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Synthesis and thermochemistry of relaxor ferroelectrics in the lead magnesium niobate–lead titanate (PMN–PT) solid solutions series Gustavo Carneiro Cardoso da Costa,* Lili Wu and Alexandra Navrotsky Received 15th September 2010, Accepted 27th October 2010 DOI: 10.1039/c0jm03090b The energetics of the (1 x)PMN–xPT solid solutions have been investigated using high temperature oxide melt solution calorimetry in 3Na2O$4MoO3 solvent at 702 C. The solid solutions show positive heats of mixing, reflecting the changes in structure from cubic to tetragonal to monoclinic and the morphotropic phase transition. The synthesis of a perovskite phase without a secondary pyrochlore phase depends on the annealing temperature and time. The enthalpies of reactions involved in synthesis and decomposition of the PMN perovskite were measured for the first time by oxide melt solution calorimetry. The decomposition of perovskite to pyrochlore plus MgO and PbO is energetically favorable, as is the formation of perovskite from columbite and lead oxide.
Introduction The relaxor ferroelectric materials based on perovskite structures ABO3 are technologically important electrochemical transducers whose physical and chemical properties change as a function of composition and structure. One of the most common relaxor ferroelectrics, lead magnesium niobium titanate Pb[(Mg1/3Nb2/3)1xTix]O3 or PMN–PT, exhibits systematic changes in structure and physical properties (such as dielectric constant and Curie temperature) as a function of PbTiO3 content.1,2 Therefore, its properties can be tailored for specific applications by varying the composition. PbMg1/3Nb2/3O3 or PMN with high dielectric constant (20 000 for single crystals) is relevant for applications in multilayer capacitors and electrostrictive devices such as actuators.3–8 The addition of small amounts of PbTiO3 shifts the Curie temperature of PMN from 10 C to 40 C and results in PMN– PT with low remnant polarization required for dynamic randomaccess memory (DRAM) devices.9,10 Compositions around the morphotropic phase boundary (MPB), located at a PbTiO3 mole fraction of approximately 0.35 and separating the relaxor side of the solid solution from the ferroelectric side, exhibit piezoelectric properties beyond typical ferroelectric behavior which makes them suitable for a broad range of applications in acoustic transduction devices and bulk acoustic devices for telecommunications.11 These rich, variable, and tunable properties of (1 x)PMN–xPT solid solutions arise from the cation size mismatch (rb0 > rb00 ) in the b sites of the structure Pb(b1/30 b2/300 )O3 (b0 ¼ Mg2+, b00 ¼ Nb5+).12 In this structure, the cations adopt 1 : 1 crystallographic order even though the b sites have 1 : 2 chemistry.13 Assuming charge balanced stoichiometry, the b sites of PMN, occupied by 1/3 of Mg2+ ions and 2/3 of Nb5+ ions, can be substituted by Ti4+ to derive PMN–PT. The electrical response of these relaxor ferroelectric materials as a function of composition and structure may be correlated to their energetics, which can be
Peter A. Rock Thermochemistry Laboratory and NEAT ORU, University of California at Davis, One Shields Avenue, Davis, California, 95616, USA. E-mail:
[email protected];
[email protected]; Fax: +1 530 752 9307; Tel: +1 530 754 2133
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studied by high temperature oxide melt solution calorimetry. Solution calorimetry has been exploited to measure the energetics of other classes of perovskites to determine chemical reactivity and stability, which are crucial to theory and modeling.14–18 Synthesis of PMN–PT has been a focus of discussion due the formation of a pyrochlore impurity phase which is undesirable for electronic applications because of its low dielectric constant, 130.19 Pyrochlore has the ideal formula Pb3Nb4O13 in which niobium can be replaced by magnesium resulting in the solid solution Pb3+(3/2)x,1(3/2)x(MgxNb4x)O13,, where ‘‘,’’ represents vacancies and 0 # x # 0.67.20,21 The phase diagram for PbO–MgO–Nb2O5 has a boundary between pyrochlore and perovskite solid solutions.21 Thus, a small change in composition during the synthesis process can lead to the formation of a pyrochlore phase. Two major factors can compromise the initial stoichiometry and phase formation of the perovskite. First, lead evaporation is a concern during high temperatures heat treatment. Second, low temperature and short heat treatment can lead to second phases since the formation of perovskite is related to the ability of the ions to diffuse through the structure of the precursor to form the phase of interest. The formation of a pyrochlore phase can apparently be avoided by adding a small excess of lead and magnesium.22,23 Another alternative to avoid pyrochlore is tailoring synthesis methods to change the chemical characteristics of the reactants. Xu et al.24 developed a particle coating method in which a magnesium citrate polymeric complex prevents direct contact between PbO and Nb2O5 and thus avoids the formation of pyrochlore. Yu et al.25 synthesized PMN–PT perovskite single phase by introducing polyethylene glycol to a mixture of MgO, PbO, Nb2O5 and TiO2. The synthesis of PMN and (1 x)PMN–xPT solid solutions without second phases can be achieved by different procedures and the formation of pyrochlore is explained based on composition changes as discussed above. However, there is no information available for the thermochemistry involved in the synthesis of (1 x)PMN–xPT as well for pyrochlore formation and stability. In the present study, oxide melt solution calorimetry has been exploited for the first time to derive the trends in energetics of (1 x)PMN–xPT system as well as to derive the J. Mater. Chem., 2011, 21, 1837–1845 | 1837
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enthalpies of formation of columbite and pyrochlore. We also provide a thermodynamic explanation for perovskite formation and decomposition.
Experimental methods PMN was synthesized by colloidal dispersion and nanoreaction methods. In the colloidal dispersion method, a precursor was prepared through a dispersion of lead hydroxide precipitate in a gel of niobium and magnesium citrates. In the nanoreaction method, magnesium niobate nanoparticles were covered with lead hydroxide precipitate to form a core–shell composite structure. The idea behind these two methods is, during heat treatment, to isolate the lead and promote reaction between magnesium and niobium precursors in order to favor the formation of an intermediate compound (columbite) which then reacts with lead oxide to form the perovskite. Lead titanate was synthesized by conventional solid state reaction and pyrochlore, Pb1.86Mg0.24Nb1.76O6.5, was synthesized by a simultaneous precipitation method. Columbite (MgNb2O6) was synthesized by the combustion of metal citrates. (1x)PMN–xPT was synthesized by combustion of citrate as well as by the columbite method. Structure, morphology and composition of the powders and precursors were characterized using X-ray diffraction (XRD), electron microscopy, electron microprobe analysis and thermal analysis DSC/TG. Trends in the drop solution enthalpies, formation enthalpies and enthalpies of mixing were derived from high temperature oxide melt drop solution calorimetry. PbMg1/3Nb2/3O3 and MgNb2O6 syntheses The first step in colloidal dispersion and nanoreaction methods involved the preparation of a stock solution containing magnesium and niobium ions in the ratio of 1.02 : 2 (2% excess of Mg2+) complexed by citric acid. To obtain this solution as described earlier,26 niobium ammonium oxalate was dissolved in a solution of citric acid (99.5%, Alfa Aesar) and hydrogen peroxide 30% (v/v) (Fisher Scientific) according to molar ratio 1 cation : 2 citric acid and 1 oxalate : 13 H2O2. The niobium solution (1.0 mol L1) was heated for 1 h at 65 C while being stirred, leading to total decomposition of oxalate. Then pH was increased to 9 with ammonia (30%, Fisher Scientific) to ensure complete citric acid ionization and the solution was stirred for another 3 h until O2 and NH3 evolution ceased. The magnesium solution (0.3 mol L1) was prepared by complexing magnesium ions from magnesium nitrate (99.9%, Alfa Aesar) with citric acid in the ratio of 1 mole of metal : 1.2 mole of citric acid. The stock solutions of magnesium and niobium were mixed according to ratio of 1 Mg2+ : 2 Nb5+ or (2% excess of Mg2+) and hereafter referred to as columbite solution. In the colloidal dispersion method, a precursor was prepared by adding lead acetate solution (0.3 mol L1) dropwise into the columbite solution at a constant pH of 10. This dispersion of lead precipitate in the citrate solution of magnesium and niobium was dried on a hot plate at 70 C until it reached the consistency of a gel. In the nanoreaction method, the columbite solution was dried on a hot plate at 70 C until it formed a gel. This precursor was annealed at 250 C for 2 h and 450 C for 1 h before DSC/TG analysis. The gel 1838 | J. Mater. Chem., 2011, 21, 1837–1845
(0.5 g) was placed directly in a furnace at 850 C for 10 min and quickly cooled to room temperature by removing the alumina crucible (volume of 50 mL) covered with lid from the furnace. The obtained powder was characterized by XRD and elemental analysis to evaluate phase formation and composition. After characterization, 0.31 g of the columbite powder was dispersed in 10 mL of ammonia solution at pH 10. To this solution kept at constant pH lead acetate (0.1 mol L1) was added dropwise according the ratio of 1 mole of Pb2+ : 1/3 mole of MgNb2O6. The dispersion of lead precipitate and columbite powder was centrifuged and washed with deionized water several times. It was dried in a vacuum oven at 100 C overnight and then ground in an agate mortar and analyzed by DSC/TG. After DSC/TG analysis, the precursors were given an additional heat treatment. The furnace was previously set at a specific temperature in the range of 600–950 C. The precursors (0.5 g) were inserted in alumina crucibles (50 mL) covered with lids and placed directly to the furnace at this temperature for 30 min followed by rapid cooling to room temperature. The annealed powders were ground in an agate mortar, uniaxially pressed in a tungsten pellet die, placed in an alumina crucible with an MgO powder bed and heated to 900 C at 10 C min1 and held for 4 h. Columbite nanocrystalline powder was obtained by annealing the powder to 850 C for 10 min, allowed by removal from the furnace and air cooling. This nanocrystalline powder was pressed and heated to 700 C at 10 C min1 and held for 10 h. Pb[(Mg1/3Nb2/3)1xTix]O3 perovskite synthesis PMN–PT was synthesized by combustion of metal citrates. Solutions of cations complexed by citric acid were mixed to provide several compositions in which x ranged from 0.35 to 0.8. Niobium and magnesium citrate solutions were prepared following the procedure described above. Lead citrate in the ratio of 1.00 Pb2+ : 1.2 citric acid was prepared by dissolving lead acetate in a solution of citric acid. Titanium solution was prepared by dissolving titanium isopropoxide (97%, Alfa Aesar) in a solution of citric acid and hydrogen peroxide 30% (v/v) in a molar ratio of 1 Ti4+ : 3 citric acid : 10 H2O2. Then, the citrate solutions were mixed according the desired mole fraction of Ti and heated at 70 C to evaporate almost all water. DSC/TG analysis was performed in the gel with x ¼ 0.35. The PMN–PT polycrystalline bulk powders were obtained from the metal citrates as described above. The metal citrates were annealed directly between 700 and 900 C for 30 min, then ground in an agate mortar, pressed in a tungsten pellet die and heated to 900 C at 10 C min1 and held for 4 h. (1 x)PMN–xPT compositions with x < 0.35 were synthesized by the columbite method since it worked well in this composition range. A slurry of oxides (0.5 g) was made by mixing columbite as prepared above, lead oxide (litharge), titanium oxide with 5 mL of polyethylene glycol (400) and 0.1 mL of propanol. The slurry was ground and homogenized in an agate mortar, uniaxially pressed in a tungsten pellet die, placed in an alumina crucible with MgO powder bed and heated to 1100 C at 10 C min1 and held for 3 h. Pb1.86Mg0.24Nb1.76O6.5 pyrochlore synthesis The pyrochlore lead magnesium niobate phase was synthesized by a simultaneous precipitation method. A peroxo-niobium This journal is ª The Royal Society of Chemistry 2011
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solution was prepared by dissolving and decomposing niobium ammonium oxalate in hydrogen peroxide 30% (v/v) solution. This solution was stirred and heated on a hot plate until the evolution of gases ceased. The other stock solutions were prepared by dissolving lead acetate and magnesium nitrate in deionized water. The resulting solutions were mixed in the molar ratio of 1.86Pb2+ : 0.24Mg2+ : 1.76Nb5+ for a final concentration of approximately 0.6 mol L1. This solution was added dropwise to a 0.5 mol L1 ammonia solution. The precipitate was centrifuged and washed with deionized water several times. It was dried in a vacuum oven at 40 C overnight and then ground in an agate mortar. After thermal characterization (DSC/TG), the precipitate was heated to 1000 C at 10 C min1 and held for 10 h. PbTiO3 synthesis Lead titanate was synthesized using conventional solid state reaction. A slurry of lead oxide (litharge) and titanium oxide (rutile) (1PbO : 1TiO2) dispersed in propanol was poured in a polyethylene jar and ball milled for 20 min. The mixture was dried at 100 C and characterized by thermal analysis. Then, it was heated to 1000 C at 10 C min1 and held for 2 h. Characterization The compositions of the synthesized samples were measured by wavelength dispersive (WDS) electron probe microanalysis with a Cameca SX100 instrument at accelerating voltage of 15 kV, beam current of 10 nA and beam size of 1 mm. Sample homogeneity was analyzed by back-scattered electron images. For microprobe analysis, the sintered pellets were polished and carbon-coated. PbTiO3, MgO, LiNbO3 standards were used for Pb, Mg, Nb and Ti. The sample compositions were calculated from an average of 10 data points. For comparison purposes, PMN perovskite and pyrochlore were analyzed by inductively coupled plasma-optical emission spectroscopy (ICP-OES) at Galbraith Laboratories, Inc. The analytical method was GLI procedure ME-70 accredited by American Association for Laboratory Accreditation (A2LA), certificate number 2777.01. Thermal analysis was performed on the precursors as well on the sintered pellets using a Netzsch STA 449 system (Netzsch GmbH). Thermogravimetry (TG) and differential scanning calorimetry (DSC) traces were recorded on heating 20–50 mg samples in platinum crucibles at 10 C min1 in 40 mL min1 oxygen flow. Buoyancy corrections were made by recording baselines with empty crucibles for all runs. Evolved gases were analyzed using a Bruker Equinox 55 IR spectrometer (Bruker Optics Inc.) (range 400–4000 cm1) attached to the thermal analyzer by a transfer line heated at 150 C. Powders and sintered pellets were analyzed by X-ray diffraction using a Bruker-AXS D8 Advance diffractometer (BrukerAXS Inc.) operated at an accelerating voltage of 40 kV and an emission current of 40 mA with CuKa radiation (l ¼ 0.15406 nm). Data were collected from 10 to 90 2q with a step size of 0.03 and a collection time of 0.5 s per step. Crystallite sizes were refined from diffraction peak broadening using a whole profile fitting procedure (Rietveld refinement) as implemented in the Jade 6.1 (MDI) software package. This journal is ª The Royal Society of Chemistry 2011
Transmission electron microscopy was performed using a Phillips CM12 instrument operated at 120 kV with LaB6 filament. Samples were dispersed in methanol, ultrasonicated and deposited on a lacey carbon grid. Magnification was calibrated using Ted Pella 603 latex spheres on grating replica standard. Calorimetry High temperature oxide melt drop solution calorimetry was performed in a custom-made isoperibol Tian-Calvet twin microcalorimeter. The equipment and experimental procedures have been described previously.27,28 The calorimeter assembly was flushed with oxygen at 40 mL min1. Oxygen was bubbled through the solvent at 3 mL min1 via a Pt-tipped alumina tube to aid dissolution. Nominal 5 mg pellets of bulk samples were loosely pressed, weighed, and dropped from room temperature into 3Na2O$4MoO3 solvent at 702 C. Standard calibration against the heat content of alpha alumina was used.
Results Thermal analysis Fig. 1A shows DSC and TG traces for the metal citrates used as precursors in the synthesis of PMN–PT. On heating to 400 C samples underwent a weight loss of approximately 80% with two corresponding heat effects. Water and carbon dioxide were detected by evolved gas analysis (FTIR) for the endothermic (water evaporation) and exothermic (organic oxidation) effects, respectively. Thus, sample crystallized at 400–600 C, as evident from an exothermic DSC peak and crystallinity confirmed by XRD as shown in Fig. 1B. This effect is accompanied by a steep weight loss of 8 wt%, also attributed after gas analysis to residual water. Samples collected at three different temperatures from the DSC/TG instrument and analyzed by XRD (Fig. 1B) confirmed evolution of the amorphous precursor to the perovskite and pyrochlore crystalline phases. No significant weight loss was observed between 600 and 900 C. Above 900 C an endothermic effect related to lead vaporization took place. Crystallization of the PMN and MN samples starting from citrate precursors showed similar thermal behavior to the PMN– PT precursor, with crystallization at 400–600 C. Residual water was not detected by DSC/TG and FTIR analyses in the synthesized bulk samples used for high temperature oxide melt solution calorimetry. Synthesis (perovskite vs. pyrochlore) Before adding an excess of MgO, the amount of perovskite phase increased with increasing heat treatment for powders synthesized by both methods. PMN precursors heat treated at 950 C for 30 min resulted in 86.6 0.7% perovskite phase for the colloidal dispersion method and 85.6 0.6% perovskite phase for the nanoreaction method. These proportions are the same within experimental error. After adding an excess of 2 mol% MgO and annealing the precursors at 850 C for 30 min, approximately 96% of the perovskite phase was obtained for both preparations. The addition of an excess of MgO resulted in a decrease of 100 C in the synthesis temperature as well as an increase in yield of the perovskite phase of 10%. Powders with 96% perovskite sintered J. Mater. Chem., 2011, 21, 1837–1845 | 1839
Fig. 1 (A) Thermogravimetry (TG) and differential scanning calorimetry (DSC) traces on heating of precursors of 0.65PMN–0.35PT obtained by the citrate method. (B) XRD patterns of 0.65PMN–0.35PT powders heat treated up to three temperatures in the DSC/TG calorimeter.
at 950 C for 4 h produced pure PMN without the second phase pyrochlore. (1 x)PMN–xPT with x $ 0.35 nanocrystalline powders free of a second phase were obtained by direct combustion of metal citrates with excess of 2 mol% MgO at 800 C for 30 min. (1 x)PMN–x powders with x < 0.35 were obtained without second phases by the columbite method when adding an excess of MgO and PbO of 2 mol% each in the precursors, and pressing and sintering at 1100 C for 3 h.
Composition and structure
The compositions of synthesized samples analyzed by microprobe analysis are the same within experimental error as the nominal compositions (Table 1). The back-scattered electron images showed homogeneous samples with no phase separation or impurity phases. In order to choose the appropriate pyrochlore composition to be studied by calorimetry, one PMN sample was annealed at 650 C for 2 h and its phases consisting of perovskite and pyrochlore were analyzed by microprobe and ICP-OES. This sample, analyzed by XRD using whole profile fitting is 87 1% pyrochlore and 12.6 0.2% perovskite. The derived compositions from microprobe analysis for these phases are Pb2.20.5Mg0.30.1Nb1.50.3O6.30.4 for pyrochlore and
1840 | J. Mater. Chem., 2011, 21, 1837–1845 — — — 5.6940(5) 5.691(2) 4.0042(2) 3.9641(2) 3.9324(1) 3.8994(4) 14.202(2) —
— — — 4.0259(5) 4.009(2) 4.0333(3) 4.0659(3) 4.0968 (2) 4.1516(5) 5.0366(9) —
c
b/ — — — 89.901(2) 89.96(3) — — — — — —
Space group Pm3m Pm3m Pm3m Cm Cm P4mm P4mm P4mm P4mm Pcan Fd3m 66.231(1) 66.032(1) 65.821(1) 130.75(3) 129.95(9) 64.667(6) 63.892(7) 63.352(4) 63.13(1) 406.82(6) 1185.15(2)
˚3 Volume/A
>100 >100 >100 85.4 6.8 61.0 4.9 58.9 5.2 83.3 4.7 92.8 5.6 >100 76.5 11.8 >100
Cryst. size XRD/nm
1.012 0.003 1.011 0.003 1.005 0.006 0.996 0.005 1.008 0.004 0.991 0.006 1.002 0.004 1.008 0.003 1.002 0.007 — 2.012 0.009
Pb
0.312 0.002 0.291 0.003 0.293 0.004 0.263 0.004 0.216 0.003 0.224 0.009 0.136 0.002 0.064 0.003 0.998 0.005 0.99 0.04 0.220 0.003
Mg
Composition (mole fraction)
0.676 0.002 0.650 0.003 0.602 0.005 0.533 0.007 0.490 0.007 0.436 0.003 0.284 0.003 0.138 0.003 — 2.01 0.03 1.768 0.005
— 0.048 0.002 0.100 0.004 0.209 0.012 0.287 0.008 0.348 0.002 0.578 0.003 0.790 0.006 — — —
Ti
3.014 0.003 3.022 0.004 3.002 0.007 3.008 0.010 3.021 0.007 3.002 0.007 3.004 0.005 2.997 0.005 2.998 0.006 6.02 0.04 6.652 0.008
O
a Compositions from ICP-OES analysis is pyrochlore (Pb2.00.1Mg0.260.02Nb1.70.1O6.510.07). b Uncertainties for the lattice parameters are given in parentheses. c MN, PDF card no 33-0875; pyrochlore, PDF card no 63-8810; PMN PDF card no 63-4648; PT PDF card no 61-4959; (1 x)PMN–xPT, x ¼ 0.05 – 0.1, ICSD 99710; (1 x)PMN–xPT, x ¼ 0.2 – 0.3 ICSD 155120; 0.65PMN–0.35PT ICD 157488; (1 x)PMN–xPT, x ¼ 0.6 – 0.8 ICSD 156342.
4.04595(4) 4.04190(3) 4.03759(4) 5.7038(5) 5.696(2) 4.0042(2) 3.9641(2) 3.9324(1) 3.8994(4) 5.701(1) 10.58257(9)
x ¼ 0.0 0.05 0.1 0.2 0.3 0.35 0.60 0.8 1.0 MgNb2O6 a Pb1.86Mg0.24Nb1.76O6.5
b
˚ Lattice parameter/A
a
b
Phase (1 x)PMN–xPT
c
Table 1 Unit-cell dimensions, crystallite sizes and compositions of columbite, pyrochlore and (1 x)PMN–xPT perovskites
Nb
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Pb0.90.1Mg0.30.1Nb0.80.1O3.20.1 for perovskite. The total composition, accounting for pyrochlore and perovskite phases, derived from ICP-OES for this sample is Pb1.000.01Mg0.360.01Nb0.910.01O3.640.03. Based on this result we chose this pyrochlore composition to be synthesized for calorimetric study. The composition of samples consisting of pure pyrochlore and pure perovskite analyzed by ICP-OES is in good agreement with values determined by microprobe analysis. Compositions derived from ICP-OES Pb1.000.07Mg0.360.03 Nb0.670.05O3.040.05 and from microprobe analysis Pb1.000.01Mg0.3260.006Nb0.6700.008O3.000.03 for one of the PMN perovskite samples are statistically indistinguishable. These compositions are also indistinguishable for the ideal composition PbMg1/3Nb2/3O3. The nominal compositions were used in the thermochemical calculations. All synthesized samples used for calorimetry were confirmed to be single phases by powder XRD as shown in Fig. 2A and B. The powder XRD patterns (Fig. 2A) as well as lattice parameters (Table 1) for (1 x)PMN–xPT samples studied here are consistent with the phase diagram and lattice parameters derived from powder neutron diffraction reported earlier29 and with (1 x)PMN–xPT (0.15 # x # 0.30) structures studied by high resolution powder X-ray diffraction.30 The composition range for PMN–PT solid solutions synthesized for the thermodynamic study covered the three different crystal systems: monoclinic, tetragonal and cubic.
Fig. 2 XRD patterns of bulk (1 x)PMN–xPT (A), pyrochlore and columbite (B) powders used for calorimetry. Crystallite size was refined from peak broadening using whole profile fitting.
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Crystallite sizes derived from whole profile fitting are >100 nm for PMN (perovskite and pyrochlore) and PT samples. Crystallite sizes for PMN–PT perovskite samples (Table 1) ranged from 58.9 5.2 nm to >100 nm and for MN (columbite) it is 76.5 11.8 nm. Since peak broadening in XRD patterns is sensitive to crystallite size rather than overall particle size, the sample 0.65PMN–0.35PT was selected for analysis by TEM (Fig. 3). The sample sintered at 900 C is bulk and has no significant presence of interfaces or grain boundaries (Fig. 3B). Annealing the metal citrates directly at 800 C for 30 min produced nanocrystalline powders with average size of 113 57 nm (Fig. 3C). The value for particle size derived from TEM being larger than that derived from XRD indicates that the particles consist of agglomerated crystallites.
Fig. 3 TEM micrographs at high magnification (scale bar 100 nm for all samples) of the 0.65PMN–0.35PT annealed at 800 C for 30 min (A) followed by pressing and sintering at 900 C for 4 h (B). (C) Size distributions in 0.65PMN–0.35PT powder annealed at 800 C for 30 min from measurement of 55 crystals in TEM.
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Energetics The enthalpies of drop solution are shown in Table 2 and Fig. 4. The values for intermediate compositions are less endothermic than those of a mechanical mixture of PMN and PT, implying that the solid solution phases are energetically less stable than a mixture of the end-members. Enthalpies of mixing of the solid solutions for PMN and PT end-members are shown in Fig. 5, again indicating an energetic destabilization. Fig. 6 shows the enthalpy of formation from PbO, MgO, Nb2O5 and TiO2 as a function of composition. It becomes less exothermic with increasing PbTiO3 content. The enthalpies of formation of pyrochlore and columbite are shown in Table 2. The tolerance factor versus enthalpy of formation for (1 x)PMN–xPT and PbZrxTi1xO3 (PZT)31 solid solutions is compared in Fig. 7A. Tolerance factor,32 t ¼ (rA + rO)/21/2(rB + rO), calculated adopting the Shannon and Prewitt ionic radii33 in
Fig. 5 Enthalpies of mixing for (1 x)PMN–xPT perovskites as a function of composition.
Table 2 Enthalpies of drop solution in sodium molybdate at 975 K, enthalpies of formation from the oxides at 298 K, and enthalpies of mixing at 975 K for (1 x)PMN–xPT perovskites
(1 x)PMN–xPT
a
DHds/kJ mol1
x ¼ 0.0 51.62 0.81(7) 0.05 47.91 0.88(9) 0.1 47.03 1.49(9) 0.2 48.66 1.53(7) 0.3 51.44 1.48(7) 0.35 52.95 1.40(9) 0.60 55.60 1.68(7) 0.8 62.95 1.30(7) 1.0 67.50 1.86(8) 163.17 2.93(6) MgNb2O6 Pb1.86Mg0.24Nb1.76O6.5 160.45 1.94(11)
DHmix/ DHf,ox/kJ mol1 kJ mol1 34.41 1.00 29.20 0.58 26.81 0.58 25.42 0.58 25.18 0.60 25.18 0.61 20.29 0.72 21.78 0.83 21.61 0.83 76.99 0.79 102.34 2.30
0.00 4.51 6.18 6.14 4.94 4.22 5.55 1.37 0.00 — —
1.17 1.67 1.70 1.68 1.63 2.04 1.98
a Mean values of the number of experiments are given in parentheses, uncertainties are calculated as two standard deviations of the mean, extra digit is retained to prevent round-off error.
Fig. 6 Enthalpies of formation for (1 x)PMN–xPT perovskites for PbO, MgO, Nb2O5, and TiO2 as a function of composition.
Fig. 4 Enthalpies of drop solution for (1 x)PMN–xPT perovskites as a function of composition. The data are fit by two straight line segments, one for cubic phase, and one for tetragonal and monoclinic phases. The dashed curve is a quadratic fit through all the data.
1842 | J. Mater. Chem., 2011, 21, 1837–1845
which rB is a weighted average of the ionic radii for the metal ions (Mg2+, Zr4+, Ti4+ and Nb5+) in the b sites (octahedral coordination). The PbZrxTi1xO3 phases are tetragonal (x ¼ 0 to 0.5), rhombohedral (x ¼ 0.5 to 0.95) and orthorhombic (x ¼ 0.95 to 1.0). For (1 x)PMN–xPT structures are cubic (x ¼ 0 to 0.1), monoclinic (x ¼ 0.2 to 0.3) and tetragonal (x ¼ 0.35 to 1.0). PZT exhibits a behavior typical of many perovskites in which the tolerance factor diminishes and the enthalpy of formation from oxides becomes more positive as a smaller ion is replaced by a larger one (e.g. Ti4+ by Zr4+, rTi4+ ¼ 0.61 and rZr4+ ¼ 0.72). In case of PMN–PT the tolerance factor becomes more positive by replacing Mg2+ and Nb5+ by Ti4+ in the b sites. The change in the tolerance factor for PMN–PT is smaller than that for PZT. A strong variation in enthalpy of formation with tolerance factor is seen for the cubic crystal structure. Fig. 7B shows different behavior for PZT and PMN–PT in terms of average cation radius in the b sites. For PMN–PT the enthalpy of formation becomes less exothermic as the average cation radius diminishes, which is opposite to that observed for PZT. This journal is ª The Royal Society of Chemistry 2011
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answer in terms of thermochemistry to this apparent instability of the perovskite phase, we can assume that the extent to which decomposition occurs is kinetically controlled and pyrochlore remains constant in composition. Starting with perovskite composition, one needs more Nb and less Mg and Pb in the pyrochlore. The reaction, balancing Nb in both phases, produces excess MgO and PbO. Complete decomposition would be 2.639PbMg0.333Nb0.667O3 / Pb1.86Mg0.24Nb1.76O6.5 + 0.777PbO + 0.631MgO (1) The enthalpy of this reaction at room temperature can be calculated using the enthalpies of formation from the oxides from Table 2 as follows DHrxn ¼ DHf;oxðpyrochloreÞ 2:639DHf;oxðperovskiteÞ DHrxn ¼ 11:52 3:48 kJ
(2)
Thus this reaction is energetically favorable. In a reaction among solid phases, the vibrational entropy change can usually be neglected. However, positional disorder in both perovskite and pyrochlore gives each configurational entropy, and the change in the configurational entropy might significantly affect the Gibbs free energy of reaction at high temperature. The change in the configurational entropy for the decomposition of perovskite can be calculated as DSrxn ¼ Sconf. pyrochlore 2.369Sconf. perovskite. The configurational entropy for PbMg1/3Nb2/3O3 is Sconf: PMN ¼ R xPb2þ ln xPb2þ þ xMg2þ ln xMg2þ þ xNb2þ ln x Nb2þ J mol1 K1 Fig. 7 Enthalpy of formation versus tolerance factor (A) and (B) versus average cation radius in the b sites.
Sconf: PMN ¼ Rð0:33ln 0:33 þ 0:67ln 0:67Þ J mol1 K1 Sconf: PMN ¼ 5:27 J mol1 K1 (3)
Discussion Synthesis (perovskite vs. pyrochlore) The perovskite contents analyzed by XRD for powders obtained by both methods used to synthesize PMN agree within experimental error. This suggests that the heat treatment affects the phase chemistry more than the precursors. Moreover, the addition of excess PbO and MgO improves the yield of perovskite phase, but the heat treatment and annealing time are dominant factors to obtain the pure perovskite phase. The addition of excess MgO and PbO for obtaining pure perovskite is explained in terms of composition limits in the phase diagram.21,22 In an earlier work,34 PMN stoichiometric samples annealed at 1200 C for 1 h or 3 h revealed a highly inhomogeneous mixture consisting of perovskite, pyrochlore and magnesium oxide. In other work,35 inclusions of MgO were also observed by EDS in the grains and grain boundaries of PMN with an excess of MgO. Evidence for Nb and Pb was also detected in these inclusions but no diffraction lines were observed for the MgO phase in the XRD pattern. From these earlier results, it is observed that secondary phases, probably MgO and PbO, are formed during synthesis or decomposition of perovskite PMN to pyrochlore. However, there is no discussion in terms of thermodynamic stability of the competing phases. To find an This journal is ª The Royal Society of Chemistry 2011
For pyrochlore (Pb3+(3/2)x,1(3/2)x(MgxNb4x)O13,, where ‘‘,’’ represents vacancies)21 assuming Pb and vacancies mix, Nb and Mg mix, oxygen sublattice is ordered or correlated with Mg, Nb, and Pb Sconf: pyrochlore ¼ R xPb2þ ln xPb2þ þ x, ln x, þ xMg2þ ln xMg2þ þ xNb2þ ln xNb2þ
Sconf: pyrochlore ¼ Rð0:93 ln 0:93 þ 0:07 ln 0:07 þ 0:12 ln 0:12 þ 0:88 ln 0:88Þ J mol1 K1 Sconf: pyrochlore ¼ 5:16 J mol1 K1 (4) Thus, the change for the configurational entropy for the decomposition of perovskite would be DSconf: rxn ¼ Sconf: pyrochlore 2:639Sconf: perovskite J K1 (5) DSconf: rxn ¼ 8:76 J K1 Considering the equation for the Gibbs free energy, DG ¼ DH TDS, the decomposition of perovskite is not favorable at temperatures above T ¼ DHrxn/DSconf. rxn ¼ 1316 K. If J. Mater. Chem., 2011, 21, 1837–1845 | 1843
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pyrochlore has no configurational entropy (Sconf. pyrochlore ¼ 0) the equilibrium temperature is 828 K. In the first case, the decomposition of perovskite to pyrochlore, MgO and PbO is favorable at all relevant synthesis temperatures. Furthermore, if free PbO is formed, it will vaporize with increasing temperature and drive reaction (1) even more to the right. The synthesis of perovskite by the columbite method can also be evaluated by thermodynamics using the following equation
3 kJ mol1. However, the extrapolated enthalpy of transition is only about 1 kJ mol1 at the morphotropic phase boundary (x ¼ 0.35), which seems reasonable. The points for the monoclinic phase fall on the line for the tetragonal phase, suggesting very small (
