- Email: [email protected]
Crystal structure and Raman spectrum of Ba2Pb(B3O6)2
Materials Chemistry and Physics 163 (2015) 501e506
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Crystal structure and Raman spectrum of Ba2Pb(B3O6)2 X.L. Tang a, D.X. Feng a, S.M. Wan a, *, L. Kang b, B. Zhang a, Z.S. Lin b, ** a b
Anhui Key Laboratory for Photonic Devices and Materials, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
The new crystal structure of Ba2Pb(B3O6)2 has been determined. The Raman spectrum of Ba2Pb(B3O6)2 has been analyzed by the site group method and first-principles calculation. The Pb2þ effect on the Raman spectrum has been interpreted.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 April 2015 Received in revised form 9 July 2015 Accepted 1 August 2015 Available online 17 August 2015
Ba2Pb(B3O6)2 polycrystalline powder was synthesized by a solid state reaction using BaCO3, Pb3O4 and H3BO3 as initial reactants. The crystal structure was solved from the powder X-ray diffraction data by the Rietveld refinement method and the DFT (density functional theory) calculation. The results show that Ba2Pb(B3O6)2 is isostructural with the high-temperature phase BaB2O4 (Ba2Ba(B3O6)2). It crystallizes in the trigonal space group R3 c with a ¼ b ¼ 7.20295(3) Å, c ¼ 37.594(1) Å, and Z ¼ 6. The structure is built up of the layers of B3O6 rings that are separated by Ba2þ or Pb2þ cations. The Raman spectrum of Ba2Pb(B3O6)2 was interpreted on the basis of the analysis through site group method. Its irreducible representation of the normal modes is 10A1g þ 11A2g þ 10A1u þ 11A2u þ 21Eg þ 21Eu among which 10A1g þ 11A2g þ 10A1u þ 10A2u þ 21Eg þ 20Eu are optical modes, where the A1g and Eg are Raman active. The DFT calculated results confirmed the results of the site group analysis and assigned all peaks in the experimental Raman spectrum. The a-BaB2O4 Raman spectrum was recorded and compared with the Ba2Pb(B3O6)2 Raman spectrum. The effect of the Pb2þ cations on the Raman intensity was discussed. © 2015 Elsevier B.V. All rights reserved.
Keywords: Ab initio calculations Raman spectroscopy and scattering Rietveld analysis Crystal structure
1. Introduction Metaborate crystals with the formula of Ba2M(B3O6)2 (M ¼ Mg, Ca, Sr, Ba, Co, Ni, Zn, Cd and Pb) are an important class of materials employed in laser technology. For example: (1) b-BaB2O4 (low-
* Corresponding author. Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, No. 350 Shushanhu Road, Hefei 230031, China. ** Corresponding author. E-mail address: [email protected] (S.M. Wan). http://dx.doi.org/10.1016/j.matchemphys.2015.08.005 0254-0584/© 2015 Elsevier B.V. All rights reserved.
temperature phase Ba2Ba(B3O6)2) crystals have been widely applied to generate the coherent light sources in the ultraviolet region and the continuously tunable coherent light sources from 412 nm to 2550 nm [1,2]. (2) Ba2Mg(B3O6)2, a-BaB2O4 (high-temperature phase Ba2Ba(B3O6)2) and Ba2Cd(B3O6)2 crystals are excellent birefringent crystals with wide transmission ranges, and suitable for fabrication of the polarizers and laser beam splitters used in the ultraviolet region [3e5]. The Ba2M(B3O6)2 crystals are also characterized by high damage thresholds which allow them to be applied in high power laser
502
X.L. Tang et al. / Materials Chemistry and Physics 163 (2015) 501e506
systems. It is well known that if the intensity of the laser beam is high enough, then SRS (simulated Raman scattering) will occur in the crystals. On one hand, the SRS process can be utilized to extend the spectral coverage of current lasers or to improve the spatial quality of the laser beams [6,7]; on the other hand, the SRS process will deplete the laser power, which is troublesome or even unwanted in the design of the high-power laser systems [8]. The SRS process is a two-photon stimulated process that grows from the spontaneous Raman scattering; thus, the spontaneous Raman spectrum is frequently used to understand the SRS process [9]. Recently, we studied the spontaneous Raman spectra of Ba2Mg(B3O6)2, Ba2Ca(B3O6)2 and a-BaB2O4 crystals, and found that their Raman peak positions and intensities are remarkably influenced by the type of the M2þ cation, and the M2þ cation effect is related to the electron density distributions in these crystals [10]. Ba2Pb(B3O6)2, as a possible Ba2M(B3O6)2-type compound, was firstly mentioned by Liebertz et al. in 1984 [11]. Recently, Li et al. reported its crystal structure and basic physical properties [12]. According to their results, PbBa2(B3O6)2 is isostructural to Ba2Mg(B3O6)2 and Ba2Ca(B3O6)2. It crystallizes in the trigonal space group R3 with a ¼ b ¼ 7.2056(8) Å, c ¼ 18.752(6) Å, and Z ¼ 3. The structure is built up of Ba2þ, Pb2þ and nearly planar B3O6 rings; all of the rings are perpendicular to the c axis. Unlike Mg2þ, Ca2þ and Ba2þ cations that have the inert gas electron configurations, Pb2þ cation has the unique 6s2 lone pair electrons that might influence the electron density distribution in Ba2Pb(B3O6)2 and then the Raman spectrum. However, little research has been carried out to investigate the Pb2þ cation effect although this issue, in a broader sense, is related to the spectral performance of other compounds containing heavy main-group elements with the s2 lone pair electrons. In our previous works, we found the PXRD (powder X-ray diffraction) and Raman spectrum of Ba2Pb(B3O6)2 very similar to that of a-BaB2O4 rather than Ba2Mg(B3O6)2 and Ba2Ca(B3O6)2, which implies Ba2Pb(B3O6)2 is probable to be isostructural to aBaB2O4. In this work, the Ba2Pb(B3O6)2 polycrystalline powder was prepared by a solid-state reaction; its crystal structure was reinvestigated by the Rietveld refinement combined with the DFT (density functional theory) calculation. The Ba2Pb(B3O6)2 Raman spectrum was analyzed on the basis of the site group method and the DFT calculation. Finally, the Pb2þ effect on the Ba2Pb(B3O6)2 Raman spectrum was discussed as compared with the a-BaB2O4 Raman spectrum.
the GSAS (generalized structural analysis system) software package [14]. The peak profile function was modeled using the pseudo-Voigt function described by Thompson et al.; the background was fitted by a Chebyshev polynomial function. The refinement involved the unit cell parameters, atomic coordinates, isotropic thermal parameters, a scale factor, background parameters, etc. Because of the complexity of the structure, soft restraints were applied to the BeO bond distances with suitable weighting factors (1.320 ± 0.015 Å, 1.400 ± 0.015 Å and 1.405 ± 0.010 Å for the BeO1, BeO2 and BeO20 bonds, respectively. See Table S1 in the supporting information for more details). A correction was made for the preferred orientation effect by using the MarchDollase approach. DFT calculations were carried out to study the crystal structure and Raman spectrum using the plane-wave pseudopotential method implemented in CASTEP (Cambridge Sequential Total Energy Package) [15,16]. The PerdewBurkeErnzerhof (PBE) version [17] of the generalized gradient approximation (GGA) was employed in conjunction with the norm-conserving pseudopotentials to describe the interactions between the ionic cores and the valence electrons. An energy cut-off of 1000 eV was used for the plane-wave basis set expansion. The sampling of the Brillouin zone was performed using a 2 2 2 Monkhorst-Pack k-point grid. The optimization met the following criteria: an energy tolerance of 1 106 eV/atom, a maximal force tolerance of 0.03 eV/Å, a maximal displacement of 1 103 Å, and a maximal stress of 0.05 GPa. The calculated Raman intensities were reduced by the BoseeEinstein population factors [18]. The energy cut-off and the kpoint grid have been tested to ensure the total energy converged in the calculations (see Fig. S1 and Table S2 in the supporting information).
3. Results and discussion Fig. 1 is the Raman spectrum of Ba2Pb(B3O6)2 recorded at room temperature. All characteristic peaks of the B3O6 ring are present in the spectrum. For example, the peaks located around 630 cm1 and 770 cm1 are related to the breathing modes of the ring; the peak located around 1510 cm1 arises from the stretching mode of the extra-ring BeO bonds [19]. The result confirms that the B3O6 rings are the most important blocking units in the Ba2Pb(B3O6)2 crystal structure. The PXRD pattern of Ba2Pb(B3O6)2 is shown in Fig. 2. It is very similar to that of a-BaB2O4, indicating that the two compounds
2. Experimental and computational details Ba2Pb(B3O6)2 was prepared by reacting a stoichiometric mixture of BaCO3 (1.974 g), Pb3O4 (1.142 g) and H3BO3 (1.892 g) (all reagents used were of analytical purity). The mixture was ground and heated at 550 C for 12 h to decompose H3BO3, followed by a heating treatment at 780 C for 12 h to decompose BaCO3 and Pb3O4. After that, the intermediate product was reground and heated again at 780 C for 12 h. The final polycrystalline powder was analyzed by PXRD and Raman spectroscopy. The PXRD data were collected at room temperature by a Rigaku D/Max-Ra powder diffractometer which used Cu Ka radiations (lKa1 ¼ 0.15406 nm and lKa2 ¼ 0.154434 nm) and operated at 200 mA and 40 kV. The data were collected in the 2q range of 10e70 with a 0.02 step width and 8 s/point. Raman spectra were recorded at room temperature on a Jobin Y'von LABRAM HR Raman spectrometer with a backscattering configuration. The 514.5 nm line of an Arþ laser was employed for excitation. The laser beam power at the sample surface was about 1 mW. All of the Raman spectra were recorded at 2 cm1 resolution from 100 to 1800 cm1. The PXRD data were analyzed by the Rietveld method [13] using
Fig. 1. Raman spectrum of the Ba2Pb(B3O6)2 polycrystalline powder.
X.L. Tang et al. / Materials Chemistry and Physics 163 (2015) 501e506
503
Table 1 Crystallographic data for the Ba2Pb(B3O6)2 crystal. Ba2Pb(B3O6)2 Trigonal R3 c a ¼ 7.20295(3) b ¼ 7.20295(3) c ¼ 37.594(1) 120 1689.14 6 4.74 5.84
Empirical formula Crystal system Space group Unit cell dimensions (Å)
g ( ) Volume (Å3) Z Rp(%) Rwp(%)
Table 2 Atomic coordinates, Wyckoff sites and temperature factors of the Ba2Pb(B3O6)2 crystal.
Fig. 2. PXRD patterns of the a-BaB2O4 and Ba2Pb(B3O6)2 polycrystalline powders.
possess a similar crystal structure. According to the PXRD result, the a-BaB2O4 crystal structure [20] reported by Mighell et al. was used as the prototype for the Ba2Pb(B3O6)2 structural refinement. With reference to the crystal structures of Ba2Ca(B3O6)2 and Ba2Mg(B3O6)2, the Ba2þ cations located at the Wyckoff site 6a in the a-BaB2O4 crystal structure were substituted by Pb2þ cations. The resulting model was refined by the Rietveld method to obtain the accurate cell parameters; and then optimized by the DFT method to determine the reasonable atomic coordinates. During the DFT optimization, the lattice parameters were fixed, but all of the atomic coordinates were allowed to be refined. Finally, the DFT-optimized structure, including the cell parameters and the atomic coordinates, was refined again by the Rietveld method. The final Rietveld plot of Ba2Pb(B3O6)2 is presented in Fig. 3, which shows a good agreement between the experimental and calculated PXRD patterns (Rp ¼ 4.74% and Rwp ¼ 5.84%) and confirms the hypothesis of the isostructural relationship between aBaB2O4 and Ba2Pb(B3O6)2. Relevant crystallographic data and atomic coordinates are summarized in Tables 1 and 2, respectively.
Fig. 3. Experimental (circles), calculated (solid line) and difference patterns (bottom line) for the Ba2Pb(B3O6)2 polycrystalline powder.
Atom
Site
x
y
z
Ueq (Å2)
Ba Pb B O1 O2
12c 6a 36f 36f 36f
0 0 0.9604(1) 0.1692(2) 0.4110(2)
0 0 0.17519(6) 0.2071(2) 0.0687(2)
0.35126(3) 0.25000 0.04069(6) 0.0417(1) 0.03758(3)
6.8(2) 10.1(2) 22.2(3) 2.6(6) 17.9(1)
The Ba2Pb(B3O6)2 crystal structure is illustrated in Fig. 4. Its fundamental building units are Ba2þ cations, Pb2þ cations and B3O6 six-membered rings. These planar rings are parallel to each other to form the B3O6 layers which are alternately separated by the Ba2þ and Pb2þ cations. All of the B3O6 rings belong to the C3 site group and are symmetrically surrounded by six Ba2þ and three Pb2þ cations; each Ba2þ/Pb2þ cation is surrounded by six oxygen atoms to form a BaO6/MgO6 octahedron (see Fig. 5). The selected bond lengths and angles of Ba2Pb(B3O6)2 are listed in Table S3 (see the supporting information). The Ba2Pb(B3O6)2 crystal structure is similar to that reported by Li et al., but the space group and the caxis length are different [12]. They considered that the crystal
Fig. 4. Trigonal crystal cell (left) and primitive cell (right) of the Ba2Pb(B3O6)2 crystal.
504
X.L. Tang et al. / Materials Chemistry and Physics 163 (2015) 501e506
00
Gv ¼ 3A1 0 þ 2A2 0 þ 2A2 þ 5E 0 þ 2E
00
where Gt, Gr and Gv represent the translational, rotational and vibrational modes, respectively. In the Ba2Pb(B3O6)2 crystal structure, the B3O6 ring has the C3 site group symmetry and the D3d unit cell group (factor group) symmetry. Scheme 1 presents the correlations of the irreducible representations between the D3h point group and the C3 site group and that between the C3 site group and the D3d unit cell group. From the scheme, we can see that the A01 A02 A01 and A02 modes convert to the A modes when the isolated ring is located at the C3 site, and then split to the A1g, A1u, A2g and A2u lattice modes when the ring is further constrained by the D3d symmetry. In the same way, the E0 and E00 modes of the isolated B3O6 ring convert to the E modes and then split to the Eg and Eu lattice modes. As mentioned above, the Ba2Pb(B3O6)2 primitive cell contains four B3O6 rings; therefore the translational modes ð4A02 þ 4E0 Þ, rotational modes ð4A02 þ 4E0 Þ and vibrational modes ð12A01 þ 8A02 þ 8A02 þ 20E0 þ 8E0 Þ of the four B3O6 rings yield 12 lattice translational modes (A1g þ A2g þ A1u þ A2u þ 2Eg þ 2Eu), 12 lattice liberational modes (A1g þ A2g þ A1u þ A2u þ 2Eg þ 2Eu) and 84 lattice internal vibrational modes (7A1g þ 7A2g þ 7A1u þ 7A2u þ 14Eg þ 14Eu). In the Ba2Pb(B3O6)2 crystal structure, the Ba2þ and Pb2þ cations occupy the C3 and D3 symmetric positions, respectively. According to the correlations between the C3/D3 site group and the D3d unit cell group, the 12 translational modes of the Ba2þ cations (4A þ 4E, four Ba2þ cations in the primitive cell) and the 6 translational modes of the Pb2þ cations (2A þ 2E, two Pb2þ cations in the primitive cell) yield 12 (A1g þ A2g þ A1u þ A2u þ 2Eg þ 2Eu) and 6 (A2g þ A2u þ Eg þ Eu) lattice translational modes, respectively. The total lattice vibrational modes of the Ba2Pb(B3O6)2 crystal are 10A1g þ 11A2g þ 10A1u þ 11A2u þ 21Eg þ 21Eu. Except three acoustical modes (A2u þ Eu), the rest (10A1g þ 11A2g þ 10A1u þ 10A2u þ 21Eg þ 20Eu) are optical modes. The lattice vibrational modes can also be divided into internal modes and external modes. The internal modes originate from the vibrations of the B3O6 rings; the external modes from the librations of the B3O6 rings and the translations of the B3O6 rings, Ba2þ cations and Pb2þ cations. According to the above results of the site group analysis, we can obtain: Fig. 5. Coordination environments around the Pb2þ cations, Ba2þ cations, and B3O6 rings.
crystallizes in the R3 space group and the c-axis length is 18.752(6) Å, only half of the value determined here. Ba2Pb(B3O6)2 is a moleculecation type crystal, its lattice vibrational modes can thus be classified by the site group method of analysis. The Ba2Pb(B3O6)2 crystal structure belongs to the space group R3 c (unit cell group D3d). Its primitive cell includes four B3O6 rings, four Ba2þ cations and two Pb2þ cations (Fig. 4). The isolated B3O6 ring with the D3h symmetry (point group) has 27 vibrational modes [21]; the corresponding irreducible representations are given by
Gring ¼ Gt þ Gr þ Gv 00
Gt ¼ A2 þ E 0 Gr ¼ A20 þ E
00
Gtotal ¼ Gint þ Gext Gint ¼ 7A1g þ 7A2g þ 7A1u þ 7A2u þ 14Eg þ 14Eu Gext ¼ 3A1g þ 4A2g þ 3A1u þ 4A2u þ 7Eg þ 7Eu where the A1g and Eg modes are Raman active, and the A2g, A2u and Eu modes are infrared active. Thus, 31 Raman peaks (10A1g þ 21Eg) are expected to be observed in the Ba2Pb(B3O6)2 Raman spectrum. In fact, the number of the Raman peaks in the experimental spectrum (Fig. 1) is less than the predicted, which is probably due to the weak scattering intensities of some modes. We used the DFT method to calculate the Raman spectrum of Ba2Pb(B3O6)2 at the same level of theory for the structural optimization. The calculated Raman spectrum, together with the experimental spectrum, is shown in Fig. 6. All calculated Raman frequencies are in good agreement with the experimental. The relative intensities of the calculated peaks are also consistent with the experimental results except for the peaks located at 303 cm1 and 734 cm1 (calculated values). The irreducible representation of Ba2Pb(B3O6)2 predicted by the site group method is also confirmed by the DFT calculation. According to the calculated results, the
X.L. Tang et al. / Materials Chemistry and Physics 163 (2015) 501e506
505
Scheme 1. Site group analysis for the Ba2Pb(B3O6)2 lattice vibrational modes.
Fig. 6. Experimental and calculated Raman spectra of Ba2Pb(B3O6)2.
experimental Raman peaks are assigned (Fig. 6). More detailed results are provided in the supporting information (Table S4). The Raman spectrum of a-BaB2O4 was recorded and compared with that of Ba2Pb(B3O6)2 (see Fig. 7). The two Raman spectra are very similar in peak number and position, which is due to their almost identical crystal structures and vibrational modes. However, the corresponding peak intensities are remarkably different. More detailed studies revealed that almost all the strong peaks in the aBaB2O4 spectrum became weaker in the Ba2Pb(B3O6)2 spectrum, or the weak peaks became stronger due to the substitution of Pb2þ for Ba2þ (see Fig. 7, only the internal modes are discussed in this paper.). This phenomenon can be explained by the formula for Raman peak intensity. Theoretical studies indicate that Raman peak intensity is linearly proportional to the square of the first derivative of electronic polarizability with respect to atomic displacements (I f (va/vq)2, where I, a and q are Raman peak intensity, electronic
Fig. 7. Raman spectra of a-BaB2O4 and Ba2Pb(B3O6)2.
polarizability and atomic displacement, respectively.) [22]. As we know, the Pb2þ cation has a unique 6s2 electron configuration which generally shows a higher tendency to polarize than the inert gas electron configuration of the Ba2þ cation ((va/vq)Pb > (va/vq)Ba). On the other hand, the effective va/vq (S(va/vq)) of the Pb2þ cations is also related to their arrangement in the crystal and the vibrational modes of the most neighboring B3O6 rings. In the Ba2Pb(B3O6)2 crystal structure, the Pb2þ cations are symmetrically arranged around the B3O6 rings (Fig. 5(c)), which leads to the (va/ vq)Pb arising from the B3O6 ring symmetrically vibrational modes to cancel each other, and thus the S(va/vq)Pb of the symmetrically A1g vibrational modes is less than that of the asymmetrically Eg vibrational modes ([S(va/vq)Pb]A1g < [S(va/vq)Pb]Eg). Two examples, corresponding to a typical A1g mode and a typical Eg mode, are
506
X.L. Tang et al. / Materials Chemistry and Physics 163 (2015) 501e506
the PXRD data with the help of the DFT structural optimization. Ba2Pb(B3O6)2 crystallizes in the space group R3 c of the trigonal system with six formula units in a unit cell; the unit cell constants a ¼ b ¼ 7.20295(3) Å and c ¼ 37.594(1) Å. The basic boronoxygen structural unit in the crystal is the planar B3O6 ring. Each B3O6 ring is symmetrically surrounded by six Ba2þ cations and three Pb2þ cations. Each Ba2þ/Pb2þ cation is surrounded by six oxygen atoms to form a BaO6/MgO6 octahedron. The vibrational modes of the Ba2Pb(B3O6)2 crystal have been classified by the site group method of analysis. The crystal has 126 vibrational modes, corresponding to the irreducible representation of 10A1g þ 11A2g þ 10A1u þ 11A2u þ 21Eg þ 21Eu. Except three acoustical modes (A2u þ Eu), the rest (10A1g þ 11A2g þ 10A1u þ 10A2u þ 21Eg þ 20Eu) are optical modes of which A1g and Eg are Raman active. The DFT calculation verified the results predicted by the site group method and assigned the vibrational modes of all the peaks in the Raman spectrum. The Ba2Pb(B3O6)2 Raman spectrum was compared with the a-BaB2O4 Raman spectrum. The substitution of Pb2þ for Ba2þ in the a-BaB2O4 crystal remarkably reduces the relative intensities of the A1g peaks. The Pb2þ effect is attributed to its unique 6s2 electron configuration and the arrangement of Pb2þ cations in the crystal structure. Fig. 8. Atomic displacements of a typical symmetrically A1g mode of which the peak is around 630 cm1 (experimental value) and a typical asymmetrically Eg mode of which the peak is around 1380 cm1 (experimental value). The right part is the electronic polarizability of the Pb2þ cations associated to the two vibrational modes.
shown in Fig. 8. Considering that (va/vq)Pb > (va/vq)Ba, [S(va/ vq)Pb]A1g < [S(va/vq)Pb])Eg and most of the A1g modes appear in the a-BaB2O4 Raman spectrum as strong peaks (Fig. 7), we can conclude that the strong peaks increase in intensity less than the weak peaks when the Ba2þ cations located at 6a Wyckoff sites in the a-BaB2O4 crystal structure are replaced by the Pb2þ cations, as shown in Fig. 7. In order to further explore the effect of the substitution of Pb2þ for Ba2þ, we analyzed the Hirshfeld charges of the atoms/cations in the a-BaB2O4 and Ba2Pb(B3O6)2 crystals by the DFT method at the same level of theory for the Raman spectrum calculation. The results are shown in Table 3. From the table, we can see that the substitution of Pb2þ for Ba2þ leads to obvious variations on the Hirshfeld charges of all the atoms/cations in Ba2Pb(B3O6)2, especially on that of Pb2þ. The electronic density redistribution will influence the electronic polarizability a, the first derivative of electronic polarizability va/vq, and then the Raman intensity I of Ba2Pb(B3O6)2. The charge analysis results further prove that the differences of Raman peak intensity between a-BaB2O4 and Ba2Pb(B3O6)2 are associated with the special electron configure of Pb2þ. 4. Conclusions Ba2Pb(B3O6)2 was synthesized via a solid state reaction. Its crystal structure was reinvestigated by the Rietveld method from Table 3 Hirshfeld charge analyses for a-BaB2O4 and Ba2Pb(B3O6)2 crystals. Crystal
a-BaB2O4 Ba2Pb(B3O6)2 a b c
Hirshfeld charge B
O1a
O2b
Ba1c
Ba2/Pb
0.26 0.25
0.19 0.20
0.34 0.33
0.53 0.48
0.51 0.68
O1 ¼ intra-ring oxygen. O2 ¼ extra-ring oxygen. The Ba2þ cations occupy two Wyckoff sites in the a-BaB2O4 crystal.
Acknowledgment The work is financially supported by the National Natural Science Foundation of China (Grant No. 51372246). The calculations were partially performed at the Center for Computational Science, CASHIPS. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.matchemphys.2015.08.005. References [1] D. Eimerl, L. Davis, S. Velsko, E.K. Graham, A. Zalkin, J. Appl. Phys. 62 (1987) 1968e1983. [2] Y.X. Fan, R.C. Eckardt, R.L. Byer, J. Nolting, R. Wallenstein, Appl. Phys. Lett. 53 (1988) 2014e2016. [3] R.K. Li, Y.Y. Ma, CrystEngComm 14 (2012) 5421e5424. [4] G.Q. Zhou, J. Xu, X.D. Chen, H.Y. Zhong, S.T. Wang, K. Xu, P.Z. Deng, F.X. Gan, J. Cryst. Growth 191 (1998) 517e519. [5] X.Y. Dong, L. Cui, Y.J. Shi, S.L. Pan, Z.X. Zhou, Z.H. Yang, B.B. Zhang, X.Z. Jiang, Y. Yang, Z.H. Chen, Z.J. Huang, Z. Anorg, Allg. Chem. 639 (2013) 988e993. [6] J.A. Piper, H.M. Pask, IEEE J. Sel. Top. Quantum Electron 13 (2007) 692e704. [7] P. Cerny, H. Jelinkova, P.G. Zverev, T.T. Basiev, Prog. Quantum Electron 28 (2004) 113e143. [8] M. Maier, W. Kaiser, J.A. Giordmaine, Phy. Rev. 177 (1969) 580e599. [9] T.T. Basiev, A.A. Sobol, P.G. Zverev, L.I. Ivleva, V.V. Osiko, R.C. Powell, Opt. Mater 11 (1997) 307e314. [10] X.L. Tang, S.M. Wan, B. Zhang, X.S. Lv, Y.L. Sun, J.L. You, Mater. Chem. Phys. 149150 (2015) 270e274. [11] J. Liebertz, R. Frohlich, Z. Krist. 168 (1984) 293e297. [12] H.Y. Li, L.Y. Dong, Y. Lu, S.L. Pan, X.Q. Lu, H.W. Yu, H.P. Wu, X. Su, Z.H. Yang, J. Alloys Compd. 615 (2014) 561e565. [13] H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65e71. [14] A.C. Larson, R.B. von Dreele, Generalised Structure Analysis System Report LAUR86-748, Los Alamos National Laboratory, Los Alamos, NM, 2004. [15] V. Milman, K. Refson, S.J. Clark, C.J. Pickard, J.R. Yates, S.P. Gao, P.J. Hasnip, M.I.J. Probert, A. Perlov, M.D. Segall, J. Mol. Struct. 954 (2010) 22e35. [16] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys. Condens. Matter 14 (2002) 2717e2744. [17] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865e3868. [18] A.K. Hassan, L.M. Torell, L. Borjesson, H. Doweidar, Phys. Rev. 45 (1992) 12797e12805. [19] X.S. Lv, Y.L. Sun, J. Han, G.X. Gu, S.M. Wan, M.J. Cheng, S.L. Pan, Q.L. Zhang, J. Cryst. Growth 363 (2013) 220e225. [20] A.D. Mighell, A. Perloff, S. Block, Acta Crystallogr. 20 (1966) 819e823. [21] J.Q. Lu, G.X. Lan, B. Li, Y.Y. Yang, H.F. Wang, B.C. Wu, J. Phys. Chem. Solids 49 (1988) 519e527. [22] T.T. Basiev, R.C. Powell, Opt. Mater 11 (1999) 301e306.
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Crystal structure and Raman spectrum of Ba2Pb(B3O6)2 X.L. Tang a, D.X. Feng a, S.M. Wan a, *, L. Kang b, B. Zhang a, Z.S. Lin b, ** a b
Anhui Key Laboratory for Photonic Devices and Materials, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
The new crystal structure of Ba2Pb(B3O6)2 has been determined. The Raman spectrum of Ba2Pb(B3O6)2 has been analyzed by the site group method and first-principles calculation. The Pb2þ effect on the Raman spectrum has been interpreted.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 April 2015 Received in revised form 9 July 2015 Accepted 1 August 2015 Available online 17 August 2015
Ba2Pb(B3O6)2 polycrystalline powder was synthesized by a solid state reaction using BaCO3, Pb3O4 and H3BO3 as initial reactants. The crystal structure was solved from the powder X-ray diffraction data by the Rietveld refinement method and the DFT (density functional theory) calculation. The results show that Ba2Pb(B3O6)2 is isostructural with the high-temperature phase BaB2O4 (Ba2Ba(B3O6)2). It crystallizes in the trigonal space group R3 c with a ¼ b ¼ 7.20295(3) Å, c ¼ 37.594(1) Å, and Z ¼ 6. The structure is built up of the layers of B3O6 rings that are separated by Ba2þ or Pb2þ cations. The Raman spectrum of Ba2Pb(B3O6)2 was interpreted on the basis of the analysis through site group method. Its irreducible representation of the normal modes is 10A1g þ 11A2g þ 10A1u þ 11A2u þ 21Eg þ 21Eu among which 10A1g þ 11A2g þ 10A1u þ 10A2u þ 21Eg þ 20Eu are optical modes, where the A1g and Eg are Raman active. The DFT calculated results confirmed the results of the site group analysis and assigned all peaks in the experimental Raman spectrum. The a-BaB2O4 Raman spectrum was recorded and compared with the Ba2Pb(B3O6)2 Raman spectrum. The effect of the Pb2þ cations on the Raman intensity was discussed. © 2015 Elsevier B.V. All rights reserved.
Keywords: Ab initio calculations Raman spectroscopy and scattering Rietveld analysis Crystal structure
1. Introduction Metaborate crystals with the formula of Ba2M(B3O6)2 (M ¼ Mg, Ca, Sr, Ba, Co, Ni, Zn, Cd and Pb) are an important class of materials employed in laser technology. For example: (1) b-BaB2O4 (low-
* Corresponding author. Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, No. 350 Shushanhu Road, Hefei 230031, China. ** Corresponding author. E-mail address: [email protected] (S.M. Wan). http://dx.doi.org/10.1016/j.matchemphys.2015.08.005 0254-0584/© 2015 Elsevier B.V. All rights reserved.
temperature phase Ba2Ba(B3O6)2) crystals have been widely applied to generate the coherent light sources in the ultraviolet region and the continuously tunable coherent light sources from 412 nm to 2550 nm [1,2]. (2) Ba2Mg(B3O6)2, a-BaB2O4 (high-temperature phase Ba2Ba(B3O6)2) and Ba2Cd(B3O6)2 crystals are excellent birefringent crystals with wide transmission ranges, and suitable for fabrication of the polarizers and laser beam splitters used in the ultraviolet region [3e5]. The Ba2M(B3O6)2 crystals are also characterized by high damage thresholds which allow them to be applied in high power laser
502
X.L. Tang et al. / Materials Chemistry and Physics 163 (2015) 501e506
systems. It is well known that if the intensity of the laser beam is high enough, then SRS (simulated Raman scattering) will occur in the crystals. On one hand, the SRS process can be utilized to extend the spectral coverage of current lasers or to improve the spatial quality of the laser beams [6,7]; on the other hand, the SRS process will deplete the laser power, which is troublesome or even unwanted in the design of the high-power laser systems [8]. The SRS process is a two-photon stimulated process that grows from the spontaneous Raman scattering; thus, the spontaneous Raman spectrum is frequently used to understand the SRS process [9]. Recently, we studied the spontaneous Raman spectra of Ba2Mg(B3O6)2, Ba2Ca(B3O6)2 and a-BaB2O4 crystals, and found that their Raman peak positions and intensities are remarkably influenced by the type of the M2þ cation, and the M2þ cation effect is related to the electron density distributions in these crystals [10]. Ba2Pb(B3O6)2, as a possible Ba2M(B3O6)2-type compound, was firstly mentioned by Liebertz et al. in 1984 [11]. Recently, Li et al. reported its crystal structure and basic physical properties [12]. According to their results, PbBa2(B3O6)2 is isostructural to Ba2Mg(B3O6)2 and Ba2Ca(B3O6)2. It crystallizes in the trigonal space group R3 with a ¼ b ¼ 7.2056(8) Å, c ¼ 18.752(6) Å, and Z ¼ 3. The structure is built up of Ba2þ, Pb2þ and nearly planar B3O6 rings; all of the rings are perpendicular to the c axis. Unlike Mg2þ, Ca2þ and Ba2þ cations that have the inert gas electron configurations, Pb2þ cation has the unique 6s2 lone pair electrons that might influence the electron density distribution in Ba2Pb(B3O6)2 and then the Raman spectrum. However, little research has been carried out to investigate the Pb2þ cation effect although this issue, in a broader sense, is related to the spectral performance of other compounds containing heavy main-group elements with the s2 lone pair electrons. In our previous works, we found the PXRD (powder X-ray diffraction) and Raman spectrum of Ba2Pb(B3O6)2 very similar to that of a-BaB2O4 rather than Ba2Mg(B3O6)2 and Ba2Ca(B3O6)2, which implies Ba2Pb(B3O6)2 is probable to be isostructural to aBaB2O4. In this work, the Ba2Pb(B3O6)2 polycrystalline powder was prepared by a solid-state reaction; its crystal structure was reinvestigated by the Rietveld refinement combined with the DFT (density functional theory) calculation. The Ba2Pb(B3O6)2 Raman spectrum was analyzed on the basis of the site group method and the DFT calculation. Finally, the Pb2þ effect on the Ba2Pb(B3O6)2 Raman spectrum was discussed as compared with the a-BaB2O4 Raman spectrum.
the GSAS (generalized structural analysis system) software package [14]. The peak profile function was modeled using the pseudo-Voigt function described by Thompson et al.; the background was fitted by a Chebyshev polynomial function. The refinement involved the unit cell parameters, atomic coordinates, isotropic thermal parameters, a scale factor, background parameters, etc. Because of the complexity of the structure, soft restraints were applied to the BeO bond distances with suitable weighting factors (1.320 ± 0.015 Å, 1.400 ± 0.015 Å and 1.405 ± 0.010 Å for the BeO1, BeO2 and BeO20 bonds, respectively. See Table S1 in the supporting information for more details). A correction was made for the preferred orientation effect by using the MarchDollase approach. DFT calculations were carried out to study the crystal structure and Raman spectrum using the plane-wave pseudopotential method implemented in CASTEP (Cambridge Sequential Total Energy Package) [15,16]. The PerdewBurkeErnzerhof (PBE) version [17] of the generalized gradient approximation (GGA) was employed in conjunction with the norm-conserving pseudopotentials to describe the interactions between the ionic cores and the valence electrons. An energy cut-off of 1000 eV was used for the plane-wave basis set expansion. The sampling of the Brillouin zone was performed using a 2 2 2 Monkhorst-Pack k-point grid. The optimization met the following criteria: an energy tolerance of 1 106 eV/atom, a maximal force tolerance of 0.03 eV/Å, a maximal displacement of 1 103 Å, and a maximal stress of 0.05 GPa. The calculated Raman intensities were reduced by the BoseeEinstein population factors [18]. The energy cut-off and the kpoint grid have been tested to ensure the total energy converged in the calculations (see Fig. S1 and Table S2 in the supporting information).
3. Results and discussion Fig. 1 is the Raman spectrum of Ba2Pb(B3O6)2 recorded at room temperature. All characteristic peaks of the B3O6 ring are present in the spectrum. For example, the peaks located around 630 cm1 and 770 cm1 are related to the breathing modes of the ring; the peak located around 1510 cm1 arises from the stretching mode of the extra-ring BeO bonds [19]. The result confirms that the B3O6 rings are the most important blocking units in the Ba2Pb(B3O6)2 crystal structure. The PXRD pattern of Ba2Pb(B3O6)2 is shown in Fig. 2. It is very similar to that of a-BaB2O4, indicating that the two compounds
2. Experimental and computational details Ba2Pb(B3O6)2 was prepared by reacting a stoichiometric mixture of BaCO3 (1.974 g), Pb3O4 (1.142 g) and H3BO3 (1.892 g) (all reagents used were of analytical purity). The mixture was ground and heated at 550 C for 12 h to decompose H3BO3, followed by a heating treatment at 780 C for 12 h to decompose BaCO3 and Pb3O4. After that, the intermediate product was reground and heated again at 780 C for 12 h. The final polycrystalline powder was analyzed by PXRD and Raman spectroscopy. The PXRD data were collected at room temperature by a Rigaku D/Max-Ra powder diffractometer which used Cu Ka radiations (lKa1 ¼ 0.15406 nm and lKa2 ¼ 0.154434 nm) and operated at 200 mA and 40 kV. The data were collected in the 2q range of 10e70 with a 0.02 step width and 8 s/point. Raman spectra were recorded at room temperature on a Jobin Y'von LABRAM HR Raman spectrometer with a backscattering configuration. The 514.5 nm line of an Arþ laser was employed for excitation. The laser beam power at the sample surface was about 1 mW. All of the Raman spectra were recorded at 2 cm1 resolution from 100 to 1800 cm1. The PXRD data were analyzed by the Rietveld method [13] using
Fig. 1. Raman spectrum of the Ba2Pb(B3O6)2 polycrystalline powder.
X.L. Tang et al. / Materials Chemistry and Physics 163 (2015) 501e506
503
Table 1 Crystallographic data for the Ba2Pb(B3O6)2 crystal. Ba2Pb(B3O6)2 Trigonal R3 c a ¼ 7.20295(3) b ¼ 7.20295(3) c ¼ 37.594(1) 120 1689.14 6 4.74 5.84
Empirical formula Crystal system Space group Unit cell dimensions (Å)
g ( ) Volume (Å3) Z Rp(%) Rwp(%)
Table 2 Atomic coordinates, Wyckoff sites and temperature factors of the Ba2Pb(B3O6)2 crystal.
Fig. 2. PXRD patterns of the a-BaB2O4 and Ba2Pb(B3O6)2 polycrystalline powders.
possess a similar crystal structure. According to the PXRD result, the a-BaB2O4 crystal structure [20] reported by Mighell et al. was used as the prototype for the Ba2Pb(B3O6)2 structural refinement. With reference to the crystal structures of Ba2Ca(B3O6)2 and Ba2Mg(B3O6)2, the Ba2þ cations located at the Wyckoff site 6a in the a-BaB2O4 crystal structure were substituted by Pb2þ cations. The resulting model was refined by the Rietveld method to obtain the accurate cell parameters; and then optimized by the DFT method to determine the reasonable atomic coordinates. During the DFT optimization, the lattice parameters were fixed, but all of the atomic coordinates were allowed to be refined. Finally, the DFT-optimized structure, including the cell parameters and the atomic coordinates, was refined again by the Rietveld method. The final Rietveld plot of Ba2Pb(B3O6)2 is presented in Fig. 3, which shows a good agreement between the experimental and calculated PXRD patterns (Rp ¼ 4.74% and Rwp ¼ 5.84%) and confirms the hypothesis of the isostructural relationship between aBaB2O4 and Ba2Pb(B3O6)2. Relevant crystallographic data and atomic coordinates are summarized in Tables 1 and 2, respectively.
Fig. 3. Experimental (circles), calculated (solid line) and difference patterns (bottom line) for the Ba2Pb(B3O6)2 polycrystalline powder.
Atom
Site
x
y
z
Ueq (Å2)
Ba Pb B O1 O2
12c 6a 36f 36f 36f
0 0 0.9604(1) 0.1692(2) 0.4110(2)
0 0 0.17519(6) 0.2071(2) 0.0687(2)
0.35126(3) 0.25000 0.04069(6) 0.0417(1) 0.03758(3)
6.8(2) 10.1(2) 22.2(3) 2.6(6) 17.9(1)
The Ba2Pb(B3O6)2 crystal structure is illustrated in Fig. 4. Its fundamental building units are Ba2þ cations, Pb2þ cations and B3O6 six-membered rings. These planar rings are parallel to each other to form the B3O6 layers which are alternately separated by the Ba2þ and Pb2þ cations. All of the B3O6 rings belong to the C3 site group and are symmetrically surrounded by six Ba2þ and three Pb2þ cations; each Ba2þ/Pb2þ cation is surrounded by six oxygen atoms to form a BaO6/MgO6 octahedron (see Fig. 5). The selected bond lengths and angles of Ba2Pb(B3O6)2 are listed in Table S3 (see the supporting information). The Ba2Pb(B3O6)2 crystal structure is similar to that reported by Li et al., but the space group and the caxis length are different [12]. They considered that the crystal
Fig. 4. Trigonal crystal cell (left) and primitive cell (right) of the Ba2Pb(B3O6)2 crystal.
504
X.L. Tang et al. / Materials Chemistry and Physics 163 (2015) 501e506
00
Gv ¼ 3A1 0 þ 2A2 0 þ 2A2 þ 5E 0 þ 2E
00
where Gt, Gr and Gv represent the translational, rotational and vibrational modes, respectively. In the Ba2Pb(B3O6)2 crystal structure, the B3O6 ring has the C3 site group symmetry and the D3d unit cell group (factor group) symmetry. Scheme 1 presents the correlations of the irreducible representations between the D3h point group and the C3 site group and that between the C3 site group and the D3d unit cell group. From the scheme, we can see that the A01 A02 A01 and A02 modes convert to the A modes when the isolated ring is located at the C3 site, and then split to the A1g, A1u, A2g and A2u lattice modes when the ring is further constrained by the D3d symmetry. In the same way, the E0 and E00 modes of the isolated B3O6 ring convert to the E modes and then split to the Eg and Eu lattice modes. As mentioned above, the Ba2Pb(B3O6)2 primitive cell contains four B3O6 rings; therefore the translational modes ð4A02 þ 4E0 Þ, rotational modes ð4A02 þ 4E0 Þ and vibrational modes ð12A01 þ 8A02 þ 8A02 þ 20E0 þ 8E0 Þ of the four B3O6 rings yield 12 lattice translational modes (A1g þ A2g þ A1u þ A2u þ 2Eg þ 2Eu), 12 lattice liberational modes (A1g þ A2g þ A1u þ A2u þ 2Eg þ 2Eu) and 84 lattice internal vibrational modes (7A1g þ 7A2g þ 7A1u þ 7A2u þ 14Eg þ 14Eu). In the Ba2Pb(B3O6)2 crystal structure, the Ba2þ and Pb2þ cations occupy the C3 and D3 symmetric positions, respectively. According to the correlations between the C3/D3 site group and the D3d unit cell group, the 12 translational modes of the Ba2þ cations (4A þ 4E, four Ba2þ cations in the primitive cell) and the 6 translational modes of the Pb2þ cations (2A þ 2E, two Pb2þ cations in the primitive cell) yield 12 (A1g þ A2g þ A1u þ A2u þ 2Eg þ 2Eu) and 6 (A2g þ A2u þ Eg þ Eu) lattice translational modes, respectively. The total lattice vibrational modes of the Ba2Pb(B3O6)2 crystal are 10A1g þ 11A2g þ 10A1u þ 11A2u þ 21Eg þ 21Eu. Except three acoustical modes (A2u þ Eu), the rest (10A1g þ 11A2g þ 10A1u þ 10A2u þ 21Eg þ 20Eu) are optical modes. The lattice vibrational modes can also be divided into internal modes and external modes. The internal modes originate from the vibrations of the B3O6 rings; the external modes from the librations of the B3O6 rings and the translations of the B3O6 rings, Ba2þ cations and Pb2þ cations. According to the above results of the site group analysis, we can obtain: Fig. 5. Coordination environments around the Pb2þ cations, Ba2þ cations, and B3O6 rings.
crystallizes in the R3 space group and the c-axis length is 18.752(6) Å, only half of the value determined here. Ba2Pb(B3O6)2 is a moleculecation type crystal, its lattice vibrational modes can thus be classified by the site group method of analysis. The Ba2Pb(B3O6)2 crystal structure belongs to the space group R3 c (unit cell group D3d). Its primitive cell includes four B3O6 rings, four Ba2þ cations and two Pb2þ cations (Fig. 4). The isolated B3O6 ring with the D3h symmetry (point group) has 27 vibrational modes [21]; the corresponding irreducible representations are given by
Gring ¼ Gt þ Gr þ Gv 00
Gt ¼ A2 þ E 0 Gr ¼ A20 þ E
00
Gtotal ¼ Gint þ Gext Gint ¼ 7A1g þ 7A2g þ 7A1u þ 7A2u þ 14Eg þ 14Eu Gext ¼ 3A1g þ 4A2g þ 3A1u þ 4A2u þ 7Eg þ 7Eu where the A1g and Eg modes are Raman active, and the A2g, A2u and Eu modes are infrared active. Thus, 31 Raman peaks (10A1g þ 21Eg) are expected to be observed in the Ba2Pb(B3O6)2 Raman spectrum. In fact, the number of the Raman peaks in the experimental spectrum (Fig. 1) is less than the predicted, which is probably due to the weak scattering intensities of some modes. We used the DFT method to calculate the Raman spectrum of Ba2Pb(B3O6)2 at the same level of theory for the structural optimization. The calculated Raman spectrum, together with the experimental spectrum, is shown in Fig. 6. All calculated Raman frequencies are in good agreement with the experimental. The relative intensities of the calculated peaks are also consistent with the experimental results except for the peaks located at 303 cm1 and 734 cm1 (calculated values). The irreducible representation of Ba2Pb(B3O6)2 predicted by the site group method is also confirmed by the DFT calculation. According to the calculated results, the
X.L. Tang et al. / Materials Chemistry and Physics 163 (2015) 501e506
505
Scheme 1. Site group analysis for the Ba2Pb(B3O6)2 lattice vibrational modes.
Fig. 6. Experimental and calculated Raman spectra of Ba2Pb(B3O6)2.
experimental Raman peaks are assigned (Fig. 6). More detailed results are provided in the supporting information (Table S4). The Raman spectrum of a-BaB2O4 was recorded and compared with that of Ba2Pb(B3O6)2 (see Fig. 7). The two Raman spectra are very similar in peak number and position, which is due to their almost identical crystal structures and vibrational modes. However, the corresponding peak intensities are remarkably different. More detailed studies revealed that almost all the strong peaks in the aBaB2O4 spectrum became weaker in the Ba2Pb(B3O6)2 spectrum, or the weak peaks became stronger due to the substitution of Pb2þ for Ba2þ (see Fig. 7, only the internal modes are discussed in this paper.). This phenomenon can be explained by the formula for Raman peak intensity. Theoretical studies indicate that Raman peak intensity is linearly proportional to the square of the first derivative of electronic polarizability with respect to atomic displacements (I f (va/vq)2, where I, a and q are Raman peak intensity, electronic
Fig. 7. Raman spectra of a-BaB2O4 and Ba2Pb(B3O6)2.
polarizability and atomic displacement, respectively.) [22]. As we know, the Pb2þ cation has a unique 6s2 electron configuration which generally shows a higher tendency to polarize than the inert gas electron configuration of the Ba2þ cation ((va/vq)Pb > (va/vq)Ba). On the other hand, the effective va/vq (S(va/vq)) of the Pb2þ cations is also related to their arrangement in the crystal and the vibrational modes of the most neighboring B3O6 rings. In the Ba2Pb(B3O6)2 crystal structure, the Pb2þ cations are symmetrically arranged around the B3O6 rings (Fig. 5(c)), which leads to the (va/ vq)Pb arising from the B3O6 ring symmetrically vibrational modes to cancel each other, and thus the S(va/vq)Pb of the symmetrically A1g vibrational modes is less than that of the asymmetrically Eg vibrational modes ([S(va/vq)Pb]A1g < [S(va/vq)Pb]Eg). Two examples, corresponding to a typical A1g mode and a typical Eg mode, are
506
X.L. Tang et al. / Materials Chemistry and Physics 163 (2015) 501e506
the PXRD data with the help of the DFT structural optimization. Ba2Pb(B3O6)2 crystallizes in the space group R3 c of the trigonal system with six formula units in a unit cell; the unit cell constants a ¼ b ¼ 7.20295(3) Å and c ¼ 37.594(1) Å. The basic boronoxygen structural unit in the crystal is the planar B3O6 ring. Each B3O6 ring is symmetrically surrounded by six Ba2þ cations and three Pb2þ cations. Each Ba2þ/Pb2þ cation is surrounded by six oxygen atoms to form a BaO6/MgO6 octahedron. The vibrational modes of the Ba2Pb(B3O6)2 crystal have been classified by the site group method of analysis. The crystal has 126 vibrational modes, corresponding to the irreducible representation of 10A1g þ 11A2g þ 10A1u þ 11A2u þ 21Eg þ 21Eu. Except three acoustical modes (A2u þ Eu), the rest (10A1g þ 11A2g þ 10A1u þ 10A2u þ 21Eg þ 20Eu) are optical modes of which A1g and Eg are Raman active. The DFT calculation verified the results predicted by the site group method and assigned the vibrational modes of all the peaks in the Raman spectrum. The Ba2Pb(B3O6)2 Raman spectrum was compared with the a-BaB2O4 Raman spectrum. The substitution of Pb2þ for Ba2þ in the a-BaB2O4 crystal remarkably reduces the relative intensities of the A1g peaks. The Pb2þ effect is attributed to its unique 6s2 electron configuration and the arrangement of Pb2þ cations in the crystal structure. Fig. 8. Atomic displacements of a typical symmetrically A1g mode of which the peak is around 630 cm1 (experimental value) and a typical asymmetrically Eg mode of which the peak is around 1380 cm1 (experimental value). The right part is the electronic polarizability of the Pb2þ cations associated to the two vibrational modes.
shown in Fig. 8. Considering that (va/vq)Pb > (va/vq)Ba, [S(va/ vq)Pb]A1g < [S(va/vq)Pb])Eg and most of the A1g modes appear in the a-BaB2O4 Raman spectrum as strong peaks (Fig. 7), we can conclude that the strong peaks increase in intensity less than the weak peaks when the Ba2þ cations located at 6a Wyckoff sites in the a-BaB2O4 crystal structure are replaced by the Pb2þ cations, as shown in Fig. 7. In order to further explore the effect of the substitution of Pb2þ for Ba2þ, we analyzed the Hirshfeld charges of the atoms/cations in the a-BaB2O4 and Ba2Pb(B3O6)2 crystals by the DFT method at the same level of theory for the Raman spectrum calculation. The results are shown in Table 3. From the table, we can see that the substitution of Pb2þ for Ba2þ leads to obvious variations on the Hirshfeld charges of all the atoms/cations in Ba2Pb(B3O6)2, especially on that of Pb2þ. The electronic density redistribution will influence the electronic polarizability a, the first derivative of electronic polarizability va/vq, and then the Raman intensity I of Ba2Pb(B3O6)2. The charge analysis results further prove that the differences of Raman peak intensity between a-BaB2O4 and Ba2Pb(B3O6)2 are associated with the special electron configure of Pb2þ. 4. Conclusions Ba2Pb(B3O6)2 was synthesized via a solid state reaction. Its crystal structure was reinvestigated by the Rietveld method from Table 3 Hirshfeld charge analyses for a-BaB2O4 and Ba2Pb(B3O6)2 crystals. Crystal
a-BaB2O4 Ba2Pb(B3O6)2 a b c
Hirshfeld charge B
O1a
O2b
Ba1c
Ba2/Pb
0.26 0.25
0.19 0.20
0.34 0.33
0.53 0.48
0.51 0.68
O1 ¼ intra-ring oxygen. O2 ¼ extra-ring oxygen. The Ba2þ cations occupy two Wyckoff sites in the a-BaB2O4 crystal.
Acknowledgment The work is financially supported by the National Natural Science Foundation of China (Grant No. 51372246). The calculations were partially performed at the Center for Computational Science, CASHIPS. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.matchemphys.2015.08.005. References [1] D. Eimerl, L. Davis, S. Velsko, E.K. Graham, A. Zalkin, J. Appl. Phys. 62 (1987) 1968e1983. [2] Y.X. Fan, R.C. Eckardt, R.L. Byer, J. Nolting, R. Wallenstein, Appl. Phys. Lett. 53 (1988) 2014e2016. [3] R.K. Li, Y.Y. Ma, CrystEngComm 14 (2012) 5421e5424. [4] G.Q. Zhou, J. Xu, X.D. Chen, H.Y. Zhong, S.T. Wang, K. Xu, P.Z. Deng, F.X. Gan, J. Cryst. Growth 191 (1998) 517e519. [5] X.Y. Dong, L. Cui, Y.J. Shi, S.L. Pan, Z.X. Zhou, Z.H. Yang, B.B. Zhang, X.Z. Jiang, Y. Yang, Z.H. Chen, Z.J. Huang, Z. Anorg, Allg. Chem. 639 (2013) 988e993. [6] J.A. Piper, H.M. Pask, IEEE J. Sel. Top. Quantum Electron 13 (2007) 692e704. [7] P. Cerny, H. Jelinkova, P.G. Zverev, T.T. Basiev, Prog. Quantum Electron 28 (2004) 113e143. [8] M. Maier, W. Kaiser, J.A. Giordmaine, Phy. Rev. 177 (1969) 580e599. [9] T.T. Basiev, A.A. Sobol, P.G. Zverev, L.I. Ivleva, V.V. Osiko, R.C. Powell, Opt. Mater 11 (1997) 307e314. [10] X.L. Tang, S.M. Wan, B. Zhang, X.S. Lv, Y.L. Sun, J.L. You, Mater. Chem. Phys. 149150 (2015) 270e274. [11] J. Liebertz, R. Frohlich, Z. Krist. 168 (1984) 293e297. [12] H.Y. Li, L.Y. Dong, Y. Lu, S.L. Pan, X.Q. Lu, H.W. Yu, H.P. Wu, X. Su, Z.H. Yang, J. Alloys Compd. 615 (2014) 561e565. [13] H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65e71. [14] A.C. Larson, R.B. von Dreele, Generalised Structure Analysis System Report LAUR86-748, Los Alamos National Laboratory, Los Alamos, NM, 2004. [15] V. Milman, K. Refson, S.J. Clark, C.J. Pickard, J.R. Yates, S.P. Gao, P.J. Hasnip, M.I.J. Probert, A. Perlov, M.D. Segall, J. Mol. Struct. 954 (2010) 22e35. [16] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys. Condens. Matter 14 (2002) 2717e2744. [17] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865e3868. [18] A.K. Hassan, L.M. Torell, L. Borjesson, H. Doweidar, Phys. Rev. 45 (1992) 12797e12805. [19] X.S. Lv, Y.L. Sun, J. Han, G.X. Gu, S.M. Wan, M.J. Cheng, S.L. Pan, Q.L. Zhang, J. Cryst. Growth 363 (2013) 220e225. [20] A.D. Mighell, A. Perloff, S. Block, Acta Crystallogr. 20 (1966) 819e823. [21] J.Q. Lu, G.X. Lan, B. Li, Y.Y. Yang, H.F. Wang, B.C. Wu, J. Phys. Chem. Solids 49 (1988) 519e527. [22] T.T. Basiev, R.C. Powell, Opt. Mater 11 (1999) 301e306.