Structure and relaxor ferroelectric behavior of novel tungsten bronze type ceramic, Sr5BiTi3Nb7O30

A novel lead-free tungsten bronze type ceramic Sr5BiTi3Nb7O30, was prepared by a conventional solid-state reaction route. The room-temperature crystal structure shows an average structure with centro-symmetric space group P4/mbm identified by synchrotron XRD. Temperature dependence of dielectric permittivity indicates that Sr5BiTi3Nb7O30 is a ferroelectric relaxor with Tm near 260 K. The ceramic displays stronger frequency dispersion and lower phase-transition temperature compared with Sr6Ti2Nb8O30. A macroscopic and phenomenological statistical model was employed to describe the temperature dependence of their dielectric responses. The calculated size of polar nanoregions (PNRs) of Sr5BiTi3Nb7O30 compared with Sr6Ti2Nb8O30 implies that the stronger diffusion phase transition for the former is related to the disorder emerged in both A and B sites. The smaller PNRs can be activated at lower temperature but have smaller electrical dipole moment. This is the origin of relaxor behavior of Sr5BiTi3Nb7O30 with lower Tm and dielectric permittivity. The PNRs is related to a local structure with a polar space group P4bm, which contributes to the dielectric frequency dispersion of relaxor behavior. This work opens up a promising feasible route to the development of relaxor ferroelectrics in tungsten bronze type oxides.


Introduction
Tungsten bronze (TB) type ferroelectrics, A12A24C4B12B28O30, with diffuse phase transition (DPT) behavior are known for their extraordinary physical properties, such as high electro-optic, piezoelectric and nonlinear optical efficiencies and have been investigated for years. 1,2The structure consists of a network of corner-sharing BO6 octahedra, which form tetragonal (A1) and pentagonal (A2) channels occupied by various distinct metal cations, respectively.Smaller triangular (C) channels are filled (or partially filled) by small low-charged cations such as, e.g., Li + ions. 36Ti2Nb6O30 (STN) is one such tungsten bronze type ferroelectric, whose structure was investigated extensively.It was reported with tetragonal P4bm symmetry, 4 Cmm2 symmetry 5 and Pba2 space-group symmetry. 68][9] However, later work by Whittle et al. 10 suggested that STN forms with Pna21 symmetry and a ~12.36×12.40×7.76Å 3 unit cell instead.3 Recently, the relaxor and ferroelectric behavior have been reported for M5RTi3Nb7O30 structures (M = Ba and Sr; R represents the larger rare earth ions ranging from La to Dy and also Bi). [14][15][16] In M5RTi3Nb7O30 tungsten bronzes, the relaxor behavior originates from disordered distribution of M and R ions on the A1 sites (tetragonal) and small size difference between M and R ions.
However, the nature of the relaxor behavior in the quaternary tungsten bronzes and its relation with compositions are not yet clear.In order to describe the dielectric response, the Curie-Weiss law was proposed to describe the temperature dependence of dielectric permittivity.Unfortunately, it is only suitable for the temperature above Tm, which means it cannot account for the mechanism correctly.Several models [17][18][19] were also proposed to quantitatively describe the temperature dependent dielectric permittivity of diffused phase transition (DPT).One of the popular models is the Gaussian function with a mean value 0 and a standard deviation to describe the character of DPT. 20,21The derived expression is: here ∞ is the contribution from electronic and ionic polarization, and 0 is a temperature and frequency-dependent parameter.Later, a new and simple empirical equation for a phenomenological description of ()near Tm was proposed by Santos and Eiras 22 : Where =1 indicates a "normal" ferroelectric phase transition, while =2 represents a so-called "complete" DPT. is considered as an empirical diffuseness parameter that indicates the degree of the DPT.The merit of this equation is that it provides a good fitting of experimental data at temperatures around and above the dielectric dispersion region.However, it has limitations in describing the entire temperature range of () and illustrating non-symmetric peaks around Tm in relaxor.
In this work, the structure of Sr5BiTi3Nb7O30 (SBTN) was determined from synchrotron X-ray diffraction and an approach based on the macroscopic and phenomenological statistical model was employed to analyze the dielectric response of Sr5BiTi3Nb7O30 ferroelectric ceramics around and above the dielectric dispersion region.The results were compared with those of Sr6Ti2Nb6O30 (STN) 8 , suggesting that stronger frequency dispersion results from the disorder existing in both A and B sites.

Experimental procedures
Sr5BiTi3Nb7O30 ceramic was prepared by solid-state reaction technique, using high-purity SrCO3, Bi2O3, TiO2, Nb2O5 powders as starting materials.After ball milling, the mixtures were sintered in high-purity alumina crucibles at 1200 o C in air for 4 h, whereafter, the disks annealed at

Results and discussion
3.1 Crystal structure and microstructure High-resolution synchrotron X-ray powder diffraction was utilized to investigate the crystal structure of SBTN ceramic.Zhu et al reported the structure of Sr4(La1-xSmx)2Ti4Nb6O30 23 belongs to space group P4bm, where La 3+ and Sm 3+ ions randomly distribute at A1 site and Ti 4+ and Nb 5+ ions randomly locate at B site.Li et al. found that Sr5RTi3Nb7O30 9,16 (R = La, Sm) belongs to a centrosymmetric space group P4/mbm.Furthermore, the Ba-containing tungsten bronzes 24 also belong to centrosymmetric space group P4/mbm, just the same as Sr5RTi3Nb7O30.
In our work, X-ray powder diffraction data of SBTN can be indexed as a tetragonal tungsten bronze structure, and refined with centrosymmetric space group P4/mbm, through the Rietveld refinement as shown in Fig. 1.Since the diffraction data were collected at room temperature above Tm (the temperature corresponding to the maximum of dielectric permittivity), it should be a paraelectric phase with a centro-symmetry.All peaks are indexed with the tungsten bronze phase with a = b= 12.34195( 6) Å and c = 3.87675(2) Å, except some weak peaks consistent with a cubic cell with a=b=c= 4.25 Å.A complete list of atomic coordinates for the refinement of SBTN against synchrotron X-ray powder diffraction data is provided in Table Ⅰ.

Dielectric characterization
Temperature-dependence of the dielectric permittivity at frequencies of 500 Hz, l kHz, 10 kHz, 100 kHz and 1 MHz for SBTN is shown in Fig. 3.It is seen that the dielectric permittivity peaks at different frequencies exhibit a broad shape, which is similar to that of other tungsten-bronze compounds with relaxor behavior. 25Moreover, the temperature corresponding to the maximum dielectric peak (Tm) moves towards higher temperature with increasing frequency.The SBTN ceramic shows a larger dielectric permittivity at 260 K, which may be attributed to thermally activated reorientation of dipole moments of polar nanoregions as well as the motions and interactions of the polar nanoregion boundaries. 26cording to Zhu et al. independent of the cation distribution in the A site, larger difference in radius of A-site ions always causes normal ferroelectric transition. 27In their study, Sr5RTi3Nb7O30 (R = La, Nd, Sm, Eu) 27 ceramics shows a larger difference in radius between the A1 and A2 sites, which reduces the overlap distribution between the two cation sites and enhances octahedral distortion, making ferroelectric transformation easier.Although a larger difference exists in A site in our work, the ceramic only exhibits relaxor-like behavior rather than a normal ferroelectric-paraelectric transition (Fig. 3), suggesting the dielectric anomaly may be dominated by the disorder in A and B sites.For tungsten bronze compounds, long-range dipolar coupling may be disrupted into polar clusters, which dominates the relaxation behavior at lower temperature.Considering the dielectric relaxation in SBTN, the disorder in A and B sites should be responsible for the removal of long-range dipolar coupling.( 2 ), and 845 cm -1 ( 1 ), corresponding to internal vibrational modes of the (Ti/Nb)O6 octahedra.
The internal mode 2 splits into two broad peaks at 515 cm -1 and 605 cm -1 , and the mode υ 1 also splits into two broad peaks at 833 cm -1 and 913 cm -1 .Owning to the broad nature of the Raman lines, deconvolution is utilized to reduce each Raman vibration.The Gaussian profile is used as the Raman vibration fitting model as shown in Fig. 5.The room-temperature spectrum is deconvoluted into eight peaks, denoted as 1, 2, 3, …, 8. Peak 3 (240 cm -1 ) belongs to the internal mode 5 , peak 5 (515 cm -1 ) and 6 (605 cm -1 ) belong to the internal mode 2 , whereas peak 7 (833 cm -1 ) and 8 (913 cm -1 ) belong to the internal mode υ 1 .The O-Ti/Nb-O stretching vibration 2 shows an asymmetric shape, which deconvolutes into two vibrations at 515 cm -1 (peak 5) and 605 cm -1 (peak 6).Two aspects should be considered for the splitting of the internal modes: (1) the influence of external vibrations, which reflect the motions of the A-site cations; (2) the distorted octahedron and deviation from the ideal octahedral symmetry.In SBTN, the radii of Sr 2+ and Bi 3+ dominate the bonding requirements of the cations and determine the tilting type and distortion extent of the oxygen octahedra, which frustrates ferroelectric long-range order and result in the relaxor behavior. where where is the static permittivity, ∞ is the permittivity at very high frequency, is the angular frequency, is the mean relaxation time, is the Cole-Cole parameter. And where s (0<s<1) is a constant, 1 (from free charge carrier) and 2 (from space charge) both are conductivity.
The room-temperature dielectric response can be described by Eqs.(4a) and (4b) as shown in Fig. 6.It is interesting to note that good agreement between experimental and calculated data over a wide frequency range for both ' and '' well supports the model.The obtained parameter (0.713) is much smaller than 1, suggesting a strong interaction between PNRs, which is the nature of relaxor ferroelectrics rather than space charge polarization or charged carries hopping.The conductivity ( 1 ) resulting from free charge carrier and the conductivity ( 2 ) due to the space charges are 8.706 x10 -12 S and 9.977 x10 -11 S, respectively.Both of them are very low, indicating an intrinsic dielectric at room temperature.

2) Fitting dielectric permittivity
To further probe the relaxor behavior, the degree of disorder or diffusivity (γ) can be obtained by the modified Curie-Weiss law 30,31 : where ' is the dielectric permittivity at Tm, ' is the Curie constant, γ is an exponent indicating diffusivity, ranging from 1 (a normal ferroelectric) to 2 (an ideal relaxor ferroelectric).The fitting result of as a function of ( − ) for SBTN at a frequency of 10 kHz is shown in Fig. ( is the Curie-Weiss temperature and C is a constant), only applies to temperatures much higher than Tm.The fitting parameters for SBTN are C=1.41×10 5 and =89.9 K.The Curie constant with a magnitude of 10 5 suggests SBTN to be a displacement-type ferroelectric.Recently, a macroscopic and phenomenological approach 32,33 was proposed to describe the dielectric response of ferroelectric relaxors in temperatures both below and above Tm.In such a model, individual dipoles which complies with the Maxwell-Boltzmann distribution at a given temperature are categorized into two groups.The first group consists of dipoles with lower kinetic energies ([N2( ,T)]) than potential wells ( ), whereas the second group ([N1( ,T)]) can escape the wells and have more freedom in terms of orientations.It is not difficult to imagine that the two distinguishing dipoles contribute significantly different amounts to the dielectric response of ferroelectric relaxors.The total number of dipoles(N) is equal to the sum of two groups.The relationship between those parameters is given by the following expressions: where is the Boltzmann constant, T is the absolute temperature, and erfc is the complementary error function.The total susceptibility is given by: here 1 , and 2 , are responses that correspond to 1 , and 2 , , respectively.
is the measurement frequency, and .
According to this model, the temperature dependence of dielectric permittivity is proposed as follow 32 : where 1 , 2 , b and are constants at a given frequency.We applied Eq. ( 9) to describe the dielectric response associated with polar nanoregions (PNRs) in SBTN ceramic and Sr6Ti2Nb8O30 (STN) 8 ceramic to better understand the ferroelectric relaxor nature.Clearly, both of them show satisfactorily fitting results in Fig. 8, which means that it is an effective way to describe the dielectric response of ferroelectric relaxors over the whole temperature range.The genesis of can be traced back to the random field attributed to cation disorder.The of SBTN and STN are 0.071 eV and 0.134 eV, respectively.According to Landau-Devonshire, 34,35 represents the energy barrier density for reorientation of a PNR ranging from 10 5 ~10 7 J m -3 .can describe as * , represents the volume of a single PNR.The volume of a PNR for STN and SBTN is calculated to be 2.15 × 10 -27 m 3 and 1.04 × 10 -27 m 3 , respectively.Corresponding the calculated size of PNRs ( 3) for STN and SBTN are 1.29 nm and 1.01 nm, respectively, which suggests that SBTN has smaller polar clusters due to the disorder in both A and B sites.Furthermore, SBTN has a greater number of dipoles that overcome potential wells than STN at room temperature.It suggests that the dielectric response of ferroelectric relaxor may be related to the active dipoles that overcome the potential wells.The dielectric permittivity is related not only to the number of active PNRs but also to the size of active PNRs (electrical dipole moment).Due to higher disorder in SBTN, the size of PNRs is smaller than that of STN, as a result, the dielectric permittivity is lower than that of later.The diffuseness exponent of the phase transition, , is calculated to be 1.42 and 1.62 for STN and SBTN, respectively, which confirms that the dielectric anomaly of SBTN could originate from the disorder at both A and B sites.
It has been stated that when 1 is close to 1 in Fig. 9(c), the corresponding temperature is the freezing temperature . 33The value of STN is close to 1 around 300 K, but drops to zero at high temperature (~600 K), resembling the Fermi-Dirac function.Due to limited temperature measurement range of dielectric permittivity, the of SBTN is below 200K.The PNRs of SBTN can be activated at lower temperature due to smaller size.As the temperature increases to higher than , the value of 1 monotonously decreases.Although the structure of SBTN belongs to centrosymmetric space group P4/mbm at room temperature, a non-centrosymmetric, could be P4bm, may exit in a local structure (PNRs), which contributes to the dielectric frequency dispersion of relaxor behavior.

1000 o C for 2 h
to obtain highly dense ceramics.The diffraction pattern of Sr5BiTi3Nb7O30 was measured using high-resolution synchrotron X-ray radiation (λ = 0.413 420 Å) at the beamline MSPD at ALBA (Barcelona, Spain).The crystal lattice parameters were refined by the Rietveld method using the FULLPROF program.The morphology of sintered sample was evaluated using secondary electrons images of Field Emission Scanning Electron Microscopy, FE-SEM (Hitachi S-4800).Dielectric properties in the range of 210 K to 690 K were measured with TZDM-200-800.P-E hysteresis loop was obtained from TFANALYZER-2000.A Thermo Scientific DXR Raman microscope (Waltham, MA) controlled by the software (Thermo Scientific Omnic) for room temperature Raman measurements was employed.The dielectric properties of the sample were measured using Impedance Analyzer (Agilent 4294A) in the frequency range from 40 Hz to 110 MHz at room temperature.

Fig. 1
Fig.1The synchrotron X-ray powder diffraction date for SBTN (black) with a simulated pattern for the P4/mbm

Fig. 3
Fig. 3 Temperature dependence of dielectric permittivity and dielectric loss for SBTN

Fig. 4 5 .
Fig. 4 Polarization (P) as function of applied electric field (E) measured at room temperature for SBTN

Fig. 6
Fig. 6 Frequency dependence of ' (a) and '' (b) at room temperature.The red solid curves are the best fits to

Fig. 8
Fig. 8 Fit of dielectric permittivity obtained at 1M Hz for SBTN ceramic (a) and STN ceramic (b)

Fig. 9
Fig. 9 The Maxwell-Boltzmann distribution versus temperature of SBTN (red line) and STN (black line) is

Table Ⅰ .
Atomic coordinates for SBTN resulting from refinement against synchrotron X-ray powder diffraction date Morphology of the sintered SBTN ceramic is shown in Fig.2.The average grain size is about 3.8 μm and exhibits a compact characteristic.Most of grians are hexagon, suggesting the grains growth is complete.