J O U R N A L O F C H E M I S T R Y Materials Crystallization behaviour of the series of solid solutions ZrxTi1-xO2 and PbyZrxTi1-xO2+y prepared by the sol–gel process Rotraut Merkle* and Helmut Bertagnolli Institut fu�r Physikalische Chemie, Universita�t Stuttgart, PfaVenwaldring 55, D-70550 Stuttgart, Germany Received 16th June 1998, Accepted 11th August 1998 A series of solid solutions of zirconium titanium oxide ZrxTi1-xO2 (0x1) and PbyZrxTi1-xO2+y (0y1.15, 0x1) up to lead zirconate titanate PbZrxTi1-xO3 was prepared from zirconium and titanium n-propoxide and lead acetate, dissolved in 2-methoxyethanol, by the sol–gel process.The crystallization was investigated by diVerential thermal analysis (DTA), and the apparent activation energies, crystallization enthalpies and Avrami exponents were determined.The crystalline phases were identified by X-ray diVraction (XRD). Within the series of solid solutions ZrxTi1-xO2, the activation energy changes from ca. 200 kJ mol-1 for samples with low (x0.14) or high (x0.9) ZrO2 content, to ca. 800 kJ mol-1 for intermediate ZrO2 contents. Within the series of solid solutions PbyZrxTi1-xO2+y, PbO lowers the activation energies and hinders the crystallite growth.solution in PrnOH, Ti(OPrn)4 98 wt% solution in PrnOH, Alfa] 1 Introduction in 2-methoxyethanol (MOE, distilled before use). During the The sol–gel process allows the simple preparation of oxidic addition of 5 mol H2O per mol Zr/Ti, a slightly turbid gel was solid solutions with a continuous variation of the stoichiometry formed. It was dried at 90 °C, 20 mbar and crushed to a fine and a homogeneous distribution of all components at the powder.For gels containing more than 10% ZrO2, a steam molecular level. It is frequently used for the synthesis of treatment7 was applied to prevent the formation of carbon electrical and magnetic ceramics with optimized properties.1 residues during pyrolysis which severely disturb the following Owing to the high homogeneity of the amorphous oxide DTA measurements. For gels with a ZrO2 content of up to mixture which is the product of the pyrolysis of the dried gels, 10% the steam treatment cannot be applied because small crystallization can occur without long range diVusion at mod- anatase crystallites are formed during this treatment.erate temperatures. Thus, desired or undesired metastable Additionally, the solvent was varied and samples of ZT(X) phases can be the first crystallization products2 which trans- were prepared with n-propanol (PrOH, distilled before use) form to the thermodynamically stable structures at higher instead of MOE. During hydrolysis, a voluminous precipitate temperatures. instead of a gel was formed.It was dried under the same In the first step, the binary system of ZrxTi1-xO2 [ZT(X) conditions as the gel samples. These samples pyrolyze without with X=100x=content of ZrO2 in %] prepared by the sol–gel any formation of carbon residues even without steam treatprocess is investigated to study the eVect of substituting Zr by ment. Samples of ZT(X) prepared in PrOH with and without Ti on the crystallization behaviour.Zr and Ti can be inter- steam treatment [labeled ZT(X)-PS and ZT(X)-P] are examchanged easily in many ternary systems, e.g. in the perovskites ined to study the eVect of the steam treatment on the ABO3 on the B sites with A=Pb, Ba or Sr. Nevertheless, in crystallization. the binary system ZrO2–TiO2 the diVerences between zir- Lead containing samples were prepared analogously to conium and titanium may have larger eVects.The hydrolysis ZT(X) by dissolving appropriate amounts of lead acetate of TiMOR groups and the condensation of TiMOH groups trihydrate (99.5%, Fluka) in methoxyethanol (100 ml per are faster than the corresponding reactions of ZrMOR and 0.1 mol of Zr/Ti alkoxide), adding Zr/Ti n-propoxide ZrMOH groups.3–5 While titanium is mostly octahedrally and hydrolyzing.After the steam treatment, samples of coordinated by oxygen, zirconium prefers larger coordination P(Y )ZT(45) with 0Y115% pyrolyze without carbon resi- numbers of 7 to 8. dues. In the series P(Y )Z, samples with a PbO content larger In the second step, the PbO content in the ternary system than 10% form carbon residues and cannot be studied further.PbyZrxTi1-xO2+y [P(Y )ZT(X) with Y=100y=content of Samples of P(Y )T must be prepared in n-propanol (with PbO in %] is varied at fixed ZrO2 content X, and gives a series anhydrous lead acetate to prevent precipitation before hydroly- of solid solutions, extending from P(Y )T, P(Y )ZT(45) to sis) without steam treatment, because they crystallize during P(Y )Z.Between ZrO2 and PZ, a complete series of solid the course of the steam treatment, and P(Y )T, prepared in solution can be prepared by coprecipitation,6 where the struc- MOE without steam treatment, forms carbon residues. ture changes from the tetragonally distorted fluorite structure Samples of P(Y )T-P with Y>15% crystallize in a diVerent for the lead poor samples to the pyrochlore structure for lead structure (PbTi3O7) and were not examined further.rich samples. The P(Y )ZT(X) series provides information A Netzsch STA 409 with Al2O3 crucibles was used for DTA about the role of the lead in the crystallization process. The measurements. The mass of the samples was 5–30 mg, the knowledge obtained from all these series can improve the furnace was purged with 0.5 l min-1 of dry air.All samples understanding of the crystallization of PZT prepared by show an exothermic DTA peak at about 300 °C due to the the sol–gel process. pyrolysis of the organic components, and a total weight loss of less than 10% for ZT(X) up to about 25% for PZT(X). After this pyrolysis step, no further weight loss occurs, which 2 Experimental indicates that the samples have reached the final composition and contain no further organic residues.Activation energies The samples ZT(X) with 0X100% were prepared from a 1 molar solution of Zr/Ti n-propoxide [Zr(OPrn)4 70 wt% were determined from DTA runs with heating rates from J. Mater. Chem., 1998, 8(11), 2433–2439 24331 K min-1 to 30 K min-1. Crystallization enthalpies were cal- preexponential factors p0, k0: culated from the integrals of the DTA peaks.Some samples have extremely narrow DTA peaks. Thus the total crystalliz- b-ln R Ea¾ # 1 n ln ap0k0 m m =ln c0¾ (5) ation heat is liberated in a very short time, and the sample is overheated which also accelerates the crystallization. This The molar volume contained in a can be estimated from the leads to unrealistically high values of the Avrami exponents volume of the unit cell, which is usually of the order of determined from the DTA peak shape.Therefore the samples some A° 3, and the geometry factor included in a is of the same were mixed with Al2O3 as an inert material in the mass ratio order of magnitude as m, thus the apparent preexponential of 152 for determining Avrami exponents from the DTA factor c0¾ approximately equals the geometrical average of the peak shape.preexponential factor of the nucleation rate per molecular unit X-Ray diVractograms were measured on a horizontal Stoe p0¾=p0/NA and of the growth rate k0: Stadi P diVractometer with a focussing germanium monoc0 ¾#(p0¾k0 m)1/n (6) chromator and a curved position sensitive detector (PSD).Cu-Ka radiation (40 kV, 35 mA) was used. The samples were An approximate value nGr of the Avrami exponent n can be pressed to tablets, fixed on a rotating sample holder and determined from the integral . h(T )dT and the maximum measured in reflection mode. The measured intensities were height h(Tm) of the DTA peak20 by the phenomenological corrected for absorption8 and polarization.9 The crystallite relation, deduced from simulated DTA curves: size L was determined from the full width at half maximum (FWHM) d(k) of the reflections on the k scale [k=4p sin(H)/l] nGr=0.02+C h(Tm)Tm2 Ea¾.h(T )dT (7) with the Scherrer equation10 L=2p/d(k).The measured d(k)exp was corrected for apparatus broadening d(k)app according to11 C is 2.211×10-4 for energies in eV,20 corresponding tod(k)=d(k)exp-d(k)app with the assumption that the peak 0.02133 for energies in kJ mol-1.For the crystallization of shapes are lorentzian. The apparatus broadening d(k)app was PZT prepared by the sol–gel process,21 a good agreement was determined from sintered PT and PZ samples with suYciently found between n determined from Avrami plots of isothermal large crystallite size so that d(k)exp equals d(k)app.crystallization measurements and approximate values of nGr DiVractograms of samples heated to 350 °C, where the from non-isothermal DTA measurements. pyrolysis of organic components is completed, prove that these samples are amorphous. DiVractograms of samples heated above the temperatures of the crystallization peaks, which 4 Solid solution series ZT(X) were observed in the DTA measurements, show the complete transformation to the crystalline phases. The crystalline phases formed in the course of the heating of the ZT(X) samples depend on the ZrO2 content X.The pure TiO2 and the titanium rich samples up to ZT(18) crystallize in the anatase structure. The formation of this metastable 3 Crystallization kinetics phase by a sol–gel process is also reported for TiO2 in The isothermal formation of a crystalline phase from an refs. 22–24. amorphous or another crystalline phase by a mechanism of In the intermediate range of ZT(25) to ZT(60), the samples nucleation and surface controlled growth can be described by crystallize in the orthorhombic srilankite structure (a-PbO2 the Johnson–Mehl–Avrami equation:12–15 structure), whose unit cell parameters vary linearly with the ZrO2 content.25 At temperatures below about 1200 °C, srilank- 1-x(t)=exp(-apkmtn/m) (1) ite TiZr2O6 is the only stable compound in this stoichiometry range, and above 1200 °C only ZrTiO4 is stable.26 For the x(t) is the fraction transformed at time t, m is the dimensionalsol –gel samples crystallizing at much lower temperatures, ity of the growth and n=m for a constant number of nuclei, the metastable srilankite is formed over a wide range.The and n=m+1 for a constant nucleation rate; a includes a diVractograms of the crystalline phases of ZT(25)–ZT(60) are geometry factor and the reciprocal of the molar volume; p collected in Fig. 1. and k are the rate constants of nucleation and linear crystallite The samples with a ZrO2 content of more than 60% crys- growth.They are assumed to follow an Arrhenius law: tallize mainly in the tetragonally distorted fluorite structure. p=p0 exp(-En/RT) (2) The formation of this phase in the course of the sol–gel process is also reported for ZrO2 in ref. 27, although this phase is k=k0 exp(-Eg/RT) (3) stable only at temperatures of 1100–2300 °C.The diVractograms of the crystalline phases of ZT(75)–ZrO2 are also The Kissinger plot16,17 which was deduced in order to collected in Fig. 1. ZT(75) and ZT(85) still show a very weak determine the activation energy of a simple, not interface srilankite (011) reflection. Shoulders at 2H=28.2° and 2H= controlled reaction from the dependence of the shift of the 31.5° besides the main (111) fluorite reflection indicate the DTA peak maximum temperature Tm from the heating rate a, presence of small amounts of the monoclinic ZrO2 phase can also be applied to crystallization processes obeying Avrami formed from the tetragonal phase during pressing of the kinetics.The plot of ln(a/T 2m) versus 1/Tm yields an apparent sample tablet.activation energy Ea¾ as the weighted average of En and Eg: Application of the Scherrer equation yields crystallite sizes of about 250 A° for TiO2 and ZT(10), and over 1000 A° for Ea¾= En+mEg n (4) ZT(18). The crystallite size is in the range 140–350 A° for the srilankite phases, and rises for the fluorite phases to 640 A° for ZT(95) and over 1000 A° for ZrO2.For the samples prepared For the crystallization of ZT(X) and P(Y )ZT(X) samples, both the nucleation (i.e. the growth of a subcritical nucleus to in PrOH, the steam treatment has no eVect on the crystallite sizes. The only exceptions are TiO2-P and ZT(10)-P, where a supercritical nucleus) and the crystallite growth require the reorientation of the (Zr/Ti)O6 network by breaking and the crystallite size increases significantly with the use of PrOH, and reaches about 1000 A° .reconstructing (Zr/Ti)MOM(Zr/Ti) bonds. Therefore, it is very likely that En#Eg and thus E¾a#En#Eg. In this case, The DTA curves of ZT(X), prepared in MOE, are shown in Fig. 2. TiO2 and ZT(10) crystallize at about 400 °C and the crystallization is isokinetic,18,19 and the following relation holds for the intercept b of the Kissinger plot and the 500 °C, respectively.The samples ZT(18)–ZT(75) with moder- 2434 J. Mater. Chem., 1998, 8(11), 2433–2439Fig. 1 DiVractograms of the crystalline phases of ZrxTi1-xO2 [ZT(X) with X=100x=ZrO2 content in %], shifted along the ordinate for clarity. Fig. 2 DiVerential thermal analysis curves of ZrxTi1-xO2 [ZT(X) with X=100x=ZrO2 content in %], prepared by a sol–gel process in 2-methoxyethanol.ate ZrO2 contents crystallize at temperatures above 650 °C and exhibit very narrow DTA peaks. The crystallization temperature decreases with increasing ZrO2 content down to about 400 °C for ZrO2. The crystallization temperature is independent of which crystal structure is formed, because the samples crystallizing above 650 °C crystallize in the anatase [ZT(18)], srilankite [ZT(25)–ZT(60)] and fluorite [ZT(75)] structures.All the crystallization enthalpies are in the range of about 14–18 kJ mol-1; only the samples TiO2 and ZT(10), prepared in MOE without steam treatment, show lower values of about 10 kJ mol-1. The apparent activation energies Ea¾, determined from the Kissinger plots (examples are shown in Fig. 3), are depicted in Fig. 4. They show the same trend as the crystallization temperatures with a distinct maximum at medium ZrO2 contents. For the samples prepared in MOE, the apparent activation energies of about 800 kJ mol-1 reach the values of the Fig. 3 Kissinger plots of ZrxTi1-xO2 [ZT(X) with X=100x=ZrO2 sublimation enthalpies of ZrO2 and TiO2 (811 kJ mol-1 and content in %], prepared by a sol–gel process in 2-methoxyethanol. 695 kJ mol-1 28).The crystallization behaviour of the samples prepared in PrOH with steam treatment is very similar to that of the samples prepared in MOE with steam treatment. Thus, must be broken in order to allow the linked (Zr/Ti)O6 the diVerent early stages (gel versus voluminous precipitate) octahedra to arrange according to the crystal structures.For have no eVect on the crystallization. The samples prepared in the pure components ZrO2 and TiO2 of the binary system PrOH without steam treatment show the same general trends (Zr/Ti)O2, the activation energies are similarly low at about in the activation energies, but the maximum values of about 200 kJ mol-1. This can be interpreted by the following, simpli- 550 kJ mol-1 for ZT(18)–ZT(75) are lower than for the steam fied model.The TiMOMTi bonds (and ZrMOMZr bonds) treated samples. can be broken with the same probability in both directions: The drastic change of the apparent activation energies with the zirconium content is not correlated with the changes in OMTiMOMTiMO�OMTiMO9 |+TiMO the final crystal structures.Therefore the reason for this change OMTiMOMTiMO�OMTi+|O9 MTiMO must be sought in the amorphous phase or the crystallization process. In the crystallization process, some (Zr/Ti)MO bonds thus the breaking of one (or very few) TiMOMTi connections J. Mater. Chem., 1998, 8(11), 2433–2439 2435l4 mol-4 s-1 was found.5 As the alkoxide exchange reaction M(OPrn)+EtOH�MOEt+PrnOH is fast, even at room temperature, 4 it can be assumed that the species which was hydrolyzed was mostly Zr(OEt)4, and therefore k3 and k¾5 can be compared to prove the faster hydrolysis of titanium alkoxides compared to the corresponding zirconium alkoxides.The condensation reaction of the TiMOH groups, which follows the hydrolysis step, TiMOr=TiMOMZr+ROH TiMOH+HOMTi=TiMOMTi+H2O occurs easier with ZrMOR than with TiMOH due to the larger basicity of the leaving group, and leads to the favoured formation of TiMOMZr bonds instead of the homocondensation to TiMOMTi and ZrMOMZr.In an EXAFS study at the Zr K-edge of PZT gel which was not dried,32 the first metal backscatterer around Zr was found to be Ti, indicating Fig. 4 Apparent activation energies of ZrxTi1-xO2 [ZT(X) with X= 100x=ZrO2 in %], with standard deviation calculated from the linear the preferred heterocondensation.Therefore already at moderregression. ate ZrO2 or TiO2 contents of about 20%, a large amount of ZrMOMTi bonds may be present and causes the change in the crystallization behaviour. yields fragments which are suitable for the progress of the The Avrami exponents nGr, determined from the DTA peak crystallite growth.shape, show no significant diVerence between the samples Ea¾ and thus En and Eg are drastically increased when more prepared in MOE or PrOH and with or without steam than about 15% of the other metal cation is present. Although treatment. nGr of the samples crystallizing in the anatase Zr and Ti are chemically similar, they disturb each other structure decreases from almost 4 for TiO2 to about 2 for markedly in the crystallization process. As a consequence of ZT(18).The samples forming the srilankite phase have Avrami the larger electronegativity and the larger positive charge exponents in the range of 3–4. nGr decreases to nGr#2 for density of Ti4+ compared to Zr4+, the TiMOMZr bonds are ZT(75) with the change to the fluorite phase, and increases broken preferably in one direction: again with increasing ZrO2 content to about 4 for ZrO2.The MOMTiMOMZrMOM�MOMTiMO9 |+ZrMOM closer the stoichiometry of a sample is to that of the ‘pure’ phase (TiO2 with anatase structure, ZrTi2O6 and ZrTiO4 with Thus mainly the fragments MOMTiMO9 | and ZrMOM are srilankite structure, ZrO2 with tetragonally distorted fluorite formed from MOMTiMOMZrMOM bonds.If other fragstructure), the higher are the Avrami exponents. The maximum ments, e.g. MOMTi or |O9 MZrMOM, are needed for the values of about 4 correspond to a crystallization mechanism reconstruction of the (Zr/Ti)O6 network during the crystallizof a constant nucleation rate with subsequent three-dimen- ation, additional bonds of a (Zr/Ti)O6 octahedron must be sional crystallite growth.When the growth is disturbed, the broken, which strongly increases the activation energy. This Avrami exponent is reduced more or less. will happen more often when the number of TiMOMZr bonds From the ordinate intercept b and the apparent activation is high, i.e. at intermediate zirconium contents. energies E¾a of the Kissinger plots, the apparent preexponential In order to estimate the probability of TiMOMZr bonds in factors c0¾#( p0¾k0 m)1/n can be calculated according to eqn.amorphous samples of ZT(X), the hydrolysis of the zirconium (5). They show a strong increase with increasing values of Ea¾. and titanium alkoxides shall be considered briefly. The struc- A similar trend was observed for the thermally activated tural aspects of the formation of oligomers and polymers diVusion in amorphous alloys.33–35 The plot of the logarithm during the hydrolysis of zirconium and titanium alkoxides of the Arrhenius preexponential factors versus the diVusion were studied extensively by Bradley and coworkers.29–31 activation energies of several iron–zirconium alloys, shown in Kinetic aspects of the diVerent steps comprising the complex ref. 33, exhibits a linear correlation approximately. This hydrolysis and condensation reactions were investigated relation can be deduced from the Eyring theory, which yields later.3–5 Owing to the larger charge density of the Ti4+, which a temperature dependence of the rate constants of makes the hydrogen atoms of coordinated water molecules in TiMOH2 more acidic, the hydrolysis of TiMOR groups to TiMOH is faster than the hydrolysis of ZrMOR groups.c= kT h exp(DS/R) exp(DH/RT) (8) For the formation of TiO2 from 0.1–0.2 molar solutions of Ti(OEt)4 in ethanol with a water5Ti ratio of 2–5, a rate law instead of the Arrhenius law.36 For a small temperature range, of t=k[H2O]3[Ti(OEt)4] (t is the time from the addition of the frequency factor kT /h is approximately constant, and the the water to the first turbidity of the solution) was found.3 It Arrhenius preexponential factor c0 can be identified as indicates that the hydrolysis reaction Ti(OR)4+3H2O�Ti(OR)(OH)3+3ROH c0= kT h exp(DS/R) (9) is the rate limiting step, and a value of k=6.6 l4 mol-4 s-1 was determined for the hydrolysis. In contrast, a rate law of containing the activation entropy DS‡.The Arrhenius activation energy Ea corresponds to the activation enthalpy t=k[H2O][Ti(OEt)4]2 is observed for dilute solutions [0.01–0.03 molar solutions of Ti(OEt)4 in ethanol ] with a DH‡. In contrast to gas reactions, usually DS‡ is positive in the solid state, because the transition state requires a high large excess of water (10–100 mol H2 per mol Ti).4 Instantaneous hydrolysis to Ti(OH)3(OEt) is proved by meas- mobility to enable a reorientation of the fragments into another structure.The increase of the activation energies Ea and uring the rapid decrease of the water content. The formation of precipitates is much slower, and the condensation reaction activation enthalpies DH‡ observed in refs. 33–35 was attributed to a larger number of atoms involved in a collective is the rate-limiting step. For the hydrolysis of 0.05–0.53 molar solutions of Zr(OPrn)4 motion during a diVusion step. This is accompanied with an increase of the activation entropy DS‡. In case of an approxi- in ethanol, a rate law of t=k¾[H2O]3[Zr(OPr)4] with k¾=0.9 2436 J. Mater.Chem., 1998, 8(11), 2433–2439Fig. 6 DiVractograms of PbyZr0.45Ti0.55O2+y [P(Y )ZT(45) with Y= Fig. 5 Logarithmic plot of the Arrhenius preexponential factor c¾O 100y=PbO content in %], shifted along the ordinate for clarity. versus activation energy E¾a for the samples ZrxTi1-xO2 [ZT(X) with X=100x=ZrO2 content in %], with standard deviation calculated from the linear regression.mate proportionality DS‡~DH‡, we get from eqn. (9) the observed linear relation ln c0~DS‡�ln c0~DH‡. This interpretation of the Arrhenius preexponential factors can be transferred to the crystallization of the ZT(X) samples. The increase of Ea¾ can be attributed to a larger number of (Zr/Ti)MOM(Zr/Ti) bonds which must be broken in the transition state, and therefore Ea¾~DS‡ can be assumed.In Fig. 5 the plot of ln c0¾ versus Ea¾ is shown, which clearly exhibits a linear relation between these quantities. The maximum eVect of the activation entropy on c0¾ can be estimated from the crystallization of ZT(18) taking place at about 650 °C. From c0¾#1052 min-1 and kT /h#1015 min-1, we get DS‡#700 J mol-1 K-1 which is still below the entropy of sublimation of about 765 J mol-1 K-1 estimated from the sublimation enthalpy of TiO2.Another example of the correlation of activation energies Fig. 7 DiVerential thermal analysis curves of PbyZr0.45Ti0.55O2+y [P(Y )ZT(45) with Y=100y=PbO content in %], prepared in 2- and Arrhenius preexponential factors can be found in ref. 37 methoxyethanol with steam treatment. for the crystallization of PbTiO3.For samples prepared by coprecipitation or sol–gel processing, activation energies of 260–270 kJ mol-1 and preexponential factors of 2×1015–7×1017 s-1 were determined. Amorphous PbTiO3, prepared from the melt by roller quenching, yields Ea¾= 633 kJ mol-1 and c0¾=4×1037 s-1. The higher activation energy of the roller quenched sample can be attributed to the stronger hindrance of movements due to the significantly higher density.The collective motion of the adjacent (Zr/Ti)O6 octahedra increases DS‡ and therefore also c0¾. d solution series P(Y)ZT(45) The samples P(Y )ZT(45), prepared in MOE with steam treatment, can be examined over the whole range 0Y100%, and additionally even with a lead excess (y= 107% and y=115%). P(5)ZT(45) and P(10)ZT(45) crystallize in the srilankite structure.At larger PbO contents, the samples form the fluorite structure with a continuous transition to the pyrochlore phase. The diVractograms are shown in Fig. 6. The Fig. 8 Apparent activation energies of PbyZr0.45Ti0.55O2+y crystallite size decreases from 350 A° [ZT(45)] and 160 A° [P(Y )ZT(45) with Y=100y=PbO content in %], prepared in 2- [P(10)ZT(45)] to 110 A° [P(40)ZT(45)] and down to 40 A° for methoxyethanol with steam treatment, with standard deviation the pyrochlore phase of P(85)ZT(45)–P(115)ZT(45). calculated from the linear regression.In Fig. 7 the DTA curves of ZT(45)–P(40)ZT(45) are depicted. With increasing PbO content, the crystallization temperature decreases and the peaks broaden. The apparent decreases with an excess of PbO to 420 kJ mol-1 for P(115)ZT(45).The transformation of the pyrochlore phase activation energies are shown in Fig. 8. A PbO content of 5% already reduces Ea¾ from 800 kJ mol-1 to below 600 kJ mol-1 to the perovskite phase, which can be observed for the samples P(85)ZT(45)–P(115)ZT(45), has a constant activation energy without changing the crystal structure.Ea¾ of the formation of the fluorite or pyrochlore phase is constant at about of 300 kJ mol-1. The crystallization enthalpy decreases strongly from 16 kJ mol-1 for ZT(45) to 8 kJ mol-1 for 530 kJ mol-1 for P(10)ZT(45)–P(100)ZT(45) and slightly J. Mater. Chem., 1998, 8(11), 2433–2439 2437Fig. 9 Schematic representation of the (Zr/Ti)MOM(Zr/Ti) bond reconstruction in the presence of PbO.M=(Zr/Ti). P(40)ZT(45) and to only 3 kJ mol-1 for the pyrochlore formation of PZT(45). The Avrami exponents nGr decrease parallel to the decrease of the crystallite size from about 4 for ZT(45)–P(10)ZT(45) to 2 for P(40)ZT(45) and about 1.5 for P(85)ZT(45)–P(115)ZT(45). The small nGr for the pyrochlore formation of P(85)ZT(45)–P(115)ZT(45) can be interpreted with a high, constant nucleation rate and subsequent growth to a maximal crystallite radius of 20 A° .21 Growth to larger Fig. 10 DiVerential thermal analysis curves of PbyTiO2+y [P(Y )T-P maximal radii corresponding to the crystallite sizes found for with Y=100y=PbO content in %], prepared in n-propanol without P(40)ZT(45) and P(25)ZT(45) yields Avrami exponents steam treatment. closer to 4.The decrease of Ea¾ and thus En and Eg can be explained by the involvement of PbO in the reconstruction of the (Zr/Ti)O6 P can be explained by a mechanism of a constant nucleation rate and subsequent crystallite growth which is more or less network. Lead has a high mobility either in the form of PbO (cf. the high vapour pressure of PbO38) or in the form of Pb2+ hindered. When the crystallite growth ceases at some large (>1000 A° ) but fixed radius, n decreases without any eVect on (cf.the high diVusion coeYcient of Pb2+ in sintered ZrTiO439). A small amount of lead is suYcient to act as a ‘catalyst’ the XRD line width. This is observed, e.g., for the perovskite formation of PZT in ref. 21. In order to explain the large and to break many bonds subsequently.The decrease of the activation energy can interpreted by the avoiding of shifts of the crystallization temperatures with increasing PbO content, a corresponding decrease of the Arrhenius pre- energetically unfavourable fragments during crystallization. The eVect of PbO is shown schematically in Fig. 9. The exponential factors p0 and k0 must also be assumed. In total, the presence of PbO in TiO2 gels seems to hinder the insertion of PbO into a OM(Zr/Ti)MOM(Zr/Ti)MO bond is energetically more favourable than the formation of crystallization.OM(Zr/Ti)MO9 |+(Zr/Ti)MO fragments which is required in the absence of lead. The PbMO bonds, which are weaker 7 Solid solution series P(Y)Z compared to (Zr/Ti)MO bonds, can be broken easily. The additional oxygen atom, introduced with the PbO, ensures The samples P(Y )Z, prepared in MOE with steam treatment with a PbO content of 0Y10%, crystallize in the tetra- that the Zr/Ti atoms are surrounded by at least 6 oxygen atoms during the rearrangement of the (Zr/Ti)O6 network.gonally distorted fluorite structure. The crystallite size decreases from over 1000 A° for ZrO2 to about 500 A° for Thus the unfavourable (Zr/Ti)MO fragments with a reduced coordination number are avoided.After the rearrangement, P(5)Z and P(10)Z. The DTA peak temperatures at a heating rate of a=3.5 K min-1 shift from 380 °C for ZrO2 to 425 °C the PbO is eliminated again, leaving the modified (Zr/Ti)O6 network. The decrease of the crystallite sizes with increasing for P(5)Z and to 455 °C for P(10)Z.All the Avrami exponents nGr have values larger than 4 due to overheating, even after lead content can also be explained by this model. If the PbO is not eliminated, then a configuration (Zr/Ti)MOM mixing with Al2O3. The apparent activation energies are constant at about 270 kJ mol-1, and the crystallization PbMOM(Zr/Ti) remains. Owing to mechanical stress caused by the volume shrinkage during crystallization, the weaker enthalpies are about 19 kJ mol-1.The eVect of the presence of PbO in ZrO2 gels is similar PbMO bonds can be broken yielding (Zr/Ti)MOM Pb+|O9 M(Zr/Ti). The continuous octahedral network is to that observed for P(Y)T-P. The activation energies of TiO2 and ZrO2 are already so low that no further decrease broken and thus the crystallite growth is stopped.The pyrochlore phase of PZT(45) is the lead rich end occurs when lead is added. It can be assumed that (Zr/Ti)MOMPbMOM(Zr/Ti) bonds are also formed in member of this solid solution series. Therefore the small crystallite size of 40 A° , the Avrami exponent of 1.5 and the these systems, and that they can be broken easily to (Zr/Ti)MOMPb+|O9 M(Zr/Ti), which stops the crystallite apparent activation energy of 500 kJ mol-1 (which is relatively high compared with Ea¾#300 kJ mol-1 for the pyrochlore to growth.Thus the crystallization is hindered by the lead addition, which is detectable in an increase of the crystalliz- perovskite transformation21) are not exceptional. ation temperatures and a decrease of the Avrami exponents and crystallite sizes. 6 Solid solution series P(Y)T The samples P(Y )T-P with 0Y15% crystallize in the 8 Summary anatase structure. The reflections are only slightly broadened, indicating a crystallite size of more than 600 A° for all samples. In the solid solution series of ZT(X), extremely high apparent activation energies, reaching the values of the sublimation The DTA curves of these samples are depicted in Fig. 10. The DTA peaks are shifted to higher temperatures and strongly enthalpies of ZrO2 and TiO2, are found for intermediate ZrO2 contents of 18–75%. The most plausible explanation is the broadened with increasing PbO content. Correspondingly, the Avrami exponents nGr decrease from 4 for TiO2-P to 1.5 for favoured formation of ZrMOMTi bonds during the gel formation. These bonds are broken with a preferred direction P(15)T-P.The apparent activation energies from the Kissinger plots are about 260 kJ mol-1, and the crystallization enthalpies yielding the fragments TiMO9 |+Zr, and thus it may be necessary to break additional bonds of a (Zr/Ti)O6 octahedron to are about 18 kJ mol-1. Both energies are independent of the PbO content. form the fragments required for the continuation of the crystallite growth.Therefore the activation energy is increased The lowering of the Avrami exponents for P(5)T-P–P(15)T- 2438 J. Mater. Chem., 1998, 8(11), 2433–243912 W. A. Johnson and R. F. Mehl, Trans. Am. Inst. Min. Eng,, 1939, strongly. A linear relation between the logarithm ln c0¾ of the 135, 416. apparent Arrhenius preexponential factor and the apparent 13 M.Avrami, J. Chem. Phys., 1939, 7, 1103. activation energy Ea¾ is found. It can be explained by the 14 M. Avrami, J. Chem. Phys., 1940, 8, 213. contribution of the activation entropy DS‡ which is increased 15 M. Avrami, J. Chem. Phys., 1941, 9, 177. parallel to the number of broken bonds and Ea¾. 16 H. E. Kissinger, Anal. Chem., 1957, 29, 1703. 17 J. W. Graydon, S.J. Thorpe and D. W. Kirk, Acta Metall. 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