I. INTRODUCTION
Eu2+-activated Li2(Ca,Sr,Ba)SiO4 phosphors are among the most promising silicates for white light-emitting diodes (LEDs) through the integration of blue LED chips because their excitation spectra extend to the longer wavelength region than 460 nm (Saradhi and Varadaraju, Reference Saradhi and Varadaraju2006; Zhang et al., Reference Zhang, He, Li, Yu and Zou2008; He et al., Reference He, Fu, Wang, Song, Pan, Zhao, Zhang and Cao2008; Kulshreshtha et al., Reference Kulshreshtha, Sharma and Sohn2009a, Reference Kulshreshtha, Shin and Sohn2009b). The crystal structures of the host materials Li2CaSiO4 and Li2SrSiO4 have been well characterized in the literatures (Gard and West, Reference Gard and West1973; Hirano et al., Reference Hirano, Iwata, Momma and Fukuda2010). Recently, Kim et al. (Reference Kim, Ahn, Kulshreshtha, Sohn and Shin2009) determined the crystal structure of Li2BaSiO4 [space group P63c m, Z=6, and unit-cell parameters a=0.810 040(1) and c=1.060 052(1) nm] by synchrotron radiation powder diffraction method for the sample containing impurities. The atomic coordinates of the initial structural model were derived from the direct methods for Ba and Si and the simulated annealing method for O. The positions of Li atoms, which were located near the Ba atoms with the closest distance of 0.327 nm, were determined by the maximum-entropy method (MEM) (Takata et al., Reference Takata, Nishibori and Sakata2001). The reliability indices of the refinement were satisfactory. However, the final structural model can still be improved partly because the interatomic distances do not agree well with those expected from the ionic radii nor bond valence sums. In order to clarify the highly efficient luminescence mechanism and further improve the performance of Li2BaSiO4:Eu2+ phosphor, a more detailed structural study of the host material will be useful.
A combined use of the Rietveld method (Rietveld, Reference Rietveld1967), MEM, and the MEM-based pattern fitting (MPF) method (Izumi et al., Reference Izumi, Kumazawa, Ikeda, Hu, Yamamoto and Oikawa2001) using X-ray powder diffraction (XRPD) data has enabled us to determine three-dimensional (3D) electron-density distributions (EDDs), which efficiently disclose structural details such as precise positions of light atoms near the much heavier ones (Izumi, Reference Izumi2004). The Rietveld method and MEM have a drawback in determining the EDD because the observed structure factors, F o(Rietveld), are biased toward the structural model assuming intensity partitioning. On the other hand, the MPF method can minimize the structural bias. Thus, the MEM and MPF analyses are alternately repeated (REMEDY cycle) until the reliability indices reach minima. Crystal structures are represented not by structural parameters but by 3D EDD in MPF.
In the present study, we have successfully prepared the powder specimen consisting exclusively of Li2BaSiO4. The coordinates of all atoms, including those of Li, have been readily derived using the direct methods. The validity of the final structural model has been confirmed by the 3D EDD determined by MPF.
TABLE I. Crystal data for Li2BaSiO4.
II. EXPERIMENTAL
A sample of Li2BaSiO4 was prepared from stoichiometric amounts of reagent-grade chemicals Li2CO3, BaCO3, and SiO2. Well-mixed chemicals were pressed into pellets (20 mm diameter and 5 mm thick), heated at 973 K for 3 h, and followed by quenching in air. The procedures of mixing and heating were repeated three times for complete homogenization. The densely sintered pellets were finely ground to obtain a powder specimen.
A diffractometer (X’Pert PRO Alpha-1, PANalytical B.V., Almelo, The Netherlands), equipped with an incident-beam Ge(111) Johansson monochromator to obtain Cu K α 1 radiation and a high-speed detector, was used in the Bragg-Brentano geometry. The X-ray generator was operated at 45 kV and 40 mA. A variable divergence slit was used to keep a constant illuminated length of 5 mm on the specimen surface. Other experimental conditions were continuous scan, experimental 2θ range from 10.0114° to 145.3058° (an accuracy of ±0.0001 °2θ), 8097 total data points, and 2.4 h total experimental time. The structure data were standardized according to rules formulated by Parthé and Gelato (Reference Parthé and Gelato1984) using the computer program STRUCTURE TIDY (Gelato and Parthé, Reference Gelato and Parthé1987). The crystal-structure models, equidensity isosurfaces of EDD, and two-dimensional (2D) EDD map were visualized with the computer program VESTA (Momma and Izumi, Reference Momma and Izumi2008). Distortion parameters for the coordination polyhedra (Makovicky and Balić-Žunić, Reference Makovicky and Balić-Žunić1998) were found using the computer program IVTON (Balić-Žunić and Vickovic, Reference Balić-Žunić and Vickovic1996).
III. RESULTS AND DISCUSSION
A. Structure refinement
Peak positions of the experimental diffraction pattern were first determined by finding minima in the second derivatives using the computer program PowderX (Dong, Reference Dong1999). The 2θ values of 40 observed peak positions were then used as input data to the automatic indexing computer program TREOR90 (Werner et al., Reference Werner, Eriksson and Westdahl1985). One hexagonal unit cell was found with satisfactory figures of merit: M40=217 and F40=428 (0.001 673, 56) (de Wolff, Reference de Wolff1968; Smith and Snyder, Reference Smith and Snyder1979). The derived unit-cell parameters of a=0.810 567(9) and c=1.060 97(2) nm could index all reflections in the observed diffraction pattern.
The observed diffraction peaks were examined to confirm the presence or absence of reflections. Systematic absences l≠2n for h h¯0l reflections were found, suggesting that possible space groups are P3c1, P3¯c1, P63c m, P6¯c2, and P63/m c m. All these space groups were tested and confirmed
TABLE II. Structural parameters and anisotropic atomic displacement parameters (105×U/nm2) for Li2BaSiO4.
Note: U(eq) is defined as one-third of the trace of the orthogonalized U i j tensor. The anisotropic displacement factor exponent takes the form −2π 2[h 2a ∗2U 11+k 2b ∗2U 22+l 2c ∗2U 33+2h k a ∗b ∗U 12+2h l a ∗c ∗U 13+2k l b ∗c ∗U 23].
Figure 1. (Color online) Crystal structure of Li2BaSiO4. Two types of basic structural layers (a) [LiSiO4]3− and (b) [LiBaO4]5− are alternately stacked in the [001] direction to form (c) a three-dimensional structure. Atom numbering corresponds to that given in Table II.
using the EXPO2004 package (Altomare et al., Reference Altomare, Burla, Camalli, Carrozzini, Cascarano, Giacovazzo, Guagliardi, Moliterni, Polidori and Rizzi1999). A unit-cell content with [12Li 6Ba 6Si 24O] was used as input data for the search of a crystal-structure model. A promising structural model, including two types of coordinates for Li atoms, with the minimum reliability index R F (Young, Reference Young and Young1993) of 7.52% was successfully obtained with the space group P63c m in a default run of the program. There were nine independent sites (i.e., two Li sites located at the Wyckoff position 6c, one Ba site at 6c, two Si sites at 4b and 2a, and four O sites at 4b, 6c, 2a, and 12d) in the unit cell. The derived structural model was isomorphous with that determined by Kim et al. (Reference Kim, Ahn, Kulshreshtha, Sohn and Shin2009).
Structural parameters of all atoms were refined by the Rietveld method using the computer program RIETAN-FP (Izumi and Momma, Reference Izumi and Momma2007) with the profile intensity data in the whole 2θ range. A Legendre polynomial with 12 adjustable parameters was fitted to background intensities. The split Pearson VII function (Toraya, Reference Toraya1990) was used to fit the peak profiles. Isotropic atomic displacement parameters (ADPs) were initially assigned to all atoms. The refinement resulted in the reliability (R) indices of R wp=7.00%, S (=R wp/Re)=1.22, R p=5.33%, R B=2.68%, and R F=1.41% (Young, Reference Young and Young1993). We subsequently assigned anisotropic ADPs to obtain the lower R indices of R wp=6.72%, S=1.17, R p=5.06%, R B=1.86%, and R F=0.98%. Crystal data are given in Table I, and the final atomic positional parameters and anisotropic ADPs are given in Table II. The ratio of the largest/smallest principal ADP components of all atoms were necessarily less than 2.44, indicating that the refinement was entirely successful to obtain the reasonable structural model (Figure 1). The two types of Li sites have been found to be located close to the Ba site: the interatomic distance of Li1-Ba was 0.325(1) nm and that of Li2-Ba was 0.333(2) nm.
The EDDs with 162×162×212 pixels in the unit cell, the spatial resolution of which is approximately 0.005 nm, were obtained from the MPF method using the computer programs RIETAN-FP and PRIMA (Izumi and Dilanian, Reference Izumi and Dilanian2002). After one REMEDY cycle, R B and R F further decreased to 1.49% and 0.69%, respectively (R wp=6.74%, S=1.17, and R p=5.10%). Subtle EDD changes as revealed by MPF significantly improve the R B and R F indices. The decreases in R indices demonstrate that the crystal structure can be seen more clearly from EDD instead of from the conventional structural parameters reported in Table II. Observed, calculated, and difference XRPD patterns for the final MPF are plotted in Figure 2.
The individual equidensity isosurfaces of 3D EDD in Figure 3 are in reasonably good agreement with the corresponding atom arrangements in Figure 1c. Bonding electrons for highly covalent bonds (Si-O) are clearly visualized; the representation of these bonds by 3D EDD must contribute to the decrease in R B. The 2D EDD map at the height of Li1, Li2, Ba, Si1, O1, and O3 sites shows that the positions of Li atoms are successfully disclosed by the EDD (Figure 4). We found the peak positions of EDD from the 3D pixel data and compared them with the coordinates of all atoms that were determined by the Rietveld method. The positional deviations of all atoms in the unit cell were found to be necessarily less than 0.003 nm, which is within the resolution limit of the 3D EDD. We therefore concluded that the present structural model would reasonably and satisfactorily represent the crystal structure of Li2BaSiO4.
B. Structure description
Selected interatomic distances and bond angles, together with their standard deviations, are listed in Table III. The average Li-O bond lengths are 0.198 nm for Li1O4 and 0.201 nm for Li2O4, which are comparable to those of the LiO4 tetrahedra in La2SrSiO4 (0.198 nm), Li2EuSiO4 (0.198 nm),
Figure 2. (Color online) Comparison of the observed diffraction pattern of Li2BaSiO4 (symbol: +) with the corresponding calculated pattern (upper solid line). The difference curve is shown in the lower part of the diagram. Vertical bars indicate the positions of possible Bragg reflections.
and Li2CaSiO4 (0.197 nm) (Hirano et al., Reference Hirano, Iwata, Momma and Fukuda2010); Haferkorn and Meyer, Reference Haferkorn and Meyer1998; Gard and West, Reference Gard and West1973). When the volume distortion parameters v are compared between the two types of tetrahedra Li1O4 and Li2O4, the extent of distortion (v value) is smaller for the former than for the latter (Table IV). The average Si-O bond lengths of 0.163 nm for Si1O4 and 0.162 nm for Si2O4 agree well with the interatomic distance of 0.164 nm calculated from the ionic radii of Si4+ and O2− in the fourfold coordination [r(Si4+(4))=0.026 nm and r(O2−(4))=0.138 nm] (Shannon, Reference Shannon1976). The average values of the O-Si-O angles are 109.5°. These interatomic distance and bond angle are in good agreement with those found in
Figure 3. (Color online) Three-dimensional electron-density distributions determined by MPF. Isosurfaces expressed in smooth shading style for an equidensity level of 0.0007 nm−3.
other silicates (Baur, Reference Baur1971). The BaO9 polyhedron showed the bond lengths ranging from 0.264 to 0.323 nm. Ionic radii of Ba2+ in the ninefold coordination [r(Ba2+(9))=0.147 nm and r(O2−(8))=0.142 nm] predict the interatomic distance of 0.289 nm for Ba-O. This predicted value is in good agreement with the corresponding average interatomic distance of 0.293 nm. Valence bond sums calculated on the basis of bond-strength analysis (Li1: 1.06, Li2: 0.97, Ba: 1.96, Si1: 3.95, and Si2: 3.98) are in good agreement with the expected
Figure 4. (Color online) A bird’s eye view of electron densities up to 3.0% of the maximum (0.512 nm−3) on the (100) plane (lower part) with the corresponding atomic arrangements (upper part). Atom numbering corresponds to that given in Table II.
TABLE III. Selected bond lengths (nm) and angles (deg) in Li2BaSiO4.
formal oxidation states of Li+, Ba2+, and Si4+ ions (Brown and Altermatt, Reference Brown and Altermatt1985; Brese and O’Keeffe, Reference Brese and O’Keeffe1991). The average bond lengths of Li-O, Si-O, and Ba-O are in agreement with those expected from the bond valence sums (Li-O: 0.1979 nm, Si-O: 0.1624 nm, and Ba-O: 0.2847 nm).
The crystal structure of lithium barium silicate consists of the five types of polyhedra, Li1O4, Li2O4, Si1O4, Si2O4, and BaO9. Three Li2O4 tetrahedra and one Si1O4 tetrahedron are connected via O1-O3 edges to form a [Li3SiO10]13− unit. Individual units are further linked through Si2O4 tetrahedra to form a basic structural layer [LiSiO4]3− parallel to (001) [Figure 1a]. The BaO9 polyhedra mutually share faces O2-O3-O4 to form a two-dimensional sheet with the composition [Ba3O11]16−. Three Li1O4 tetrahedra are linked via O1 vertexes to form a [Li3O10]17− unit. The [Li3O10]17− units and [Ba3O11]16− sheet are joined by sharing faces O3-O4-O4 to build up the other basic layer [LiBaO4]5− parallel to (001) [Figure 1b]. These two types of basic layers are alternately stacked in the [001] direction with two layers each per unit cell to form a three-dimensional structure [Figure 1c].
We compared the present structural model with that determined by Kim et al. (Reference Kim, Ahn, Kulshreshtha, Sohn and Shin2009) to find that the unit-cell dimensions as well as the coordinates of relatively heavy atoms such as Ba, Si, and O were almost comparable between the two structures. For example, the distances from O1 atoms, which are located at the origin of the coordinate axes, to Ba atoms were 0.4296(4) nm for the former structural model and 0.4346(14) nm for the latter, with the deviation being less than 1.3%. On the other hand, the coordinates of Li atoms were quite different; the Li1-O1 and Li2-O1 distances determined in the present study (Table III) were longer than those of the previous study by 12.6% and 9.1%, respectively.
IV. CONCLUSION
We successfully refined the crystal structure of lithium barium silicate Li2BaSiO4, having a hexagonal unit cell with space group P63c m. The basic structural layers of the crystal structure were [LiSiO4]3− and [LiBaO4]5−, comprising five types of polyhedra, Li1O4, Li2O4, Si1O4, Si2O4, and BaO9. These two types of basic layers were alternately stacked in the [001] direction with two layers each per unit cell to form a three-dimensional structure. The validity of this structural model was confirmed by the EDD determined by MPF. The 2D EDD map at the height of Li sites showed that the positions of Li atoms were successfully disclosed by the EDD.
TABLE IV. Polyhedral distortion parameters.
Note: Δ=eccentricity; r S=radius of sphere fitted to ligands; V S=sphere volume; σ=sphericity; V P=volume of coordination polyhedron; v=volume distortion; and σ for coordination number four is 1 by definition.
