The existence of local tetragonal distortions is evidenced in the BaTiO3xBi(Zn1/2Ti1/2)O3 (BT–xBZT) relaxor dielectric material system at elevated temperatures. The local and average structures of BT-xBZT with different compositions are characterized using in situ high temperature total scattering techniques. Using the box-car fitting method, it is inferred that there are tetragonal polar clusters embedded in a non-polar pseudocubic matrix for BT-xBZT relaxors. The diameter of these polar clusters is estimated as 2–3 nm at room temperature. Sequential temperature series fitting shows the persistence of the tetragonal distortion on the local scale, while the average structure transforms to a pseudocubic paraelectric phase at high temperatures. The fundamental origin of the temperature stable permittivity of BT-xBZT and the relationship with the unique local scale structures are discussed. This systematic structural study of the BT-xBZT system provides both insight into the nature of lead-free perovskite relaxors, and advances the development of a wide range of electronics with reliable high temperature performance.

Many emerging technologies such as micro-flight systems, electric-powered vehicles, and renewable energy generation devices have electrical energy storage requirements that are not met by existing materials and devices.1,2 Existing energy storage technologies require a tradeoff between power density and energy density. For example, fuel cell and battery technologies provide high energy densities, but have limited power densities because of the sluggish nature of their charge storage mechanism.1,3 Therefore, there is a demand to develop new energy storage materials that exhibit both high power density and high energy density. One promising class of materials for the new generation of energy storage materials is ceramic capacitors. The most common currently used material in this class is the BaTiO3 (BT)-based multilayer ceramic capacitors, which can reach the X9R level of the Electronic Industries Association standards by chemical modification, in which X9R represents ±15% variability of capacitance over the −55 to 175 °C temperature range.4–7 However, traditional ferroelectric-based dielectric materials suffer a significant permittivity drop and an increase of dielectric loss when the temperature exceeds 200 °C. Considering the growing demands of electronic devices that operate in harsh environments, efforts have been made to discover new materials with properties that persist at higher temperatures.

The concept of complex solid solutions with the perovskite ABO3 structure has been a mainstay of the capacitor community and new materials with a relatively high permittivity, temperature insensitivity, and frequency dependent character have been reported.8–10 The in-service temperature can be extended to above 200 °C, which is an improvement in conventional BT-based dielectric materials. These materials are referred to as temperature-stable relaxor dielectrics due to the broad frequency-dependent permittivity. In general, two types of lead-free perovskite systems have been widely examined for high temperature performance: BT-based11–14 and Na1/2Bi1/2TiO3(NBT)-based15–18 solid solutions. Zeb and Milne provided a systematic performance study of the different temperature-stable relaxor dielectrics.19 To obtain BT-based relaxor dielectrics, the general method is to modify the normal ferroelectric BT with Bi(M)O3, where M indicates the trivalent equivalent cations on the B-site of the perovskite structure, such as Fe3+, Sc3+, (Zn1/2Ti1/2)3+, and (Mg2/3Nb1/3)3+. The performance of various BT-Bi(M)O3 relaxor dielectrics has been reported and summarized by others.19–22 

Traditional ferroelectric-based dielectrics with high temperature properties may be strongly contributed by compositional segregation in a core-shell microstructure.4,21 However, this core-shell type of microstructure has not been comprehensively reported in the new generation of temperature-stable relaxor dielectrics. Even though the compositions of relaxor dielectrics are similar to those of normal ferroelectric compounds, in which the high permittivity arises from domain interactions, the lack of hysteresis and the negligible saturation indicate the absence of domain interactions in relaxor dielectrics.23,24 Therefore, relaxor dielectrics are fundamentally different from traditional ferroelectric-based dielectrics although they exhibit similar high temperature properties. It has been hypothesized that the mixed site occupancy, lattice scale heterogeneity, and subtle compositional variations might be the chemical and structural origins of these unique properties. Due to the lack of fundamental studies of the structure-property relationships in this class of materials, the mechanism underlying these anomalous dielectric properties is not entirely known.

In this study, one BT-Bi(M)O3 solid solution that has been reported to have desirable high temperature stable performance, (1–x)BT-xBi(Zn1/2Ti1/2)O3 (BT-xBZT), is examined.23–26 Previous dielectric measurements show a crossover from normal ferroelectric-like behavior to relaxor-like behavior when the BZT concentration is increased to x =9% and above. Laboratory X-ray diffraction (XRD) suggests a phase transition from a tetragonal to ‘rhombohedral-like’ (or pseudocubic) structure with increasing BZT concentration in this solid solution, and a critical composition for this transition is around x =0.09.23,24,27 Usher et al. presented a detailed structural description for the BT-xBZT system at room temperature using high resolution XRD, neutron diffraction, and neutron pair distribution function (PDF).28 However, in situ crystal structure studies at elevated temperatures of BT-xBZT and other BT-Bi(M)O3 material systems are yet unavailable. In situ XRD and total scattering techniques enable the crystallographic study of various materials under different stimuli (temperature, pressure, stress, electric field, etc.), which can offer valuable information to interpret structure-property relationships.29–33 Here, we conducted in situ high-temperature synchrotron total scattering experiments on the BT-xBZT material system with selected compositions. The purpose of this study is to examine the local environment on the A-site, to study the distortions at the local scale, and furthermore, to elucidate the average and local structure for compositions across the BT-xBZT phase diagram, both at room temperature and at elevated temperatures. The average and local structural changes with increasing temperature and varying composition can give insight into the mechanism of high temperature relaxor dielectrics, which may help to interpret and to engineer the properties.

Bulk polycrystalline ceramics of BT-xBZT with compositions of x =0.06, 0.08, 0.10, and 0.20 were prepared using a conventional solid state synthesis technique. The details of reactants and synthesis procedures are described elsewhere by Triamnak et al. and Usher et al.28,34 Ceramic pellets were obtained after sintering at 1200 °C for 2 h. The bulk samples were polished, painted with silver paste, and then examined by using a LCR meter (Agilent 4284A model, Agilent Technologies, Inc., Santa Clara, CA). The permittivity and dielectric loss of the BT-xBZT samples were recorded upon cooling over a wide temperature range of −150 to 200 °C with frequencies of 25–250 kHz. The sintered pellets were crushed into powders and then annealed at 400 °C for 3 h to reduce the induced stress for the following X-ray investigation. In addition, the bulk ceramic samples were polished and thermally etched at 800 °C for 30 min, and then cooled to room temperature with a 5 °C/min cooling rate. The microstructures were investigated with a field-emission scanning electron microscope (FE-SEM) (Verios XHR model, FEI, Corp., Hillsboro, OR). The grain size was determined from stereological analyses of the FE-SEM images using the ImageJ program.35 

In situ X-ray total scattering measurements were performed at beamline 11-ID-B of the Advanced Photon Source at Argonne National Laboratory, with an X-ray wavelength of 0.13702 Å (90.49 keV). The powder samples were loaded in quartz capillaries, and heated from room temperature to 500 °C with a ramp rate of 5 °C/min using resistive heating coils in the sample environment. Total scattering patterns were recorded on a Perkin Elmer flat-panel amorphous-silicon 2-D detector with a collection rate of 20 s per pattern. This method can capture structure changes in a temperature increment as small as 1.67 °C during the in situ heating procedure. The 2-D total scattering images were integrated and reduced to 1-D patterns using Fit2D.36 Within the PDFgetX3 package,37 background subtraction, normalization, and Fourier transform were performed on each 1-D total scattering structure function S(Q), converting the data to a G(r) PDF pattern. The maximum scattering vector (Qmax) used for Fourier transform is above 23 Å−1, which is suitable for PDF analysis.38–40 Peak fitting of selected PDF peaks was conducted using a Gaussian profile. Real-space refinements of the in situ PDF patterns were carried out in PDFgui using the least-squares minimization method.41 

The dielectric properties of BT-xBZT were characterized as a function of temperature and frequency. Figure 1 shows the real part of dielectric relative permittivity (ε) and dielectric loss (tanδ) for BT-xBZT samples at various frequencies (f) and temperatures (T). BT-0.06BZT exhibits classic ferroelectric-like behaviors: a sharp peak of permittivity as a function of temperature, the temperature of maximum permittivity (Tm) is frequency independent, and the ε versus T curves do not exhibit obvious frequency dispersion. With a BZT concentration of 0.08, the permittivity peak becomes broad as a function of temperature, Tm decreases with increasing frequency, and a strong frequency dispersion of ε and tanδ is observed. These behaviors suggest relaxor-like dielectric behavior for BT-0.08BZT. With a BZT content of 0.10, the frequency dispersion of ε and tanδ is enhanced and the permittivity peak is broader still. For BT-0.20BZT, the diffusive permittivity peak is further broadened, and a temperature-insensitive plateau develops. The relative permittivity of BT-0.20BZT remains around 1500 for temperatures up to 200 °C, while the dielectric loss is relatively small, confirming that BT-0.20BZT belongs to the class of temperature-stable relaxor dielectrics.

FIG. 1.

Temperature dependent dielectric permittivity (ε) and dielectric loss (tanδ) at various frequencies for BT-xBZT, where x =0.06, 0.08, 0.10, and 0.20, respectively (arrows indicate the direction of increasing frequency).

FIG. 1.

Temperature dependent dielectric permittivity (ε) and dielectric loss (tanδ) at various frequencies for BT-xBZT, where x =0.06, 0.08, 0.10, and 0.20, respectively (arrows indicate the direction of increasing frequency).

Close modal

For a normal ferroelectric material, the permittivity follows the Curie-Weiss (CW) law above the Curie temperature (TC), as shown by the linear response of inverse permittivity (1/ε) versus T.42 The (1/ε) as a function of T for BT-xBZT measured at 100 kHz is shown in Fig. S1 in the supplementary material. Deviation from the CW law is observed for all the compositions above Tm. For example, BT-0.06BZT has a Tm of 71 °C, while the linear fitting of (1/ε) versus T shows that the deviation temperature (Tdev) is 136 °C, which is well above Tm. The deviation from CW law in BT-0.06BZT reveals the minor relaxor character in this ferroelectric-like material. With increasing BZT concentration from 0.06 to 0.10, the deviation from the CW law becomes larger, and Tdev decreases from 136 °C to 131 °C. In addition, the TC obtained by fitting the CW law (x-intercept of the fit line) decreases significantly with a small amount of BZT modification: TC decreases from 20 °C to −123 °C when BZT content changes from 0.06 to 0.10. Notably, the linear fitting of BT-0.20BZT (1/ε) versus T curve gives a line nearly parallel to the x-axis, with a slope of 2.38 × 10−7 and x-intercept of −2505 °C as shown in Fig. S1 (supplementary material). Clearly, these physically impossible values indicate the strong temperature stable character in BT-0.20BZT composition. Due to the high resistivity in BT-0.20BZT, the dielectric measurement can be performed at higher temperatures. Therefore, for BT-0.20BZT, the maximum measurement temperature was extended to 500 °C, and the new (1/ε) versus T curve is presented in Fig. S2 (supplementary material), in which the permittivity begins to follow the CW law at above 405 °C. It is worthwhile to note that other compositions with relaxor behavior (e.g., x =0.08, 0.10) may also not strictly follow the fitted line in Fig. S1 (supplementary material) with further increase in the dielectric measurement temperatures. This is because the CW law was originally used to describe a ferroelectric in the paraelectric phase, and the pseudocubic phases in relaxors are fundamentally different from the paraelectric phase of traditional ferroelectrics. To better describe the dielectric behaviors in the high temperature region, a modified CW law was proposed and employed for the dielectric relaxors.10,25,43 Further extension of the dielectric measurement temperature for x =0.06 to 0.10 was not successful due to the significant decrease in resistivity and increase in dielectric loss. Nonetheless, Fig. S2 (supplementary material) demonstrates excellent high temperature stable permittivity in BT-0.20BZT compared to other compositions. The grain size for all compositions is about 1–2 μm, and the representative SEM images are shown in Fig. S3 in the supplementary material. The samples with x =0.08, 0.10, and 0.20BT show clear microstructures and grain boundaries, while for x =0.06, segregation is observed at the grain boundaries. According to the study of Triamnak et al.,34 the sintering temperature increases with decreasing BZT concentration, suggesting that the thermal etching temperature for low-BZT compositions should also be a little higher than that for the high-BZT compositions. However, in this study the thermal etching temperature was fixed to 800 °C for all compositions. The segregation in BT-0.06BZT grain boundaries might come from insufficient diffusion and redistribution of atoms, and a cleaner boundary is expected for BT-0.06BZT with a slight increase in the thermal etching temperature, prolonging the annealing time, or decreasing the cooling rate.

To summarize, with increasing BZT concentration in BT, a transition from a classic ferroelectric-like to relaxor-like material then to temperature stable relaxor is observed according to the dielectric measurements. The incorporation of BZT into BT may involve compositional and site disorder on the A- and B-sites of the perovskite structure. Considering that the properties of a ferroelectric or dielectric material are strongly correlated with the crystal structure, the study of the local and long-range structure as a function of temperature is necessary and important.

The experimental PDF, G(r), is obtained by a direct Fourier transform of the total scattering structure function, S(Q), as

Gr=2π0QSQ1sinQrdQ,

where Q is the scattering vector or momentum transfer, and r is the atom-atom distances.44 Figure 2(a) shows the reduced structure function, Q(S(Q)1), of BT-0.06BZT at room temperature. The inset is a magnification of the high-Q region, indicating a good signal-to-noise ratio. The signal only begins to decay at Q 23 Å−1, which is suitable for PDF analysis. Figure 2(b) shows a representative G(r) pattern covering the range from sub-ångström up to 50 Å, showing the connection from the local structure to long-range structure. The inset of Fig. 2(b) shows the magnification of the local PDF peaks: the first characteristic peak (at r 2.8 Å) represents the A-sites to oxygen (A-O) pairs, followed by the nearest A-B pairs at r 3.4 Å and the nearest A-A and B-B pairs at r 4.0 Å. The peak representing the shortest B-O pairs should be at r 2 Å, but is obscured by the intrinsically weak scattering of Ti/Zn-O when using X-ray radiation and the presence of termination ripples (a normal artifact due to the Fourier transform) at low-r.

FIG. 2.

(a) Reduced structure function, Q(S(Q)1), of BT-0.06BZT at room temperature. The inset is a magnification of the high-Q region, indicating a good signal-to-noise ratio. (b) PDF of BT-0.06BZT at room temperature after Fourier transform, the inset shows the magnified area of low-r PDF data, and the major atom pairs which contribute to the local PDF peaks are indicated.

FIG. 2.

(a) Reduced structure function, Q(S(Q)1), of BT-0.06BZT at room temperature. The inset is a magnification of the high-Q region, indicating a good signal-to-noise ratio. (b) PDF of BT-0.06BZT at room temperature after Fourier transform, the inset shows the magnified area of low-r PDF data, and the major atom pairs which contribute to the local PDF peaks are indicated.

Close modal

The room temperature PDF patterns for all the BT-xBZT compositions are shown in Fig. S4 in the supplementary material. At the local scale, i.e., r range of 2–6 Å as shown in Fig. S4(a), the peaks overlay each other for different compositions with almost no peak position difference, suggesting the local structure has no obvious changes as a function of composition. Peak fitting of the first three PDF peaks confirmed this statement: as shown in Fig. S4(b) (supplementary material), the position difference for a specific set of low-r PDF peaks is within the error bars. The peaks in a high-r range shift to the right side, suggesting that the addition of BZT into BT expands the lattice, and the expansion of the unit cell accumulates at a longer length scale, resulting in obvious peak shifts at high-r. This observation agrees well with other reported average structure studies of BT-xBZT at room temperature.23,24,28 Another interesting observation is the increase in peak width and decrease in height with increasing BZT concentration. A previous PDF study suggested that this decrease in peak height is partially due to the change in scattering factors as a function of composition.28 To test this theory, an ABO3 model with a pseudocubic structure was created, in which the composition is allowed to vary but the structure remains unchanged. The corresponding PDF patterns were then calculated to investigate the effect of scattering factors on the peak shape. Figure S4(c) shows that the X-ray scattering factor difference between Ba2+ and Bi3+ or between Ti4+ and Zn2+ has negligible impact on the PDF peak heights (supplementary material). Instead, it is likely that static disorder induced by BZT modification dominates this broadening effect.

To determine the structure of BT-xBZT at room temperature, PDF refinements were conducted for all compositions at two different length scales: 2–10 Å for the local scale, and 10–30 Å for the intermediate scale. Four plausible phases were used for refinements: cubic Pm3¯m, rhombohedral R3m, orthorhombic Amm2, and tetragonal P4mm. These four phases were selected because these structures are widely reported in BT-based perovskite structure studies, e.g., BT has a Pm3¯mP4mmAmm2 → R3m phase transformation with decreasing temperature,45,46 the local structure of Sn-doped (Ba,Ca)TiO3 is reported to be R3m at high temperature and P4mm at lower temperature,47 Zr-doped BT has a R3m local structure,48 Nb-doped BT is reminiscent of a local R3m phase at all temperatures,49 and pure BZT assumes a highly distorted perovskite P4mm structure.50 Therefore, it is reasonable that BZT-modified BT will inherit part of the BT or BZT crystallographic character for local and long-range structures. The fits of each phase to the BT-0.06BZT room temperature PDF pattern are shown in Fig. 3 in the two respective ranges. At the intermediate length scale, tetragonal P4mm gives the best fit indicated by the minimized difference curve and best goodness of fit (GoF) value. The structure represented by the intermediate range PDF data agrees with the average structure XRD studies. This suggests that the intermediate scale structure from PDF approximates to the average structure obtained from XRD refinements. At the local scale, P4mm also gives the best fit compared to other models. The Amm2 model also results in a reasonable GoF, but by examining the actual fit at the local scale, it is clear that the low GoF is a result of the better fit of the termination ripples at around 2 Å, while the fit of PDF peaks is inferior to P4mm, e.g., the fit of the peak at r 9 Å is poor. The same refinement routine was conducted for all compositions, and P4mm is the best model in the local and intermediate scale with all BZT additions. Figure S5 (supplementary material) shows the fit of the BT-0.20BZT PDF data using different models as a representative example of fitting other compositions. It was found that at the intermediate scale, either P4mm or Pm3¯m gives a good fit of the PDF data, but P4mm has a lower GoF value, indicating that a subtle and not negligible tetragonal distortion may exist in the BT-0.20BZT relaxor, corresponding to the “pseudocubic” average structure reported from previous diffraction studies.23,25 At the local scale of the BT-0.20BZT PDF pattern, P4mm is a better fit than Pm3¯m and the GoF difference between these two models is larger than that at the intermediate scale, suggesting that at the local scale, it is more likely tetragonal than cubic.

FIG. 3.

The fits of the BT-0.06BZT room temperature PDF pattern over a range of 2–10 Å and 10–30 Å using four plausible phases: P4mm, R3m, Amm2, and Pm3¯m. The goodness of fit value for each fit is listed.

FIG. 3.

The fits of the BT-0.06BZT room temperature PDF pattern over a range of 2–10 Å and 10–30 Å using four plausible phases: P4mm, R3m, Amm2, and Pm3¯m. The goodness of fit value for each fit is listed.

Close modal

To characterize the length scale dependence of the crystal structure in BT-xBZT at room temperature, a sequential fitting of increasing r-ranges (box-car method) was performed on each PDF dataset. This approach is beneficial when studying how the structure evolves at different length scales, and has been applied to various material systems.28,51–53 In this study, the r-window was fixed to 10 Å, with an increment of 5 Å for the starting and end position of the r-window: 1–10 Å, 5–15 Å, 10–20 Å, etc. The tetragonal P4mm model was adopted for this box-car sequential fitting of all BT-xBZT compositions. The initial parameter values for each individual fitting were input from the refinement results of whole profile fitting (1–50 Å), and the parameters refined during the sequential fitting were: scale factor, lattice parameters (a and c for P4mm), atomic positions, and atomic displacement parameters (ADP). Figure 4 summarizes the box-car fitting results of the lattice parameters for BT-xBZT. The black and red shaded regions in each subplot represent the a and c lattice parameters with standard deviation obtained from whole profile fitting of PDF data (1–50 Å), which can be approximated to the average structure of this material. With increasing BZT concentration, the tetragonality (c/a) decreases, and for BT-0.20BZT, the tetragonality is nearly unity, meaning a cubic-like average structure. Interestingly, all compositions show a structure evolution with increasing length scale: an enhancement of tetragonality is observed for the local scale structure, while the structure in the high-r region is closer to the average structure. This transition is demonstrated in Fig. 4.

FIG. 4.

The box-car fitting results of the lattice parameters a and c for BT-xBZT using P4mm model. The black and red shade lines in each subplot represent the a and c values with standard deviation obtained from whole profile fitting of PDF data (1–50 Å).

FIG. 4.

The box-car fitting results of the lattice parameters a and c for BT-xBZT using P4mm model. The black and red shade lines in each subplot represent the a and c values with standard deviation obtained from whole profile fitting of PDF data (1–50 Å).

Close modal

It is interesting to note that the lattice parameters of local structures have similar values for different compositions (a 3.995 Å and c 4.040 Å), indicating that the local structure across the BT-xBZT system is similar, and the addition of BZT affects the structure only at a longer length scale. The lattice parameters of the BT-xBZT local structure at RT are also in excellent agreement with the long-range structure of undoped BT (a =3.966 Å and c =4.035 Å from Ref. 54 by first-principles calculations, and a =3.992 Å and c =4.036 Å from Ref. 46 by Rietveld refinement of neutron diffraction data). This suggests that the local structure of BT-xBZT (or more generally, the BT-xBi(M)O3 solid solutions) is inherently inherited from the major BT end-member, while addition of other elements on A/B-sites only disrupts the long-range order and not the local atom pair correlations. Similar box-car fitting of PDFs of classic ferroelectrics, e.g., BT or PbTiO3, would likely yield significantly less deviation of the local structure from the long-range structure compared to the chemically modified solid solutions.

We hypothesize that the observed significantly enhanced tetragonal distortion at the local scale for BT-0.10BZT and BT-0.20BZT correlates with the polar nano-region (PNR) theory in the relaxor ferroelectrics literature. According to the PNR theory, nanoscale clusters with a polar phase are embedded in the non-polar matrix and contribute to the anomalous dielectric and ferroelectric behaviors for relaxor ferroelectrics.8,10 The PDF results in this study support the fact that the polar phase of the clusters exists as regions characterized by tetragonal distortions, while at a longer length scale the distortions average out as the matrix. The tetragonal distortion and permittivity are found to be positively correlated. Based on first-principles calculations and experimental measurements of a variety of ferroelectric solid solutions, the tetragonality is coupled to the cation displacements, and therefore coupled to the polarization of the unit cell.55–57 This spontaneous polarization creates dipoles, and dipole moments under an external stimulus, e.g., electric field, result in the high permittivity of dielectrics. It is likely that the observed tetragonal distortions are the origin of the anomalous dielectric permittivity in BT-xBZT, similar to the dielectric observations in the canonical relaxor Pb(Mg1/3Nb2/3)O3 which is attributed to different types of PNR responses.9,10

In addition, the structures from box-car fitting begin to follow the average structure in around the 20–30 Å range, suggesting that the possible polar clusters have a limited diameter of 2–3 nm. Since PDF is a bulk average probe that is sensitive to local structures, the determined polar cluster size is an estimation based on the total scattering from the bulk sample. It is likely that there is a distribution of the polar cluster size across the sample. The box-car fitting method was used with an interval (r-window) of 10 Å and a step increment of 5 Å; a better estimation of the PNR size might be achieved by decreasing the r-window and the step increment in the box-car fitting, but at the cost of fewer data points for each sequential fitting and larger uncertainty of the fitting results. Confidence in the PNR size estimate could also be improved by utilizing an instrument with finer resolution, which would result in observable pair correlations at higher r, although likely at the cost of rapid in situ measurements. Another point to note: it is expected that the tetragonality inside a PNR is not uniform due to the inhomogeneity from charge and compositional disorder in BT-xBZT, but the PDF cannot readily detect the tetragonality distribution within the PNR due to the averaging effect. As the model length scale increases, the longer correlation lengths will contain more atom-atom pairs from matrix-matrix or matrix-PNR correlations than those from the PNR itself, thus resulting in the decreasing tetragonality with increasing r. In addition, inherently local probes, e.g., transmission electron microscopy and scanning probe microscopy, could offer complementary information on the structure and structural fluctuation within the PNRs.

The room temperature X-ray PDF result is consistent with a similar study by Usher et al. using neutron PDF, in which the polar clusters were also shown.28 In the present work, the use of a synchrotron source has the advantage of rapid acquisition time58 compared to a neutron source, which allows parametric in situ studies under external stimuli, such as increasing temperature. The local structural changes with increasing temperature can be captured and studied, as shown in Sec. III C.

The PDF patterns of BT-0.06BZT at selected temperatures obtained by the in situ high temperature scattering technique are shown in Fig. 5. The in situ PDF patterns for other compositions are included in Fig. S6 in the supplementary material. Two features are prominent in Fig. 5: the peaks shift to higher r with increasing temperature, especially for the peaks above 10 Å, and peak broadening occurs. The peak shifts are due to the positive thermal expansion coefficient of BT-xBZT, while the peak broadening is mainly attributed to enhanced thermal motion at higher temperatures, giving rise to a wider distribution of atom-atom distances (r). Whole profile refinement was conducted at selected temperatures using the four plausible single phase models, and Fig. S7 (supplementary material) shows the refined results for BT-0.06BZT at 475 °C as an example. At 475 °C, which is much higher than TC or Tm of this composition, the material should be in its paraelectric phase with a Pm3¯m cubic average structure. However, the phase determination using the least-squares fitting method suggests that tetragonal P4mm remains the most likely representation of the local and intermediate scale PDF data. The reason might be that P4mm allows atomic displacements along the c-axis while in the Pm3¯m prototype perovskite structure the atom coordinates are fixed. Such atomic displacements appear to occur in BT-xBZT even at high temperatures. Using different plausible single phase models to fit PDF patterns at selected elevated temperatures has also been trialed for other BT-xBZT compositions, and the results show that P4mm gives better fits than other structures. Therefore, P4mm is sufficient to describe the most likely phases occurring in the studied temperature range, and was adopted in the following sequential fitting of the temperature series for all the BT-xBZT compositions.

FIG. 5.

The PDF patterns of BT-0.06BZT at selected temperatures obtained by the in situ high temperature total scattering technique.

FIG. 5.

The PDF patterns of BT-0.06BZT at selected temperatures obtained by the in situ high temperature total scattering technique.

Close modal

Crystallographic structure information was determined by sequential fitting of the temperature series (from 25 °C to 475 °C) of BT-0.06BZT, and is presented in Fig. 6. The fitting range is from 1 to 50 Å, and the refined results can be used to approximate the average structure as described in the above section. Figure 6(a) represents the changes in the lattice parameters a and c as a function of temperature: from 25 °C to ∼125 °C, c decreases while a increases, corresponding to the tetragonality decrease in Fig. 6(b). At around 125 °C, the difference between a and c is subtle (<0.15%), and the tetragonality approaches unity. Above 125 °C, increasing temperature only results in a linear increase of c and a, and the tetragonality remains nearly unity. The slopes of a and c curves at high temperature have similar values, suggestive of isotropic thermal expansion above 125 °C. The unit cell volume and isotropic ADP of A-sites atoms have a linear correlation with temperature as shown in Figs. 6(c) and 6(d), with no sharp changes near 125 °C observed. The unit cell behavior of BT-0.06BZT at elevated temperatures suggests that a second-order phase transformation occurs in the vicinity of 125 °C, which can be described as the tetragonal to cubic average structure phase transition. In the sequential fitting, a temperature increment of 50 °C was used to detect the general trend. Thereafter, sequential fitting with an increment of 10 °C was performed on patterns measured from 50 °C to 150 °C to show more details about the structural changes in the vicinity of transformation temperature. The refinement results in the magnified temperature range are shown in Figs. 6(e) and 6(f). It follows the same general trend, and the transition temperature is narrowed to between 125 and 135 °C. The transition temperature identified using whole PDF profile refinement is much higher than Tm of the same composition (71 °C), but has a better agreement with the deviation temperature from the CW law (136 °C). Therefore, our results suggest that the tetragonal distortion persists to above Tm for BT-0.06BZT in the scale range up to 50 Å, resulting in the deviation from the CW law in the temperature range from Tm to Tdev for BZT modified BT samples.

FIG. 6.

Structure information of BT-0.06BZT as a function of temperature extracted from sequential whole profile fitting of temperature series PDF patterns: (a) lattice parameters a and c; (b) tetragonality (c/a); (c) unit cell volume; (d) anisotropic ADP of A-sites atoms where U11=U22≠U33 for P4mm. (e) and (f) show lattice parameters and tetragonality in a magnified temperature range from 50 °C to 150 °C.

FIG. 6.

Structure information of BT-0.06BZT as a function of temperature extracted from sequential whole profile fitting of temperature series PDF patterns: (a) lattice parameters a and c; (b) tetragonality (c/a); (c) unit cell volume; (d) anisotropic ADP of A-sites atoms where U11=U22≠U33 for P4mm. (e) and (f) show lattice parameters and tetragonality in a magnified temperature range from 50 °C to 150 °C.

Close modal

The long-range lattice parameters as a function of temperature for all compositions are summarized in Fig. 7. The unit cell changes of BT-0.08BZT and BT-0.10BZT (in the vicinity of the critical transition point), which show traditional relaxor-like behaviors, are presented. These changes follow the same trend as in BT-0.06BZT, indicating that a tetragonal to cubic transition occurs above the Tm of these compositions. In addition, the transition temperature decreases with increasing BZT concentration, as shown in Fig. 7, suggesting that the addition of BZT disrupts the typical tetragonal distortion in a ferroelectric material, lowering the polar to non-polar transition temperature. For BT-0.20BZT, the average structure is nearly cubic at room temperature, and during heating only a near-linear increase is observed, with the lattice parameters a and c overlaying each other. This behavior indicates that the average structure of the BT-0.20BZT relaxor remains pseudocubic with negligible changes at elevated temperatures. Clearly, the negligible changes with increasing temperature in the pseudocubic average structure are not directly responsible for the high dielectric permittivity. Considering the possible existence of nano clusters (or local tetragonal distortions) in these materials and the fact that these local structures may be closely related to the dielectric permittivity, it is crucial to have a systematic study of the local structural changes as a function of temperature. These results are reported in Sec. III D.

FIG. 7.

The lattice parameters of BT-xBZT average structures as a function of temperature, where x =0.06, 0.08, 0.10, and 0.20.

FIG. 7.

The lattice parameters of BT-xBZT average structures as a function of temperature, where x =0.06, 0.08, 0.10, and 0.20.

Close modal

Referring to the in situ PDF patterns in Fig. 5, it is important to reiterate that the low-r PDF peaks have different behaviors compared to the high-r PDF peaks: peak broadening occurs with increasing temperature for low-r peaks, but the peak position appears unchanged, especially for the first three peaks. Fitting the first three PDF peaks of all the PDF patterns using a Gaussian function confirmed this observation: as shown in Fig. S8(a) (supplementary material) using BT-0.06BZT as an example, the positions of local PDF peaks remain at almost the same value with increasing temperature. In addition, a linear decrease in the peak height and increase in peak width for low-r peaks were also confirmed by this peak fitting method, as shown in Figs. S8(b) and S8(c) (supplementary material). The same trend of low-r peak behaviors with increasing temperature was obtained for all the other compositions. If a phase transition happens at the local scale, we would expect to see shifts of local PDF peak positions, and abrupt changes in the peak shape instead of the linear gradual peak broadening effect. These observations indicate that the local scale structure in BT-xBZT may persist at high temperatures.

Sequential temperature series fitting of BT-xBZT local PDF data was conducted with a scale range from 1 to 10 Å, and the refinement results are summarized in Fig. 8. The maximum temperature for the local PDF refinements is limited to 225 °C rather than 475 °C because significant total scattering signal decay occurs at elevated temperatures due to the increased Debye-Waller factor. Figure S9 (supplementary material) shows the reduced total scattering function Q(S(Q)1) at 225 °C, and the inset clearly shows that the signal terminates at Qmax≈20 Å−1, beyond which is mainly amplified noise. In general, with lower Qmax, the real-space resolution decreases. Therefore, less detailed structural information can be obtained from the higher-temperature data due to the reduced effective Qmax (<20 Å−1).38,44 Consequently, refinements using an r-range of 1–10 Å for PDF patterns above 225 °C give structural information with large standard deviations, and are unsuitable for drawing conclusions concerning the local structure. Therefore, the maximum temperature for local PDF refinements was limited to 225 °C in this study. This limit of 225 °C is higher than the Tm or Tdev of these BT-xBZT compositions and the local scale structure in this temperature range can be used to investigate the temperature-stable permittivity in BT-xBZT relaxor dielectrics.

FIG. 8.

The lattice parameters of BT-xBZT local structures as a function of temperature, where x =0.06, 0.08, 0.10, and 0.20.

FIG. 8.

The lattice parameters of BT-xBZT local structures as a function of temperature, where x =0.06, 0.08, 0.10, and 0.20.

Close modal

Compared to Fig. 7, the local structures as a function of temperature in Fig. 8 exhibit totally different behaviors from the average structure: for all the compositions, the lattice parameter c remains nearly constant with increasing temperature, while the lattice parameter a gradually and slightly increases. The error bars increase at higher temperature due to the enhanced atomic thermal vibration. One important thing to note is that at temperatures as high as 225 °C, the local tetragonal distortion persists, even though the average structure approaches cubic. It is interesting that the local distortion within the 10 Å range is composition independent as well as temperature insensitive. These in situ high temperature PDF measurements suggest the persistence of the BT-xBZT local structures at elevated temperatures, which corresponds to the existence of polar nanoscale clusters according to the PNR explanation. In addition, the box-car method was performed for the PDF of BT-0.20BZT at 125 and 225 °C, respectively, and the lattice parameters a and c at different length scales are shown in Fig. S10 (supplementary material). Even though the local tetragonal distortion persists at elevated temperatures for BT-0.20BZT, e.g., 125 and 225 °C, the tetragonality converges to near unity at a shorter atom-atom distance (r). This infers a decrease in the size of nanoscale polar clusters among the non-polar matrix upon heating.

To summarize, the presence of a local tetragonal distortion in relaxors decreases smoothly with increasing temperature, but can maintain its existence at temperatures above Tm. Box-car fitting of high temperature PDF suggests that the persistence of local polar clusters at elevated temperatures is accompanied by a shrinkage of the cluster size. These nanoscale clusters with tetragonal distortions may be responsible for the large relative permittivity in BT-BZT due to being highly responsive to an external stimulus, e.g., electric-field. Therefore, our systematic PDF study assists in the interpretation of the high temperature dielectric permittivity of the relaxor compositions. In addition, for the ferroelectric-like compositions (e.g., x =0.06), a combination of average and local structure changes with temperature shows evidence that the polar to non-polar phase transformation is order-disorder type, demonstrates how global symmetry may emerge from local symmetry-breaking distortions, and agrees with other theoretical and experimental studies of similar BT-based systems.59–62 The detected local ferroelectric distortions in the current study might be partially induced by the pseudo Jahn-Teller effect,62,63 in which the off-center displacements of the Ti4+ are thought to be maintained in all the phases and phase transitions in BT-xBZT. In addition, the strong covalent driving forces in the Zn-O bond, as well as the tendency of Bi3+ to occupy an offset position, might also be responsible for the local tetragonal distortions. The effects of Zn2+ and Bi3+ on the enhanced tetragonality have been studied and reported in other perovskite systems.53,64–66 On the other side, the addition of Bi3+ on A-sites and Zn2+ on B-sites also starts to break the long-range dipole order and inhibits the formation of a long-range ferroelectric phase, attributed to the higher degree of diffuseness and stronger relaxor character. In general, this study suggests that the local scale ferroelectric distortions (especially in 1–10 Å range) are not affected by the increased disorder at elevated temperatures, resulting in the temperature-stable feature of the dielectric permittivity in BT-xBZT relaxors.

BaTiO3xBi(Zn1/2Ti1/2)O3 polycrystalline ceramics (x =0.06, 0.08, 0.10, and 0.20) were examined by synchrotron total scattering techniques at room temperature and elevated temperatures (25–475 °C), together with dielectric measurements and surface microstructure characterization. For BT-xBZT at room temperature, with increasing BZT concentration, a tetragonal to cubic-like average structure transition was determined, and the local structure within the 10 Å range was identified as P4mm tetragonal for all compositions. Using the box-car fitting method, the evolution from local tetragonal distortion to an average pseudocubic matrix was evidenced, and the size of possible polar clusters was estimated to be 2–3 nm. During heating, a polar to non-polar phase transformation was captured for the ferroelectric-like compositions by whole profile fitting of the in situ PDF data, while the relaxor-like compositions show negligible average structure changes. Examination of the local scale PDF data presents the persistence of tetragonal distortion at elevated temperatures to at least 225 °C, indicating that stable polar clusters exist in BT-xBZT. The persistence of these polar clusters may be the key to the mechanism of temperature-stable dielectric relaxors. Based on the results, the effect of chemical doping Bi3+ and Zn2+ on A- and B- sites was discussed, relating to the increased disorder, off-center displacements of Ti4+, and local ferroelectric distortion. This study demonstrates that the in situ PDF technique can be used to investigate the fundamental mechanism of anomalous properties found in dielectric and ferroelectric materials, and can be extended to research of other functional ceramics.

See supplementary material for additional analysis of the dielectric permittivity, surface microstructure characterization, and refinements of PDF patterns.

This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. This work was performed in part at the Analytical Instrumentation Facility (AIF) at North Carolina State University, which is supported by the State of North Carolina and the National Science Foundation (Award No. ECCS-1542015). The AIF is a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), a site in the National Nanotechnology Coordinated Infrastructure (NNCI). D.H. thanks financial support from China Scholarship Council. T.-M.U. acknowledges support from the U.S. Department of Commerce under Award No. 70NANB13H197. This material is based on work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC05-00OR22725.

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Supplementary Material