2364 E.R. Andrievskaya Journal of the European Ceramic Sociery 28(2008)2363-2388 ternary diagram. Thus, the present paper aims to show the main the mentioned systems belong to the limited solubility type of phase relations in the binary and ternary compositions consid- diagrams. The main features inherent in these systems are poly ered prospective for new materials. -82 morphism of REO, zirconia(hafnia) and intermediate phases as and advanced coatings. In many applications, the ternary solid compensate the excess charge on defects and this makes oxides solutions of fluorite-type, C-type of the REO and intermediate sensitive with respect to environment (i.e. phase transformations pyrochlore-type phase are the targeted materials. In some cases, become dependable on oxygen partial pressure) high strength of ceramics is necessary to combine with high ionic The key feature of all solid solutions in these phase diagram onductivity or low thermal conductivity. Such a combination is is the prevalence of a steric factor over energetic. The linear not attainable in a two-component solid solution, but becomes dependences of temperature-concentration coordinates versus realistic in three-component systems. Summary of current and ionic radii of rare-earth elements were revealed for many phase potential applications of ceramics based on the systems with diagram elements. All phase diagrams of the binary systems different lanthanides ZrO2(HfO2-Y2O3-Ln2O3 is presented in HfO2(ZrO2-Ln2O3 are of eutectic type(Figs. 1-4). The min- Table 1 imal liquidus temperature in the ZrO2(HfO2--Ln2O3 systems HfO2-Y2O3-Ln2O3 and ZrO2-k he ternary systems correspond to the reactions of eutectic type F+XLfor lan- The phase relations ies in the wide range of temperature and concentrations using subgroup XRD, DTA in He at temperatures up to 2500C, thermal anal- The coordinates(temperature and concentration) of eutectic ysis in air(including solar furnace up to 3000C), petrography points vary linearly with effective ionic radius of lanthanide. The and electron microscopy. 83-87 temperature of reaction increases and the concentration of lan- REO selected are representatives of lanthanides from the thanide oxide ineutectic point decreases with ion radius decrease beginning, the middle and end of the raw. This allows deducing (Table 2, Fig. 5) the main regularities of constitution in the series of the ternary Note, that under effective ionic radius in solid solution of diagrams HfO2(ZrO2H-Y203-Ln2O3. The comparison of the substitution type Mel-rLnr O2 we understand the ratio of addi phase diagrams based on zirconia and hafnia permits lucida- tivity: Reff=xRLn++(1-xRMe+ where u is a concentration tion the difference between the phase diagram constitution of the in mol%, R is the cation radius. The linear approximation is systems included the components--crystallographic analogs but sufficient, taking into account low accuracy of temperature mea- differed by cation radius. surement above 2000C, as well as the tendency for some oxides The crystallization of the alloys in the ZrO2 to change oxidation degree in vacuum or inert gas medium. The (HfO2-Y203-Ln2O3 systems was investigated using the eutectic reactions in the systems with HfO2 occur at tempe data liquidus and solidus surfaces. The crystallization atures 50-100C higher, than that in systems based on ZrO2 paths for the alloys and the schematics of the reactions were which correspond to difference in melting points for pure hafnia constructed. The equilibrium phase diagrams have been and zirconia(Table 2) deduced In the selected systems, the substitution-type solid solu- Basic interest to this research originates from the diversity tions are known to be formed by components and intermediat of polymorphic modifications inherent to the mentioned oxides, phases. The substantial phenomenon in the solid solutions intermediate phases and solid solutions stable or metastable, as the non-stoichiometry. Thus, the solid solutions based on cubic well as from the effect of electronic structure and ionic radii modifications of HfO,(ZrO,) form so called"defect fluorite of lanthanides on phase stability and boundaries of phase fields. structure.227 The substitution of hafnium or zirconium ions The overview of general regularities in constitution of phase dia- by lanthanide ion leads to increased concentration of oxygen grams of the ternary systems HfO2(ZrO2)-Y2O3-Ln2O3 seems vacancies--the defects compensating the lack of positive ionic to be logically starting from the analysis of the bounded binary charge in the cation sublattice. 28 The formation of solid solu- systems; then discuss several ternary systems and consider the tions also occurs by substitution of lanthanide ion by hafnium character of phase crystallization, and then introduce some or zirconium ion, provided the electron compensation of excess potential system for directional solidification study charge, 62 The model of substitution-type solid solution based on 2. General characteristics and regularities of phase MeO2 (Me=Hf, Zr)can be presented by Kroger-Vink formula: reactions in the systems HfO2-Ln203 and ZrO2-Ln20 Me++1- Ln+102-2-(/2). This formula seems to be correct for all three types of solid solutions based on monoclinic(M), tetrag- Phase interaction of zirconia, hafnia and practically all lan- onal (T) and cubic(fluorite-type, F)polymorphs of MeO2 thanide oxides(REO)(except Pm2O3, CeO2)are thoroughly Additives of the REO markedly decrease temperatures of phase studied in the temperature range from 1500C up to melting transformations T Tt F in hafnia and zirconia In the 2900 C4.57-60,63,65,67,68, 88-22 At temperatures below 1500.C series of phase diagrams, temperature of melting and solid-state these systems are studied a little, because the diffusion mobility transformations directly depends on the ratio between ionic radi is extremely low and the rate of solid solution and intermedi- of cations rHf++/rLn". The solubility in the monoclinic phase ate phase formation is infinitesimal. The phase diagrams of all as a rule, does not exceed 2 mol%, and in the tetragonal it is less2364 E.R. Andrievskaya / Journal of the European Ceramic Society 28 (2008) 2363–2388 ternary diagram. Thus, the present paper aims to show the main phase relations in the binary and ternary compositions consid￾ered prospective for new materials.4–82 From the practical use viewpoint, these systems are worth studying because of needs in new structural, functional ceramics and advanced coatings. In many applications, the ternary solid solutions of fluorite-type, C-type of the REO and intermediate pyrochlore-type phase are the targeted materials. In some cases, high strength of ceramics is necessary to combine with high ionic conductivity or low thermal conductivity. Such a combination is not attainable in a two-component solid solution, but becomes realistic in three-component systems. Summary of current and potential applications of ceramics based on the systems with different lanthanides ZrO2(HfO2)–Y2O3–Ln2O3 is presented in Table 1. The phase relations in the ternary systems HfO2–Y2O3–Ln2O3 and ZrO2–Y2O3–Ln2O3 were stud￾ies in the wide range of temperature and concentrations using XRD, DTA in He at temperatures up to 2500 ◦C, thermal anal￾ysis in air (including solar furnace up to 3000 ◦C), petrography and electron microscopy.83–87 REO selected are representatives of lanthanides from the beginning, the middle and end of the raw. This allows deducing the main regularities of constitution in the series of the ternary diagrams HfO2(ZrO2)–Y2O3–Ln2O3. The comparison of the phase diagrams based on zirconia and hafnia permits elucida￾tion the difference between the phase diagram constitution of the systems included the components—crystallographic analogs but differed by cation radius. The crystallization of the alloys in the ZrO2 (HfO2)–Y2O3–Ln2O3 systems was investigated using the data on liquidus and solidus surfaces. The crystallization paths for the alloys and the schematics of the reactions were constructed. The equilibrium phase diagrams have been deduced. Basic interest to this research originates from the diversity of polymorphic modifications inherent to the mentioned oxides, intermediate phases and solid solutions stable or metastable, as well as from the effect of electronic structure and ionic radii of lanthanides on phase stability and boundaries of phase fields. The overview of general regularities in constitution of phase dia￾grams of the ternary systems HfO2(ZrO2)–Y2O3–Ln2O3 seems to be logically starting from the analysis of the bounded binary systems; then discuss several ternary systems and consider the character of phase crystallization, and then introduce some potential system for directional solidification study. 2. General characteristics and regularities of phase reactions in the systems HfO2–Ln2O3 and ZrO2–Ln2O3 Phase interaction of zirconia, hafnia and practically all lan￾thanide oxides (REO) (except Pm2O3, CeO2) are thoroughly studied in the temperature range from 1500 ◦C up to melting 2900 ◦C.4,57–60,63,65,67,68,88–221 At temperatures below 1500 ◦C these systems are studied a little, because the diffusion mobility is extremely low and the rate of solid solution and intermedi￾ate phase formation is infinitesimal. The phase diagrams of all the mentioned systems belong to the limited solubility type of diagrams. The main features inherent in these systems are poly￾morphism of REO, zirconia (hafnia) and intermediate phases as well as aleovalent character of ion substitution in the majority of solid solutions.57,58,222–226 Ionic or electronic charge carriers compensate the excess charge on defects and this makes oxides sensitive with respect to environment (i.e. phase transformations become dependable on oxygen partial pressure). The key feature of all solid solutions in these phase diagrams is the prevalence of a steric factor over energetic. The linear dependences of temperature–concentration coordinates versus ionic radii of rare-earth elements were revealed for many phase diagram elements. All phase diagrams of the binary systems HfO2(ZrO2)–Ln2O3 are of eutectic type (Figs. 1–4). The min￾imal liquidus temperature in the ZrO2(HfO2)–Ln2O3 systems correspond to the reactions of eutectic type F + X L for lan￾thanide oxides of cerium subgroup and F + H L—for yttrium subgroup. The coordinates (temperature and concentration) of eutectic points vary linearly with effective ionic radius of lanthanide. The temperature of reaction increases and the concentration of lan￾thanide oxide in eutectic point decreases with ion radius decrease (Table 2, Fig. 5). Note, that under effective ionic radius in solid solution of substitution type Me1−xLnxO2 we understand the ratio of addi￾tivity: Reff = xRLn 3+ + (1 − x)RMe 4+, where ч is a concentration in mol%, R is the cation radius. The linear approximation is sufficient, taking into account low accuracy of temperature mea￾surement above 2000 ◦C, as well as the tendency for some oxides to change oxidation degree in vacuum or inert gas medium. The eutectic reactions in the systems with HfO2 occur at temper￾atures 50–100 ◦C higher, than that in systems based on ZrO2, which correspond to difference in melting points for pure hafnia and zirconia (Table 2). In the selected systems, the substitution-type solid solu￾tions are known to be formed by components and intermediate phases. The substantial phenomenon in the solid solutions is the non-stoichiometry. Thus, the solid solutions based on cubic modifications of HfO2(ZrO2) form so called “defect fluorite” structure.227 The substitution of hafnium or zirconium ions by lanthanide ion leads to increased concentration of oxygen vacancies—the defects compensating the lack of positive ionic charge in the cation sublattice.228 The formation of solid solu￾tions also occurs by substitution of lanthanide ion by hafnium or zirconium ion, provided the electron compensation of excess charge.62 The model of substitution-type solid solution based on MeO2 (Me = Hf, Zr) can be presented by Kroger-Vink formula: ¨ Me4+1−xLn3+xO2−2−(x/2). This formula seems to be correct for all three types of solid solutions based on monoclinic (M), tetrag￾onal (T) and cubic (fluorite-type, F)—polymorphs of MeO2. Additives of the REO markedly decrease temperatures of phase transformations T M and T F in hafnia and zirconia. In the series of phase diagrams, temperature of melting and solid-state transformations directly depends on the ratio between ionic radii of cations rHf4+/rLn 3+. The solubility in the monoclinic phase, as a rule, does not exceed 2 mol%, and in the tetragonal it is less