Morphotropy, Isomorphism, and Polymorphism of Ln 2 M 2 O 7 -Based (Ln = La Lu, Y, Sc; M = Ti, Zr, Hf, Sn) Oxides

Transcription

1 ISSN , Crystallography Reports, 23, Vol. 58, No. 4, pp Pleiades Publishing, Inc., 23. Original Russian Text A.V. Shlyakhtina, 23, published in Kristallografiya, 23, Vol. 58, No. 4, pp STRUCTURE OF INORGANIC COMPOUNDS Morphotropy, Isomorphism, and Polymorphism of Ln 2 M 2 O 7 -Based (Ln = La Lu, Y, Sc; M = Ti, Zr, Hf, Sn) Oxides A. V. Shlyakhtina Semenov Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, Moscow 999, Russia annash@chph.ras.ru, annashl@inbox.ru Received June, 2 Abstract Structural studies of compounds of variable composition and measurements of their conductivity have made it possible to identify new oxygen-ion-conducting rare-earth pyrochlores, Ln 2 Ti 2 O 7 (Ln = Dy Lu) and Ln 2 Hf 2 O 7 (Ln = Eu, Gd), with intrinsic high-temperature oxygen ion conductivity (up to.4 2 S/cm at 8 C). Twenty six systems have been studied, and more than 5 phases based on the Ln 2 M 2 O 7 (Ln= La Lu; M = Ti, Zr, Hf) oxides have been synthesized and shown to be potential oxygen ion conductors. The morphotropy and polymorphism of the Ln 2 M 2 O 7 (Ln = La Lu; M = Ti, Zr, Hf) rare-earth pyrochlores have been analyzed in detail for the first time. Thermodynamic and kinetic (growth-related) phase transitions have been classified with application to the pyrochlore family. DOI:.34/S INTRODUCTION In the 98s, the Ln 2 Zr 2 O 7 (Ln = Nd, Sm, Gd) rare-earth zirconates with the pyrochlore structure were first shown to undergo a pyrochlore defect fluorite (order disorder) phase transition [], resulting in rather high oxygen ion conductivity of their high-temperature phase [2], comparable to the conductivity of 9 mol % Y 2 O 3 -stabilized ZrO 2. The Ln 2 Hf 2 O 7 (Ln = Nd, Sm Gd) hafnates and R 2 Ti 2 O 7 (R = Y, Gd Lu) titanates with the pyrochlore structure have been studied in much less detail. Also, there is insufficient, fragmentary information about the phase transitions and the associated high-temperature oxygen ion conductivity of the rare-earth pyrochlores. This paper summarizes and systematizes the results of many years of a targeted search for pyrochlore-structure solid electrolytes in the Ln 2 O 3 MO 2 (Ln = Sm Lu; M = Ti, Zr, Hf) systems, which involved structural characterization of rare-earth pyrochlores synthesized at different temperatures and measurements of their electrical conductivity. Efforts in this direction have enabled the preparation of new pyrochlore-structure oxygen ion conductors, stable in the range 7 to 9 С and potentially attractive for practical applications as electrolytes and anodes of solid oxide fuel cells (SOFCs). Studies of a wide range of compounds of variable composition have made it possible to classify the thermodynamic and kinetic (growth-related) phase transitions of the Ln 2 M 2 O 7 (Ln =La Lu, M = Ti, Zr, Hf) mixed oxides and understand distinctive features of the morphotropy and polymorphism of these compounds.. MORPHOTROPY IN RARE-EARTH TITANATE, ZIRCONATE, AND HAFNATE SERIES Morphotropy is an abrupt change in crystal structure in a systematic series of chemical compounds, with no changes in the quantitative relationship between their structural units [3]. The morphotropic phase transitions in series of rare-earth compounds involve structural changes to different degrees, of which the most significant are structural transformations involving changes in the coordination number (CN) of the rare-earth atoms [3]. A key crystal-chemical property of rare-earth compounds is that the CNs of their constituent atoms decrease in going from La to Lu. For example, in the Ln 2 Ti 2 O 7 titanates of the lighter rare earths (Ln = La Nd), the rare-earth atoms have a 2-vertex coordination polyhedron, and these compounds have a distorted pyrochlore structure whose diffraction pattern can be indexed in a monoclinic unit cell, whereas the rare-earth atoms in the Ln 2 Ti 2 O 7 titanates of the heavier rare earths (Ln = Sm Lu) have CN = 8, and these compounds are cubic pyrochlores. According to an assumption made by Bandurkin et al. [4], large CNs correspond to a larger contribution of the 4f orbitals to the bonding in the compound, and the decrease in CN from 2 to 8 in going from La to Lu in the Ln 2 Ti 2 O 7 series reflects a sharp drop in this contribution. In the Ln 2 Zr 2 O 7 (Ln = La Lu) series, the Ln 2 Zr 2 O 7 (Ln = La Gd) zirconates have the pyrochlore structure (Fd3m) and the LnZrO 4 δ zirconates of the smaller lanthanides (Ln = Tb Lu) have the fluorite structure (Fm3m) (which is accompanied by a 548

2 MORPHOTROPY, ISOMORPHISM, AND POLYMORPHISM 549 change in the CN of the zirconium atoms from six to four, whereas that of the lanthanide atoms remains unchanged). In the Ln 2 Hf 2 O 7 (Ln = La Lu) series, the Ln 2 Hf 2 O 7 (Ln = La Tb)) hafnates have the pyrochlore structure (Fd3m) and the LnHfO 4 δ hafnates of the heavier lanthanides (Ln = Dy Lu) have the fluorite structure (Fm3m). When the compounds of a morphotropic series are similar in crystal structure, the concept of morphotropy is identical to that of structural homology. In particular, the changes in crystal structure across the Ln 2 Ti 2 O 7 (Ln = La Lu), Ln 2 Zr 2 O 7 (Ln = La Lu), and Ln 2 Hf 2 O 7 (Ln = La Lu) series reflect the different degrees of order in the fluorite structure, so the concepts of morphotropy and structural homology are here identical. 2. BROAD ISOMORPHISM IN THE Ln 2 O 3 MO 2 (Ln = Sm Lu; M = Ti, Zr, Hf) SYSTEMS Broad isomorphism is typical of most systems under consideration [5 ]. The phase diagrams of the Ln 2 O 3 TiO 2 (Ln = Gd Lu) systems, which contain pyrochlore-structure Ln 2 Ti 2 O 7 (Ln = Gd Lu) compounds and pyrochlore-like and fluorite-like Ln 2 (Ti 2 x Ln x )O 7 δ (Ln =Gd Lu; x =.8) solid solutions were considered in detail by Komissarova et al. [5] and can be divided into two groups. One type of phase diagram is encountered in the R 2 O 3 TiO 2 systems with R = Gd, Dy, Ho (the middle of the lanthanide series), and Y. The salient feature of these systems is that they contain broad Ln 2 Ti 2 O 7 Ln 2 O 3 isomorphism ranges: there are Ln 2+x Ti 2 x O 7 δ (Ln = Gd Ho), or Ln 2 (Ti 2 x Ln x )O 7 δ (Ln =Gd Ho; x =.8), substitutional solid solutions, which undergo a transition with increasing x, from pyrochlore Ln 2 Ti 2 O 7 and pyrochlore-like Ln 2 (Ti 2 x Ln x )O 7 δ ( < x <.67) solid solutions to fluorite Ln 2 (Ti 2 x Ln x )O 7 δ (x =.67.8) solid solutions, as evidenced by X-ray diffraction (XRD) data. As the radius of the rare-earth cation decreases, the isomorphous miscibility range of Ln 2 (Ti 2 x Ln x )O 7 δ (Ln = Gd, Dy, Ho; x =.8) increases, from 2 mol % in the Gd 2 O 3 TiO 2 system to 3 mol % in the Ho 2 O 3 TiO 2 system at 6 С [5]. According to isomorphism theory, when a lanthanide (Ln 3+ ) is heterovalently substituted for titanium (Ti 4+ ) in the Ln 2 (Ti 2 x Ln x )O 7 δ (Ln =Gd Ho; x =.8) solid-solution series, their miscibility region should increase in going from Gd to Ho because this is accompanied by a decrease in ionic radius mismatch between the B cations. This does occur in the systems under consideration, where the ionic radius of the rare-earth atoms decreases in going from Gd ( r 3+ Gd =.53 Å) to Ho ( r 3+ Ho =.5 Å). The Ln 2 (Ti 2 x Ln x )O 7 δ (Ln = Gd Ho; x =.8) solid-solution range increases with increasing temperature, in accord with the well-known temperature effect on the degree of isomorphic substitution. It is worth noting the formation of β-ln 2 TiO 5 (Ln = Dy, Ho), a phase that exists in these systems up to 5 9 С, together with pyrochlore Ln 2 Ti 2 O 7 (Ln = Dy, Ho). The other type of phase diagram is encountered in the Ln 2 O 3 TiO 2 systems with Ln = Er Lu (heavy rare earths). The principal distinction from the former type of phase diagram is that there is no β-ln 2 TiO 5 (Ln = Er Lu) phase [5]. The Ln 2 O 3 TiO 2 (Ln = Er Lu) systems contain only one compound, pyrochlore Ln 2 Ti 2 O 7 (Ln = Er Lu), and there is Ln 2 Ti 2 O 7 Ln 2 O 3 isomorphous miscibility in a wide temperature range [5]. The phase diagrams of the zirconate and hafnate systems Ln 2 O 3 МO 2 (Ln = Nd, Sm Gd; M = Zr, Hf) have features similar to those mentioned above for the titanate systems [6, ]. They also show broad Ln 2 (M 2 x Ln x )O 7 δ (Ln = Nd, Sm Gd; M = Zr, Hf; x =.29) isomorphous miscibility ranges, in which a pyrochlore-to-fluorite phase transition occurs with increasing rare-earth concentration. At 6 С, these ranges, 8 mol % in width, are however narrower than those in the titanate systems. The width of the Ln 2 M 2 O 7 Ln 2 O 3 (M = Zr, Hf) isomorphous miscibility range in the zirconate and hafnate systems decreases with a decrease in the ionic radius of the lanthanides, in contrast to what occurs in the rare-earth titanate systems. In the Ln 2 O 3 ZrO 2 (Ln = Sm Gd) zirconate systems, the composition range of the pyrochlore Ln 2 ± x Zr 2 ± x O 7 ± δ (Ln = Nd, Sm Gd) substitutional solid solutions is symmetric about the stoichiometric composition Ln 2 Zr 2 O 7 (Ln = Nd, Sm Gd). Thus, the isomorphous miscibility range in these systems lies on both sides of the stoichiometric composition, in contrast to that in the titanate and hafnate systems, where the isomorphous miscibility range lies predominantly at Ln 2 O 3 (Ln = Dy Lu) compositions. An important point, mentioned by a number of researchers, is that the nominally stoichiometric compounds Ln 2 Zr 2 O 7 (Ln = Nd, Sm Gd) actually contain cation antistructure pairs and oxygen vacancies; that is, these compounds are inherently nonstoichiometric and possess intrinsic ionic conductivity [6, 7]. This feature of the zirconates was commonly attributed to the fact that Ln 3+ and Zr 4+ differ very little in ionic radius. The processes in question can be represented by the following general formulas: x x Ln + M Ln' + M Ln M M Ln, () x Oo VO (48 f ) + O'' i(8 b). (2) The isomorphous miscibility range in the Ln 2 O 3 HfO 2 (Ln = Sm Gd) systems, Ln 2 (Hf 2 x Ln x )O 7 δ (Ln = Nd, Sm Gd; x =.29), resembles that in the titanate systems, but it includes compositions starting at 3 mol % Ln 2 O 3 (Ln = Sm Gd), whereas the sub-

3 55 SHLYAKHTINA Table. Pyrochlore defect fluorite (order disorder) phase transition temperatures (t PT ) and melting points of Ln 2 M 2 O 7 (Ln = Nd, Sm Lu; M = Ti, Zr, Hf) t PT, С Melting point, С Solid-state reaction Compound Coprecipitation Nd 2 Zr 2 O 7 23 [] 24 [6] Sm 2 Zr 2 O 7 22 [] 23 [6] Gd 2 Zr 2 O 7 53 [] 25 [6] Nd 2 Hf 2 O 7 24 [6] 27 [6, ] Sm 2 Hf 2 O [9, 3] 255 [9] 25 [3] Gd 2 Hf 2 O 7 24 [9, ] 27 [9, ] Dy 2 Ti 2 O 7 4 [4] 2 [5] 65 [4] Ho 2 Ti 2 O 7 4 [4] 29 [5] 65 [4] Er 2 Ti 2 O 7 6 [5] 25 [5] ~7 [5] Tm 2 Ti 2 O [6] 29 [5] ~7 [6] Yb 2 Ti 2 O 7 6 [7] 26 [5] ~7 [7] Lu 2 Ti 2 O [8] 99 [8] ~7 [8] stitutional solid solutions in the titanate systems exist starting at the stoichiometric composition Ln 2 Ti 2 O 7, containing ~33.3 mol % Ln 2 O 3 (Ln = Dy Lu). Attention should be paid to the fact that wide solidsolution ranges with Ln 3+ heterovalent substitutions on the M 4+ (Ti, Zr, Hf) site, resulting in the formation of Ln 2 (Ti 2 x Ln x )O 7 δ (Ln = Dy Lu; x =.67) and Ln 2 (M 2 x Ln x )O 7 δ (Ln = Nd, Sm Gd; M = Zr, Hf; x =.29), are rather uncommon because the fractional difference between the ionic radii of Ln 3+ and M 4+ is 42.3 and 69.8% relative to the smaller radius (Ti 4+ ) in lutetium and dysprosium titanates, respectively, 46.3 and 49.9% relative to the smaller radius (Zr 4+ ) in gadolinium and samarium zirconates, respectively, and 48.3 and 52% relative to the smaller radius (Hf 4+ ) in gadolinium and samarium hafnates, respectively, rather than the 5% predicted by isomorphism theory [, 2]. For example, in the Yb 2 (Ti 2 x Yb x )O 7 δ (x =.67) solid-solution series, the considerably larger cation Yb +3 ( r =.985 Å) substitutes for Ti Yb ( r 4+ Ti =.65 Å). It seems likely that this substitution is possible owing to some specific features of the pyrochlore structure, which contains rather large channels (with a hexagonal cross section up to 5 Å in diameter). This allows large-sized cations to be accommodated on sites normally occupied by cations with a smaller ionic radius. Some disagreement with isomorphism theory seems to arise from the fact that its ideas rely on experimental data obtained previously for binary sys- tems, and results on substitutions in the Ln 2 O 3 MO 2 (Ln = Sm Lu; M = Ti, Zr, Hf) systems should be systematized separately. One important distinction of the zirconate and hafnate systems Ln 2 O 3 МO 2 (Ln = Sm Gd; M = Zr, Hf) from the titanate systems Ln 2 O 3 TiO 2 (Ln = Gd Lu) is that these latter contain no fluorite solidsolution series at low (~8 2 mol %) Ln 2 O 3 (Ln = Gd Lu) contents [5, 6]. 3. POLYMORPHISM OF THE Ln 2 M 2 O 7 (Ln = La Lu, M = TI, ZR, HF) COMPOUNDS OF VARIABLE COMPOSITION 3.. Temperature Effect on the Crystal Structure of Ln 2 M 2 O 7 (Ln = Nd, Sm, Eu, Gd; M = Zr, Hf) and Ln 2 Ti 2 O 7 (Ln = Dy Lu) 3... Thermodynamic order disorder transitions. The Ln 2 M 2 O 7 (Ln = Sm Lu; M = Ti, Zr, Hf) compounds in the Ln 2 O 3 MO 2 (Ln = Sm Lu; M = Ti, Zr, Hf) systems exhibit not only isomorphism but also complex polymorphism. In particular, the nominally stoichiometric (Ln : M = : ) zirconates and hafnates Ln 2 M 2 O 7 (Ln = Nd, Sm, Gd; M = Zr, Hf) have been clearly shown to undergo a pyrochlore defect fluorite (order disorder) phase transition, which takes place at temperatures from 53 to 23 С and leads to the formation of an oxygen-ion-conducting phase [, 7,, 6, 9, 2]. Table lists the melting points and pyrochlore defect fluorite (order disorder) phase transition temperatures of Ln 2 M 2 O 7 (Ln = Nd, Sm, Gd; M = Zr, Hf). Such transformations were first identified in the Gd 2 Zr 2 O 7, Sm 2 Zr 2 O 7, and Nd 2 Zr 2 O 7 zirconates in the pioneering work of Michel et al. []. They were the first to study the ( x)zro 2 xln 2 O 3 (Ln = La, Nd, Sm, Gd) systems, using Raman spectroscopy and electron microscopy. They assumed the presence of pyrochlore-structure local order regions in the high-temperature, oxygen-ion-conducting phase, µm in size in Sm 2 Zr 2 O 7 and down to. µm in size in Gd 2 Zr 2 O 7. The size of the pyrochlore-structure local order regions (antiphase microdomains) was shown to decrease with a decrease in the ionic radius of the lanthanides. Later, van Dijk et al. [9] studied Tb 2 Zr 2 O 7 by electron microscopy and also assumed the presence of pyrochlore-structure antiphase microdomains in the fluorite matrix of the high-temperature phase. In the literature, the high-temperature phase transition in the Ln 2 O 3 MO 2 (Ln = Sm Tb; M = Zr, Hf) systems is referred to as a pyrochlore defect fluorite (order disorder) phase transition. The phase transition temperature of Gd 2 Zr 2 O 7 is known to be ~53 C (Table ) []. Van Dijk et al. [2] quenched polycrystalline Gd 2 Zr 2 O 7 from a considerably higher temperature of 7 C. The resultant Gd 2 Zr 2 O 7 material consisted of a fluorite phase and

4 MORPHOTROPY, ISOMORPHISM, AND POLYMORPHISM 55 pyrochlore-structure local order regions. The diffuse scattering features observed in the electron diffraction pattern of the high-temperature phase of Gd 2 Zr 2 O 7 were tentatively attributed by van Dijk et al. [2] to the formation of pyrochlore-structure antiphase microdomains in the fluorite matrix. By contrast, Scheetz and White [22] suggested that the observed broadening of lines in the Raman spectra of Ln 2 Zr 2 O 7 (Ln = Nd, Sm, Gd, Dy, Er, Yb) was due to disorder in both the cation and anion sublattices and not to antiphase microdomain boundaries. A detailed study of pyrochlore- and fluorite-structure Gd 2 Zr 2 O 7 single crystals [2] confirmed the conclusion [2] that fluorite Gd 2 Zr 2 O 7 contained pyrochlore-structure local order regions. Thus, the high-temperature phase that resulted from phase transitions typically was not a true fluorite phase but consisted of a fluorite matrix and pyrochlore-ordered local regions embedded in the matrix; that is, it was a defect fluorite phase. Using electron diffraction, Michel et al. [] identified antiphase microdomains not only in the nominally stoichiometric phases Ln 2 Zr 2 O 7 (Ln = Nd, Sm, Gd) but also in Ln 2 ± x Zr 2 ± x O 7 ± δ nonstoichiometric pyrochlores prepared at temperatures near the order disorder phase transition and showed that the domain size decreased in going from Nd to Gd. According to Uehara et al. [23], the domain size in Gd 2 Zr 2 O 7 was 7 8 Å, that is, ten times smaller than that reported by Michel et al. []. When antiphase boundaries lie in the () plane, the lattice energy of such a defect structure only slightly exceeds the energy of a perfect pyrochlore phase. This means that a structure containing such antiphase boundaries should be stable and that oxygen diffusion along such boundaries is optimal [24]. Uehara et al. [23] believe that the CN of the lanthanide cations on an antiphase boundary is less than eight, in contrast to the typical coordination of the lanthanides in pyrochlores. Thus, the antiphase domain boundary decreases in size with a decrease in the ionic radius of the rare earth and/or a reduction in the stability of the typical coordination of the lanthanides in the pyrochlore structure. Gallardo-Lopez et al. [25] compared diffuse scattering data for a pyrochlore-like Zr 2.4 Gd.86 O 7.4 solid solution prepared at 5 and 6 С, that is, above and below the temperature of the pyrochlore fluorite phase transition, 53 С. According to their results, the pyrochlore microdomain size decreases with increasing annealing temperature, and the superlattice reflections in the XRD pattern of the solid solution become weaker. The Ln 2 Hf 2 O 7 (Ln = Nd, Sm, Gd) hafnates are known to have higher pyrochlore defect fluorite (order disorder) phase transition temperatures (~2 24 С) in comparison with their zirconate analogs (Table ) [6, 9, ]. Because of this, significantly less work has been directed toward the study of the structure of hafnates prepared at high temperatures [9,, 26, 27] in comparison with the zirconates I hkl /I I 33 /I 222 I 3 /I t, C Fig.. Relative intensity of the (3) and (33) pyrochlore superstructure lines as a function of temperature for Yb 2 Ti 2 O 7. [28 38]: the hafnates are difficult to prepare at the very high temperatures where such transitions occur, and, more importantly, are expected to have low electrical conductivity. The pyrochlore defect fluorite (order disorder) phase transitions of the Ln 2 M 2 O 7 (Ln = Nd, Sm, Gd; M = Zr, Hf) materials seem to be second-order, as suggested by the fact that they are accompanied by relatively small changes in crystal structure (fluorite and pyrochlore are structural homologues). Pyrochlore defect fluorite (order disorder) phase transitions had long been thought to take place only in the Ln 2 M 2 O 7 (Ln = Nd, Sm, Gd; M = Zr, Hf) rare-earth zirconates and hafnates, and no such transitions had been detected in systems with a smaller ionic radius of М 4+, such as Ln 2 O 3 TiO 2 ( r 4+ =.65 Å < r 4+ = Ti CN 6 Ti CN 6.72 Å), for a large number of Ln 2 Ti 2 O 7 (Ln = Gd Lu) pyrochlores. Only comparatively recently have pyrochlore defect fluorite (order disorder) phase transitions been identified as well in the Ln 2 Ti 2 O 7 (Ln =Dy Lu) rare-earth titanates (Table ) [4 8, 39 47]. Pyrochlore (P) to disordered pyrochlore (PII, >% cation antistructure pairs) (order disorder) thermodynamic phase transitions were first identified in the Ln 2 Ti 2 O 7 (Ln = Tm, Yb, Lu) rare-earth titanates prepared from coprecipitated precursors near the melting points of the titanates (Table ). Oxygen ion conduction was found in the metastable high-temperature form (PII) of Ln 2 Ti 2 O 7 (Ln = Tm Lu) prepared at 6 67 C, which has reduced room-temperature intensities of the (3) and (33) pyrochlore superstructure lines, as evidenced by the reduced I 3 /I 222 and I 33 /I 222 intensity ratios (Fig. ). The pyrochlore structure has a rather complex unit cell, with 88 atoms per cell, so oxygen disorder persists after cooling. Thus, at high synthesis temperatures (t 6 С) the

5 552 SHLYAKHTINA Table 2. Characteristics of Ln 2 Ti 2 O 7 (Ln = Yb, Lu) and an Yb 2 Ti 2 O 7 -based solid solution synthesized under different conditions (XRD data were obtained at room temperature) Compound Synthesis procedure, t syn, cooling Phase Lu 2 Ti 2 O 7 C, 86 C, PI.828(3)Lu +.82Ti Lu 2 Ti 2 O 7 C, 5 C, PI.933(3)Lu +.67Ti Lu 2 Ti 2 O 7 C, 6 C, 2 P.992(4)Lu +.8Ti Site composition Ln M.828Ti +.82Lu.933Ti +.67Lu.992Ti +.8Lu a, Å ρ, % Color.2() 45 White 9.998() 46.8 White.4(4) 9.5 Beige Yb 2 Ti 2 O 7 C, 4 C, 2 P.25() 92.5 Beige Yb 2 Ti 2 O 7 C, 6 C, 2 PII 93 Light brown Yb 2 Ti 2 O 7 C, 67 C, 2 PII.8(2) 93 Dark pink Yb 2 Ti 2 O 7 M, 6 C, 2 PII.955(3)Yb +.45Ti (Yb.9 Sc.9 ) 2 Ti 2 O 7 δ C, 6 C, 2 PII.875(3)Yb +.35Ti +.9Sc Yb 2 Ti 2 O 7 S, 6 C, 2 PII.993Yb +.7Ti Yb 2 Ti 2 O 7 S, 6 C, 3 PII.987Yb.3Ti Yb 2 Ti 2 O 7 S, 6 C, 4 PII.986Yb +.4Ti.955Ti +.45Yb.965Ti +.35Yb.993Ti +.7Yb.987Ti +.3Yb.986Ti +.4Yb.24(4) 92 Dark lilac.82(5) 9.2 Brown.34() Brown.34() Brown.35(2) Brown Note: In the synthesis procedure description, C = coprecipitation, M = mechanical activation, S = solid-state reaction, = quenching in N 2, 2 = cooling at 2.2 C/min, 3 = cooling at 3 C/min, and 4 = cooling at C/min. thermodynamic order disorder transition yields Ln 2 Ti 2 O 7 (Ln = Tm Lu) with a disordered pyrochlore structure (PII), which contains cation antistructure pairs and associated oxygen vacancies, as represented by schemes () and (2) (Table 2). Such results were first obtained for (Sc x Yb x ) 2 Ti 2 O 7 (x =,.9,.2,.3) samples prepared by the Pechini process at С and characterized by high-temperature neutron diffraction in the range 8 45 С [48]. The transition involves changes in both the oxygen and cation sublattices, but the Ln Ti + TiLn antistructure pairs in the titanates of the heavy rare earths often disappear during slow cooling or prolonged storage because of the considerable ionic radius mismatch between Ln 3+ ( r 3+ =.994 Å; r 3+ =.985 Å; r 3+ = Tm CN 8 Yb CN 8 Lu CN Å [49] and Ti 4+ ( r 4+ =.65 Å) (Table ). Ti CN 6 The phase transition temperature of Ln 2 Ti 2 O 7 (Ln =Ho Lu) decreases with an increase in the ionic radius of the lanthanides and is 4 C for Ho 2 Ti 2 O 7 (Table ). For t 7 C, high-temperature polymorphs with the defect fluorite structure have been obtained for none of the Ln 2 Ti 2 O 7 (Ln = Dy Lu) titanates synthesized through coprecipitation: the rare-earth titanates melted at these temperatures (Table ). The Ln 2 Ti 2 O 7 (Ln = Dy Lu) compounds with the pyrochlore structure, which contains oxygen vacancies, are potentially attractive oxygen ion conductors. Figure 2 shows the Arrhenius plots of bulk and grainboundary conductivities for Yb 2 Ti 2 O 7 prepared at 67 C. The activation energy for bulk conduction is.87 ev (Fig. 2), which is close to the level of oxygen ion conductors with the pyrochlore structure [9]. Figure 3 shows the 75 C bulk conductivity of Ln 2 Ti 2 O 7 (Ln = Ho Lu) synthesized at 65 C (Fig. 3, curve ) and a lower temperature of 6 C (Fig. 3, curve 2). Analysis of the bulk conductivity data for Ln 2 Ti 2 O 7 (Ln = Ho Lu) indicates that the conductivity of Ln 2 Ti 2 O 7 (Ln = Ho Lu) increases with a decrease in the ionic radius of the rare earths, reaching the highest level in Yb 2 Ti 2 O 7 and Lu 2 Ti 2 O 7. The oxygen ion conductivity of Ln 2 Ti 2 O 7 (Ln = Ho Lu) is determined by the synthesis temperature of the rareearth titanates. High conductivity is offered by Ln 2 Ti 2 O 7 (Ln =Ho Yb) prepared through coprecipitation followed by annealing at 6 С (Table ). Lu 2 Ti 2 O 7 has high oxygen ion conductivity after heat treatment at 65 С. Annealing Ln 2 Ti 2 O 7 (Ln =Er Lu) at t 7 С led to melting of the samples. Thus, Ln 2 Ti 2 O 7 (Ln = Er Lu) oxygen ion conductors can be

6 MORPHOTROPY, ISOMORPHISM, AND POLYMORPHISM 553 lgσt [S K/cm] /T, K Fig. 2. Arrhenius plots of () bulk and (2) grain-boundary conductivities for Yb 2 Ti 2 O 7 prepared at 67 С. σ при 75 C, S/cm Lu 2 Yb Tm Er Ho rln 3+, Å Fig С conductivity vs. ionic radius of Ln for Ln 2 Ti 2 O 7 (Ln = Ho Lu) synthesized at () 65 and (2) 6 С. obtained in a rather narrow temperature range (Table ). Prolonged (24 h) heat treatment at a typical working temperature of SOFCs, ~86 С, produced no significant changes in the Arrhenius plot of conductivity for Tm 2 Ti 2 O 7 synthesized at 67 С, and its 75 С ionic conductivity (measured at MHz) remained at the same level, ~2 3 S/cm, meaning that the order disorder phase transition of this material was irreversible Kinetic (growth-related) disordering transitions. In addition to the known, well-studied pyrochlore defect fluorite (order disorder) phase transition in the Ln 2 O 3 ZrO 2 (Ln = Nd, Sm, Gd) and Ln 2 O 3 HfO 2 (Ln = Nd, Gd) systems, there is evidence that Sm 2 Zr 2 O 7, Gd 2 Zr 2 O 7, and solid solutions based on these zirconates undergo a transition from a metastable fluorite-like phase (F*) to a pyrochlore phase at 7 С [29, 3]. In particular, Fomina and Pal guev [29] reported the formation of fluorite-like metastable phases at 7 C for Sm 2 Zr 2 O 7 and Gd 2 Zr 2 O 7 prepared through coprecipitation followed by high-temperature heat treatment. Clearly, at temperatures as low as ~7 C ordering processes are extremely slow. In the synthesis of the Gd 2 (Ti.65 Zr.35 ) 2 O 7 δ pyrochlore solid solution with the use of mechanical activation, Moreno et al. [3] have recently detected, using XRD, the formation of a fluorite-like phase at temperatures in the range ~7 8 C. It seems likely that the Ln 2 O 3 ZrO 2 (Ln =Sm, Gd) materials undergo kinetic (growth-related) disordering transitions: during crystallization of an amorphous phase, the atoms have no time to occupy sites corresponding to the ordered pyrochlore structure in the surface layer before the formation of the next atomic layer [5 52]. This is possible at a small ionic radius mismatch between the Ln 3+ and M 4+ cations in the pyrochlore structure. The result is the formation of fluorite-like metastable phases containing pyrochlorestructure local order regions. The Ln 2 Hf 2 O 7 (Ln = La Er) hafnates synthesized through coprecipitation were also reported to have a tendency toward the formation of a fluorite-like phase at ~8 С [53, 54]. In the case of the Ln 2 Ti 2 O 7 (Ln = Dy Lu) rare-earth titanates prepared through coprecipitation [5, 55 6] and the Ln 2 Hf 2 O 7 (Ln = Eu, Gd) rare-earth hafnates prepared using the mechanical activation of oxide mixtures [6, 62], kinetic (growth-related) disordering transitions have been identified comparatively recently (Table ). It is worth pointing out that the temperatures of the kinetic (growth-related) transition in hafnates prepared by different techniques (using coprecipitation and mechanical activation) differ markedly (8 С after coprecipitation and 2 С after mechanical activation). According to XRD data, reaction between coprecipitated precursors with Ln : Ti = (Ln = Tm, Yb, Lu) at С yields a fluorite-like phase, F*, instead of a pyrochlore-like phase (Fig. 4a) [5, 55 6]. The absorption bands at 3 and 6 cm, typical of the pyrochlore structure, are missing in the IR spectra of F* Ln 2 Ti 2 O 7 (Ln = Tm Lu) but the spectra contain a very weak line at 38 cm, which suggests that the F* phase may contain pyrochlore-ordered local regions (antiphase microdomains) [29, 3]. Heat treatment at higher temperatures in the range t < С leads to the formation of the pyrochlore structure, PI, which is only partially ordered and has reduced intensities of the (), (3), and (33) pyrochlore superstructure lines. The phase with the perfect

7 554 SHLYAKHTINA I, rel. units (a) 74 C-2h + 95 C-2h 8 C-2h 74 C-2h I,rel. units C-24h 2 65 C-h θ, deg (b) 3 4 2θ, deg 85 C-2h 74 C-2h 55 C-2h 35 C-2h Fig. 4. XRD patterns of freeze drying products with (a) Lu : Ti = : and (b) Gd : Ti = : heat-treated at temperatures from 65 to 95 С.. pyrochlore structure, P, exists only in a narrow temperature < t < 2 С [5, 55 58]. The disordered pyrochlore phase, PI, which forms above 74 С, was studied in detail by XRD, using the Rietveld method for Lu 2 Ti 2 O 7 (Table 2) [58, 6]. Samples quenched in liquid nitrogen from 86 and 5 С were found to contain 8.2 and 6.7% Lu Ti + Ti Lu antistructure pairs, respectively (Table 2). Thus, there is solid evidence for the existence of disordered pyrochlores, PI, containing antistructure pairs in their cation sublattice. Oxygen ion conduction in the compounds with the PI structure has not been studied because attempts to prepare high-density samples needed for conductivity measurements at temperatures from 74 to C have so far been unsuccessful. In the case of the lighter rare-earth titanates Ln 2 Ti 2 O 7 with Ln = Gd Er, no F* fluorite-like phase formation was detected in the range С, and X-ray amorphous precursors crystallized into Ln 2 Ti 2 O 7 (Ln = Gd Er) with a disordered pyrochlore structure (Fig. 4b). Thus, the Ln 2 M 2 O 7 (Ln = Sm Lu; M = Ti, Zr, Hf) rare-earth pyrochlores exhibit complex polymorphism, which involves a kinetic (growth-related) disordering transition and a high-temperature, pyrochlore to defect fluorite or disordered pyrochlore (order disorder) phase transition. The temperature of the kinetic (growth-related) transition depends on the synthesis procedure used to prepare the compound (solid-state reaction, coprecipitation, or mechanical activation). During synthesis from coprecipitated precursors, most of the rare-earth titanates, zirconates, and hafnates with the pyrochlore structure undergo a kinetic (growth-related) disordering transition of the form F* PI P (fluorite-like phase to low-temperature disordered pyrochlore to ordered pyrochlore transition). The temperature of the kinetic (growthrelated) transition in these materials is 7 8 С. In the Ln 2 (Hf 2 x Ln x )O 7 δ (Ln =Eu, Gd; x =,.) rare-earth hafnates synthesized using mechanical activation in the range С, no ordered pyrochlore (P) phase field has been detected. The F* PI (fluorite-like phase to high-temperature disordered pyrochlore (>% antistructure pairs)) kinetic (growthrelated) transition occurs at temperatures above 2 С, whereas the temperature of this transition in the hafnates prepared through coprecipitation is substantially lower: ~ 8 С [53, 54]. Thus, independent of the synthesis procedure, all of the Ln 2 (M 2 x Ln x )O 7 δ (Ln = Sm Lu; M = Ti, Zr, Hf; x =,.) rare-earth pyrochlores undergo thermodynamic P PII (ordered pyrochlore to hightemperature disordered pyrochlore) order disorder transitions, which yield an oxygen-ion-conducting phase with the PII structure. The PII phase persists metastably at room temperature. The transition temperature is 4 24 С, depending on the system and the procedure used to prepare the compounds of variable composition. In addition, a fluorite-like phase, F*, was reported to form in the zirconate and hafnate systems at high, near-melting temperatures. The ordered Ln 2 Ti 2 O 7 (Ln = Dy Lu) pyrochlores have been shown to undergo a P PII order disorder transition below their melting point. The phase transition temperature of the Ln 2 Ti 2 O 7 (Ln = Dy Lu) titanates approaches their melting point as the ionic radius of the rare earths decreases.

8 MORPHOTROPY, ISOMORPHISM, AND POLYMORPHISM High-Pressure and Radiation-Induced Pyrochlore Fluorite (Order Disorder) Phase Transitions Pyrochlore fluorite (order disorder) secondorder thermodynamic phase transitions can be induced not only by heating but also by high pressures and irradiation. The influence of high pressures on pyrochlorestructure compounds has been the subject of several studies. In particular, Kumar et al. [3] investigated the effect of high pressures on the structure of the Tb 2 Ti 2 O 7, Tb 2 Sn 2 O 7, and Tb 2 SnTiO 7 pyrochlores using synchrotron radiation and Raman spectroscopy. Increasing the pressure led to distortion of the pyrochlore structure and a transition to a monoclinic phase (isostructural with Ln 2 Ti 2 O 7 (Ln = La, Nd) under ordinary conditions). At pressures of ~ GPa, complete amorphization was observed. Near the transition to the amorphous phase, the parameter X (variable positional parameter of O2 (48f) in the pyrochlore structure) changed sharply, without reaching that in the fluorite structure:.375. Kumar et al. [3] believe that the pressure-induced order disorder transition begins with significant changes in oxygen position. Similar results were reported by Zhang and Saxena [32], who studied the high-pressure behavior of Gd 2 Ti 2 O 7 and Sm 2 Ti 2 O 7. Their structure was probed by Raman spectroscopy, which showed that disordering first developed on the oxygen site: when the anions were already disordered, the cation order persisted. Eventually, both Gd 2 Ti 2 O 7 and Sm 2 Ti 2 O 7 were completely amorphized, but no defect fluorite phase was detected. It is of interest to note that this result is in complete contrast to what was reported on the influence of different types of radiation, which caused predominantly cation disordering [33 37]. The effect of ion bombardment (-MeV Kr +, 2-MeV Au 2+,.6-MeV Bi +,.5-MeV Xe +, and.6-mev Ar + ) on the R 2 Ti 2 O 7 (R = Y, Sm, Gd, Lu), Gd 2 (Zr x Ti x ) 2 O 7, and Gd 2 Zr 2 O 7 pyrochlores has been the subject of extensive studies [33 37]. Results for Gd 2 Ti 2 O 7 depended on the type of radiation. Wang et al. [34] reported that irradiation with -MeV Kr + ions to a fluence of cm 2 converted pyrochlore Gd 2 Ti 2 O 7 to an amorphous phase, with no fluorite formation, whereas exposure to.6-mev Ar + ions (5 4 cm 2 ) at room temperature led to the formation of a fluorite phase, as determined by electron diffraction, which was evidenced by the disappearance of the pyrochlore superstructure lines, accompanied by amorphization [37]. Irradiation of Gd 2 Ti 2 O 7 with -MeV Kr + ions to a fluence of cm 2 resulted in cation disordering, which led to a considerable increase in fluorite cell volume [34]. The fluorite phase formed from pyrochlore Gd 2 Ti 2 O 7 was energetically unstable to amorphization. Gd 2 Zr 2 O 7 exhibited a different behavior. Hard radiations induced a sharp pyrochlore fluorite (order disorder) phase transition in this zirconate. The fluorite phase formed retained short-range order in the cation sublattice. Hess et al. [38] studied vibrational spectra of the Gd 2 (Ti y Zr y ) 2 O 7 series before and after irradiation and showed that cation disorder, rather than anion disorder, played a dominant role in the radiation-induced order disorder transition. Their results demonstrate high stability of Gd 2 Zr 2 O 7 to amorphization after exposure to heavy ions, which is its important advantage over the titanate pyrochlores, suggesting that the zirconate pyrochlores are potential materials for radioactive waste burial Iso- and Heterovalent Substitution-Induced Pyrochlore Defect Fluorite (Order Disorder) Phase Transitions Van Dijk et al. [2] studied the formation of pyrochlore microdomains in the fluorite-like lattice of (Tb x Gd x ) 2 Zr 2 O 7+y ( x, y.25) by electron diffraction at different temperatures both above and below the temperature of the pyrochlore defect fluorite (order disorder) phase transition. Their results demonstrate that the transition can be induced by both heating and isovalent substitution of terbium for gadolinium. The change in the crystal structure of (Tb x Gd x ) 2 Zr 2 O 7+y ( x, y.25) is a pyrochlore defect fluorite morphotropic phase transition, where the two structures belong to the same homologous series. Samples quenched from 7 С and terbium-rich samples consisted of a fluorite matrix containing pyrochlore-structure local order regions. When domains increase and come into contact with each other, as in samples obtained at temperatures below 53 С or in gadolinium-rich samples, the material has a pyrochlore structure with a high degree of order. Thus, the above results are the first to demonstrate that pyrochlore defect fluorite (order disorder) phase transitions in (Tb x Gd x ) 2 Zr 2 O 7+y ( x, y.25) can be induced not only by heating but also by cation substitutions on the lanthanide or zirconium site of pyrochlore Ln 2 Zr 2 O 7 that reduce the cation size mismatch and cause cation disordering, which is obviously favorable for defect formation in the anion sublattice, as evidenced by the considerable increase in high-temperature oxygen ion conductivity. That a decrease in cation size mismatch in the pyrochlore structure leads to an order disorder transition was first suggested in a review by Subramanian et al. [63]. An important study concerned with the influence of composition and temperature on the structure and oxygen ion conductivity of pyrochlore-like solid solutions was carried out for several systems: Y 2 (Zr y Ti y ) 2 O 7, Y 2 (Sn y Ti y ) 2 O 7, Y 2 (Zr y Sn y ) 2 O 7, and Gd 2 (Sn y Ti y ) 2 O 7 (y = ) [64]. Substitution of a larger sized cation (Zr) on the M (M = Ti, Sn) site of pyrochlore Ln 2 M 2 O 7 (Ln = Y, Gd; M = Sn, Ti) increases the ionic conduc-

9 556 SHLYAKHTINA Oxygen site occupancy. O Onset of A and B cation intermixing O O y Fig. 5. Oxygen site occupancies against the degree of for Y 2 (Zr y Ti y ) 2 O 7 (O, position 8а; O2, position 48f; O3, position 8b) [64]. tivity of the material to a level comparable to the conductivity of 8 mol % Y 2 O 3 -stabilized ZrO 2 : ~ S/cm at С. In all cases except for Y 2 (Sn y Ti y ) 2 O 7 and Gd 2 (Sn y Ti y ) 2 O 7, there was a sharp increase in ionic conductivity for y >.4, in parallel with ion intermixing on the lanthanide and M sites. In particular, in Y 2 (Zr y Ti y ) 2 O 7 the normally vacant O3 (8b) site of the pyrochlore structure was occupied by oxygen from the O2 (48f) and O3 (8a) sites (Fig. 5). Figure 5 shows the variation in the occupancy of position 8b with zirconium concentration in Y 2 (Zr y Ti y ) 2 O 7. Figure 6 plots the variable positional parameter X and ionic conductivity against zirconium content for Y 2 (Zr y Ti y ) 2 O 7. In addition to the relationship between the ionic radii of the atoms on the lanthanide and M (M = Ti, Zr, Hf, Sn) sites, an important role is played by the M О bond covalence. Attempts to replace titanium ( r 4+ Ti =.65 Å) in Y 2 (Sn y Ti y ) 2 O 7 by the larger sized cation r 4+ Sn =.69 Å, intermediate in ionic radius between Ti 4+ ( r =.65 Å) and Zr Ti ( r 4+ Zr =.72 Å), were unsuccessful. No increase in ionic conductivity was detected for y >.4. By contrast, the conductivity decreased, and Y 2 Sn 2 O 7 remained fully ordered throughout the temperature range С. Clearly, an important role is played by the M O (M = Ti, Zr, Hf, Sn) bond covalence. In particular, the Sn O bond in Y 2 Sn 2 O 7 is much stronger than the M O bond in Y 2 (Zr.6 Ti.4 ) 2 O 7 [65]. The ionic conductivity of Gd 2 (Sn y Ti y ) 2 O 7 was also found to drop for y >.4, like that of Y 2 (Sn y Ti y ) 2 O 7. The results of Wuensch et al. [64] were confirmed by Moreno et al. [65, 66], who prepared solid solutions using mechanical activation of oxide mixtures, whereas Wuensch et al. [64] synthesized the Gd 2 (Zr y Ti y ) 2 O 7 and Dy 2 (Ti y Zr y ) 2 O 7 (y = ) solid solutions by the Pechini process. Moreno et al. [65, 66] prepared Gd 2 (Zr y Ti y ) 2 O 7 and Dy 2 (Ti y Zr y ) 2 O 7 through mechanical activation of oxide mixtures, followed by annealing at 5 С for 36 h. Ionic conductivity measurements showed a jump for y >.4, like in the case of Y 2 (Zr y Ti y ) 2 O 7 [65]. The oxygen ion conductivity of solid solutions containing isovalent and heterovalent substituents on the Ln and Ti sites of the Ln 2 Ti 2 O 7 (Ln = Dy Lu) rareearth titanates has been studied in detail [8, 4 47]. The structure and conductivity of solid solutions based on oxygen-ion-conducting Ln 2 Ti 2 O 7 (Ln = Dy Lu) rare-earth titanates have been studied for heterovalent and isovalent substitutions in the two cation sublattices of the pyrochlore structure. Extrinsic (impu- Positional parameter X of O 2.42 (a).4 Ionic conductivity σ, S/cm 2 (b) y y Fig. 6. (a) Variable positional parameter X of O 2 (48f) and (b) ionic conductivity against the degree of substitution, y, for Y 2 (Zr y Ti y ) 2 O 7 [64].

10 MORPHOTROPY, ISOMORPHISM, AND POLYMORPHISM 557 N, % σ, S/cm.4 E a, ev 2. Ion transport number, ti Lu 2 Ti 2 O 7 x, % Fig. 7. () 8 С bulk conductivity (σ), (2) activation energy, (3) percentage of Lu Ti antisite defects, and (4) percentage of Lu Ti + Ti Lu antistructure pairs as functions of mol % Lu 2 O 3 for Lu 2 (Ti 2 x Lu x )O 7 δ with x =.44. x = corresponds to Lu 2 Ti 2 O 7 (33 mol % Lu 2 O 3 ) lgp O2, Pa Fig. 8. Ion transport number as a function of oxygen partial pressure for () Lu 2 (Ti 2 x Lu x )O 7 δ with x =. and (2) Lu 2 (Ti 2 x Lu x )O 7 δ with х =.29. rity) conduction in mixed oxides can be due to heterovalent cation substitutions, and useful oxygen vacancies can form through the following mechanisms: heterovalent substitution of Ln 3+ trivalent cations on the M 4+ site, e.g., Ln 2 (M 2 x Ln x )O 7 δ (Ln = Sm Lu; M = Ti, Zr, Hf) (this mechanism is responsible for oxygen vacancy generation in the well-known solid electrolyte ZrO 2 9 mol % Y 2 O 3 ): ( 2 xm ) O2 + ( + x/2) Ln2O3 x x ( 2 x) M M + xlnm + 2LnLn (3) x + ( 7 x/2) O O + x/2vo ; heterovalent substitution of D 2+ divalent cations on the Ln 3+ site,[ital] e.g., (Ln 2 x D x )Ti 2 O 7 δ (D = Ca, Mg, Zn): x x x 4DO+ 4LnLn + 2TiTi + 3OO (4) 4DLn ' + 2LnTi ' + 3VO + Ln2Ti2O7; heterovalent substitution of D 2+ divalent cations on the M 4+ site, e.g., Ln 2 (Ti 2 x D x )O 7 δ (D = Ca, Mg, Zn): x x x 4DO+ 2LnLn + 4TiTi + 3OO (5) 4DTi '' + 2TiLn + 3VO + Ln2Ti2O7. Isovalent substitutions in the pyrochlore structure of Ln 2 M 2 O 7 (Ln = Sm Lu; M = Ti, Zr, Hf) were performed so as to reduce the ionic radius mismatch between the cations on the Ln 3+ and M 4+ sites and create conditions for defect formation in the pyrochlore structure according to schemes () and (2) [4, 42, 45]. Extensive studies were concerned with the synthesis and characterization of Ln 2 (Ti 2 x Ln x )O 7 δ solid solutions, with heterovalent substitutions of Ln 3+ trivalent cations for Ti 4+ (3) in the broad Ln 2 Ti 2 O 7 Ln 2 O 3 (Ln = Ho Lu) isomorphous miscibility ranges [7, 8, 43, 44, 46, 47]. The conductivity of Lu 2 (Ti 2 x Lu x )O 7 δ (x =,.5,.,.29,.44,.63) solid solutions prepared at 6 С using coprecipitation followed by freeze drying was determined for the first time using impedance spectroscopy [8, 42]. The data in Fig. 7 illustrate the relationship between the 8 С conductivity (σ), activation energy for conduction (E a ), percentage of Lu Ti ' + Ti Lu antistructure pairs, that of Lu Ti ' antisite defects, and composition for the Lu 2 (Ti 2 x Lu x )O 7 δ (x =.44) solid solutions. As seen, the highest conductivity is offered by the Lu 2 (Ti.9 Lu. )O 6.9 (x =.) pyrochlore-like solid solution, which has the lowest activation energy for ionic conduction:.3 ev. According to XRD data, the oxygen-ion-conducting solid solutions with х =. and.29 contained.8 and 2.4% oxygen vacancies on the O2 (48f) site [8, 42]. Combining total conductivity versus oxygen partial pressure data and electronic conductivity measurements by the Hebb Wagner blocking electrode technique has made it possible to estimate ion transport numbers (Fig. 8) and to demonstrate for the first time that the Lu 2 (Ti.9 Lu. )O 6.9 (x =.) and Lu 2 (Ti.7 Lu.29 )O 6.86 (x =.29) solid solutions are purely ionic conductors (with ion transport numbers of ~) at С and oxygen partial pressures above 5 Pa. Experimental data have been obtained that show for the first time that the Lu 2 O 3 TiO 2 system has a wide composition range of oxygen ion conduction, which can be thought of as superionic according to its

11 558 SHLYAKHTINA Table 3. Characteristics of Ln 2 (Ti.9 Ln. )O 6.9 (Ln = Er, Ho) solid solutions prepared from coprecipitated precursors at 85, 4, and 6 C (according to room-temperature XRD data) Composition t syn * Phase M Site composition a, Å Color Er 2 (Ti.9 Er. )O C PI.85(3)Er +.85Ti.767Ti +.233Er.5(2) Pink 6 C PII.97Er +.29Ti.923Ti +.77Er.965(3) Dark pink Ho 2 (Ti.9 Ho. )O C PII.985(3)Ho +.5Ti.937Ti +.63Ho.39(4) Yellow-green 6 C PII.957(5) Ho +.43Ti.99Ti +.9Ho.475(6) Yellow-green * Cooling mode 2: cooling rate, 2.2 C/min. Ln magnitude and activation energy over most of this composition range. This range lies within the Lu 2 Ti 2 O 7 Lu 2 O 3 isomorphous miscibility range (33.3 to 44 mol % Lu 2 O 3 ) and the corresponding materials are superionic oxygen ion conductors after high-temperature annealing between 4 and 75 С, depending on composition. The highest ionic conductivity is offered by the stoichiometric and near-stoichiometric materials Lu 2 (Ti 2 x Lu x )O 7 δ with x = and. synthesized at temperatures in the range 6 65 С. The new materials are comparable in ionic conductivity to the well-known solid electrolyte ZrO 2 9 mol % Y 2 O 3. The ion transport number was determined for solid solutions of holmium and erbium titanates in the isomorphous miscibility ranges of the Ln 2 O 3 TiO 2 (Ln = Ho, Er) systems [5, 47]. The ion transport number versus oxygen partial pressure data lg[σ S/cm] 2 3 x = x =. x =.8 x = lg[p O2 Pa] Fig. 9. Total conductivity (filled data points) and n-type electronic conductivity (open data points) as functions of oxygen partial pressure for Yb 2 (Ti 2 x Yb x )O 7 δ (x =,.,.8,.29) synthesized through coprecipitation followed by heat treatment at 6 С [7]. obtained for Er 2 (Ti.9 Er. )O 6.9 and Ho 2 (Ti.9 Ho. )O 6.9 by the Hebb Wagner blocking electrode technique demonstrate that Er 2 (Ti.9 Er. )O 6.9 is a purely ionic conductor (with an ion transport number of ~) at С and oxygen partial pressures (Р О2 ) above 5 Pa and that Ho 2 (Ti.9 Ho. )O 6.9 synthesized at 6 С has a purely ionic conductivity of 2 2 S/cm at С and Р О2 > 3 Pa. Table 3 presents data on the defect structure of these solid solutions. Figure 9 presents the key dependences of conductivity on oxygen partial pressure for Yb 2 (Ti 2 x Yb x )O 7 δ (x =,.,.8,.29) [7, 44]. There is a plateau of predominantly ionic conductivity ( Pa < Р О2 < 5 Pa) and an appreciable n-type electronic conductivity, responsible for the increase in total conductivity under strongly reducing conditions. The р-type electronic conductivity remains insignificant throughout the range of oxygen pressures examined, including oxidizing conditions. The activation energy for grainboundary conduction was found to depend little on Yb 2 O 3 concentration. The generation of oxygen vacancies in Yb 2 (Ti 2 x Yb x )O 7 δ (x =.29) follows scheme (3). The vacancy concentration increases with Yb 2 O 3 content, which might be expected to ensure an increase in oxygen ion conductivity. Moreover, partial occupancy of the titanium site by ytterbium cations, which have a large ionic radius, may contribute to oxygen vacancy formation according to schemes () and (2), as was found for Y 2 (Zr y Ti y ) 2 O 7 [64]. The highest conductivity was, however, found in Yb 2 Ti 2 O 7, and the conductivity decreases with increasing Yb 2 O 3 concentration (Fig. 9). This is most likely due to defect association in Yb 2 (Ti 2 x Yb x )O 7 δ (x =.29) according to the scheme Yb Ti + (Yb Ti V O ). (6) V O The drop in ionic conductivity with increasing Yb concentration is due to a reduction in oxygen vacancy mobility and not to a decrease in oxygen vacancy concentration. A similar variation in conductivity with Er 2 O 3 concentration was found in Er 2 (Ti 2 x Er x )O 7 δ (x =,.) [5]. It seems likely that the increase in ionic conductivity according to scheme (3) occurs in

12 MORPHOTROPY, ISOMORPHISM, AND POLYMORPHISM lg[σ b T, Ω cm K] E a =.94 ev E a =.86 ev Ho 2 Ti 2 O 7, 6 C Ho 2. Ti.99 O 7, 6 C Ho 2.2 Ti.98 O 6.99, 6 C E a =.4 ev E a =.6 ev /T, K Fig.. Arrhenius plots of bulk conductivity for Ho 2 (Ti 2 x Ho x )O 7 x/2 (x =,.,.2) in air. N, % σ, S/cm E a, ev.5. Lu Yb Tm Er Ho Dy rln 3+, Å Fig.. () 8 С bulk conductivity, (2) activation energy, and (3) percentage of antistructure pairs vs. ionic radius of Ln for Ln 2 (Ti.9 Ln. )O 6.9 pyrochlore-like solid solutions (coprecipitation, 6 С)...5 these systems at very low dopant (Er) concentrations in the titanium sublattice. Indeed, according to recent ionic conductivity data for the Ho 2 (Ti 2 x Ho x )O 7 δ (x =,.,.2,.) solid solutions [47] (Fig. ), the ionic conductivity of Ho 2 (Ti.99 Ho. )O 7 δ is three times that of the stoichiometric material Ho 2 Ti 2 O 7, whereas the ionic conductivity of Ho 2 (Ti.98 Ho.2 )O 7 δ is markedly lower. The conductivity of Ho 2 (Ti.9 Ho. )O 6.9 is slightly lower than that of Ho 2 (Ti.99 Ho. )O 7 δ. The conductivity of Ho 2 (Ti.9 Ho. )O 6.9, Er 2 (Ti.9 Er. )O 6.9, and Yb 2 (Ti.9 Yb. )O 6.9 is predominantly ionic and remains constant in a wide range of oxygen partial pressures. At low oxygen partial pressures, these materials have a considerable n-type conductivity. Figure plots the 8 С bulk conductivity and activation energy against the ionic radius of the rare earth for the Ln 2 (Ti.9 Ln. )O 6.95 (Ln = Dy Lu) pyrochlore-like solid solutions [5, 8, 43, 47]. The highest ionic conductivity (4.7 3 S/cm at 8 С) and lowest activation energy (~ ev) are offered by the Yb 2 (Ti.9 Yb. )O 6.9 solid solution. Fluorite-like Ln 2 (Ti 2 x Ln x )O 7 δ (Ln = Er Lu;.44 < x 67) materials have a considerably lower conductivity than do the pyrochlore-like Ln 2 (Ti 2 x Ln x )O 7 δ (Ln = Er Lu; x =.) solid solutions, because of the insufficient concentration of oxygen vacancies in positions 48f and 8b, which are necessary for oxygen ion transport in the pyrochlore structure. In the Ho 2 (Ti 2 x Ho x )O 7 δ (x =.8) system (like Dy and Gd, Ho is located in the middle of the lanthanide series), high conductivity is offered by the pyrochlore-like solid solutions with x =. and In the Y 2 (Ti 2 x Y x )O 7 δ system (the Shannon ionic radius of Y 3+ ( r Y 3+ КЧ 8 =.9 Å) differs little from that of Ho 3+ ( r Ho 3+ КЧ 8 =.5 Å) [49]), high conductivity was also reported for the pyrochlore solid solutions with х =.3.48 [5]. Their high conductivity is attributable to the presence of oxygen vacancies not only in position 48f [see schemes (2) and (8)] but also in position 8b [67], as represented by scheme (9): x x Ho Ti Ti Ho Ho + Ti Ho' + Ti, Ho TiO 2Ho' + + TiO +3/2O2, V 2 5 Ti O(48 f ) 2 (7) (8) Ho ' + V 2TiO5 2HoTi O( 8b) + TiO2 + 3/2O2. (9) Shlyakhtina et al. [4, 42] studied in detail the effect of the synthesis procedure (mechanically activated or coprecipitated precursors) and Sc 3+ isovalent substitution for Yb on the conductivity of Yb 2 Ti 2 O 7 and (Yb x Sc x ) 2 Ti 2 O 7 (х =,.9,.3). The high-temperature ionic conductivity of (Yb x Sc x ) 2 Ti 2 O 7 (х =,.9,.3) was shown to be influenced by cation antistructure pairs in the solid solutions. High oxygen ion conductivity was offered by Yb 2 Ti 2 O 7 synthesized using mechanical activation and the (Yb.9 Sc.9 ) 2 Ti 2 O 7 solid solution prepared from coprecipitated precursors. Both titanates contained ~ % cation antistructure pairs (Table 2). Oxygen ion conductivity data for LnYTi 2 O 7 (Ln = Dy, Ho) were presented in Ref. [45]. These double rare-earth titanates constitute an example of solid solutions with isovalent Ln (Dy, Ho) substitution on the Y site of Y 2 Ti 2 O 7. The double titanates DyYTi 2 O 7 and HoYTi 2 O 7 were synthesized at 6 С using mechanically activated oxides in order to accelerate the phase formation process and optimize the defect density in