Correlation among Dielectric Properties, Vibrational Modes, and

Article pubs.acs.org/JPCC

Correlation among Dielectric Properties, Vibrational Modes, and Crystal Structures in Ba[SnxZn(1−x)/3Nb2(1−x)/3]O3 Solid Solutions Chuanling Diao and Feng Shi* College of Physics and Electronics, Shandong Normal University, Jinan 250014, P. R. China ABSTRACT: Ba[SnxZn(1−x)/3Nb2(1−x)/3]O3 (x = 0.0, 0.16, 0.226, 0.32, 0.4) solid solution ceramics were synthesized by the conventional solid-state reaction method. Crystal structures are studied by X-ray diffraction, and vibrational modes are obtained by Raman spectroscopy and Fourier transform far-infrared reflection spectroscopy. The correlation among dielectric properties, lattice vibrational modes, and crystal structures are discussed by analyses of vibrational modes. Spectroscopic and structural data show sensitivity of dielectric properties to structures of samples with Sn4+ concentration, and optimized dielectric properties of Ba[SnxZn(1−x)/3Nb2(1−x)/3]O3 are found where x = 0.32. The changes of unit cell parameters and the bulk densities of the samples with Sn4+ concentration are discussed. The changes of dielectric properties with the Raman modes and their full width at half-maximum are obtained. The frequencies of phonon modes are determined, and the widths of phonon modes are related to ionic radii for the Sn4+ substitution in the B-site. The disappearance of the imaginary part of the dielectric constant peaks may be closely related to the dielectric properties of the BSZN system.

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INTRODUCTION Ba(B′1/3B″2/3)O3-type microwave dielectric ceramics (B′ = Mg, Zn, Ni, or Co; B″ = Ta and Nb) are promising materials that could be used widely as components of resonators and filters (since they have the advantages of a suitable dielectric constant εr, a near zero value for the temperature coefficient of the resonant frequency τf, and a high quality factor Q.1,2 Ba(Zn1/3Nb2/3)O3 (BZN) ceramics, with a cubic lattice constant of a = 4.094 Å, have microwave dielectric properties of εr = 41, Q = 5600 at 10 GHz, and τf = 28 × 10−6/°C reported by Kim et al.,3 while BaSnO3 ceramics (εr = 14), with a cubic lattice constant of a = 4.1163 Å, have a high positive value of the temperature coefficient of the capacity (τc) due to its temperature coefficient of the dielectric constant, τε = +180 × 10−6/°C. Both BZN and BaSnO3 belong to the simple perovskite cubic structures (Pm3m̅ ); therefore, a wide range of solid solutions may be prepared by the substitution of quadrivalent Sn4+ ions for divalent Zn2+ and pentavalent Nb5+ ions in the B-sites simultaneously to form BaSnxZn(1−x)/3Nb2(1−x)/3O3 (BSZN).4 According to the equation τε = τc − αL, where αL is the coefficient of linear thermal expansion, it is possible for BSZN ceramics to have an ideal τf value (2τf = −τc − αL). X-ray diffraction (XRD), Raman, and Fourier transform farinfrared (FTIR) reflection spectroscopic techniques are useful tools to investigate the phonon modes and the crystal structures of the solid solutions.5−8 For example, XRD and Raman spectroscopy were used by Dias et al.9 to evaluate the crystal structures and the phonon modes of (Ba1−xSrx)(Mg1/3Nb2/3)O3 microwave dielectric ceramics and to verify the presence of the phase transition. Masaaki et al.10 studied the (Ba 1−xSrx) (Mg 1/3Ta 2/3)O 3 solid solutions with Raman © 2012 American Chemical Society

spectroscopic techniques and observed an abnormal behavior of the dielectric constants and obtained the relationship with the structural changes. Dias et al.11 used FTIR spectroscopic techniques to evaluate the dielectric properties of Ba(Mg1/3Nb2/3)O3 and determined which phonon and vibrational modes made great contributions to the dielectric properties. Wang et al.12 studied the far-infrared reflection spectrum and IR-active modes of MgTiO3 and concluded that the optical modes have great influence on the microwave dielectric constant and the dielectric loss. Toru et al.13 studied the anomaly in the infrared active phonon modes and the relationship with the dielectric constants of the (Ba1−xSrx)(Mg1/3Ta2/3)O3 compounds, finally verifying that the tilting of the oxygen octahedron clearly affects the polar phonon modes of the compounds. Poulet et al.14 determined which of the lattice vibrational modes are either infrared active or Raman active according to the selection rules. Subsequently, Dong et al.15,16 in our group used Raman and FTIR together to study the vibrational spectra and the structural characteristics of the Ba[(Zn1−xMgx)1/3Nb2/3]O3 as well as the (Ba1−xSrx)(Zn1/3Nb2/3)O3 solid solutions, and they finally obtained the correlation between the vibrational modes and the structural characteristics. However, so far, there is no report about applying the lattice vibrational modes to study the relationship between the crystal structures and the dielectric properties in the Ba[SnxZn(1−x)/3Nb2(1−x)/3]O3 solid solutions. Received: December 21, 2011 Revised: January 27, 2012 Published: February 29, 2012 6852

dx.doi.org/10.1021/jp2123289 | J. Phys. Chem. C 2012, 116, 6852−6858

The Journal of Physical Chemistry C

Article

To clarify the concrete relationship among the crystal structures, the lattice vibrational spectra, and the dielectric properties, Raman and FTIR spectra are employed together to study BSZN, i.e., Ba[SnxZn(1−x)/3Nb2(1−x)/3]O3 (x = 0.0, 0.16, 0.226, 0.32, 0.4), solid solutions in this article. The results are discussed in terms of the variation of the crystal structures and the dielectric properties caused by the substitution in the B-site, which could also correlate with the X-ray diffraction (XRD) data. We hope that our work provides some reference values relevant to research concerning the correlation among the lattice vibration modes, the crystal structures, and the dielectric properties for the Ba(B′1/3″B2/3)O3-type microwave dielectric ceramics.

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EXPERIMENTAL SECTION

The raw materials were analytically pure (AR) BaCO3, SnO2, ZnO, and Nb2O5 powders. Ba[SnxZn(1−x)/3Nb2(1−x)/3]O3 (BSZN, x = 0.0, 0.16, 0.226, 0.32, 0.4) solid solutions were synthesized by a conventional solid-state sintering technique. Oxide compounds were mixed for 12 h in polyethylene jars with zirconia balls and then dried and calcined at 1100 °C for 2 h. After remilling, the powders were dried and pressed into discs of 15 mm × 1 mm and next sintered at 1500 °C for 3 h. A Hewlett-Packard 4278A capacitance meter was used to test capacitance (C) and dielectric loss (tan δ, Q = 1/tan δ) at 1 MHz. The dielectric constant (εr) was calculated by the equation εr = (14.4Cd)/D2, where D and d are the average diameter and the thickness of the sample, respectively. The temperature coefficient of the capacitance (τc) was calculated by the equation (C85 − C25)/60C25, where C85 and C25 are the capacitances of the samples at 85 and 25 °C, respectively. Archimedes’ principle was used to test the bulk density (ρv) of all the samples using the equation ρv = (m0/m1 − m2)ρwater, where m0, m1, and m2 are the weight after drying, the weight in the air, and the weight in water, respectively. X-ray diffraction analyses (XRD) were carried out on a Rigaku D/max-rB X-ray diffractometer with CuKα incident source, in the 10−120° 2θ range (0.02°, 2θ step size, and 1 s per step). Raman scattering spectra were collected at room temperature using a Nexus 670 spectrometer, equipped with a liquid-N2-cooled CCD detector and an Olympus BXL microscope (100× and 20× objectives). The measurements were done in backscattering geometry using a Nd:YVO4 laser at 514 nm line as the excitation source (10 mW). The accumulation times were typically 10 collections of 5 s, and the spectral resolution was better than 2 cm−1. The FTIR spectra were obtained at room temperature using a Bruker IFS 66v FTIR spectrometer with high sensitivity DTGS detector, and the laser source is He−Ne. The reflection method used in IR measurement is of specular-reflection. The surface of the pellet was carefully polished using micrometer-scale Al2O3 powders (which rubbed off about 20 μm) before testing the XRD, Raman, and FTIR.

Figure 1. XRD patterns for the BSZN solid solutions sintered at 1500 °C for 3 h. The values of x are indicated in the figure.

peaks of a second phase appear for the samples where x = 0 or x = 0.16, which are considered to be Ba5Nb4O15 (No.14-0028) caused by Zn loss. The (420) peaks (shown in the inset image) shift to lower angle with increasing Sn4+ concentration, which indicates an increase in the lattice constants and the lattice volumes. Figure 2 presents the unit cell volumes, the lattice constants, and the dielectric constants εr of the BSZN solid solutions, which were calculated according to the cubic structures. The radii of Zn2+, Nb5+, and Sn4+ ions are 74, 64, and 69 pm, respectively, and the calculated average ionic radii in the B-site of the BSZN solid solutions with the SnxZn(1−x)/3 Nb2(1−x)/3 formula are given in Table 1. It is obvious that the lattice constants (a) as well as the cell volumes increase with the increasing Sn4+ ions, consistent with the changes shown in Figure 2, and the average radius of the B-site increases steadily with the substitution of the Sn4+ ions for Zn2+ and Nb5+ ions, as shown in Table 1. According to the logarithm admixture law, the dielectric constant decreases with the increases in the Sn4+ content because the dielectric constant of the BZN ceramic is 41, while that of the BS ceramic is only 14, which is similar to the study reported by Sun et al.17 Raman spectra are widely used to determine the relationship between the lattice vibrational modes and the resonant patterns. Raman spectra of the BSZN system are shown in Figure 3, over the range 50 to 900 cm−1, and are assigned according to the related compounds of Ba(Zn1/3Ta2/3)O318 and Ba(Mg1/3Ta2/3)O3.1 There are five main assigned peaks, which are concerned with the spectra of the 1:1 nanoscale regions of the Fm3m symmetry.1 In addition, two other peaks are observed, i.e., Eg(O) at about 170 cm−1 and A1g(Nb) at about 290 cm−1, which correspond to the 1:2 ordered structures. The changes of Raman shifts and the full width at halfmaximum (fwhm) values are two important parameters to distinguish Raman normal modes. All phonon modes (frequencies and fwhm values) are shown in Table 2.

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RESULTS AND DISCUSSION The XRD patterns of different Sn4+ content BSZN ceramics, shown in Figure 1, were indexed according to the JCPDS cards (Joint Committee on Powder Diffraction Standard) No.170182 and No.15-0780. It is observed that the main phases of the samples are the BSZN solid solutions with cubic symmetry structures. A few 6853



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Figure 2. Correlation of unit cell volumes, crystal constants, and dielectric constants εr of the BSZN solid solutions with Sn4+concentration.

Setter et al.23 have verified that the changes of the lattice constants are related to the difference in the ionic radii in the Bsites. It is obvious from the calculated B-site radii in Table 1 that the radii of the B-site ions increase steadily due to the replacement of the Zn2+ and Nb5+ ions by Sn4+. The ordering degree increases, and the dielectric loss values reduce accordingly with the increases in the Sn4+ content according to ref 23. However, the dielectric loss values of the samples increase greatly for 0.32 ≤ x ≤ 0.4. It is suggested that this abnormal behavior is caused by an increased porosity due to lower bulk densities as compared with the sample x = 0.32. With the increasing Sn4+ content, the bulk densities ρv increase steadily, where x ≤ 0.32. However, when x ≥ 0.32, the values of the bulk densities of the samples decrease rapidly and reach a minimum value for x = 0.4. The changes of the bulk density ρv are sensitive to the Sn4+ content in the BSZN solid solutions (Figure 4), which may be one of the reasons that the BSZN solid solutions have the lowest dielectric loss value, where x = 0.32 due to lowest porosity, and of course, higher porosity will decrease the dielectric constant of the system with different Sn4+ content, which is one of the reasons that the sample x = 0.32 has the largest dielectric constant value. In Table 2, a maximum value of 46.9 in the fwhm of the A1g(Nb) modes is found at x = 0.226. The values of τc increase from −68.8 × 10−6/°C to 5.9 × 10−6/°C, while the dielectric constants decrease from 37.6 to 30.1, in agreement with the logarithm admixture law. To sum up, the BSZN ceramics where x = 0.226 and x = 0.32 have the excellent dielectric properties. The relationship among Raman shifts, fwhm values, and the dielectric properties (dielectric constant εr, temperature coefficient of the capacitance τc, and dielectric loss tan δ) in BSZN solid solutions are shown in detail in Figure 5. Figure 5a shows the correlation among Raman shifts of the A1g(Nb) modes, the εr, and the temperature coefficient of the capacitance τc. The Raman modes and the εr decrease synchronously with the increase in the Sn4+ content, which indicate that the Raman modes of A1g(Nb) correlate closely with the dielectric constants and that the results agree with the results of Webb et al.18 With the increasing Sn4+ content the τc values decrease accordingly, which indicate that the Raman shifts of the A1g(Nb) modes and the τc values have an opposite

As shown in Table 2, no change in the frequencies and the fwhm values of the F2g(Ba) [F2g(Ba) = Eg(Ba) + A1g(Ba)] modes is observed. Region A in Figure 3 shows the 1:2 ordered structure-related vibrations,19 and the Eg(O) and A1g(Nb) modes that shift to the lower frequencies. The Eg(O) modes have small red-shifts for x ≤ 0.16, and more significant redshifts for x ≥ 0.226 and 0.32. However, for the samples with x ≥ 0.32, this trend reverses with a small blue-shift for x = 0.4. It is worth noting that a splitting appears in the F2g(O) [F2g(O) = A1g(O) + Eg(O)] modes in Region B. On the basis of the analyses of the crystal symmetries, the localized 1:1 ordered F2g mode splits into A1g and Eg modes when the long-range 1:2 order is preserved.20 The splitting of the F2g(O) modes with red-shift shows the appearance of the 1:2 ordered structures, and the fwhm values of Eg(O) modes, which are related to the O2− ions in BaSnO3 at about 390 cm−1, reach a minimum value of 18.4 for x = 0.32. The frequencies of the Eg(O) modes, which correlate with O2− ions in BZN at about 435 cm−1, almost have no change, while the fwhm values show a slight increase for x ≥ 0.16. The modes near 720 cm−1 with red-shift in Figure 3 are the oxygen-octahedral stretch A1g(O) modes of BSZN (the O2− ions located in the face-centered sites of the cubic structure, i.e., O(3e)), which shift to the lower frequency with the increase in the Sn4+ content, and the other A1g(O) modes at about 788 cm−1 are related to the O2− ions (O(6i)) in the oxygen octahedra of the BSZN system, which have almost the same frequencies with the increase in Sn4+ content, i.e., no oxygen octahedron distortion occurs on the whole BSZN system, which also proves that the BSZN system keeps the same cubic structure, in accord with the XRD results. The modes at about 500 cm−1 have not been discussed yet,21,22 but it is clear that the intensities and the fwhm values of the modes are sensitive to the content of Sn4+ ions, and the oxygen-octahedral stretch modes play an important role on the microwave properties.21 As shown in region B of Figure 3 and in Table 2, the Eg(O) mode of the sample x = 0.32 possesses the strongest intensity with the lowest fwhm value of the five samples, which indicates that this sample has the highest ordering degree in these five samples and, accordingly, has the lowest dielectric loss value. 6854



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Table 1. Ionic Radii of the B-Site in BSZN Solid Solutions radius of B-site Sn4+ content (mol %)

pm

0 0.16 0.226 0.32 0.4

67.3 67.6 67.7 67.9 68.0

Figure 4. Relationship between the bulk density ρv and the Sn4+ content in the BSZN solid solutions.

From Table 2 and the Raman spectral analyses, we can conclude that Raman shifts of the A1g(Nb) modes are related to the dielectric constants εr and the temperature coefficient of the capacitance τc, the Raman shifts of the Eg(O) modes and the fwhm values of the A1g(Nb) modes are related to the tan δ values. In short, the relationship among the Raman shifts, the fwhm values, and the dielectric properties were obtained by the analyses of the Raman spectra. Infrared reflection spectra caused by the absorption of the polar lattice vibration24 enable us to have a complete understanding of the lattice vibration. Fourier transform infrared reflection spectra ranging from 50 to 700 cm−1 are presented in Figure 6. The spectral profiles are similar to each other, as shown in Figure 6. However, the substitutions of Sn4+ ions cause a variation in intensity and position of the reflection bands. According to the analyses of Ba(Zn1/3Ta2/3)O320 and Ba(Mg1/3Ta2/3)O3,25 the modes below 160 cm−1 are related to the vibration of the Ba2+ ions. The modes above 500 cm−1 are related to the O−(ZnNb)−O, O−(ZnSn)−O, and O−(SnNb)−O bending modes. The modes between 180 and 300 cm−1 are concerned with the (ZnNb)O6, (ZnSn)O6, and (SnNb)O6 stretching modes. In comparison to BZN, new polar modes appear at 250 cm−1 for the BSZN solid solutions where x ≥ 0.16,

Figure 3. Raman spectra of the BSZN samples in the range 100−900 cm−1. The assignments for the phonon modes are indicated in the figure.

changing trend. The changes of the tan δ values, the frequencies of the Eg(O) modes,18 and the fwhm values of the A1g(Nb) modes are also obtained with increasing Sn4+ content, as shown in Figure 5b. Obviously, the tan δ values reach a minimum value at x = 0.32, similar to the shifts of the Eg(O) modes. The fwhm values of A1g(Nb) modes increase where x ≤ 0.226 and then decrease where x ≥ 0.226, showing an opposite trend as compared with that of the tan δ values, which is caused by more ordered phases in the samples where x = 0.226 and x = 0.32. This phenomenon shows that the dielectric loss values are closely related to the fwhm values, which is consistent with the results of Webb et al.18

Table 2. Phonon Mode Parameters (Frequencies and fwhm Values) from Raman Data BZN A1g (Ba) Eg(Ba) Eg(O) A1g(Nb) A1g(O) Eg(O) Eg(O) A1g(O) A1g(O) εr τca tan δb a

0.16

0.226

0.32

0.4

frequency (cm−1)

fwhm

frequency (cm−1)

fwhm

frequency (cm−1)

fwhm

frequency (cm−1)

fwhm

frequency (cm−1)

fwhm

105.5 116.9 170.4 293.2 374.7

12.4 7.8 15.6 34.3 26.8

434.4

20.0

784.8 41.2 −68.8 1.85

30.2

105.5 116.9 168.4 284.7 360.5 391.4 435.8 721.5 784.8 37.6 −43.6 0.61

12.4 7.7 11.4 39.2 17.8 25.0 14.6 30.3 31.4

105.5 117.8 154.9 277.2 360.5 393.3 435.8 716.9 786.8 34.9 −16.1 0.5

12.4 7.5 12.6 46.9 12.9 22.4 16.5 31.2 30.6

105.5 116.9 140.7 271.8 356.4 391.4 435.8 716.9 788.7 32.9 −11.5 0.45

12.9 7.7 12.1 44.5 16.8 18.4 16.7 30.9 28.8

105.5 116.9 142.6 268.0 354.4 387.6 435.8 714.6 788.7 30.1 5.9 2

13.4 7.6 10.8 41.3 33.2 19.9 16.9 31.6 27.4

Value × 10−6/°C. bValue × 10−4. 6855



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Figure 5. Relationship among A1g(Nb) phonon modes, fwhm values, and the microwave dielectric properties for the BSZN solid solutions: (a) Raman shifts and dielectric constant; (b) fwhm value and capacitance temperature coeffecient value of τc; (c) Raman shifts, fwhm value, and dielectric loss.

with the other modes. They almost disappear for x ≥ 0.226, which may be closely related to the dielectric properties because excellent dielectric properties appear for x = 0.226 and x = 0.32. As for εi = ((εs − ε∞)εT2γ)/(ε[4(εT − ε)2 + γ2]), the resonant frequency ωT of the vibrator can be determined from the imaginary part of the dielectric constant when εi(ω) reaches a maximum value. Six obvious peaks are observed in Figure 7 ranging from 50 to 700 cm−1 through Lorenz fitting, which shift to lower frequencies with the increase in the Sn4+ content. In Figure 8, the y axis {ω(x) − ω(0)}/ω(0) represents the peak frequencies shift normalized to the peaks frequency of BZN. The frequencies of the peaks 1, 2, and 5 increase with the increasing Sn4+ content, while the other peaks decrease accordingly. All of the peaks present a linear change with the increase in the Sn4+ content.

as shown by the downward arrows in Figure 6, and the polar modes with higher intensities at about 475 cm−1 shift to lower frequencies with increasing Sn4+ content. The equation of the dielectric constant frequency is ε(ω) = εr(ω) + iεi(ω), where the imaginary part characterizes the absorption characteristics of the vibrator to the electromagnetic wave. One of the widely adopted standard methods to obtain the vibrator parameters from the reflection spectra is Kramers− Krönig analysis (K−K analysis for short). We just use the K−K analysis to obtain the imaginary parts of the dielectric constants, which are described in Figure 7 (the peaks are numbered from lower to higher frequency as 1 to 6). The peaks change in shape, intensity, and position with the increase in the Sn4+ content. It is noted that the modes 3 and 4, as shown by the downward arrows in Figure 7, have lower intensities as compared 6856



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CONCLUSIONS The Ba[SnxZn(1−x)1/3Nb2/3]O3 (BSZN, x = 0.0, 0.16, 0.226, 0.32, 0.4) solid solution ceramics were synthesized by a conventional solid-state reaction method at 1500 °C for 3 h. The crystal structures were evaluated by X-ray diffraction (XRD); Raman and Fourier transform far-infrared (FTIR) reflection spectroscopy techniques were used together to investigate their vibrational phonon modes. Changes of the crystal unit cell constants were indicated by the XRD peaks, which shift to the lower angle, and the changes of dielectric properties with the crystal constants are discussed. The splitting of F2g(O) modes was found in Raman spectra. Changes of the dielectric constant εr, the temperature coefficient of the capacitance τc, and the dielectric loss tan δ with the Raman modes and their full width at half-maximum values were obtained. The appearance of new polar modes in FTIR and the disappearance of the imaginary parts of the dielectric constant peaks were discussed. In short, the concrete relationship among the crystal structures, the lattice vibrational spectra (phonon modes), and the dielectric properties were clearly clarified.

Figure 6. Fourier transform far-infrared reflectivity between 50 and 700 cm−1 for the BSZN solid solutions.

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AUTHOR INFORMATION

Corresponding Author

*Tel/Fax: + 86 531 86182521. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Figure 7. Imaginary part of dielectric constants εi(ω) calculated from Kramers−Krönig analysis for the BSZN solid solutions in the far-IR region (50−700 cm−1).

Figure 8. Variation in the frequencies of the peaks in εi(ω) of BSZN with Sn4+ concentration. 6857



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Correlation among Dielectric Properties, Vibrational Modes, and

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