program of Higher Education of China (Contract no.200806991032), the Doctorate Foundation of Northwestern Poly-technical University (Contract no. cx201005), the NorthwesternPolytechnical University (NPU) Foundation for Fundamental Re-search (Contract no. NPU-FFR-W018108) and the 111 Project(Contract no. B08040).
 C.H. Chen, W.G. Zhu, T. Yu, X.F. Chen, X. Yao, Appl. Surf. Sci. 211 (2003)244249.
 D. Miu, J.C. Martinez, M. Maier, H. Adrian, J. Optoelectron. Adv. Mater. 8 (2006)2426.
 S.Q. Hu, S.H. Li, Eng. Chem. Metall. 16 (1995) 3641. W.J. Zheng, C. Liu, W.Q. Pang, J. Inorg....