Article pubs.acs.org/cm
La-Driven Morphotrophic Phase Boundary in the Bi(Zn1/2Ti1/2)O3− La(Zn1/2Ti1/2)O3−PbTiO3 Solid Solution Valentino R. Cooper,*,† James R. Morris,†,‡ Shigeyuki Takagi,§ and David J. Singh† †
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States Department of Physics, University of Tennessee, Knoxville, Tennessee, United States § Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan ‡
ABSTRACT: We explore the Bi(Zn 1/2 Ti 1/2 )O 3 −La(Zn1/2Ti1/2)O3−PbTiO3 pseudoternary phase diagram using density functional theory and a solid solution model. We find a region of stability against phase segregation that contains a morphotropic phase boundary. On the basis of the results, we identify a ferroelectrically active composition-dependent region that is likely to show strong electro-mechanical response. Furthermore, we find that La replacement for Bi not only lowers the polarization as might be expected, but also shifts the balance from tetragonality toward rhombohedral distortions. This may be of general use in modifying phase diagrams of A-site driven perovskite ferroelectric solid solutions to generate new morphotropic phase boundary systems. KEYWORDS: ferroelectric, piezoelectric, electronic structure, solid solution model
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INTRODUCTION The study of the electro-mechanical couplings in ABO3 perovskite oxides has seen a resurgence in recent decades. This is partly due to the wide variety of device applications, such as piezoelectric fuel injectors where electro-mechanical responses can be exploited for the precise control of fuel delivery in automotive engines. A useful strategy for designing high piezoresponse compounds borrows lessons from the prototypical piezoelectric Pb(Zr,Ti)O3 (PZT), a solid-solution of the tetragonally distorted PbTiO 3 (PT), and the antiferrodistorted PbZrO3 (PZ). The key to the success of PZT lies in the combination of compounds with two very distinct phases leading to a composition-dependent region, the morphotropic phase boundary (MPB), where the crystal structure undergoes a transition (mediated by a monoclinic phase1) between the macroscopic phases of the parent compounds2 (i.e., the rhombohedral phase of the PZ rich compound and the tetragonal phase of the PT rich compound at roughly 50% PT-50% PZ). In general, ferroelectric alloys near MPBs exhibit enhanced electromechanical responses when the parent compounds have high remnant polarizations.3 Thus, the discovery of new morphotropic phase boundary systems and chemical control of their properties is important. A relatively recent direction is the exploration of Bi containing perovskites, as Bi can produce very high polarization. However, the understanding of how to produce and manipulate MPBs in these materials is less complete than in the more common Pb based materials. Bi’s stereochemical activity (resulting in large Born effective charges, Z*) and smaller ionic radius (allowing for large ionic displacements) makes it a good © 2012 American Chemical Society
alternative to Pb; producing compounds with high polarization, P⃗.4 Recent theory and experiments have demonstrated that it is possible to find Bi based perovskites at both ends of the MPB spectrum (i.e., tetragonal or rhombohedral ground states). For example, in a previous study, we predicted that the double perovskites (Bi 1/2 Sr 1/2 )(Zn 1/2 Nb 1/2 )O 3 (BSZN) and (Bi1/2M1/2)(Sc1/2Nb1/2)O3 (where M = Na, K, Rb; BMSN) all have pseudocubic structures with relatively high, rhombohedrally oriented, remnant polarizations (>73 μC/cm2).5,6 Similarly, it has been shown that BiCoO3,7 BiZn1/2Ti1/2O3 (BZT),8 BZT-PT9,10 and appropriately strained BiFeO311 all have tetragonally distorted structures. (Note: the supertetragonality of these materials limits their usefulness as ferroelectrics as they will require strong and possibly unattainable electric fields to switch the polarization.) This wide array of Bi-based oxides has spurred research related to the discovery of morphotropic phase boundaries in Bi-based ferroelectrics such as the recently explored BSZN-BZT solid solution.12 Here, we use first principles density functional theory (DFT) to explore the ternary phase diagram of the BZT-La(Zn1/2Ti1/2)O3 (LZT)-PT solid solution. For each composition we examine the magnitude and orientation of the polarization. We find that the region bounded by compositions of 75% BZT25% PT, 25% BZT-75% PT, and LZT ≤ 25% should be the most responsive/usable piezoelectric.2 In particular, we find a Received: September 21, 2012 Revised: November 7, 2012 Published: November 7, 2012 4477
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Table 1. Structural Parameters for the Ternary Solid Solutions Identified in the Region of High Piezoelectric Responsea label
% LZT
% BZT
% PT
a
b
c
c/a
Ω
LZT BZT PT A B C D E F
100.0 0.0 0.0 0.0 12.5 25.0 0.0 12.5 25.0
0.0 100.0 0.0 75.0 62.5 50.0 50.0 37.5 25.0
0.0 0.0 100.0 25.0 25.0 25.0 50.0 50.0 50.0
3.91 3.74 3.85 3.78 3.90 3.91 3.82 3.82 3.83
3.91 3.75 3.85 3.78 3.92 3.91 3.86 3.85 3.87
3.91 4.58 4.03 4.33 3.93 3.93 4.22 4.16 4.11
1.00 1.23 1.05 1.14 1.01 1.01 1.11 1.08 1.07
59.93 64.07 59.93 61.98 60.11 60.05 62.12 61.17 60.87
a
Labels A−F correspond to the specific compositions identified in Figure 1. The structural parameters a, b, c are the pseudo-orthogonal lattice parameters in units of angstrom (Å). The volume (Ω) is in units of Å3. Values for the pure end member compounds are given for comparison.
Figure 1. Ternary diagram for (a) |P| and (b) the estimated Tc = γP2 in the BZT-LZT-PT solid solution. Red and blue regions indicate areas of high P(Tc) and low P(Tc), respectively. Black squares denote the compositions modeled. The dashed diamond defines the predicted optimal piezoelectric region. Polarizations are in C/m2. Temperatures are in K. γ = 1189 K/(C/m2)2.5,25. assume that the A-site lattice consisting of Pb, Bi, and La is chemically ordered. However, an additional constraint comes from the fact that with multiple A-site ions it is possible to choose cells that have polar space groups just because of the cation ordering and not because of lattice instability. This would not represent ferroelectricity but would rather be an artifact of the selected order. Therefore, even though Bi and Pb are not expected to chemically order in the solid solutions, we consider them in a highly ordered state within our supercells. Here, we select a rocksalt ordering of Pb versus Bi/La on the A site. For a 50% Pb/50% Bi composition, the cation ordering on the A-site with this choice has symmetry F4̅3m, which is nonpolar. Thus any polarization or off-centering is a consequence of lattice instability and not the choice of cation ordering. For other concentrations, we start with the 50/50 ordering and then fill any deficient sites with the remaining species (as described above), so as to maintain the highest crystal symmetry. While cation ordering can play a role in defining the magnitude and orientation of the polarization, this approach helps to avoid computational artifacts, such as polarization because of the particular symmetry-breaking chemical ordering in a given supercell. This approach was also successful in exploring the properties of PZT, BSZN-BZT, and BZT.10,12,32 Multiple initial displacement patterns of the cations were explored. All lattice vectors and ionic coordinates were relaxed until the stresses (σ) and Hellman-Feynman forces (F) on the ions were less than 0.5 kbar and 10−3 Ry/bohr, respectively. Polarizations, P, were computed using the Berry phase method.23 Tc’s were estimated using the model of Grinberg and co-workers24,25 in which Tc = γP2 (derived from Landau theory26). We used the proportionality constant, γ = 1189 K/[(C/m2)2],24 which has previously been successful for Bi-based perovskites.27 We adopted a solution model with an ideal entropy of mixing to investigate the stability against segregate into the end member compounds. We assume that BZT, LZT, and PT are simply three separate components that form a random solution. In this regard the change in the Gibbs
monoclinic phase indicative of the morphotropic phase boundaries observed in high response regions in many piezoelectrics. Furthermore, using a solid solution model we demonstrate that this region should be stable against phase segregation into the end members. Finally, our estimates of the ferroelectric transition temperature, Tc show that the relevant ferroelectric transition temperatures should be greater than 600 K, suggesting that these materials will be useful at typical device operation temperatures.
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METHODOLOGY
We perform DFT supercell calculations for ternary compounds of xBZT-yLZT-zPT, where x + y + z = 1, using the local density approximation (LDA) and ultrasoft pseudopotentials13 as implemented in the Quantum Espresso simulation package (v. 4.3.2).14 We modeled 2 × 2 × 2 (40 atom) unit cells employing a 50 Ry planewave energy cutoff with a 4 × 4 × 4 Monkhorst−Pack k-point mesh. The large charge difference between Zn2+ and Nb5+ is expected to lead to a strong ordering tendency on the B site. This is the case in the relaxor systems Pb(Zn,Nb)O3, Pb(Mg,Nb)O3, and Pb(Sc,Nb)O3.15−20 Theory has demonstrated that this is a direct consequence of the electrostatic interactions between the A- and B-site ions.21,22 Note, there is a considerable size difference between the radius of Zn (rZn = 0.74 Å) and Nb/Ti (rNb = 0.64 Å, rTi = 0.605 Å) which also contributes to ordering. Hence, B-cations were arranged such that the Zn and Nb/Ti were on separate rocksalt-ordered sublattices placing excess cations on the deficient site. For non 1 Zn:1 Nb/Ti stoichiometries, cations were arranged first by filling in an equal amount of Nb/Ti on one of the rocksalt sublattices and Zn cations on the other, in such a way as to have the highest symmetry possible. This leaves one sublattice with a deficient amount of cations. These sites are then filled with excess cations. In contrast, there is no a priori reason to 4478
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Figure 2. Ternary phase diagram for (a) P·[001] and (b) P·[111]. Red regions are indicative of the (a) strongly tetragonal and (b) rhombohedral phases. In both diagrams, blue regions correspond to paraelectric phases and yellow regions monoclinically oriented compositions. Black squares denote the compositions modeled. The dashed diamond defines the predicted optimal piezoelectric region. free energy of the system, ΔG = ΔH − kBTS, is used to determine the stability of a given phase in each region. Here, ΔH is the enthalpy of mixing relative to the end member compounds: ΔH = Extotal BZT − y LZT − z PT − (xE BZT + yE LZT + zE PT)
Figure 2a and b depict the projections of the polarization onto the [001] and [111] directions. As expected, the BZT-PT compositional line remains strongly tetragonal (P·[001] ≈ 1), while a rhombohedral phase (P·[111] ≈ 1) is observed for compositions of roughly PT ≤ 25% and 37.5% ≤ LZT ≤ 67.5%. Between these extremes we see the emergence of a monoclinic region denoting the presence of a morphotropic phase boundary. Similar to PZT and other ferroelectric materials, this monoclinic region is expected to have a high piezoelectric response as the polarization can rotate in the monoclinic plane. An important point to note here is that the incorporation of the larger (relative to Bi), nonstereochemically active La cations not only reduces the polarization/tetragonality within the solid solution but also results in a rotation of the polarization away from the [001] direction. This effect of chemical pressure has recently been proposed as a complementary effect to the polarization rotation argument commonly used to explain the high piezoresponse in PZT near the morphotropic phase boundary.29 In other words, in PZT, the incorporation of the large Zr cations (relative to Ti) resulted in displacement of cations away from the [001] directions (due to repulsive interactions with the larger cation), thus bringing about the transition from tetragonal phases in PT rich compositions to a rhombohedrally oriented polarization in PZ rich compositions.30,31 Table 2 lists the polarization, average Born effective charges (Z*), average off-center displacements with respect to the center of the oxygen cages (δ), and average angle of rotation away from [001] (θ) for each cation in the six solid solutions identified in the region of high piezoelectric response. (see A−F in Figure 1). First, as expected, increases in the LZT fraction result in decreases in the total polarization of the material. Although La has a Born effective charge comparable to that of Bi, we see that, on average, its displacements are much smaller than for Bi. Since P = Z*δ/Ω and there is only a relatively small change in the volume of the solid solutions (see Table 1), increases in the LZT/BZT ratio will have dramatic effects on P. This is due to both the lower stereochemical activity of La3+ (i.e., no lone pairs) as well as the larger ionic radius of La (relative to Bi), which will decrease off-centering due to steric repulsions. Of course Pb has a larger ionic radius. However, the deficiencies in substituting Pb for La (i.e., comparable displacements and lower Born effective charge of Pb) are
(1)
determined directly from the DFT calculations, T is temperature and S is the entropy which is estimated from an ideally random mixture as follows
S /kB = − (x ln x + y ln y + z ln z)
(2)
where x, y, and z are the fractions of BZT, LZT, and PT, respectively. This is a simplified form, which ignores the entropy of mixing on the B-site, but provides a useful measure of local stability of the compound phase. Including contributions to entropy of mixing on the B-site would further stabilize the mixture phases. The structural parameters for the end member compounds are listed in Table 1. For BZT our tetragonal in-plane lattice constant of a = 3.74 Å, c/a = 1.23, and polarization of 1.42 C/m2 are in excellent agreement with previous experiment and theory.9,10 Note: previously, a number of different B-cation arrangements were explored for the BZT structure, all giving similar values for c/a and polarization.10 For PT we obtain a tetragonally distorted ground state with lattice constants (a = 3.85 Å, c/a = 1.05) and polarization (0.79 C/m2) in typical LDA agreement with experiment. For the LZT structure we performed relaxations starting from a number of different starting configurations (including one with the experimental Glazer tilt patterns of a+b−b+28). Our theoretical ground state was indeed a cubic, nonpolar ground state (ao = 3.91 Å) in good agreement with recent experimental characterization.28
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RESULTS AND DISCUSSION Figure 1a depicts the magnitude of the polarization as a function of composition for the ternary solid solution. As expected, compositions with a large fraction of BZT have extremely high P ≥ 1.20 C/m2. Such large P are usually accompanied by substantial barriers, making them difficult to switch and therefore unusable for many applications. Conversely, large fractions of LZT severely reduce P. Compositions with LZT ≤ 25% and PT ≥ 25% have P that are comparable to PT. This may be the compositional region that is most amenable for practical use. Commensurate with the higher P, we see that Tc's for LZT ≤ 25% are predicted to be greater than ∼600 K (see Figure 1b). These high transition temperatures point to a useful regime in which the polarizations would be sustainable at typical operating temperatures for ferroelectric/piezeoelectric devices. 4479
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17 34 0.38 0.32 4.34 4.37
37 54 0.26 0.25 4.39 4.35
overcome by the fact that there are now more Ti, B-site, cations which enhance P when substituted for Zn. Second, the overall direction of the polarization is driven by a strong competition between the incorporation of PT vs the substitution of Bi with La. For example in compositions D, E, and F (50% PT) we see that the solid solutions are mostly tetragonal (with a large component along [001]), irrespective of their La content. However, for compositions with only 25% PT the overall direction of polarization depends upon the incorporation of La, which rotates the polarization toward the [111] direction. Again, this is reminiscent of PZT where the polarization direction is controlled by the competition between the B-cation size disorder (i.e., Zr vs Ti) and the A-site cation simply aligning itself with the overall direction of the polarization.32 (Of course in this case the size disorder is on the A-site rather than the B-site). It should be noted that, unlike previous studies33 where size disorder on the A-site enhances P, we find a decrease in P. This is due to the very different nature of the local chemistry/environment of Bi versus that of La. Specifically, Bi's large off-center displacements result in 8-fold coordinated Bi cations (similar to compressively strained BiFeO311 and BiCoO37) as opposed to the typical 12-fold coordination of A-site cations. As previously mentioned, La’s larger ionic radius and absence of lone pair physics limit the magnitude of off-center displacements. This effect is over emphasized in the BZT-LZT compounds as La cations restrict the displacement of Bi cations thus resulting in a large reduction in P, even up to 75% BZT concentrations (see Figure 1a). This also suggests that, unlike STO, LZT has a much steeper ferroelectric potential energy well than BZT. This is similar to previous predictions of ferroelectric/ferroelectric superlattices in which the interlayer couplings resulted in enhancements in the piezoelectric, d33, coefficients of the superlattice,34 implying that La may foster similar improvements in the piezoresponse of these solid solutions. Finally, we explore the stability against phase separation using a simplified solution model. Figure 3 depicts the temperature in units of kT at which each composition is stabilized against segregation into the end member compounds. First, we predict that for BZT-PT there is a region of instability
a Labels A−F correspond to the specific compositions in Figure 1. Px, Py, Pz and Ptot are the x, y, z-components and total P in units of C/m2. Off-center displacements (δ) are in units of Å. Values for the pure end member compounds are given for comparison.
4 52 51 9 10 11 0.56 0.29 0.25 0.54 0.52 0.47 2.62 2.76 2.76 2.63 2.66 2.68 0 7 49 50 17 8 8 0.40 0.42 0.31 0.28 0.43 0.44 0.40 3.71 3.53 3.59 3.58 3.59 3.63 3.65 0.71 0.55 0.52 0.68 0.63 0.72 4.54 4.67 4.62 4.41 4.45 4.33
6 0.89 4.45
7 50 50 14 17 26
θ
0 17 0 7 46 48 14 7 8 0.00 0.48 0.27 0.34 0.21 0.20 0.29 0.36 0.22
δ Z* δ Z* θ δ θ
0
Z* δ
0.00 4.19
Z* Ptot
0.00 1.44 0.79 1.15 0.82 0.71 1.04 0.90 0.76 0.00 1.42 0.79 1.14 0.54 0.45 0.98 0.89 0.76
Pz Py
0.00 0.26 0.00 0.12 0.43 0.42 0.35 0.09 0.01 0.0 0.0 100.0 25.0 25.0 25.0 50.0 50.0 50.0
0.00 0.00 0.00 0.10 0.43 0.35 0.02 0.11 0.01
% PT
100.0 0.0 0.0 0.0 12.5 25.0 0.0 12.5 25.0
0.0 100.0 0.0 75.0 62.5 50.0 50.0 37.5 25.0
% LZT label
LZT BZT PT A B C D E F
% BZT
Px
Article
5.53 4.50 6.16 5.15 5.46 5.47 5.58 5.69 5.76 0 1
θ δ
0.00 0.70
θ
Z*
2.76 2.51
Ti Zn Pb Bi La
Table 2. Polarization, Average Born Effective Charges (Z*), Average off-Center Displacements (δ), and Average Angle of Rotation Away from [001] (θ) for Each Cation in the Ternary Solid Solutions Identified in the Region of High Piezoelectric Responsea
Chemistry of Materials
Figure 3. Ternary diagram for the solution model for the BZT-LZTPT solid solution. Red and blue regions indicate relatively high and low temperatures at which entropy stabilizes the solid solution, respectively. Black squares denote the compositions modeled. All temperatures are in meV. The dashed diamond defines the predicted optimal piezoelectric region. 4480
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between 50% BZT−50% PT and 35% BZT−65% PT. This phase stability limit seems to correlate well with previous work on the xBi(Mg1/2Ti1/2)O3−yBi(Zn1/2Ti1/2)O3−zPbTiO3 perovskite ternary solid solution where mixed phases (i.e., phase segregation) were observed for BZT-PT compositions with greater than 40% BZT.35 Furthermore, along the binary LZTPT phase diagram and for BZT rich binary compositions of LZT-BZT, our results point to regions of extreme instability. Moreover, apart from these highly unstable regions, the majority of the ternary mixture is predicted to be stable against segregation into the end member compounds. Here, the two main stable regions are composed of one band in the upper half of the ternary phase diagram and one for high concentrations of PT (i.e., blue regions in Figure 3). One caveat, however, relates to the extremely stable regions observed along the binary BZTPT composition line for BZT concentrations greater than 50%, which seem to contradict previous experimental evidence.35 We emphasize the fact that our results are relative to the end members of BZT and PT and not the PbO2 (Scrutinyte) and Bi2O3 compounds observed in the experiment. Furthermore, it is known that the preparation of pure BZT requires a high pressure synthesis (up to 6 GPa), whereas the aforementioned effort relied on a conventional solid state processing route with a maximum pressure of 200 MPa. Hence, it stands to reason that BZT-PT solutions with high BZT content may be synthesized under similar conditions as pure BZT. Nevertheless, the solid solution model predicts that the regions around the morphotropic phase boundary should be synthesizable when employing high-pressure synthesis techniques.
Article
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS V.R.C. acknowledges C. Bridges and Z.-G. Ye for very helpful comments. This work was supported by the Materials Sciences and Engineering Division, Office of Basic Energy Sciences, U.S. Department of Energy (V.R.C., J.R.M., D.J.S.). This research used resources of the National Energy Research Scientific Computing Center, supported by the Office of Science, U.S. Department of Energy under Contract No. DEAC0205CH11231.
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REFERENCES
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CONCLUSION In summary, we have explored the phase diagram of the BZTLZT-PT ternary solid solution. On the basis of our examination of the magnitude and orientation of the polarization as well as our predicted Tc and phase stability, we speculate that the region of the phase diagram bounded by 25% ≤ PT ≤ 50% and 0% ≤ LZT ≤ 25% should be the most likely compositions to find a high response piezoelectric (see dashed diamond in Figure 1−Figure 3). In this region, we find suitably high polarizations (0.71 C/m2 ≤ P ≤ 1.14 C/m2) with moderate phase stability and appropriate Tc > 500 K. Furthermore, we see that while the rotation of the polarization from the tetragonal phase to the rhombohedral phase is accompanied by a small change in volume (∼3% when going from the 50% BZT-50% PT binary compound to the 25% LZT-50% BZT25% PT ternary solution; see Table 1) there is a significant change in the lattice parameters (e.g., nearly 7% along the c-axis when going from the 50% BZT-50% PT binary compound to the 25% LZT-50% BZT-25% PT ternary solution; see Table 1). This suggests large mechanical responses may be achievable for phases in the region between these two compositions. The fact that the polarization is also higher than that of PZT at the morphotropic phase boundary may further enhance the coupling of lattice and polarization. A crucial factor in modulating the polarization is the role of the La cations within these materials. Here, it is clear that mixing in the cubic LZT structure reduces the overall polarization as expected, but most importantly provides chemical pressure to foster a rotation of the polarization, which is key to the emergence of the morphotropic phase boundary. Exploitation of this behavior may allow for significant progress in the discovery of new practical electromechanical materials, perhaps including Pb-free compositions. 4481
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(33) Singh, D. J.; Park, C. H. Phys. Rev. Lett. 2008, 100, 087601. (34) Cooper, V. R.; Rabe, K. M. Phys. Rev. B 2009, 79, 180101(R). (35) Dwivedi, A.; Qu, W.; Randall, C. A. J. Am. Ceram. Soc. 2011, 94, 4371.
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