2 ceramics

Journal of Alloys and Compounds 786 (2019) 1030e1039

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Optical vibrational properties of Bi2-xCaxSn2O7-x/2 ceramics
ria M. Lima a, Rafael M. Almeida b, *, Alysson Steimacher a, Adenilson O. Santos a, Vale Diego A.B. Barbosa c, Anderson Dias d, Roberto L. Moreira e ~o, 65900-410, Imperatriz, MA, Brazil CCSST, Universidade Federal do Maranha ~o Ci^ ~o, Campus Sa ~o Luís - Maracana ~, 65095-460, Sa ~o Luís, MA, Brazil Instituto Federal de Educaça encia e Tecnologia do Maranha c ~o do Curso de Licenciatura em Ci^ ~o, Campus Bacabal, 65700-000, Bacabal, MA, Brazil Coordenaça encias Naturais, Universidade Federal do Maranha d Departamento de Química, ICEx, Universidade Federal de Minas Gerais, 31270-901, Belo Horizonte, MG, Brazil e Departamento de Física, ICEx, Universidade Federal de Minas Gerais, 30123-970, Belo Horizonte, MG, Brazil a

b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 1 December 2018 Received in revised form 28 January 2019 Accepted 30 January 2019 Available online 2 February 2019

Bi2-xCaxSn2O7-x/2 ceramics were synthesized by solid-state reactions and sintered at 1050
C. Raman and infrared spectroscopies were used to investigate the optical vibrational properties of pure Bi2Sn2O7 ceramics, as well as to understand the influence of Ca2þ substitution for Bi3þ on the vibrational characteristics of the Bi2-xCaxSn2O7-x/2 system (for x  0.02). First, we demonstrate that partial substitution of Bi3þ with Ca2þ ions does not promote the b-phase, as it is commonly reported for other cationic substituents. The results of Raman and infrared spectroscopies showed that 34 bands were observed by Raman scattering, and 22 modes were observed by infrared spectroscopy. It was also verified that Raman scattering was quite sensitive to the morphological features of the samples, which was not the case for infrared spectroscopy. Scanning electron microscopy on the sintered samples showed that such sensitivity is partially linked to the grain sizes, which are larger than the incident light beamwidth, but smaller than the infrared beamwidth. Thus, infrared spectroscopy takes contributions from the average of a number of grains, while Raman spectroscopy evaluates contributions of single grains. The dielectric merit factors of the Bi2Sn2O7 ceramics were also obtained from infrared spectroscopy, namely 30 ¼ 24.2 and Quf ¼ 56.9 THz. Finally, it is worth noting that this paper presents the first investigation of infrared spectra of Bi2-xCaxSn2O7-x/2 materials. © 2019 Elsevier B.V. All rights reserved.

Keywords: Bi2Sn2O7 Ca-doped Vibrational properties Raman scattering Infrared spectroscopy Microstructure

1. Introduction Bi2Sn2O7 ternary oxide belongs to the pyrochlore family with a general formula A2B2O7, where the A- and B-cations are metals. The A2þ-B5þ pair of cations corresponds to III-V pyrochlore, and A3þ-B4þ corresponds to III-IV pyrochlore. Bi2Sn2O7 is a III-IV pyrochlore with cubic structure belonging to the Fd3m (#227, O7h) space group, which is thermodynamically stable above 626
C [1]. In this structure, the Bi3þ cation has an eight-fold coordination, while Sn4þ is six-fold coordinated. This pyrochlore phase is referred to as gBi2Sn2O7 or high-temperature phase, while the two other reported symmetry phases at lower temperatures, are known as b-Bi2Sn2O7 and a-Bi2Sn2O7, or intermediate- and room-temperature phases, respectively. Recently, these materials have received much attention due to their many technological applications; in particular,

* Corresponding author. E-mail address: [email protected] (R.M. Almeida). https://doi.org/10.1016/j.jallcom.2019.01.375 0925-8388/© 2019 Elsevier B.V. All rights reserved.

they are being extensively investigated as photocatalysts [2,3]. This property has been considerably improved by heterojunctions assemblies, such as in Bi2Sn2O7/Ag@AgCl, which is effective for the degradation of acid red 18 and methylene orange as organic pollutants in water [4,5]. The degradation by photocatalysis of other water pollutants has also been demonstrated, e.g., methylene blue (MB) and acid red 18 by Bi2Sn2O7/g-C3N4 composites [6]; rhodamine B (RhB) by BiOCl/Bi2Sn2O7 [7]; BiOBr/Bi2Sn2O7 [8]; BiOI/ Bi2Sn2O7 [9]; Bi2S3/Bi2Sn2O7 [10]; ZnO/Bi2Sn2O7 [11]; TiO2/Bi2Sn2O7 [12]; or RhB by In2O3/Bi2Sn2O7 composites [13]; RhB and phenol by Bi2Sn2O7/reduced graphene oxide [14]; RhB and 2,4dichlorophenol (2,4-DCP) by praseodymium doped Bi2Sn2O7 [15]; MB by Pd/b-Bi2O3-Bi2Sn2O7 or Pt/SnO2-Bi2Sn2O7 [16]; MB by C3N4/ Bi2Sn2O7 [17]; and 2-naphthol by the solid solutions (Bi2-dYd)Sn2O7, with d ¼ 0, 0.5, 1.0, 1.5, or 2.0 [18]. The compounds used together with Bi2Sn2O7 as heterojunctions are narrow band gap semiconductors, and their main function is to reduce the electron-hole recombination rate and to increase visible light absorption, which in turn improves the photocatalytic activity up to nine times [4] as

V.M. Lima et al. / Journal of Alloys and Compounds 786 (2019) 1030e1039

compared to pure Bi2Sn2O7. In addition, nanocrystalline Bi2Sn2O7 is also a promising visible-light photocatalyst for indoor air purification against gaseous pollutants such as nitrogen oxide [19] or arsenic, As(III), and the removal from aqueous solutions [20]. Finally, it must be emphasized that Bi2Sn2O7 has also catalytic activity [21], e.g., in isobutene oxidation [22e25], and semiconductor gas sensor operation [26,27] with a particular selectivity for CO [28e32]. The Bi2O3-SnO2 ceramic system was first described by Coffen [33], and Roth [34] was the first to identify the Bi2Sn2O7 compound. Brisse and Knop [35] reported a systematic study of the Bi2Sn2O7 structure, and Vetter et al. [36] identified two different thermodynamically accessible phases: a tetragonal one, below 740
C, and an ideal cubic pyrochlore in the range 740e1450
C. It was subsequently established that the upper limit temperature of the Bi2Sn2O7 existence was ~1365
C when it decomposes into SnO2 and Bi2O3 starting oxides [37]. Shannon et al. [38] studied polymorphism in Bi2Sn2O7 ceramics and distinguished three distinct phases: a low-temperature phase (<90
C) called the a-phase; an intermediate-temperature phase between 90
C and 680
C called the b-phase; and a high-temperature phase (>680
C) that is isostructural to the mineral pyrochlore called the g-phase. They also suggested that in polycrystalline samples, the a / b transition takes place at 135
C and is ferroic in nature, whereas the b / g transition should have a second-order character. The same authors reported that the a- and b-phases are optically active for second harmonic generation (SHG), which is evidence for the absence of an inversion symmetry center in both groups. Neutron diffraction measurements carried out by two different groups [1,39] confirmed that the g-phase has symmetry F3dm, while thermal measurements revealed the first order nature of the b / g transition and an onset temperature of 626
C [1]. Kennedy et al. [40] used neutron and X-ray diffraction to demonstrate that the b-phase structure crystallizes according to a cubic structure with F43c symmetry, which is a centrosymmetric space group and therefore is opposite to the SHG activity observed by Shannon et al. [38]. On the other hand, Evans et al. [41] carried out combined measurements of neutron and XRD followed by Rietveld refinements, and demonstrated the a-phase with Pc symmetry. The authors made three assumptions to obtain this result: a group-subgroup relationship between the a-phase and parent pyrochlore structure (g-phase); an apparent cubic structure for the b-phase; and SHG activity of the aand b-phases. Furthermore, they highlighted that a / b and b / g phase transitions occur with a cell volume drop, an effect known as negative thermal expansion (or NTE effect). Some years later, Salamat et al. [42], supported by XRD investigations, stated that the actual structure of b-Bi2Sn2O7 should be trigonal with space group P31. They also reported that by the application of pressure three phase transitions occur: the a / b transition between 11.6 and 13.6 GPa; the b / g transition between 18.4 and 20.7 GPa; and a transition from g-Bi2Sn2O7 to a fluorite phase, above 34 GPa. Recently, Lewis et al. [43] demonstrated, by an exhaustive and automated symmetry-mode method combined with X-ray and neutron diffraction, that the correct structure for the b-phase is orthorhombic with the space group Aea2 (#41, C17 2v), whilst for the a-phase the structure is monoclinic with Cc (#9, C4s ) symmetry. These space groups are in accordance with SHG activity and the group-subgroup relationship between the a- and b-phases but are in disagreement with those attributed by Salamat et al. [42] for the b-phase, and by Evans et al. [41] for the a-phase. However, Lewis et al. [43] pointed out that Salamat et al. [42] did not assume that the b-phase presents SHG activity, while Evans et al. [41] assumed that such a phase has face-centered cubic symmetry, which is totally incompatible with the high resolution XRD data of

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Lewis et al. [43]. In addition, Evans et al. [41] used this symmetry hypothesis (face-centered cubic) for the b-phase, and wrongly derived the Pc symmetry for the a-phase. In addition to the temperature or pressure, the phase stability of Bi2Sn2O7 depends also on doping. Shannon et al. [38] showed that when the aliovalent ions Pb2þ or Cd2þ are used as substitutional defects at the Bi3þ cation sites, the b-Bi2Sn2O7 phase is promoted for both cases. Ismunandar et al. [44] showed that the substitutional doping at the Bi3þ cation sites for the Y3þ ions in Bi2Sn2O7 stabilizes the b-phase of this material under ambient pressure and temperature. In addition, Subramanian et al. [45] reinforced the work of Ismunandar et al. [44] stating that in general the stabilization of the b-phase of Bi2Sn2O7 occurs under doping of the Bi cation site with aliovalent ions, regardless of the doping content. In particular, Payne [46] doped Bi2Sn2O7 with calcium at the bismuth cation site, obtaining the b-Bi2Sn2O7 phase for all compositions in the series Bi2-xCaxSn2O7-x/2, with 0  x  0.8, that was sometimes accompanied by the secondary phase CaSnO3 (for x  0.3). By using hydrothermal synthesis, g-Bi2Sn2O7 (pyrochlore phase) was stabilized [4,7,8,10,14,15,19]. Previous works [47e49] have investigated the vibrational properties of doped pyrostannates and other pyro-compounds by 3d metals, frequently replacing the Sn ions rather than the Bi ions. In these works, it was then established a correlation between the vibrational modes and the anomalies observed in the magnetic susceptibility, permittivity, and absorption line intensity as a function of the doping level. In the present work, we aim to investigate the defect substitution of Bi3þ ions by Ca2þ ions in sintered ceramics with nominal composition Bi2-xCaxSn2O7-x/2 (x ¼ 0.005, 0.01, 0.015 and 0.02). The influence of Ca-doping on the Bi2Sn2O7 phase stabilization, phonon modes, and microstructure were investigated by XRD, Raman scattering, infrared spectroscopy, and scanning electron microscopy. 2. Experimental Polycrystalline ceramic samples of Bi2-xCaxSn2O7-x/2 (x ¼ 0.005, 0.01, 0.015 and 0.02) were synthesized using the solid-state route, by mixing stoichiometric amounts of Bi2O3 (99.9%, Sigma-Aldrich), SnO2 (99.9%, Sigma-Aldrich), and CaCO3 (99.9%, Sigma-Aldrich) with acetone in an agate mortar for 10e15 min, according to the reaction: (1-x/2) Bi2O3 þ x CaCO3 þ 2 SnO2 / Bi2-xCaxSn2O7-x/2 þ x CO2. (1) The mixed oxides were calcined under four stages of temperature (from 750
C up to 975
C in steps of 75
C), for times in the range 12e24 h, and powders of yellowish white color were obtained. For the sintering process, powders of each composition (~1 g) were pressed at 3 tons for 5 min into pellets of 10 mm of diameter and fired at 1050
C for 10 h in sealed alumina crucibles. The final densities of all sintered samples were obtained by the Archimedes' method using distilled water as the immersion liquid and taking the average of three measurements for each synthesized specimen. The XRD data were collected in a Rigaku X-ray diffractometer (Miniflex II model) aligned in the geometry of BraggBrentano (q:2q), with Soller slits of 2.5
, divergence slit of 2.5
(fixed), anti-scatter slit of 1.25
(fixed), and a pyrolytic graphite diffracted beam monochromator using CuKa radiation (l ¼ 1.5418 Å), operating with 30 kV and 15 mA. The measurements were performed using an angular step of 0.02
2q and acquisition time of 2 s/step varying an angular range of 10e90
2q. Raman spectroscopy measurements were carried out in a Jobin-Yvon spectrometer (T64000 model) coupled to a LN2-cooled CCD detector and a confocal Olympus microscope (100 objective). By

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taking the average of 10 accumulations of 15 s each, the Raman spectra were obtained using the 532 nm line of a Coherent-Verdi laser and corrected by the Bose-Einstein thermal factor [50] in the spectral range 50e1000 cm1 with a spectral resolution of 2 cm1. Infrared reflectivity spectra from the polished ceramic bodies were obtained using a Fourier-Transform Nicolet spectrometer (Nexus 470 model), equipped with a Centaurus microscope (magnification of 10 and incident light beam of 350 mm diameter), in the frequency range 50e4000 cm1. For the midinfrared spectral region (550e4000 cm1), a KBr:Ge beamsplitter and MCT detector were used. For the far-infrared region (<600 cm1), the following accessories were used: a solid-state Si beamsplitter and Si-bolometer detector. Both infrared spectral regions utilized a Globar (carbide silicon laser) as the excitation source to collect the data under nitrogen purge, taking into account an average of 64 scans, an observation area with dimensions of 250  250 mm2, and a spectral resolution of 2 cm1. The morphological features of the sintered samples were investigated by scanning electron microscopy (SEM). Quanta FEG 3D (FEI) fieldemission gun SEM (FESEM) equipment was used under highvacuum conditions, with applied voltages in the range 10e30 kV. Freshly fractured surfaces were produced by placing the sintered samples into liquid nitrogen, followed by carbon film coating immediately after their fracture. 3. Results and discussion The room-temperature XRD data of all samples investigated in the present work, besides the diffraction patterns of the a-Bi2Sn2O7 and b-Bi2Sn2O7 phases, are presented in Fig. 1. The diffraction patterns of the ceramic powders agree well with the patterns of the a-Bi2Sn2O7 phase, which has a monoclinic symmetry, belonging to the Cc space group (#9, C4s ). On the right of Fig. 1, a certain XRD plane was focused to show its displacement to higher angles (2 theta) for higher amounts of calcium, which proves the proper calcium doping of our samples. Fig. 2 shows the XRD pattern of the sintered pellet of pure BSO and its respective Rietveld refinement based on the space group Cc (#9, C4s ). The Rietveld patterns of the sintered pellets of Bi2-xCaxSn2O7-x/2 are very similar to the one of pure BSO and for this reason they are presented in Fig. S1 (Supporting Information). Detailed information about the Rietveld refinements, like software used and refinement strategy are also given in the Supporting Information, along with the atomic coordinates and refined parameters (Tables S1eS5). The goodness of fit (GOF) and weighted profile R-factor (Rwp) have values of approximately 2 and 23%, respectively, for the five sintered

Fig. 2. Rietveld refinements of the Bi2Sn2O7 ceramics. The circle symbols are the experimental data and the red line is the calculated fit. The blue line is the difference between the experimental and calculated data. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

ceramics analyzed. The angular range used to the data collection (10e90
2q) was sufficient to perform the Rietveld refinements of the investigated parameters, since in this range there are more than 450 reflections available. In addition, to ensure reliability, it is only necessary to have (nþ1) peaks to refine n parameters, and most of the peaks further have very small intensities and do not decisively contribute to increase fitting quality. Regarding the Rwp value being around 23%, this is very common when dealing with polycrystalline samples synthesized by solid-state reaction methods. The lattice parameters obtained from the Rietveld refinement of pure and doped Bi2Sn2O7 are presented in Table 1 and are close to those reported by Lewis et al. [43] for the aeBSO phase, with discrepancies of ~1%. It is worth noting that the beBSO phase cannot be identified in the diffractograms of the solid solutions, since there is a peak splitting at around 33.5
2q, which is typical of the aeBSO phase and that carries influence of all the cell parameters. Such peak splitting in the diffractogram of each sample is highlighted in Fig. S1. It is noted that the higher the concentration of Ca2þ ions in the Bi2-xCaxSn2O7-x/2 ceramics, the higher the density of the sample, however saturation was reached before the highest level of substitution, i.e., for the sample Bi1.985Ca0.015Sn2O6.9925. For this

Fig. 1. XRD patterns of the investigated Bi2-xCaxSn2O7-x/2 ceramics. The diffraction patterns of the a- and b-Bi2Sn2O7 phases are also shown for comparison. On the right, a certain XRD plane was focused to show its upshift with increasing calcium contents.

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Table 1 Unit cell parameters of the Bi2-xCaxSn2O7-x/2 ceramics and the theoretical values of Bi2Sn2O7 for comparison. The maxima relative percentage errors of the sample lattice parameters as compared with the theoretical values of pure BSO are provided in brackets beside each sample cell parameter. Cell parameters

Theoretical Bi2Sn2O7

x ¼ 0.000 [% error]

x ¼ 0.005 [% error]

x ¼ 0.010 [% error]

x ¼ 0.015 [% error]

x ¼ 0.020 [% error]

a (Å) b (Å) c (Å) V (Å3) a ¼ g (
) b (
)

13.15493(6) 7.54118(4) 15.07672(7) 1224.998(11) 90.0 125.0120(3)

13.166(4) [0.12] 7.5497(5) [0.12] 15.088(5) [0.11] 1227.90(12) [0.25] 90.0 [0.01] 125.041(7) [0.03]

13.162(3) [0.08] 7.5514(5) [0.14] 15.090(5) [0.12] 1227.69(11) [0.23] 90.0 [0.01] 125.059(6) [0.04]

13.155(5) [0.04] 7.5526(6) [0.16] 15.092(7) [0.15] 1227.37(13) [0.21] 90.0 [0.01] 125.061(10) [0.05]

13.164(5) [0.10] 7.5580(7) [0.23] 15.098(7) [0.19] 1229.18(16) [0.35] 90.0 [0.01] 125.087(6) [0.07]

13.165(4) [0.11] 7.5537(7) [0.18] 15.112(6) [0.27] 1228.34(15) [0.28] 90.0 [0.01] 125.178(7) [0.14]

sample, the density was 7.78 g/cm3, which is equivalent to 93.5% of the theoretical density. In general, considering the percentage errors, the density increased from 7.03 to 7.78 g/cm3, as showed in Fig. 3. This behavior was probably due to CaCO3 acting as a sintering aid in the Bi2Sn2O7 samples, similar to Bi2O3 in ZnO varistor ceramics [51]; MgO or CaO in GdSmZr2O7 pyrochlore ceramics [52,53], transparent YAG ceramics [54] and SiC [55]; CuO in AgSbO3 n-type semiconductor ceramics [56]; LiF in MgAl2O4 spinels [57]; or CaO in zirconia toughened alumina (ZTA) [58]. The calcium carbonate with an aragonite structure used in the doped-Bi2Sn2O7 has a melting point of ~800
C, and it had the potential to promote the liquid phase sintering of the Bi2Sn2O7 samples, since they were heated to 1050
C. In this process, the sintering aid has a melting point lower than the host material; it works as a wetting liquid for the solid grains of this material; and it generally enhances the mass transportation by point defect formation similar to oxygen vacancies [59]. An increase in conductivity is also a consequence of the addition of the sintering aid in the material [60,61], by virtue of these point defects. It is noteworthy that a conductivity elevation should be observed in samples reported here, since it was observed for the aliovalent doping of pyrochlore samples [62]. In a work to be published elsewhere, the dielectric response of the Bi2Sn2O7 samples and conductivity dependence will be reported. Fig. 4 presents the microstructures of all of the investigated Bi2xCaxSn2O7-x/2 ceramics. The FESEM images corroborate the results for the density discussed above: higher values were observed for higher Ca-doping levels. Also, the FESEM images exhibit the morphology of the samples, i.e., the grain size distribution. In general, the samples contained grains that were quite uniform (regular shape), with no signatures of secondary phases, which is in accordance with the XRD results. Note that the pure sample

Fig. 3. Density evolution of the Bi2-xCaxSn2O7-x/2 ceramics with increasing calcium concentration (the red line is a general guide). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

(x ¼ 0.000) had a certain number of pores, since the grains were large and therefore did not allow greater compactions. In fact, the density of this sample was ~84.5% of the theoretical density, and when the calcium ions replaced the bismuth ions in Bi2Sn2O7, the grains were considerably reduced by comparing the pure sample (Bi2Sn2O7) with any of the doped ones. This behavior can be explained by the occurrence of liquid phase sintering due to the presence of CaO, which promoted Bi2Sn2O7 pulverization, improved compaction, reduced pores, and thus increased the final density. In fact, this corresponds to the behavior observed in Fig. 3, which showed the density dependence of the material with the Ca2þ concentration. Comparing the samples, from the sample with the lowest concentration of Ca2þ ions (x ¼ 0.005) to the highest one (x ¼ 0.020), the grains slightly grew by agglutination with their neighbors, reducing the porosity and increasing the pellet compaction. The morphological characteristics of the samples promoted the formation of more defined grains with the increasing doping of the structure, thus confirming a denser material for a higher doping level. The coalescence (formation of necks) between the grains in the sample with x ¼ 0.020 shows that the synthesis process by liquid phase sintering cannot extend the densification. According to Lewis et al. [43], the a-Bi2Sn2O7 phase crystallizes within a monoclinic structure belonging to the space group C4s (#9, Cc), containing eight motifs per unit cell (Z ¼ 8). Their atoms occupy the 4a-Wyckoff sites, with C1 site symmetry, giving rise to 129 optical vibrational modes (64A0 4 65A00 ) at the Brillouin-zone center, according to the nuclear site method of Rousseau et al. [63]. These modes are simultaneously active in both Raman and infrared spectroscopies. The b-Bi2Sn2O7 phase crystallizes into an orthorhombic structure that belongs to the C17 2v space group (#41, Aea2) [43], with Z ¼ 16, where the ions occupy the 8b and 4a Wyckoff atomic sites, with C1 and C2 symmetries, respectively. Such occupied Wyckoff-site symmetries yield a total of 261 Raman modes (63A1 4 66B1 4 64A2 4 68B2), of which 129 are also infrared active (63A1 4 66B1) [60]. Finally, the space group of the gBi2Sn2O7 phase is O7h (#227, Fd3m), with Z ¼ 8, which have the following occupied Wyckoff sites: 16c, 16d, 48f, and 8a for the atoms Bi, Sn, O1, and O2, respectively. In turn, the Wyckoff site symmetries are D3d for 16c or 16d; Cd2v for 48f; and, Td for 8a. These atomic site distributions provide 63 optical vibrational modes, of which 6 are Raman active (A1g 4 Eg 4 4F2g), 7 are infrared active (7F1u), and 12 are silent (3A2u 4 3Eu 4 2F1g 4 4F2u) [60]. Previously reported group-theory calculations for Bi2Sn2O7 considered different space groups for the a- and b-phases: symmetries C2s (#7 or Pc) [41] and C23 (P31 or #145) [42], respectively. For the first phase, 1053 (526A0 4 527A00 ) vibrational modes were predicted at the center of Brillouin zone, while 262 (131A 4 131E) were foreseen for the last phase. Compared with the space groups proposed here for these phases (C4s and C17 2v), the predicted number of vibrational modes was reduced from 1053 and 262 to 129 and 261, respectively. Fig. 5 presents the group-subgroup relationships between the three structural phases, based on the nuclear sitemethod of Rousseau et al. [63]. The transitions a / b and b / g

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Fig. 4. FESEM images (secondary electrons) for the Bi2-xCaxSn2O7-x/2 ceramics: (a) x ¼ 0.000; (b) x ¼ 0.005; (c) x ¼ 0.010; (d) x ¼ 0.015; and (e) x ¼ 0.020.

have group-subgroup relationships of indexes 2 and 48, respectively, according to a calculation performed through the Program SUBGROUPGRAPH of the Section Group-Subgroup Relations of Space Groups in Bilbao Crystallographic Server site [64]. A transformation order (or index) of a subgroup into a group, t, is related to the number of motifs per cell of both structures whose space groups have group-subgroup relationships, according to the relation [65]:

t ¼ ZðHÞ  jPðGÞj = ZðGÞ  jPðHÞj:

(2)

In this equation, jP(G)j and jP(H)j are the point group orders, i.e., the number of symmetry operations of the point groups that are related to the space groups G and H, respectively, while Z(G) and Z(H) are the number of motifs per cell of the groups G and H,

respectively. Fig. 6 shows the Raman spectra of the Bi2-xCaxSn2O7-x/2 ceramics studied here. The inset shows the wavenumber region 50e300 cm1, where the main differences in the vibrational modes were detected after Ca2þ substitution. The Raman spectroscopy was very sensitive to the increase of Ca content at the Bi cation sites, with the bands becoming increasingly broad and less intense with doping, as a general trend. This behavior demonstrates that the phonon lifetime was shortened with increasing of calcium concentration in the Bi2Sn2O7 ceramics. However, there is no evidence for the b-Bi2Sn2O7 phase, inasmuch that the main evidence of the a / b transition is the appearance of a unique and broad mode in the range 50e100 cm1 [66]. Regarding the band intensities that decrease as the calcium concentration increases, this is related to

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Fig. 5. Normal modes of vibration for the three phases of BSO and the correlations among their irreducible representations.

Fig. 6. Raman spectra of the Bi2-xCaxSn2O7-x/2 ceramics. The inset shows the wavenumber range 50e300 cm1 highlighting the differences exhibited by the Ca2þ substitution into the lattice.

the polarizability reduction that accompanies the substitution of Bi3þ (a ¼ 6.12 Å3) for the Ca2þ ion (a ¼ 3.17 Å3), since the Raman intensity is dependent on the ionic polarizabilities. It is worth noticing that the number and frequencies of the observed Raman bands did not change with Ca2þ doping, within the experimental resolution. This is because the system didn't show appreciable changes in the crystal structure and cell volume, respectively (see Tables S1eS5). A sum of Lorentzian curves was used to fit the Raman spectra of Bi2Sn2O7 in Fig. 7(aed). For the four spectral regions highlighted in Fig. 7, panel b (130e320 cm1) presents the largest number of Raman bands (16 depicted modes). The bands in this region are related to the bending of structures, such as OeBieO and OeSneO, or the stretching of the BieSnO6 structure [67]. Baseline and BoseEinstein corrections of the Raman spectra were performed prior to the adjustments, which allowed us to depict 34 bands out of the 129 predicted modes, as shown in Table 2. Such a reduced number of bands occurs because many modes have either too close wavenumbers or too weak intensities, and so cannot be resolved. On the other hand, they contribute to a natural broadening of some bands and, as a result, a reduced number of features are observed in the spectra. Compared to our previous work [66], 16 new Raman modes were observed, which could be due to the denser samples and better signal-to-noise ratio obtained in the present work.

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Conversely, the overtones or combination bands previously observed at 825 cm1 did not appear in the current spectra. The tentative assignment of the room-temperature phase (a-Bi2Sn2O7 phase) was gathered from our previous work [66] and is also presented in Table 2. Such an assignment was based on the attribution of the Raman and infrared modes for the 13 previously identified vibrational modes of geBi2Sn2O7, and for this reason 21 out of 34 bands were not attributed. In centrosymmetric materials, based on symmetry, the selection rules for Raman and infrared spectroscopies are mutually exclusive, i.e., they cannot be broken, and the Raman modes cannot be seen in the infrared spectrum and vice-versa. However, this rule can be broken if defects are present in the material, when some modes of the infrared spectrum can appear in the Raman spectrum and viceversa. In bismuth-based pyrochlore materials, which have the centrosymmetric space group Fd3m (O7h or #227), the random displacement disorder of the bismuth ion from its ideal site position can result in a relaxation of the symmetry and, in turn, the selection rules. In fact, some bismuth-containing oxide pyrochlores, such as Bi2Ti2O7 [67,68], leak infrared modes in the Raman spectra below 200 cm1, which should also be the case for Bi2Sn2O7. The displacement of the BSO ions from their ideal pyrochlore site positions is such that the space group Cc (C4s or #9) is assumed by the room-temperature phase of BSO, instead of preserving the symmetry Fd3m. In addition, according to Fig. 5, the infrared modes belonging to the ideal pyrochlore structure of Bi2Sn2O7 (F1u) are correlated to the A0 and A00 modes of the room-temperature phase, allowed by symmetry in the Raman spectra of this last phase (in fact, the A0 and A00 modes of a-BSO are simultaneously active in Raman and infrared spectra). To the best of our knowledge, this is the first time that the infrared spectra of the Bi2-xCaxSn2O7-x/2 ceramics (shown in Fig. 8) have been obtained. The infrared reflectivity spectra show very subtle differences with the increase of calcium ion concentration at the bismuth cation sites, in contrast to the Raman spectra. The infrared beamwidth (250 mm) is larger than the grain sizes (~1 mm) of the Bi2Sn2O7 ceramics, according to the FESEM images showed in Fig. 4, and the reflected signal collected at the detector is an average of the grain contributions. Therefore, the infrared reflectivity spectra correspond well to the oriented-averaged spectra of all directions of the polycrystalline sample. The small Ca concentration did not sufficiently change the dielectric function to significantly influence the main polar mode responses. As the samples presented quite similar infrared spectra, the Bi2Sn2O7 sample was used for an analysis within the fourparameter semiquantum (FPSQ) model [69], and good agreement with the infrared reflectivity data was obtained, according to Fig. 9. In such a model, the light reflectivity for low incidence angles approximately obeys Fresnel law,



pffiffiffiffiffiffiffiffiffiffi
εðuÞ  1
2

R ¼
pffiffiffiffiffiffiffiffiffiffi
:
εðuÞ þ 1


(3)

3 (u) in this approach is the frequency-dependent dielectric function and according to the FPSQ model is given by

εðuÞ ¼ ε∞

2 N U2 Y j;LO  u þ iugj;LO j¼1

U2j;TO  u2 þ iugj;TO

:

(4)

The band profiles of the infrared spectrum are then modeled by Lorentzians and the parameters ULO and UTO stand for the frequencies of the longitudinal and transversal optical branches of the jth phonon, respectively. The complex dielectric function, 3 (u), has poles at the frequencies UTO, while it has zeros at the frequencies

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V.M. Lima et al. / Journal of Alloys and Compounds 786 (2019) 1030e1039

Fig. 7. Raman spectra of the Bi2Sn2O7 sintered ceramics: (a) 50e130 cm1; (b) 140e320 cm1; (c) 320e450 cm1; and (d) 480e625 cm1. The experimental data are shown as the black squares, and the red line is the fitting curve. The individual Lorentzian lines are shown in dark green. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

ULO. Furthermore, gLO and gTO correspond in this order to the dampings (full widths at half maxima) of ULO and UTO. To obtain the € nig transstarting parameters for modelling 3 (u), the Kramers-Kro formation of the infrared reflectivity is usually performed. With this procedure, the optical functions, including the imaginary parts of the dielectric constant, Im[3 (u)], and its reciprocal, h”(u) ¼ Im[1/ 3 (u)], are calculated. Then, at the peaks of Im[3 (u)] and h”(u), the frequencies in these positions coincide with the poles and zeros of 3 (u), respectively. Finally, taking the frequencies and corresponding full widths at half maxima at these positions, the initial parameters are obtained for adjusting 3 (u) with the four-parameter semiquantum model. Adopting the FPSQ model [69], it was possible to depict 22 out of the 129 (64A0 4 65A00 ) foreseen modes for this phase, according to Table 3. This table also presents the effective dielectric strength of the jth phonon, D3 j, which can be calculated by the following expression

Dεj ¼

ε∞

U2j;TO

Q  Q

k

ksj

U2k;LO  U2j;TO





U2k;TO  U2j;TO

:

(5)

If the high frequency dielectric constant, 3 ∞, is summed together with the phonon dielectric strengths, the static dielectric constant in the microwave region, 3 0, is obtained. The Clausius-Mossotti prediction for the static dielectric constant of the a-Bi2Sn2O7 phase yields 3CM ¼ 21.9, which corresponds to a reflectivity of R0 ¼ 0.42 at low frequencies. This is in full agreement with the experimental infrared data (30 ¼ 24.2),

according to Fig. 9 and Table 3. For the calculations of 3CM, it was assumed that the polarizability of the a-Bi2Sn2O7 ceramic is 31.97 Å3, with a molar volume is 153.1 Å3. On the other hand, the experimental values found in this work for the high frequency dielectric constant and unloaded quality factor were 3∞ ¼ 5.3 and Quf ¼ 56.9 THz, respectively. The last parameter is the reciprocal of the dielectric loss tangent and along with 3 0 are important merit factors to evaluate if a material has a potential application in MW circuitry. The dielectric merit factors (30 and Qu  f) of BSO are very similar to those of the mullite BiMn2O5 (BMO) addressed in a previous work [70], for which 30 ¼ 28.4 and Quf ¼ 55.4 THz. Such values for the quality factor and dielectric constant of BSO and BMO are relatively high and suitable for applications in MW circuitry, as long as the temperature coefficients of the resonant frequency (tf) are near zero [71]. Furthermore, the quality factor has a strong dependence on porosity since moisture in the pores decreases the Quf value [71]. As both BSO and BMO have densities of ~90% of the theoretical density, this is one of the reasons for the relatively high value for this parameter. Finally, as the bands in the Raman and infrared spectra of the aBi2Sn2O7 ceramic have the same symmetry, we present all of the vibrational modes in Table 4 obtained from both techniques. A total of 45 modes were obtained for the room-temperature phase of Bi2Sn2O7, from which 11 appeared simultaneously in the Raman and infrared spectra. Note that the frequencies of the transverse optical phonon branch, UTO, were used to characterize the infrared modes (these are the frequencies that correspond to the absorption of the infrared light due to the lattice vibrations).

V.M. Lima et al. / Journal of Alloys and Compounds 786 (2019) 1030e1039

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Table 2 Raman active phonons of pure Bi2Sn2O7 depicted after the fitting of the experimental curve with Lorentzian lines. The assignments are related to the ideal pyrochlore structure. Mode # Wavenumber (cm1)

Assignments [63]

Current work Previous work [66] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

58 62 71 79 89 94 97 101 114 143 151 154 157 163 170 177 188 198 209 228 242 252 260 282 288 339 359 383 396 414 494 519 539 615 e

e e 73 82 e 92 e 104 e 139 147 155 e e e e 193 e 208 230 e 248 e 274 e 338 e 382 400 e 506 e 532 600 825

O0 eBieO0 bending (F1u) A2u

A2u O-Bi-O bending (F1u) O-Bi-O bending (F1u)

Bi-SnO6 stretching (F1u)

Fig. 9. Reflectivity spectrum of Bi2Sn2O7 ceramics at room-temperature (the experimental data are showed as black squares) and its fitting (red line) with the fourparameter semi-quantum model [69]. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

F2g Eg O-Sn-O bending (F1u)

Bi-O stretching (F1u) O motion in SnO60 polyhedra (F2g) Bi-O0 stretching (F1u) O0 -vacancy stretching (A1g) Overtone or combination

Table 3 Dispersion parameters of the complex dielectric function for the Bi2Sn2O7 ceramics, obtained from the adjustment of the infrared-reflectivity data with the fourparameter semi-quantum model. Mode #

Uj,TO

gj,TO

Uj,LO

gj,LO

D3j

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

83.2 137.5 142.0 163.7 183.3 202.0 217.6 241.5 252.5 265.0 320.1 331.5 371.0 395.8 419.9 491.8 515.4 557.5 589.5 605.4 679.8 726.2

10.9 30.6 16.2 5.2 15.5 16.4 9.4 18.9 9.9 11.0 14.8 19.2 25.1 19.7 32.3 21.2 34.8 18.5 14.7 31.3 24.2 20.0

87.0 137.9 159.0 164.0 185.0 216.0 225.5 250.2 258.1 266.8 325.4 363.8 389.8 403.8 461.9 493.5 542.9 559.0 590.1 657.8 683.0 727.4

8.4 15.7 22.5 7.2 10.4 9.7 20.9 10.1 14.5 11.2 13.6 24.5 19.8 28.6 32.9 19.8 35.0 14.9 13.3 24.8 24.0 20.0

2.532 0.683 5.590 0.025 0.496 3.368 0.171 0.870 0.116 0.067 1.604 1.652 0.314 0.106 0.469 0.033 0.351 0.012 0.018 0.403 0.009 0.006

3∞

Fig. 8. Infrared reflectivity spectra of the Bi2-xCaxSn2O7-x/2 ceramics. The experimental data for different compositions are presented as a stack sequence (step 0.04) for better visualization: x ¼ 0.000 (black line); x ¼ 0.005 (red line); x ¼ 0.010 (blue line); x ¼ 0.015 (green line); and x ¼ 0.020 (orange line). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

4. Conclusions Bi2-xCaxSn2O7-x/2 ceramics were obtained by solid-state synthesis and sintered at a high temperature. Raman and infrared

¼ 5.3;

30

¼ 3∞þSD3 ¼ 24.2; Qu  f ¼ 56.9 THz.

spectroscopies were performed to analyze their vibrational properties, in which 34 bands were depicted by Raman scattering and 22 modes were detected using infrared spectroscopy. It was also verified that, converse to infrared spectroscopy, Raman scattering is quite sensitive to the morphological features of the samples. FESEM micrographs of the sintered samples showed that such sensitivity is linked to the grain size, which were larger than the visible incident beamwidth in Raman scattering, but smaller than the infrared observation region. Therefore, infrared spectroscopy includes contributions from the average of several grains, while Raman spectroscopy evaluates contributions from single grains. The dielectric merit factors of the Bi2Sn2O7 ceramics were also obtained from infrared spectroscopy, namely 30 ¼ 24.2 and Quf ¼ 56.9 THz. Finally, it is worth noting that this work reports the first investigation of infrared spectra of Bi2-xCaxSn2O7-x/2 materials.

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V.M. Lima et al. / Journal of Alloys and Compounds 786 (2019) 1030e1039

Table 4 Vibrational modes (frequencies in cm1) of the Bi2Sn2O7 ceramics from the Raman (R) and infrared (IR) spectroscopies. Mode #

R

IR

Mode #

R

IR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

58 62 71 79 89 94 97 101 114 e 143 151 154 157 163 170 177 188 198 209 e 228 242

e e e 83 e e e e e 138 142 e e e 164 e e 183 202 0 218 e 242

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

252 260 282 288 e e 339 359 e 383 396 414 e 494 519 539 e e e 615 e e

253 265 e e 320 332 e e 371 e 396 0 420 492 515 e 558 590 605 e 680 726

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