Phase equilibria and crystallographic structure of samarium-doped zirconate titanate (Pb(1-1.5x)SmxZr(1-y)TiyO3)

Michelle M. Nolan (Chemistry) Advisor: Jacob L. Jones (Materials Science and Engineering)

Abstract Samarium-doped (PZT) is a piezoelectric ceramic of fundamental interest; it shows an uncharacteristic relaxation in its piezoelectric coefficient with frequency and a uniquely large piezoelectric coefficient at high temperatures compared to other donor-doped PZT compositions. It is also of commercial importance in surface acoustic wave and hydrophone devices. In this work, the of Sm3+ in tetragonal PZT was determined by synthesizing several unique compositions of this material varying Ti:Zr ratio and Sm3+ doping concentration. Structures were measured by powder X-ray diffraction. Solubility of Sm3+ in PZT was found to 3+ increase with increasing mol% PbTiO3: the solubility of Sm in pure PbTiO3 was found to be 8 3+ at%, whereas the solubility of Sm in PbZr0.45Ti0.55O3 was found to be 4 at%. For practical applications, lead titanate based materials are almost always used with Mn-doping to decrease conductivity and facilitate poling of the material. It was found that the solubility of Sm3+ in Mn- doped lead titanate is 15 at%. Structural analysis was carried on high resolution neutron diffraction patterns using the Rietveld refinement method, and it was determined that Sm3+ cannot solely substitute on the B-site; it may occupy the A-site, or have a mixed occupancy of the A- and B-sites.

Introduction

Samarium-doped lead zirconate titanate (Pb(1-1.5x)SmxZr(1-y)TiyO3) is a piezoelectric ceramic of fundamental scientific interest as it exhibits uncharacteristic behavior with frequency and high temperature compared to other donor-doped PZT compositions. In addition to the industrial applications of PZT in power sources, sensors, and actuators1,2, Sm-PZT is also of commercial importance in surface acoustic wave and hydrophone devices.3 Piezoelectric ceramics are materials which develop an electric polarization when subjected to mechanical stress, and conversely strain in the presence of an electric field.4 The direct piezoelectric effect is observed upon the application of a mechanical stress to a sample: the

Nolan 1 external force induces a displacement of the central ion of the unit cell, forming an electric dipole moment, as shown in Figure 1. The resulting electric field generates an electric potential on the faces of the sample. These materials also exhibit the opposite behavior. When subjected to an electric field, the volume of the piezoelectric sample changes; if this deformation is constrained (for example, if the sample was attached to an immobile Figure 1: The spontaneous polarization of a material), a mechanical strain is generated. A key tetragonal perovskite (ABO3), such as PZT aspect of this effect is that the applied stress and the resulting electric dipole are parallel to one another.4 The magnitude of the material's piezoelectric response is described by the piezoelectric coefficient, or d33. (1)

In the above equation, E is the applied electric field and ε is the strain, both of which are in the 3 direction. was initially thought to only exist in single crystals because in bulk ceramics, the random orientation of unit cells result in no net dipole moment. However, if a strong electric field is temporarily applied over the sample in a processed called poling, these diploes can be aligned. Currently, PZT dominates in industrial applications due to its superior piezoelectric 5,6 properties. PZT is a solid solution of PbZrO3 and 7 PbTiO3, as illustrated by the phase diagram in Figure 2. Because compositions of different Zr:Ti ratios have significantly different properties, especially near the morphotropic phase boundary (MBP), it is a highly customizable smart material.

However, it is rarely used in its pure form: chemical y = modification of the composition, or doping, is key to Figure 2: Phase diagram of pure PZT. tailoring the properties of PZT to a particular application. The substitution of Sm (III) ion is an example of soft-doping. Soft-doping involves

Nolan 2 the addition of donor-ions, which create cation vacancies.4 These compositions typically have high d33, high relative permittivities, and large electromechanical coupling factors. Most donor-doped PZT compositions exhibit decreasing logarithmic relationships between piezoelectric coefficient and frequency.8 However, Sm-PZT shows an uncharacteristic relaxation in d33. This relationship is illustrated below in Figure 3.

Figure 3: Comparison of the logarithmic variation in piezoelectric coefficient with frequency for

8 typical piezoelectric materials (left) with the unique variation in d33 for Sm-doped lead titanate (PT)

Earlier studies by the author also show that Sm-PZT has an unexpected and unique d33 temperature dependence: the d33 of Sm-doped PZT varies significantly with increasing temperature compared to that of La- and Nb-doped PZT, both of which are also soft-dopants. At its maximum, Sm-PZT has roughly double the d33 of the other two compositions. These properties are illustrated below in Figure 4.

900 800 2% Sm 48/52 700 2% La 48/52

600 2% Nb 48/52

500

400

(pm/V)

33 300 d 200 100 0 0 100 200 300 400 Temperature (ºC)

Figure 4: Comparison of the relationships between d33 and temperature for 2 at% Sm-doped,

2 at% La-doped, and 2 at% Nb-doped PbZr0.48Ti0.52O3

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Although it is known that the addition of dopants can improve piezoelectricity through the creation of point defects and defect dipoles5, there has not yet been a systematic investigation linking different types and concentrations of dopants with macroscopic properties. Understanding the link between microscopic structure and macroscopic properties of PZT is essential to designing more efficient and commercially applicable materials. To further investigate the structure of Sm-PZT, this work determines the solubility of Sm (III) in tetragonal PZT and the site the Sm (III) ion occupies. For practical applications, lead titanate (PT) based materials are almost always used with Mn-doping to decrease conductivity and facilitate poling of the material. The solubility of Sm (III) in 2 at% Mn-PT is also assessed.

Experimental Samples were made of several PZT compositions with varying Ti:Zr ratio and Sm-doping. Compositions were limited to tetragonal PZT (y = 0.55 to y = 1.00) in order to avoid the complications of compositions near the morphotropic phase boundary. Samarium-doped PZT was synthesized by the standard two step mixed-oxide synthetic route. The raw materials used were PbO (Alfa Aesar, 99.99% purity), TiO2 (Alfa Aesar,

99.6% purity), ZrO2 (Alfa Aesar, 99.7% purity), and Sm2O3

(Alfa Aesar, 99.99% purity) powders. First, a precursor was synthesized to reduce the development of an undesirable pyrochlore phase impurity. Then, PbO and Sm2O3 were added to synthesize Sm-PZT, as shown by the following reactions.

(I)

(II)

In the precursor preparation (Reaction I), ZrO2 and TiO2 were mixed in a laboratory ball-mill for 12 hours using ethyl alcohol solution and zirconia milling media; this process homogenizes Figure 5: Processing scheme for Sm-PZT samples

Nolan 4 the powder and reduces particle size. The powder was then dried, ground in a pestle and mortar, sieved to a fine powder, and calcined at 1300ºC for four hours with a heating ramp rate of

4ºC/min. The calcined precursor powder was then combined with PbO and Sm2O3 (Reaction II). Due to the high volatility of PbO at sintering temperatures9, a 2 wt% excess of PbO was added to prevent lead deficiency in the final samples. The powders were wet milled in the same fashion for 12 hours, dried, ground, and sieved. Then the powder was calcined at 950ºC for two hours with a heating ramp rate of 4ºC/min. The calcined PZT powder was wet milled for an additional 12 hours, dried, and pressed into pellets using both uniaxel and isostatic pressing. The pellets were sintered on a bed of sacrificial powder at 400ºC for 1.5 hours, and then at 1200ºC for two hours using a ramp rate of 4ºC/min. This synthetic route is summarized by in Figure 5. For Sm-PT samples (when y = 1), the precursor synthesis is not necessary. Appropriate amounts of PbO, TiO2, and Sm2O3 were mixed directly. For Sm-doped 2 at% Mn-PT samples,

MnO2 was also added at this step, as shown below in Reaction III. The rest of the procedure was then followed directly.

(III)

The phase purity of each sample was determined using a laboratory powder X-ray diffractometer. All patterns were collected at room temperature and atmospheric pressure. Based on the diffraction patterns of the initial samples, more compositions were processed with adjusted Sm-doping concentration until the solubility limit was determined. To establish whether Sm3+ substitutes on the A-site or the B-site, neutron diffraction patterns of a Pb0.85Sm0.10Mn0.02Ti0.98O3 sample were recorded using the HB-2A high resolution neutron diffractometer at Oak Ridge National Laboratory with a wavelength of 1.5378 Å. Rietveld refinement using the General Structure Analysis System (GSAS) was applied.

Discussion X-ray diffraction patterns of each composition were compared in order to find the maximum samarium doping concentration at which no secondary peaks were observed within the detection limit of the diffractometer. This process is illustrated in Figure 6, which represents all of the Pb(1-1.5x)SmxZr0.2Ti0.8O3 samples with varying Sm-doping concentration. The peaks due to secondary phases are highlighted, and this phase was identified to be a pyrochlore phase.

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Figure 6: An example series of X-ray diffraction patterns for Pb(1-1.5x)SmxZr0.2Ti0.8O3. Peaks arising from secondary phases are labeled by asterisks. From these patterns, it can be concluded that 6 at% is the solubility limit of Sm in Pb(1-1.5x)SmxZr0.2Ti0.8O3 within the detection limit of the diffractometer.

perovskite

+ pyrochlore

perovskite

Figure 7: Phase diagram of Sm-PZT at room temperature and atmospheric temperature. Compositions with observed secondary phases are marked with red dots, whereas those which appear to be phase pure are marked with green squares. The dotted line is used to delineate the observed solubility limit. Nolan 6

The completed phase diagram is shown in Figure 7. Every composition synthesized for this study is shown: compositions with observable secondary phases are marked with a red dot, and compositions without observable secondary phases are marked with green squares. A dotted line is used to delineate the observable solubility limit of Sm (III) ion. Below the dotted line, compositions appear to be phase-pure perovskite; above the line is a mixed-phase region, with both perovskite and pyrocholore phases observed. It is clear from this phase diagram that the solubility of Sm (III) in PZT decreases with decreasing mol% PbTiO3: the solubility of Sm (III) in pure PbTiO3 was found to be 8 at%, whereas the solubility in PbZr0.45Ti0.55O3 was found to be only 4 at%. The solubility of Sm in

PbMn0.02Ti0.98O3 was determined to be 15 at%, which is significantly higher than the 8 at% limit in pure PbTiO3. Rietveld refinement was used to determine the site Sm (III) occupies in the ABO3 structure (shown in Figure 1). As shown in Figure 8, GSAS was used to refine a theoretical diffraction pattern to match the measured for Pb0.85Sm0.10Mn0.02Ti0.98O3 at Oak Ridge National Laboratory. During the refinement process, the program determines the crystallographic structure of the sample through the optimization of several parameters, including atomic position, thermal energy, and occupancy of each site.

Figure 8: The Rietveld refinement method. The collected neutron diffraction data is shown as the "intensity" scatter plot and the simulated diffraction pattern is shown as a fitted red line. Below, a difference plot in blue shows the difference between the two patterns. The tick marks indicate the Miller indices for the tetragonal unit cell.

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(a) (b) (c)

Figure 9: Sm substitution possibilities on the (a) A-site, (b) B-site, and (c) mixed A- and B-sites

Three possibilities were considered for the occupancy of the Sm (III) ion: Sm substitution on the A-site (Figure 9a), on the B-site (Figure 9b), or on both sites (Figure 9c).

In the refinement data below, the Rp value is a statistical quantity representing how accurately the fitted pattern represents the collected pattern; an Rp value below 6.0% is respectable for Rietveld analysis. The X, Y, and Z columns represent the atomic position in the unit cell, and only one position is shown for each element. The two rows represent the four equatorial oxygen ions surrounding the B-site ion (called O1) and the two axial oxygen ions

(called O2), which behave differently when the unit cell is polarized. The Ui/Ue parameter represents thermal energy, and specifically quantifies the vibration distance of an ion in angstroms. The occupancy column describes the mol fraction the specified ion on that atomic site. Standard deviations are given where relevant.

Table 1: Rietveld refinement data for Sm occupancy of the A-site only. The bolded occupancies both contain the expected values of 0.85 for Pb and 0.10 for Sm within their standard deviations.

Profile Fit: Rp 5.16%

Name X Y Z Ui/Ue Occupancy Pb 0.000 0.000 0.000 0.3 ± 0.1 0.87 ± 0.02 Sm 0.000 0.000 0.000 0.3 ± 0.1 0.08 ± 0.02 Ti 0.500 0.500 0.535 ± 0.003 0.8 ± 0.2 0.9800 Mn 0.500 0.500 0.535 ± 0.003 0.8 ± 0.2 0.0200

O1 0.500 0.000 0.474 ± 0.001 1.3 ± 0.2 1.0613

O2 0.500 0.500 0.094 ± 0.001 0.5 ± 0.2 0.9884

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Table 2: Rietveld refinement data for Sm occupancy of the B-site only. When the user inputs the Sm occupancy at 0.1000, the thermal parameters are negative (bolded on the left). When the program refines the thermal parameters to positive values, it computes a negative occupancy (bolded on the right).

Profile Fit: Rp 5.15%

Name X Y Z Ui/Ue Occupancy Ui/Ue Occupancy Pb 0.000 0.000 0.000 0.9 ± 0.1 0.9500 0.6 ± 0.2 0.914 Sm 0.500 0.500 0.535 ± 0.003 −0.4 ± 0.2 0.1000 0.02 ± 0.2 −0.14 ± 0.02 Ti 0.500 0.500 0.535 ± 0.003 −0.4 ± 0.2 0.8800 0.02 ± 0.2 0.89± 0.02 Mn 0.500 0.500 0.535 ± 0.003 −0.4 ± 0.2 0.0200 0.02 ± 0.2 0.0259

O1 0.500 0.000 0.475 ± 0.002 1.1 ± 0.1 1.0613 1.3 ± 0.2 1.0781

O2 0.500 0.500 0.095 ± 0.002 0.3 ± 0.3 0.9884 0.3 ± 0.2 0.9818

Table 3: Rietveld refinement data for Sm occupancy of both the A-site and B-site. The bolded thermal parameters contain both positive and negative values within the standard deviation, making this refinement ambiguous.

Profile Fit: Rp 5.15%

Name X Y Z Ui/Ue Occupancy Pb 0.000 0.000 0.000 0.6 ± 0.2 0.91 ± 0.02 Sm (A) 0.000 0.000 0.000 0.6 ± 0.2 0.06 ± 0.02 Sm (B) 0.500 0.500 0.536 ± 0.003 0.1 ± 0.4 0.06 ± 0.03 Ti 0.500 0.500 0.536 ± 0.003 0.1 ± 0.4 0.93 ± 0.03 Mn 0.500 0.500 0.536 ± 0.003 0.1 ± 0.4 0.0200

O1 0.500 0.000 0.474 ± 0.002 1.3 ± 0.2 1.0806

O2 0.500 0.500 0.094 ± 0.002 0.3 ± 0.3 0.9826

Table 1 represents the refinement data for Sm occupying the A-site. The occupancies of Pb and Sm are very reasonable, and both contain the expected occupancies of 0.85 for Pb and 0.10 for Sm within their standard deviations. The profile fit parameter shows that this model very closely matches the collected diffraction pattern. These data indicate that Sm may occupy the A- site exclusively. The refinement data for Sm occupying the B-site is much more problematic. The refinement calculations work by first having the user input estimate values, which the program then refines to a more and more accurate fit; it does not discriminate against physically

Nolan 9 impossible parameters while calculating the most optimal simulated diffraction pattern. When the user initially sets the Sm occupancy to 0.1000 (as expected from the ), GSAS calculates a negative thermal energy, as shown on the left side of Table 2. When the program refines these data to positive values, it compensates by changing the Sm occupancy to a negative value, as shown on the right side of Table 2. Since neither thermal energy nor occupancy can physically be a negative number, these data show that Sm cannot occupy the B- site exclusively. The refinement of Sm having a mixed-occupancy on both the A- and B-sites is more ambiguous than the previous two modes of substitution. The bolded thermal energy parameters on Table 3 show large standard deviations, containing both positive and negative values within the margin of error. Depending on where the "true" value lies, this occupancy may or may not be physically possible, so it cannot be ruled out without further investigation. The refinement program assumed that the Sm ion would be evenly split between the A- and B-sites: it is possible that the data may become more conclusive by changing the ratio of A-site to B-site occupancy. Neutron diffraction studies of another Sm-PT composition may also provide more insight to this case.

Conclusions

Solubility of Sm (III) ion in PZT was found to increase with increasing mol% PbTiO3: the solubility limit in pure PbTiO3 was observed at 8 at%, whereas the solubility limit in

PbZr0.45Ti0.55O3 was observed at 4 at%. Commercially, lead titanate typically contains Mn- doping to minimize conductivity: the solubility of Sm (III) in PbMn0.02Ti0.98O3 was determined to be 15 at%. Structural analysis using the Rietveld refinement method showed that Sm (III) may occupy the A-site alone, but it is physically impossible for it to occupy the B-site exclusively. Samarium (III) might have a mixed occupancy of the A- and B-sites, but further studies are necessary to fully assess this possibility.

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Acknowledgements This work was supported by the National Science Foundation Award DMR-0746902 and the University of Florida University Scholars Program (USP). The neutron diffraction research at Oak Ridge National Laboratory’s High Flux Isotope was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. This work also acknowledges the contributions of Shruti B. Seshadri, Bruna Bregadiolli, and Dr. Jennifer S. Forester.

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