- Email: [email protected]
Structural study of Ca doped barium titanate
Nuclear Instruments and Methods in Physics Research B 284 (2012) 44–48
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Structural study of Ca doped barium titanate Jong-Seo Park, Yun-Hee Lee, Ki-Bok Kim, Yong-Il Kim ⇑ Korea Research Institute of Standards and Science, P.O. Box 102, Yuseong, Daejeon 305340, Republic of Korea
a r t i c l e
i n f o
Article history: Available online 11 August 2011 Keywords: Ca-doped BaTiO3 Combined structural refinement Site preference Virtual crystal approximation
a b s t r a c t Both the combined structural refinement and the geometry energy calculation based on quantum mechanics were applied to determine the site preference and occupancies of Ca atom as a dopant in Ca-doped BaTiO3 prepared by the hydrothermal process. Of possible models based on cation disorder and anion vacancy, the best structural refinement result was obtained from the model, in which Ca atoms co-substituted for Ba and Ti atoms, and vacancies of the two O sites were created for charge compensation due to the substitution of Ca2+ ions for Ti4+ ions. The model proposed by the combined structural refinement was verified by the virtual crystal approximation method dealing with the disorder of atoms based on the first principle calculation. The final weighted R-factor and the goodness-of-fit for both data was 6.78% and 1.42%. The occupancies of Ca atoms distributed over Ba and Ti sites were 0.086(2) at Ba site and 0.027(2) at Ti site, and the vacancies of O atoms at O(1) and O(2) sites were 0.011(2) and 0.019(2), respectively. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Multi-layer ceramic capacitors (MLCCs) produced from BaTiO3 powder have been widely used in the electronic industry for various applications like infrared detectors, piezoelectric transducers, waveguide modulators, gate dielectrics, ferroelectric memories and so on. These MLCCs based the X7R specification are required to extend their working range up to 150 °C because the present electronic devices become much smaller in size and higher in performances than ever before [1]. In order to attain these industrial requirements, many studies have been performed to find a way of extending working temperature of MLCC by doping of metal ions such as Co2+, Fe3+ and Mn3+ into the BaTiO3 host lattice [2]. In addition, it is well known that alkaline earth metals as dopants produce various physical properties of BaTiO3-based materials, including ferroelectricity, conductivity, structural transformations and so forth [3]. Among these alkaline metals, the substitution of Ca and Sr atoms for every cation in BaTiO3 have a significant effect on the Curie temperature (TC) and electrical properties of BaTiO3 with the solid solution limit of each site [4–6]. Although many reports have noted that Ca atoms possibly play a key role in the reduction of electrical resistance and the formation of other phases, most of the studies concerning the amount of Ca atoms substituting for cationic atoms have focused chemically on the quantities of Ca atoms in the compound. Determining the quantities of Ca atoms in the crystal lattice is an important
⇑ Corresponding author. Tel.: +82 42 868 5448; fax: +82 42 869 5635. E-mail address: [email protected] (Y.-I. Kim). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.07.107
thing because the amount of Ca atoms doped into the crystal lattice of BaTiO3 is directly related in predicting the ferroelectric properties and modified electronic structure of BaTiO3. Furthermore, the behavior of Ca atom as a dopant in the host lattice is important to understand the spontaneous polarization at room temperature. However, the studies on the behavior of Ca atoms in Ca-doped BaTiO3 are lacking relative to the studies on preparation. Therefore, this work has attempted to perform the combined structural refinement for Ca-doped BaTiO3 system using X-ray and neutron powder diffraction in order to determine the preferential site of Ca atom and to quantify the amount of constituent atoms. Two kinds of diffraction data in this study were used to get complementary information on every atom in Ca-doped BaTiO3 due to the different scattering properties of neutrons versus X-rays, even though the neutron diffraction is very similar to X-ray diffraction.
2. Experimental The samples (BaTiO3:Cax) were synthesized by a hydrolysis method using barium hydroxide monohydrate [Ba(OH)2H2O, Aldrich, 98.0%), titanium isopropoxide [Ti(OCH(CH3)2)4, Aldrich, 99.9%] and calcium chloride [CaCl2, Aldrich, 99.9%] as precursors with x ranging from 0 to 0.15. And then, the washing, filtering, and drying process were carried out. Finally, the resultants were heat-treated at 1050 °C for 6 h in the air. Neutron powder diffraction data were measured over scattering angles between 0° and 160° with a 2h step of 0.05° using 1.8343 Å on the High Resolution Powder Diffractometer (HRPD) at Hanaro
45
J.-S. Park et al. / Nuclear Instruments and Methods in Physics Research B 284 (2012) 44–48
Center of the Korea Atomic Energy Research Institute (KAERI). X-ray diffraction data were obtained from the powder diffractometer (Dmax 2200, Rigaku, Japan) in the step scan mode (15° 6 2h 6 130° at a 2h step of 0.02°) using copper radiations with a graphite monochromator in the reflection geometry at room temperature. The structural refinement was carried out with the EXPGUI program, a graphical user interface for General Structure Analysis System (GSAS) [7,8]. The peak profile function was modeled using the convolution of the Thompson-Cox-Hastings pseudo-Voigt (pV-TCH) with the asymmetry function described by Finger et al. [9]. The geometry energy calculation was performed using the Cambridge Serial Total Energy Package (CASTEP) developed by Payne et al., which employs a plane wave basis set to treat valence electrons and pseudo-potentials to approximate the potential field of ion cores [10]. Ultra-soft pseudo-potentials and the Perdew– Burke–Emzerhof (PBE) generalized gradient approximation (GGA) functions were used for all calculations. The energy cutoff was set to be above 340 eV for every element [11,12]. 3. Results and discussion The X-ray diffraction patterns for Ca-doped BaTiO3 (BaTiO3:Cax, x = 0–0.15) samples were shown in Fig. 1. All samples, (BaTiO3:Cax, x = 0–0.15), were indexed by the tetragonal crystal system of BaTiO3 and the lattice parameters of these samples were slightly smaller than those of undoped BaTiO3. However, the diffraction peaks corresponding to CaTiO3 phase for the sample with 15 at.% Ca (BaTiO3:Cax, x = 0.15) were observed. In addition, a peak splitting behavior of (0 0 2) and (2 0 0) reflections which typically indicate the tetragonal phase of BaTiO3 converged into nearly one peak. These mean that the substitutional limit of Ca atom as a dopant in Ca-doped BaTiO3 sample synthesized in this study is about 12 at.%. Consequently, the (BaTiO3:Cax, x = 0.12) sample which was shown in the maximum substitutional limit of Ca atom was used to investigate the behavior of Ca atom as a dopant in Cadoped BaTiO3. The initial structural refinement requires a crystal structural model that contains a reasonable approximation of the actual
crystal structure. The initial crystal structural model of Ca-doped BaTiO3 was constructed with crystallographic data based on the space group P4mm [13,14]. The crystal structure of BaTiO3 composed of two cations and one anion may be viewed as Ban+[TiO3]n where the corner-shared linkage of TiO6 octahedral forms a framework extending in an elongated octahedral configuration. Considering the crystal structure of BaTiO3 mentioned above, order–disorder models between Ca and two atoms (Ba and/or Ti) in BaTiO3 are possible when Ca atoms are doped into BaTiO3. In addition, there are other possibilities of Ca atoms to partially occupy two cationic sites (Ba and Ti sites) in the BaTiO3 lattice. If Ca atoms (Ca2+) partially occupied at Ti site, it gives rise to form the oxygen vacancies at two oxygen sites [(O(1) and O(2)) for charge compensation. Finally, there are seven kinds of models to be possible, assuming the substitution of Ca atoms for two cations (Ba and/or Ti) and the generation of oxygen vacancies at two different anionic sites [O(1) and O(2)]: the substitution of Ca atoms for only Ba atoms at 1a site (0, 0, 0) (B model), the substitution of Ca atoms for only Ti atoms at 1b site (1/2, 1/2, z) and the generation of oxygen vacancies at only O(1) site (1b site: 1/2, 1/2, z) (T-O1 model), the substitution of Ca atoms for only Ti atoms and the generation of oxygen vacancies at only O(2) site (2c site: 1/2, 0, z) (T-O2 model), the substitution of Ca atoms for only Ti atoms and the generation of oxygen vacancies at the two O sites (O(1) and O(2)) (T-O12 model), partially cosubstitution of Ca atoms for two cations (Ba and Ti sites) and the generation of oxygen vacancies at only O1 site (BT-O1 model), partially co-substitution of Ca atoms for two cations (Ba and Ti sites) and the generation of oxygen vacancies at only O(2) site (BT-O2 model), and finally partially co-substitution of Ca atoms for two cations (Ba and Ti sites) and the generation of oxygen vacancies at all O sites (O(1) and O(2)) (BT-O12 model) (Table 1).
Table 1 Geometry energy calculation for possible order–disorder models of Ca atoms in Cadoped BaTiO3 system. Model
Atomic site
Mixture atom (%)
B
1aa 1bb 1bc 2cd 1a 1b 1b 2c 1a 1b 1b 2c 1a 1b 1b 2c 1a 1b 1b 2c 1a 1b 1b 2c 1a 1b 1b 2c
Ba: 88, Ca: 12 Ti: 100 O: 100 O: 100 Ba: 100 Ti: 88, Ca: 12 O: 88 O:100 Ba: 100 Ti: 88, Ca: 12 O1: 100 O2: 94 Ba: 100 Ti: 88, Ca: 12 O1: 94 O2: 97 Ba: 94, Ca: 6 Ti: 94, Ca: 6 O1: 94 O2: 100 Ba: 94, Ca: 6 Ti: 94, Ca: 6 O1: 100 O2: 97 Ba: 94, Ca: 6 Ti: 94, Ca: 6 O1: 97 O2: 98.5
T-O1
T-O2
T-O12
BT-O1
BT-O2
BT-O12
a b
Fig. 1. X-ray diffraction patterns of Ca-doped BaTiO3 (BaTiO3:Cax, x = 0–0.15) samples at room temperature as a function of Ca contents.
c d
1a site (0, 0, 0). 1b site (1/2, 1/2, z). 1b site (1/2, 1/2, z). 2c site (1/2, 0, z).
Energy (eV) 3.550194783 103
3.552168544 103
3.552329413 103
3.5512701245 103
3.551250523 103
3.550203571 103
3.549933760 103
46
J.-S. Park et al. / Nuclear Instruments and Methods in Physics Research B 284 (2012) 44–48
The structural refinement using X-ray diffraction data was carried out on the assumption that there was no substitution of Ca atoms for all cations in BaTiO3. The instrument-induced zero-point shift was corrected by X-ray powder diffraction data of a standard reference material (SRM) 640c (NIST). After a good match of the peak positions was achieved, the peak profile parameters including the peak asymmetry were refined. All reflection peaks could be indexed by tetragonal phase of BaTiO3 which was used to build the starting crystal structure model. The neutron diffraction data may be useful to accurately determine the occupancies of individual atoms in Ca-doped BaTiO3 due to the large difference of neutron scattering length between constituent atoms: Ba (5.07 10 12 cm), Ti ( 3.438 10 12 cm), Ca (4.70 10 12 cm) and O (0.5803 10 12 cm). Consequently, the combined structural refinement using X-ray and neutron diffraction data was carried out to determine the preferential site of Ca atom in Ca-doped BaTiO3 by considering both Xray and neutron diffraction patterns with equal weight to both. A shifted-Chebyshev function was employed to fit the background to both X-ray and neutron powder diffraction data. The observed Bragg peaks were modeled with Thompson-Cox-Hastings pseudo-Voigt profile function. It is referred to as No. 3 in GSAS. First, in order to determine the purity of the sample as well as the lattice parameters, the structural refinement using X-ray diffraction data was carried out on the assumption that there was no substitution of Ca atoms for every cation in BaTiO3. The structural refinement for neutron diffraction data was started assuming the lattice parameters obtained from the previous refinement using the X-ray data. The next refinement procedure requires to refine constant neutron wavelength to be used for collecting neutron diffraction data. Once convergence had been reached, the subsequent step for neutron data is to refine the scale factor, background parameters and peak shape profile parameters along with other instrumental factors. Once the preliminary structural refinement using respective Xray and neutron data had converged through the refinement of the parameters, including the background, the scale factor, the lattice parameters, the profile shape parameters and so on, the possibility of disorder for the Ca atom based on the seven kinds of models mentioned above was considered through the final combined structural refinement. The occupancies of every cationic site in all models were constrained so that the sites were fully occupied and the total occupancy of Ba, Ti and Ca atoms was maintained to be unity. In addition to the above things, isotropic atomic displacement parameters of the atoms for all cationic sites to be considered were same on the condition that both Ba/Ca and Ti/Ca atoms occupied identical positions. After the preliminary combined structural refinement had converged, the occupation factor of all cationic atoms was refined with the constraints of each occupancy and isotropic atomic displacement parameter for seven models. Among the converged R-factors obtained from the structural refinement for seven models using neutron powder diffraction data, the final weighted R-factor, Rwp, for B, T-O1, T-O2, T-O12, BT-O1, BT-O2 and BT-O12 models was converged to 6.85%, 7.01%, 6.96%, 6.93%, 6.85%, 6.82% and 6.78%, respectively. Even if there is no large difference between seven models based on only final refinement patterns, from the viewpoint of final weight R-factor, it may be concluded that the BT-O12 model was most suitable as a site preferential model of Ca atoms in Ca-doped BaTiO3 system at room temperature. Fig. 2 shows the combined structural refinement patterns of the BT-O12 model using X-ray and neutron powder diffraction data. The final weighted R-factor, Rwp, and the goodness-of-fit, S (=Rwp/Re), indicating the quality of a refined model for both data was 6.78% and 1.42%, respectively: Rwp = 5.01%, Rp = 3.90%, RF = 2.17% and Re = 3.35% for neutron
Fig. 2. Combined structural refinement patterns of Ca-doped BaTiO3 (BaTiO3:Cax, x = 0.12) using (a) X-ray and (b) neutron diffraction data. Plus signs (+) represent the observed intensities; the solid line defines calculated ones. A difference plot (obs.-cal.) is shown beneath. Tick marks above the difference indicate the reflection positions.
diffraction data and Rwp = 9.86%, Rp = 7.10%, RF = 3.69% and Re = 7.38% for X-ray diffraction data. In order to confirm the preferential substitution site of Ca atoms in Ca-doped BaTiO3 from the geometry energy point of view, CASTEP as a first principle method based on the density-functional theory was applied to the Ca-doped BaTiO3 system. In CASTEP, a mixture of atoms may be used to simulate the case where one atomic site is randomly occupied by two or more different types of an atom. Also, atomic site in a disordered crystal can be described in terms of a hybrid atom, which consists of two or more element types. There are a number of different approaches for dealing with the disorder based on the first principle calculation methods, for example, virtual crystal approximation (VCA), the large ordered supercell model, coherent potential approximation and computational alchemy [15]. Of these methods, the VCA was used to calculate the total energy difference between the possible cationdisorder models of Ca atoms in the Ca-doped BaTiO3 system. Table 1 lists the calculated geometry energy of each model described above. Comparing with the only cation disorder in Table 2, the Ca atoms as dopants in BaTiO3 preferentially occupy Ba site rather than to Ti one. Also, the possibility of O atom at O(2) site to be formed vacancies states is higher than that of O(1) at O(1) site in order for charge compensation in Ca-doped BaTiO3 due to the partial substitution of Ca atoms for Ti ones.
47
J.-S. Park et al. / Nuclear Instruments and Methods in Physics Research B 284 (2012) 44–48
Table 2 Selected interatomic distances and bond angles for undoped BaTiO3 and Ca-doped BaTiO3 (BaTiO3:Cax, x = 0.12) obtained from the combined structural refinement using X-ray and neutron powder diffraction data measured at room temperature. Interatomic distances (Å) Number of bond distance (Å) BaTiO3 Polyhedron Ba-O(1)a Ba-O(2)b Ba-O(2)
4 4 4
Average Ti-O(1)
4
2 1
Average a b c d
2.0005(1)
1.8876(1) 2.1432(1)
4 4 4
2.8303(1) 2.7729(1) 2.8975(1)
4
2.0004(1)
60.679(1) 89.954(1) 58.754(1)
O(2)-Ba-O(2)
4
89.839(1)
O(2)-Ba-O(2)
2
180
O(1)-M(1)-O(1) O(2)-M(1)-O(2) O(2)-M(1)-O(2)
4 4 4
61.335(1) 89.934(1) 58.434(1)
O(2)-M(2)-O(2)
4
89.987(1)
O(2)-M(2)-O(2)
2
180
2.8336(1)
Average M(2)-O(2) M(2)-O(2)
4 4 4
2.0154(1)
Average M(2)d-O(1)
Polyhedron O(1)-Ba-O(1) O(2)-Ba-O(2) O(2)-Ba-O(2)
1.9738(1)
Average Ca-doped BaTiO3 M(1)c-O(1) M(1)-O(2) M(1)-O(2)
Angle(°)
2.8401(1)
Average Ti-O(2) Ti-O(2)
2.7965(1) 2.8262(1) 2.8795(1)
Bond angles (°) Bond type No.
2.0004(1) 1 1
1.9707(1) 2.0462(1) 2.0085(1)
O(1) : O at 1b site. O(2) : O at 2c site. M(1) : Ba and Ca at 1a site. M(2) : Ti and Ca at 1b site.
Of the possible models listed in Table 1, the BT-O12 model, in which the O vacancies are created for all O sites due to the partial distribution of Ca atoms over Ba and Ti sites is most stable in the aspect of geometry energy. The result of the geometry energy calculation based on the distribution models of Ca atom in the Cadoped BaTiO3 system is in good agreement with the model suggested by the combined structural refinement. Since the bond lengths between cation and anion have a reverse-relation to the bond energies, the occurrence possibility of vacancies at O sites may be understood in terms of the average interatomic lengths between Ti and O atoms. Table 2 presented the difference of mean interatomic distances between undoped BaTiO3 and Ca-doped BaTiO3. The selected atomic distances indicate that the probability of vacancies to be created at O(2) site may be much higher than that at O(1) site. The same tendency was observed from the geometry energy calculation result, representing the lower energy of O(2) than that of O(1). The combined structural refinement result as listed in Table 3 presents that the Ca atoms were distributed over Ba and Ti sites. The occupancy of Ca atom for Ba and Ti sites was 0.086(2) and 0.027(2), respectively. The occupancy of O atom was 0.989(2) at O(1) site and 0.981(2) at O(2) site. The result is in good accordance with the reports that Ca atoms distribute over Ba and Ti sites [4,5,16–18]. When considering the ionic radius of Ba2+ (1.49 Å), Ca2+ (1.14 Å), and Ti4+ (0.745 Å) [19] and the cell volumes of between undoped BaTiO3 (64.3539 Å3) and Ca-doped BaTiO3 (64.2800 Å3) obtained from the structural refinement results of this study, smaller Ca ions more likely substitute onto Ba sites where they will be smaller than Ba ions and hence result in decreasing the cell volume. From the viewpoint of the occupancy of Ca ions for Ba sites based on the structural refinement, it may be expected that the cell volume of Ca-doped BaTiO3 will largely decrease due to the highoccupancy of Ca ions for Ba sites. However, the difference of cell volume based on the refined lattice parameters of between
Table 3 Refined structural parameters for Ca-doped BaTiO3 (BaTiO3:Cax, x = 0.12) obtained from the combined structural refinement using X-ray and Neutron powder diffraction data measured at room temperature. The symbol, g, is the occupation factor. The numbers in parentheses are the estimated standard deviations of the last significant figure. Atom Ba Ca(1) Ti Ca(2) O(1) O(2)
Site 1a 1a 1b 1b 1b 2c
x/a 0.0 0.0 0.5 0.5 0.5 0.5
y/b 0.0 0.0 0.5 0.5 0.5 0.0
z/c 0.0 0.0 0.486(1) 0.486(1) 0.024(1) 0.478(1)
100 Uiso/Å2
g a
0.914(2) 0.086(2) 0.973(2)b 0.027(2) 0.989(2) 0.981(2)
0.44(1)c 0.44(1) 1.12(3)d 1.12(3) 1.39(1) 1.11(3)
Space group : P4mm (No. 99) and Z = 1 a = b = 4.0003(1) Å, c = 4.0169(1) Å, a = b = c = 90° a b c d
Constraint Constraint Constraint Constraint
on on on on
occupancy: g(Ba) + g(Ca(1) = 1.0. occupancy: g(Ti) + g(Ca(2)) = 1.0. isotropic atomic displacement: UisoBa = UisoCa(1). isotropic atomic displacement: UisoTi = UisoCa(2).
undoped BaTiO3 and Ca-doped BaTiO3 was only about 0.15%. This may make sense that Ca ions co-occupy both Ba and Ti sites because the larger ionic radius of Ca than Ti ion makes a contribution for increasing of the cell volume of Ca-doped BaTiO3. Consequently, the result supports that the BT-O12 model suggested by the geometry energy calculation, in which Ca atoms partially occupy two cationic sites (Ba and Ti sites) is most reasonable in the possible order–disorder models for Ca-doped BaTiO3. 4. Conclusion When Ca atoms as a dopant substituted for cations in BaTiO3, they preferentially substituted for Ba atoms at 1a (0, 0, 0) site surrounded by 12 oxygen atoms, and then occupied at Ti site (1b, 1/2, 1/2, z) creating oxygen vacancies of the two oxygen sites simulta-
48
J.-S. Park et al. / Nuclear Instruments and Methods in Physics Research B 284 (2012) 44–48
neously. The behavior of Ca atoms as dopants in Ca-doped BaTiO3 was successfully determined through the combined structural refinement and the virtual crystal approximation method based on the first principle calculation. The approach may be applied to investigate the behavior of dopants to be used for enhanced material properties. Acknowledgements This research was supported by the Converging Research Center Program through the Ministry of Education, Science and Technology (2011K000600), and the Center for Nano scale Mechatronics & Manufacturing, one of the 21st Century Frontier Research Programs, which are supported by Ministry of Education, Science and Technology, Korea. References [1] H. Kishi, Y. Mizuno, H. Chazono, Jpn. J. Appl. Phys. Part 1 42 (2003) 1.
[2] M.T. Buscaglia, V. Buscaglia, M. Viviani, P. Nanni, M. Hanuskova, J. Eur. Ceram. Soc. 20 (2000) 1997. [3] K. Asokan, J.C. Jan, J.W. Chiou, W.F. Pong, P.K. Tseng, I.N. Lin, J. Synchrotron Rad. 8 (2001) 839. [4] L. Zhang, O.P. Thakur, A. Feteira, G.M. Keith, A.G. Mould, D.C. Sinclair, A.R. West, App. Phys. Lett. 90 (2007) 142914. [5] D.F.K. Hennings, H. Schreinemacher, J. Eur. Ceram. Soc. 15 (1995) 795. [6] S. Lee, C.A. Randall, Appl. Phys. Lett. 92 (2008) 111904. [7] B.H. Toby, J. Appl. Cryst. 34 (2001) 210. [8] A.C. Larson, R.B. Von Dreele, Los Alamos National Laboratory Report LAUR 86 (1994) 748. [9] L.W. Finger, D.E. Cox, A.P. Jephcoat, J Appl. Cryst. 27 (1994) 892. [10] M.C. Payne, M.P. Peter, D.C. Allan, T.A. Arias, J.D. Joannopoulos, Rev. Modern Phys. 64 (1992) 1045. [11] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [12] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 16 (1997) 1748. [13] J. Harada, T. Pedersen, Z. Barnea, Acta Cryst. A 26 (1970) 336. [14] R.H. Buttner, E.M. Maslen, Acta Cryst. B 48 (1992) 764. [15] N.J. Ramer, A.M. Rappe, Phys. Rev. B 62 (2000) R743. [16] Z.Q. Zhuang, M.P. Harmer, D.M. Smyth, R.E. Newnham, Mater. Res. Bull. 22 (1987) 1329. [17] Y.H. Han, J.B. Appleby, D.M. Smyth, J. Am. Ceram. Soc. 70 (1987) 96. [18] T.T. Fang, J.T. Shuei, J. Mater. Res. 14 (1999) 1910. [19] R.D. Shannon, Acta Cryst A32 (1976) 751.
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Structural study of Ca doped barium titanate Jong-Seo Park, Yun-Hee Lee, Ki-Bok Kim, Yong-Il Kim ⇑ Korea Research Institute of Standards and Science, P.O. Box 102, Yuseong, Daejeon 305340, Republic of Korea
a r t i c l e
i n f o
Article history: Available online 11 August 2011 Keywords: Ca-doped BaTiO3 Combined structural refinement Site preference Virtual crystal approximation
a b s t r a c t Both the combined structural refinement and the geometry energy calculation based on quantum mechanics were applied to determine the site preference and occupancies of Ca atom as a dopant in Ca-doped BaTiO3 prepared by the hydrothermal process. Of possible models based on cation disorder and anion vacancy, the best structural refinement result was obtained from the model, in which Ca atoms co-substituted for Ba and Ti atoms, and vacancies of the two O sites were created for charge compensation due to the substitution of Ca2+ ions for Ti4+ ions. The model proposed by the combined structural refinement was verified by the virtual crystal approximation method dealing with the disorder of atoms based on the first principle calculation. The final weighted R-factor and the goodness-of-fit for both data was 6.78% and 1.42%. The occupancies of Ca atoms distributed over Ba and Ti sites were 0.086(2) at Ba site and 0.027(2) at Ti site, and the vacancies of O atoms at O(1) and O(2) sites were 0.011(2) and 0.019(2), respectively. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Multi-layer ceramic capacitors (MLCCs) produced from BaTiO3 powder have been widely used in the electronic industry for various applications like infrared detectors, piezoelectric transducers, waveguide modulators, gate dielectrics, ferroelectric memories and so on. These MLCCs based the X7R specification are required to extend their working range up to 150 °C because the present electronic devices become much smaller in size and higher in performances than ever before [1]. In order to attain these industrial requirements, many studies have been performed to find a way of extending working temperature of MLCC by doping of metal ions such as Co2+, Fe3+ and Mn3+ into the BaTiO3 host lattice [2]. In addition, it is well known that alkaline earth metals as dopants produce various physical properties of BaTiO3-based materials, including ferroelectricity, conductivity, structural transformations and so forth [3]. Among these alkaline metals, the substitution of Ca and Sr atoms for every cation in BaTiO3 have a significant effect on the Curie temperature (TC) and electrical properties of BaTiO3 with the solid solution limit of each site [4–6]. Although many reports have noted that Ca atoms possibly play a key role in the reduction of electrical resistance and the formation of other phases, most of the studies concerning the amount of Ca atoms substituting for cationic atoms have focused chemically on the quantities of Ca atoms in the compound. Determining the quantities of Ca atoms in the crystal lattice is an important
⇑ Corresponding author. Tel.: +82 42 868 5448; fax: +82 42 869 5635. E-mail address: [email protected] (Y.-I. Kim). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.07.107
thing because the amount of Ca atoms doped into the crystal lattice of BaTiO3 is directly related in predicting the ferroelectric properties and modified electronic structure of BaTiO3. Furthermore, the behavior of Ca atom as a dopant in the host lattice is important to understand the spontaneous polarization at room temperature. However, the studies on the behavior of Ca atoms in Ca-doped BaTiO3 are lacking relative to the studies on preparation. Therefore, this work has attempted to perform the combined structural refinement for Ca-doped BaTiO3 system using X-ray and neutron powder diffraction in order to determine the preferential site of Ca atom and to quantify the amount of constituent atoms. Two kinds of diffraction data in this study were used to get complementary information on every atom in Ca-doped BaTiO3 due to the different scattering properties of neutrons versus X-rays, even though the neutron diffraction is very similar to X-ray diffraction.
2. Experimental The samples (BaTiO3:Cax) were synthesized by a hydrolysis method using barium hydroxide monohydrate [Ba(OH)2H2O, Aldrich, 98.0%), titanium isopropoxide [Ti(OCH(CH3)2)4, Aldrich, 99.9%] and calcium chloride [CaCl2, Aldrich, 99.9%] as precursors with x ranging from 0 to 0.15. And then, the washing, filtering, and drying process were carried out. Finally, the resultants were heat-treated at 1050 °C for 6 h in the air. Neutron powder diffraction data were measured over scattering angles between 0° and 160° with a 2h step of 0.05° using 1.8343 Å on the High Resolution Powder Diffractometer (HRPD) at Hanaro
45
J.-S. Park et al. / Nuclear Instruments and Methods in Physics Research B 284 (2012) 44–48
Center of the Korea Atomic Energy Research Institute (KAERI). X-ray diffraction data were obtained from the powder diffractometer (Dmax 2200, Rigaku, Japan) in the step scan mode (15° 6 2h 6 130° at a 2h step of 0.02°) using copper radiations with a graphite monochromator in the reflection geometry at room temperature. The structural refinement was carried out with the EXPGUI program, a graphical user interface for General Structure Analysis System (GSAS) [7,8]. The peak profile function was modeled using the convolution of the Thompson-Cox-Hastings pseudo-Voigt (pV-TCH) with the asymmetry function described by Finger et al. [9]. The geometry energy calculation was performed using the Cambridge Serial Total Energy Package (CASTEP) developed by Payne et al., which employs a plane wave basis set to treat valence electrons and pseudo-potentials to approximate the potential field of ion cores [10]. Ultra-soft pseudo-potentials and the Perdew– Burke–Emzerhof (PBE) generalized gradient approximation (GGA) functions were used for all calculations. The energy cutoff was set to be above 340 eV for every element [11,12]. 3. Results and discussion The X-ray diffraction patterns for Ca-doped BaTiO3 (BaTiO3:Cax, x = 0–0.15) samples were shown in Fig. 1. All samples, (BaTiO3:Cax, x = 0–0.15), were indexed by the tetragonal crystal system of BaTiO3 and the lattice parameters of these samples were slightly smaller than those of undoped BaTiO3. However, the diffraction peaks corresponding to CaTiO3 phase for the sample with 15 at.% Ca (BaTiO3:Cax, x = 0.15) were observed. In addition, a peak splitting behavior of (0 0 2) and (2 0 0) reflections which typically indicate the tetragonal phase of BaTiO3 converged into nearly one peak. These mean that the substitutional limit of Ca atom as a dopant in Ca-doped BaTiO3 sample synthesized in this study is about 12 at.%. Consequently, the (BaTiO3:Cax, x = 0.12) sample which was shown in the maximum substitutional limit of Ca atom was used to investigate the behavior of Ca atom as a dopant in Cadoped BaTiO3. The initial structural refinement requires a crystal structural model that contains a reasonable approximation of the actual
crystal structure. The initial crystal structural model of Ca-doped BaTiO3 was constructed with crystallographic data based on the space group P4mm [13,14]. The crystal structure of BaTiO3 composed of two cations and one anion may be viewed as Ban+[TiO3]n where the corner-shared linkage of TiO6 octahedral forms a framework extending in an elongated octahedral configuration. Considering the crystal structure of BaTiO3 mentioned above, order–disorder models between Ca and two atoms (Ba and/or Ti) in BaTiO3 are possible when Ca atoms are doped into BaTiO3. In addition, there are other possibilities of Ca atoms to partially occupy two cationic sites (Ba and Ti sites) in the BaTiO3 lattice. If Ca atoms (Ca2+) partially occupied at Ti site, it gives rise to form the oxygen vacancies at two oxygen sites [(O(1) and O(2)) for charge compensation. Finally, there are seven kinds of models to be possible, assuming the substitution of Ca atoms for two cations (Ba and/or Ti) and the generation of oxygen vacancies at two different anionic sites [O(1) and O(2)]: the substitution of Ca atoms for only Ba atoms at 1a site (0, 0, 0) (B model), the substitution of Ca atoms for only Ti atoms at 1b site (1/2, 1/2, z) and the generation of oxygen vacancies at only O(1) site (1b site: 1/2, 1/2, z) (T-O1 model), the substitution of Ca atoms for only Ti atoms and the generation of oxygen vacancies at only O(2) site (2c site: 1/2, 0, z) (T-O2 model), the substitution of Ca atoms for only Ti atoms and the generation of oxygen vacancies at the two O sites (O(1) and O(2)) (T-O12 model), partially cosubstitution of Ca atoms for two cations (Ba and Ti sites) and the generation of oxygen vacancies at only O1 site (BT-O1 model), partially co-substitution of Ca atoms for two cations (Ba and Ti sites) and the generation of oxygen vacancies at only O(2) site (BT-O2 model), and finally partially co-substitution of Ca atoms for two cations (Ba and Ti sites) and the generation of oxygen vacancies at all O sites (O(1) and O(2)) (BT-O12 model) (Table 1).
Table 1 Geometry energy calculation for possible order–disorder models of Ca atoms in Cadoped BaTiO3 system. Model
Atomic site
Mixture atom (%)
B
1aa 1bb 1bc 2cd 1a 1b 1b 2c 1a 1b 1b 2c 1a 1b 1b 2c 1a 1b 1b 2c 1a 1b 1b 2c 1a 1b 1b 2c
Ba: 88, Ca: 12 Ti: 100 O: 100 O: 100 Ba: 100 Ti: 88, Ca: 12 O: 88 O:100 Ba: 100 Ti: 88, Ca: 12 O1: 100 O2: 94 Ba: 100 Ti: 88, Ca: 12 O1: 94 O2: 97 Ba: 94, Ca: 6 Ti: 94, Ca: 6 O1: 94 O2: 100 Ba: 94, Ca: 6 Ti: 94, Ca: 6 O1: 100 O2: 97 Ba: 94, Ca: 6 Ti: 94, Ca: 6 O1: 97 O2: 98.5
T-O1
T-O2
T-O12
BT-O1
BT-O2
BT-O12
a b
Fig. 1. X-ray diffraction patterns of Ca-doped BaTiO3 (BaTiO3:Cax, x = 0–0.15) samples at room temperature as a function of Ca contents.
c d
1a site (0, 0, 0). 1b site (1/2, 1/2, z). 1b site (1/2, 1/2, z). 2c site (1/2, 0, z).
Energy (eV) 3.550194783 103
3.552168544 103
3.552329413 103
3.5512701245 103
3.551250523 103
3.550203571 103
3.549933760 103
46
J.-S. Park et al. / Nuclear Instruments and Methods in Physics Research B 284 (2012) 44–48
The structural refinement using X-ray diffraction data was carried out on the assumption that there was no substitution of Ca atoms for all cations in BaTiO3. The instrument-induced zero-point shift was corrected by X-ray powder diffraction data of a standard reference material (SRM) 640c (NIST). After a good match of the peak positions was achieved, the peak profile parameters including the peak asymmetry were refined. All reflection peaks could be indexed by tetragonal phase of BaTiO3 which was used to build the starting crystal structure model. The neutron diffraction data may be useful to accurately determine the occupancies of individual atoms in Ca-doped BaTiO3 due to the large difference of neutron scattering length between constituent atoms: Ba (5.07 10 12 cm), Ti ( 3.438 10 12 cm), Ca (4.70 10 12 cm) and O (0.5803 10 12 cm). Consequently, the combined structural refinement using X-ray and neutron diffraction data was carried out to determine the preferential site of Ca atom in Ca-doped BaTiO3 by considering both Xray and neutron diffraction patterns with equal weight to both. A shifted-Chebyshev function was employed to fit the background to both X-ray and neutron powder diffraction data. The observed Bragg peaks were modeled with Thompson-Cox-Hastings pseudo-Voigt profile function. It is referred to as No. 3 in GSAS. First, in order to determine the purity of the sample as well as the lattice parameters, the structural refinement using X-ray diffraction data was carried out on the assumption that there was no substitution of Ca atoms for every cation in BaTiO3. The structural refinement for neutron diffraction data was started assuming the lattice parameters obtained from the previous refinement using the X-ray data. The next refinement procedure requires to refine constant neutron wavelength to be used for collecting neutron diffraction data. Once convergence had been reached, the subsequent step for neutron data is to refine the scale factor, background parameters and peak shape profile parameters along with other instrumental factors. Once the preliminary structural refinement using respective Xray and neutron data had converged through the refinement of the parameters, including the background, the scale factor, the lattice parameters, the profile shape parameters and so on, the possibility of disorder for the Ca atom based on the seven kinds of models mentioned above was considered through the final combined structural refinement. The occupancies of every cationic site in all models were constrained so that the sites were fully occupied and the total occupancy of Ba, Ti and Ca atoms was maintained to be unity. In addition to the above things, isotropic atomic displacement parameters of the atoms for all cationic sites to be considered were same on the condition that both Ba/Ca and Ti/Ca atoms occupied identical positions. After the preliminary combined structural refinement had converged, the occupation factor of all cationic atoms was refined with the constraints of each occupancy and isotropic atomic displacement parameter for seven models. Among the converged R-factors obtained from the structural refinement for seven models using neutron powder diffraction data, the final weighted R-factor, Rwp, for B, T-O1, T-O2, T-O12, BT-O1, BT-O2 and BT-O12 models was converged to 6.85%, 7.01%, 6.96%, 6.93%, 6.85%, 6.82% and 6.78%, respectively. Even if there is no large difference between seven models based on only final refinement patterns, from the viewpoint of final weight R-factor, it may be concluded that the BT-O12 model was most suitable as a site preferential model of Ca atoms in Ca-doped BaTiO3 system at room temperature. Fig. 2 shows the combined structural refinement patterns of the BT-O12 model using X-ray and neutron powder diffraction data. The final weighted R-factor, Rwp, and the goodness-of-fit, S (=Rwp/Re), indicating the quality of a refined model for both data was 6.78% and 1.42%, respectively: Rwp = 5.01%, Rp = 3.90%, RF = 2.17% and Re = 3.35% for neutron
Fig. 2. Combined structural refinement patterns of Ca-doped BaTiO3 (BaTiO3:Cax, x = 0.12) using (a) X-ray and (b) neutron diffraction data. Plus signs (+) represent the observed intensities; the solid line defines calculated ones. A difference plot (obs.-cal.) is shown beneath. Tick marks above the difference indicate the reflection positions.
diffraction data and Rwp = 9.86%, Rp = 7.10%, RF = 3.69% and Re = 7.38% for X-ray diffraction data. In order to confirm the preferential substitution site of Ca atoms in Ca-doped BaTiO3 from the geometry energy point of view, CASTEP as a first principle method based on the density-functional theory was applied to the Ca-doped BaTiO3 system. In CASTEP, a mixture of atoms may be used to simulate the case where one atomic site is randomly occupied by two or more different types of an atom. Also, atomic site in a disordered crystal can be described in terms of a hybrid atom, which consists of two or more element types. There are a number of different approaches for dealing with the disorder based on the first principle calculation methods, for example, virtual crystal approximation (VCA), the large ordered supercell model, coherent potential approximation and computational alchemy [15]. Of these methods, the VCA was used to calculate the total energy difference between the possible cationdisorder models of Ca atoms in the Ca-doped BaTiO3 system. Table 1 lists the calculated geometry energy of each model described above. Comparing with the only cation disorder in Table 2, the Ca atoms as dopants in BaTiO3 preferentially occupy Ba site rather than to Ti one. Also, the possibility of O atom at O(2) site to be formed vacancies states is higher than that of O(1) at O(1) site in order for charge compensation in Ca-doped BaTiO3 due to the partial substitution of Ca atoms for Ti ones.
47
J.-S. Park et al. / Nuclear Instruments and Methods in Physics Research B 284 (2012) 44–48
Table 2 Selected interatomic distances and bond angles for undoped BaTiO3 and Ca-doped BaTiO3 (BaTiO3:Cax, x = 0.12) obtained from the combined structural refinement using X-ray and neutron powder diffraction data measured at room temperature. Interatomic distances (Å) Number of bond distance (Å) BaTiO3 Polyhedron Ba-O(1)a Ba-O(2)b Ba-O(2)
4 4 4
Average Ti-O(1)
4
2 1
Average a b c d
2.0005(1)
1.8876(1) 2.1432(1)
4 4 4
2.8303(1) 2.7729(1) 2.8975(1)
4
2.0004(1)
60.679(1) 89.954(1) 58.754(1)
O(2)-Ba-O(2)
4
89.839(1)
O(2)-Ba-O(2)
2
180
O(1)-M(1)-O(1) O(2)-M(1)-O(2) O(2)-M(1)-O(2)
4 4 4
61.335(1) 89.934(1) 58.434(1)
O(2)-M(2)-O(2)
4
89.987(1)
O(2)-M(2)-O(2)
2
180
2.8336(1)
Average M(2)-O(2) M(2)-O(2)
4 4 4
2.0154(1)
Average M(2)d-O(1)
Polyhedron O(1)-Ba-O(1) O(2)-Ba-O(2) O(2)-Ba-O(2)
1.9738(1)
Average Ca-doped BaTiO3 M(1)c-O(1) M(1)-O(2) M(1)-O(2)
Angle(°)
2.8401(1)
Average Ti-O(2) Ti-O(2)
2.7965(1) 2.8262(1) 2.8795(1)
Bond angles (°) Bond type No.
2.0004(1) 1 1
1.9707(1) 2.0462(1) 2.0085(1)
O(1) : O at 1b site. O(2) : O at 2c site. M(1) : Ba and Ca at 1a site. M(2) : Ti and Ca at 1b site.
Of the possible models listed in Table 1, the BT-O12 model, in which the O vacancies are created for all O sites due to the partial distribution of Ca atoms over Ba and Ti sites is most stable in the aspect of geometry energy. The result of the geometry energy calculation based on the distribution models of Ca atom in the Cadoped BaTiO3 system is in good agreement with the model suggested by the combined structural refinement. Since the bond lengths between cation and anion have a reverse-relation to the bond energies, the occurrence possibility of vacancies at O sites may be understood in terms of the average interatomic lengths between Ti and O atoms. Table 2 presented the difference of mean interatomic distances between undoped BaTiO3 and Ca-doped BaTiO3. The selected atomic distances indicate that the probability of vacancies to be created at O(2) site may be much higher than that at O(1) site. The same tendency was observed from the geometry energy calculation result, representing the lower energy of O(2) than that of O(1). The combined structural refinement result as listed in Table 3 presents that the Ca atoms were distributed over Ba and Ti sites. The occupancy of Ca atom for Ba and Ti sites was 0.086(2) and 0.027(2), respectively. The occupancy of O atom was 0.989(2) at O(1) site and 0.981(2) at O(2) site. The result is in good accordance with the reports that Ca atoms distribute over Ba and Ti sites [4,5,16–18]. When considering the ionic radius of Ba2+ (1.49 Å), Ca2+ (1.14 Å), and Ti4+ (0.745 Å) [19] and the cell volumes of between undoped BaTiO3 (64.3539 Å3) and Ca-doped BaTiO3 (64.2800 Å3) obtained from the structural refinement results of this study, smaller Ca ions more likely substitute onto Ba sites where they will be smaller than Ba ions and hence result in decreasing the cell volume. From the viewpoint of the occupancy of Ca ions for Ba sites based on the structural refinement, it may be expected that the cell volume of Ca-doped BaTiO3 will largely decrease due to the highoccupancy of Ca ions for Ba sites. However, the difference of cell volume based on the refined lattice parameters of between
Table 3 Refined structural parameters for Ca-doped BaTiO3 (BaTiO3:Cax, x = 0.12) obtained from the combined structural refinement using X-ray and Neutron powder diffraction data measured at room temperature. The symbol, g, is the occupation factor. The numbers in parentheses are the estimated standard deviations of the last significant figure. Atom Ba Ca(1) Ti Ca(2) O(1) O(2)
Site 1a 1a 1b 1b 1b 2c
x/a 0.0 0.0 0.5 0.5 0.5 0.5
y/b 0.0 0.0 0.5 0.5 0.5 0.0
z/c 0.0 0.0 0.486(1) 0.486(1) 0.024(1) 0.478(1)
100 Uiso/Å2
g a
0.914(2) 0.086(2) 0.973(2)b 0.027(2) 0.989(2) 0.981(2)
0.44(1)c 0.44(1) 1.12(3)d 1.12(3) 1.39(1) 1.11(3)
Space group : P4mm (No. 99) and Z = 1 a = b = 4.0003(1) Å, c = 4.0169(1) Å, a = b = c = 90° a b c d
Constraint Constraint Constraint Constraint
on on on on
occupancy: g(Ba) + g(Ca(1) = 1.0. occupancy: g(Ti) + g(Ca(2)) = 1.0. isotropic atomic displacement: UisoBa = UisoCa(1). isotropic atomic displacement: UisoTi = UisoCa(2).
undoped BaTiO3 and Ca-doped BaTiO3 was only about 0.15%. This may make sense that Ca ions co-occupy both Ba and Ti sites because the larger ionic radius of Ca than Ti ion makes a contribution for increasing of the cell volume of Ca-doped BaTiO3. Consequently, the result supports that the BT-O12 model suggested by the geometry energy calculation, in which Ca atoms partially occupy two cationic sites (Ba and Ti sites) is most reasonable in the possible order–disorder models for Ca-doped BaTiO3. 4. Conclusion When Ca atoms as a dopant substituted for cations in BaTiO3, they preferentially substituted for Ba atoms at 1a (0, 0, 0) site surrounded by 12 oxygen atoms, and then occupied at Ti site (1b, 1/2, 1/2, z) creating oxygen vacancies of the two oxygen sites simulta-
48
J.-S. Park et al. / Nuclear Instruments and Methods in Physics Research B 284 (2012) 44–48
neously. The behavior of Ca atoms as dopants in Ca-doped BaTiO3 was successfully determined through the combined structural refinement and the virtual crystal approximation method based on the first principle calculation. The approach may be applied to investigate the behavior of dopants to be used for enhanced material properties. Acknowledgements This research was supported by the Converging Research Center Program through the Ministry of Education, Science and Technology (2011K000600), and the Center for Nano scale Mechatronics & Manufacturing, one of the 21st Century Frontier Research Programs, which are supported by Ministry of Education, Science and Technology, Korea. References [1] H. Kishi, Y. Mizuno, H. Chazono, Jpn. J. Appl. Phys. Part 1 42 (2003) 1.
[2] M.T. Buscaglia, V. Buscaglia, M. Viviani, P. Nanni, M. Hanuskova, J. Eur. Ceram. Soc. 20 (2000) 1997. [3] K. Asokan, J.C. Jan, J.W. Chiou, W.F. Pong, P.K. Tseng, I.N. Lin, J. Synchrotron Rad. 8 (2001) 839. [4] L. Zhang, O.P. Thakur, A. Feteira, G.M. Keith, A.G. Mould, D.C. Sinclair, A.R. West, App. Phys. Lett. 90 (2007) 142914. [5] D.F.K. Hennings, H. Schreinemacher, J. Eur. Ceram. Soc. 15 (1995) 795. [6] S. Lee, C.A. Randall, Appl. Phys. Lett. 92 (2008) 111904. [7] B.H. Toby, J. Appl. Cryst. 34 (2001) 210. [8] A.C. Larson, R.B. Von Dreele, Los Alamos National Laboratory Report LAUR 86 (1994) 748. [9] L.W. Finger, D.E. Cox, A.P. Jephcoat, J Appl. Cryst. 27 (1994) 892. [10] M.C. Payne, M.P. Peter, D.C. Allan, T.A. Arias, J.D. Joannopoulos, Rev. Modern Phys. 64 (1992) 1045. [11] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [12] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 16 (1997) 1748. [13] J. Harada, T. Pedersen, Z. Barnea, Acta Cryst. A 26 (1970) 336. [14] R.H. Buttner, E.M. Maslen, Acta Cryst. B 48 (1992) 764. [15] N.J. Ramer, A.M. Rappe, Phys. Rev. B 62 (2000) R743. [16] Z.Q. Zhuang, M.P. Harmer, D.M. Smyth, R.E. Newnham, Mater. Res. Bull. 22 (1987) 1329. [17] Y.H. Han, J.B. Appleby, D.M. Smyth, J. Am. Ceram. Soc. 70 (1987) 96. [18] T.T. Fang, J.T. Shuei, J. Mater. Res. 14 (1999) 1910. [19] R.D. Shannon, Acta Cryst A32 (1976) 751.