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