On the phase relations in the ZrO2–YO1.5–AlO1.5 system

On the phase relations in the ZrO2–YO1.5–AlO1.5 system

Journal of Alloys and Compounds 420 (2006) 237–245 On the phase relations in the ZrO2–YO1.5–AlO1.5 system S. Lakiza a,b,c , O. Fabrichnaya b,c,∗ , M...

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Journal of Alloys and Compounds 420 (2006) 237–245

On the phase relations in the ZrO2–YO1.5–AlO1.5 system S. Lakiza a,b,c , O. Fabrichnaya b,c,∗ , M. Zinkevich b,c , F. Aldinger b,c a

I.M. Frantsevich Institute for Materials problems, Krzhyzhanovskiy Str. 3, 03680 Kiev, Ukraine b Max-Planck-Institut f¨ ur Metallforschung, Stuttgart, Germany c Institut f¨ ur Nichtmetallische Anorganische Materialien, Universit¨at Stuttgart, Heisenbergstr. 3, 70569 Stuttgart, Germany Received 22 August 2005; accepted 29 September 2005 Available online 20 December 2005

Abstract Experimental studies of samples with the composition 23.5 mol% ZrO2 , 59.2 mol% YO1.5 and 17.3 mol% AlO1.5 indicated a change of tie-lines in the temperature range 1523–1613 K due to the invariant reaction YAM + F = YAP + ␦ as predicted by Calphad method. The thermodynamic description of the ZrO2 –YO1.5 –AlO1.5 system based on the modelling of fluorite (F) and bixbyite (C) structures as different phases is derived. The isothermal sections at 1523, 1573 and 1623 K are calculated and two invariant solid state reactions are indicated: YAM + F = YAP + ␦ at 1614 K and F = ␦ + YAM + C at 1602 K. Ternary interaction parameter in liquid phase is assessed to get an improved fit of experimental data on liquidus surface. The calculated liquidus surface is in a good agreement with experimental data. Reasonable agreement with experimental data on isoplethal sections is obtained. The T0 -lines for fluorite ⇔ tetragonal and tetragonal ⇔ monoclinic transformations are calculated in the ZrO2 –YO1.5 –AlO1.5 system. © 2005 Elsevier B.V. All rights reserved. Keywords: Oxide materials; X-ray diffraction; Phase diagrams; Thermodynamic modelling

1. Introduction Yttria stabilised zirconia (YSZ) has various industrial applications [1,2]. For example, the phase with fluorite structure is used as a solid electrolyte [3]. The tetragonal phase with 6–8 wt.% Y2 O3 is used for thermal barrier coating (TBC) on metal substrates [4,5]. During thermal cycling, thin layer of ␣-Al2 O3 (thermally grown oxide, TGO) forms between metallic bond coating (BC) and TBC. Therefore, phase relations in the ZrO2 –YO1.5 –AlO1.5 system are important to understand the interactions between TBC and TGO. Multilayer coatings Y3 Al5 O12 (YAG)/YSZ are suggested to enhance bond coat oxidation resistance [6]. Hence phase relations of the ternary system could elucidate stability issues of such coatings. The system ZrO2 –YO1.5 –AlO1.5 was studied experimentally in several works [7–12]. Isothermal sections of this system are available at 1523 K [10], 1923 K [8] and 2073 K [9]. Liquidus surface and isoplethal sections were constructed by Lakiza and Lopato [11] using experimental results obtained from high-



Corresponding author. Tel.: +49 711 6893106; fax: +49 711 6893131. E-mail address: [email protected] (O. Fabrichnaya).

0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.09.079

temperature DTA, microstructural studies and by petrographic analysis. The phase formation of three-phase composites of the ZrO2 –YO1.5 –AlO1.5 system was studied by rapid solidification from melt in work [12] in order to determine the compositional ranges of existing phase fields at the subsolidus conditions and to investigate presence of solidified eutectics. The solidified phases were determined by X-ray diffraction and Raman spectroscopy. There are several recent thermodynamic assessments of the ZrO2 –YO1.5 system [1,2,13] and one assessment of the ZrO2 –YO1.5 –AlO1.5 system [2]. The calculations at 1523 K by Fabrichnaya and Aldinger [2] indicated that the tie-lines between Zr3 Y4 O12 (␦), YAP, YAM and fluorite structure are different from those obtained in work [10]. The calculations showed that the invariant reaction YAM + F = YAP + ␦ takes place at 1587 K and the tie-lines at 1600 K coincide with ones obtained by Lopato et al. [10] at 1523 K. The present study aims to check the tie-lines at 1523 K and to determine whether the above mentioned invariant transformation proceeds and at which temperature. Another aim is to derive thermodynamic description for the ZrO2 –YO1.5 –AlO1.5 system compatible with ones obtained for the ZrO2 –GdO1.5 –AlO1.5 system [14] and ZrO2 –GdO1.5 –YO1.5 system [15] and to combine them into thermodynamic database

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for the ZrO2 –GdO1.5 –YO1.5 –AlO1.5 system, which is applicable for the modelling of phase relations between TBC and TGO. 2. Experimental procedure A sample for experimental study was taken in the tie-line triangle YAP—␦—YAM and at the same time on the tie line YAM—F (ZrO2 + 50.8 mol% YO1.5 ) (Fig. 1). The composition was 23.5 mol% ZrO2 , 59.2 mol% YO1.5 and 17.3 mol% AlO1.5 . The samples were prepared using chemical route from powders of Al(NO3 )3 ·9H2 O, ZrO(NO3 )2 ·2H2 O and yttria with purity of 99.9% by dissolving in water with some droplets of concentrated nitric acid added. The obtained solution was then dried, the yield was calcined at 1173 K in air and pressed into pellets 5 mm in diameter and 5 mm in height. Individual samples were annealed in air at temperatures from 1523 to 1923 K for at least 120 h—the time necessary to attain equilibrium. The specimens were investigated by X-ray analysis (D5000, Simens AG with position sensitive detector, Cu K␣ radiation).

3. Thermodynamic modelling The Calphad method [16] based on computer coupling of thermochemistry and phase diagram is used in this study to assess thermodynamic parameters in binary and ternary systems. The programs from Thermo-Calc software package are used for assessment of thermodynamic parameters and phase diagram calculations [17]. The phases stable in the system ZrO2 –YO1.5 –AlO1.5 and thermodynamic models used to describe them are shown in Table 1. Most of the solid phases are described by the compound energy formalism [18]; the remaining solid phases are treated as stoichiometric compounds. The liquid phase is described by two-sublattice ionic liquid model [18]. Since no ternary compounds were found in the system, this allows extrapolation from binary systems into ternary system.

Table 1 The phases stable in the system ZrO2 –YO1.5 –AlO1.5 Phase, abbreviation

Model

Liquid (L) Fluorite (F) Bixbyite (C) Tetragonal (T) Hexagonal (H) Monoclinic (M) ␦-Zr3 Y4 O12 (␦) YAM YAP YAG Corundum (AL)

(Y+3 , Zr+4 )P (O−2 , AlO1.5 )Q (Al+3 , Y+3 , Zr+4 )1 (O−2 , Va)2 (Y+3 , Zr+4 )2 (O−2 )3 (O−2 , Va)1 (Al+3 , Y+3 , Zr+4 )1 (O−2 , Va)2 (Y+3 , Zr+4 )2 (O−2 )3 (O−2 , Va)1 (Al+3 , Y+3 , Zr+4 )1 (O−2 , Va)2 Zr3 Y4 O12 Y4 Al2 O9 YAlO3 Y3 Al5 O12 Al2 O3

The thermodynamic parameters for the system ZrO2 –YO1.5 were derived by Fabrichnaya and Aldinger [2], where cubic phases with fluorite and bixbyite structures were considered as one phase having a miscibility gap. Later, the parameters were re-assessed by Fabrichnaya et al. [15], using different models to describe the fluorite (F) and bixbyite (C) solid solutions. This approach is more consistent with the crystal structure of these phases. The phase with fluorite structure can be described by two sublattices. The first sublattice is filled by Zr+4 , Y+3 and Al+3 cations; the second one contains disordered oxygen anions and oxygen vacancies, i.e., (Zr+4 , Al+3 , Y+3 )1 (O−2 , Va)2 . In the C-phase with bixbyite structure, vacancies are ordered and anionic sublattice is subdivided into two sublattices, i.e., one completely filled by oxygen anions and another one partly vacant (Y+3 , Zr+4 )2 (O−2 )3 (O−2 , Va)1 . Solid solutions based tetragonal and monoclinic ZrO2 are described with the same model as fluorite, while the hexagonal solid solutions based on YO1.5 is described similarly to C-phase. The remaining phases in Table 1 are regarded as stoichiometric compounds and their Gibbs energy is a function of temperature only. The Gibbs energy of a solution phase with mixing in two sublattices is expressed as    G = Yis Yjt Gi,j + RT αs Yis ln Yis + Gex i

j

s

i

where Gi,j are the Gibbs energies of the end-member compounds, Yis is the mole fraction of a constituent i in sublattice s, αs is the number of sites on sublattice s per mole of formula unit of phase and Gex is excess Gibbs energy of mixing expressed as  Gex = Yis Yjs Lsi,j + Gex,tern s

Lsi,j =

Fig. 1. Composition of the ZrO2 –YO1.5 –AlO1.5 system selected for experimental study (1). The phase diagram at 1523 K is from [10]. The dash lines are possible tie-lines between YAM and fluorite phases according to [10] and YAP and ␦ phases according to [2].

 n

(Yis − Yjs )n Li,j ,

where Li,j are binary interaction parameters in the sublattice s and Gex,tern is contribution from ternary interactions. For solid solutions ternary interaction parameters are assumed to be zero. Liquid phase is described by the partially ionic sublattice model (Y +3 , Zr+4 )P (O−2 AlO1.5 )Q ,

S. Lakiza et al. / Journal of Alloys and Compounds 420 (2006) 237–245

Fig. 2. The phase diagram of the ZrO2 –AlO1.5 system calculated with two sets of parameters in comparison with experimental points. Phase diagram calculated with dataset-1 is shown by solid lines, while the calculations with dataset-2 are shown by dash line.

where P and Q are the number of sites on the cation and anion sublattices, respectively. The stoichiometric factors P and Q vary with composition in order to maintain electroneutrality. For liquid phase ternary interaction is assessed from experimental data of Lakiza and Lopato [11] and ternary interaction term is expressed as Gex,tern = YY +3 YZr+4 YO−2 YAlO1.5 LY +3 ,Zr+4 :O−2 ,AlO1.5 , where L is the ternary interaction parameter. 4. Results and discussions 4.1. Binary systems The thermodynamic parameters in binary systems were already assessed in previous works: YO1.5 –AlO1.5 [2], ZrO2 –YO1.5 [15] and ZrO2 –AlO1.5 [14]. The mixing parameters of fluorite and tetragonal phases in the ZrO2 –AlO1.5 system were assessed in work [14] using estimates of the AlO1.5 solubility in these phases by Lakiza and Lopato [11]. However, there is still discussion in the literature on how much alumina

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Fig. 3. Phase equilibrium between corundum and fluorite phase in the ZrO2 –YO1.5 –AlO1.5 system at YO1.5 content in fluorite of 17.4 mol% calculated with two sets of parameters of ZrOr–AlO1.5 system, superimposed with experimental data of [20].

can be dissolved in fluorite and tetragonal phases [19]. In this work the influence of reduced solubility of AlO1.5 in tetragonal and fluorite phases on equilibria in the ZrO2 –AlO1.5 and ZrO2 –YO1.5 –AlO1.5 systems is investigated. Calculations made with dataset-1 from [14] and dataset2 resulting in a lower solubility of the Al2 O3 in fluorite and tetragonal phases derived in this study are presented in Fig. 2 and Table 2. The comparison of these calculations with experimental data for the ZrO2 –AlO1.5 system shows that dataset1 (solid lines) reproduce experimental results slightly better. The extrapolation of binary descriptions to the ternary system ZrO2 –YO1.5 –AlO1.5 and further calculations of equilibrium between corundum and fluorite phase confirm that using of the dataset-1 leads to a better consistency with experimental data [20] (see Fig. 3). 4.2. Ternary system 4.2.1. Experimental results The composition selected to check tie-lines between YAP, YAM, fluorite and ␦ phases is shown in Fig. 1 along with an experimental phase diagram at 1523 K [10]. The tie-lines

Table 2 Invariant reactions in the ZrO2 –AlO1.5 system Set 1: 0 LF = 3625, 0 LT = 9261

Set 2: 0 LF = 35000, 0 LT = 50000

Experiment

T (K)

x(AlO1.5 )

T (K)

x(AlO1.5 )

T (K)

x(AlO1.5 )

F=T+L

2587

0.058

0.051

0.4

2599

0.020

0.012

0.361

2533

0.113

0.095

0.333 [11]

L = T + AL

2130

0.767

0.087

1

2115

0.746

0.018

1

2133 2183 2143 2139 2163

0.773 0.764 0.773 0.784 0.780

0.095 – – 0.013 0.154

1 [11] – [21] – [22] 1 [19] 1 [23]

Reaction

Set 1: accepted parameters; set 2: parameters giving low content of AlO1.5 in F and T phases.

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Table 3 The phase composition of the sample 23.5 mol% ZrO2 –59.2 mol% YO1.5 –17.3 mol% AlO1.5 annealed at different temperatures No.

Annealing temperature, (K)

Phase composition by XRD

1 2 3

1523 1573 1613

YAM + ␦ + YAP YAM + ␦ + YAP YAM + YAP + F

between fluorite and YAM phases indicated by Lopato et al. [10] and between ␦ and YAP phases predicted by Fabrichnaya and Aldinger [2] are shown by dashed lines. The XRD results of the chemically prepared samples annealed at 1523, 1573, 1613 K are shown in Table 3 and in Fig. 4. They confirm that up to 1573 K YAP and YAM are in equilibrium with ␦-phase as it was predicted by Fabrichnaya and Aldinger [2]. However, YAM and YAP phases are in equilibrium with fluorite phase at 1613 K. This equilibrium was indicated by Lopato et al. [10] to occur at 1523 K. Probably the equilibrium at 1523 K was not

reached in experiments of Lopato et al. [10], since the kinetics of the fluorite to ␦-phase transformation is very sluggish. 4.2.2. Calculation results Two invariant reactions between solid phases proceed in a narrow temperature range (Table 4). One of them YAM + F = YAP + ␦ (1) was predicted by calculations [2]. Another reaction F = ␦ + YAM + C (2) appears when the line of univariant reaction F + ␦ + C, started in the binary system ZrO2 –YO1.5 , intersects the line of univariant reaction F + C + YAM started from ternary eutectic L = F + C + YAM. It is interesting to note that the temperature of reaction (2) is higher than (1) in assessment [2], while in the present assessment temperature of reaction (1) is higher than (2). Since the reactions proceed in a narrow temperature range it is difficult to justify the obtained results experimentally. The calculated isothermal sections at 1523, 1623 and 1923 K are presented in Fig. 5a–c. It can be noticed that with the

Fig. 4. The XRD pattern for samples annealed at 1250, 1300 and 1340 ◦ C.

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Table 4 Subsolidus invariant reactions in the ZrO2 –YO1.5 –AlO1.5 system Reaction

T (K), phase composition x(YO1.5 ), x(AlO1.5 ): [2]

T (K), phase composition x(YO1.5 ), x(AlO1.5 ): this study

YAM + F = YAP + ␦

T = 1587 F: 0.5130, 2 × 10−5

T = 1614 F: 0.5740, 0.0018

F = ␦ + YAM + C

T = 1619 F: 0.6314, 3 × 10−6 C: 0.9261, 1 × 10−9

T = 1602 F: 0.6056, 1.4 × 10−3 C: 0.8927, 0.0a

a

According to model accepted for C-phase in this study it does not contain AlO1.5 .

temperature increase the invariant reactions (1) and (2) proceeding between solid phases in the range 1602–1614 K are already completed at 1623 K. Since the temperature of calculated invariant reaction (1) is 1614 K (1 K higher than upper limit of experimentally studied range) the calculation is performed at 1623 K to demonstrate tie lines above invariant reaction (1). At temperature 1657 K ␦-phase transforms to fluorite structure due to thermal disordering and at the temperatures between 1657 and 1984 K (lowest eutectics) the topology of isothermal sec-

tion is the same as it is at 1923 K. There is still remarkable inconsistency regarding the composition of fluorite phase, which participates in the three-phase equilibria listed in Table 5. For example, according to works [8,10], the YO1.5 content in the fluorite phase in equilibrium with corundum and YAG decreases with temperature, while results of study [7] indicated an opposite tendency. The comparison of calculated and experimental compositions of the fluorite phase participating in three phase equilibria is presented in Table 5. The calculations for the equi-

Fig. 5. (a–c) Calculated isothermal sections of the ZrO2 –YO1.5 –AlO1.5 system at 1523, 1623 and 1923 K.

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Table 5 Composition of the fluorite phase in three-phase equilibria Equilibrium

T (K)

x(YO1.5 ) x(AlO1.5 ) x(ZrO2 ) calculated

F + YAG + AL

1473 1523 1873 1923 1973 2073 1984 1988

0.200 0.198 0.184 0.182 0.179 0.174 0.178 0.178

0.008 0.010 0.032 0.036 0.041 0.051 0.042 0.042

0.792 0.792 0.784 0.782 0.780 0.775a 0.779 0.779

0.272 0.230 0.276 0.214 0.310 0.305 0.270 0.322

F + YAG + YAP

1523 1873 1923 2073 2123 2103

0.390 0.367 0.363 0.353 0.349 0.351

0.002 0.009 0.011 0.017 0.019 0.018

0.607 0.624 0.626 0.630 0.631 0.631

0.471 0.424 0.540 0.424 0.390 0.564

F + YAG + YAM

1523 1873 1923 2073 2146 2123

0.570 0.494 0.485 0.458 0.446 0.450

0.001 0.005 0.006 0.010 0.013 0.012

0.429a 0.501 0.509 0.531 0.541 0.538

0.496 0.551 0.587 0.551 0.440 0.580

a

x(YO1.5 ) x(AlO1.5 ) x(ZrO2 ) experimental – – – – ∼0.030 – – –

Refs.

0.728 0.770 0.724 0.786 0.760 0.695 0.73 0.678

[7] [10] [9] [8] [7] [9] [12] [11]

– – – – – –

0.527 0.576 0.460 0.576 0.610 0.436

[10] [9] [8] [9] [12] [11]

– – – – – –

0.504 0.449 0.413 0.449 0.560 0.420

[10] [9] [8] [9] [12] [11]

Metastable equilibrium.

librium F + YAG + AL are in reasonable agreement with data of works [8,10], but disagree with data of works [7,9,11]. The fluorite composition determined in studies of [12] and [11] indicated higher YO1.5 content in the fluorite phase than calculated in the present work, but lower than measured in works of [7,9]. The calculation of equilibrium F + YAG + YAP and F + YAP + YAM demonstrated a good agreement of fluorite composition in subsolidus equilibria determined by CalderonMoreno and Yoshimura [12]. According to measurements made in work [9] the YO1.5 content in fluorite in equilibrium with YAG + YAP and YAP + YAM is higher than in the present work, but lower than determined in studies of [8,11]. It should

be pointed out that the difference between the experimental data of [12] and [10,11] is large and cannot be attributed to the temperature difference in these experiments. The reasons of inconsistency between calculated and experimental data could be partial ordering in fluorite structure which is not accounted in calculations as well as uncertainty of thermodynamic data for yttrium aluminates on the one side and uncertainty of experimental determination of fluorite composition on the other side. In spite of some uncertainty in the thermodynamic data of yttrium aluminates, they are based on available experimental data on phase relations and thermodynamic values and they are a part of high-order system. Since new data contradicting

Table 6 Invariant equilibia in the ZrO2 –YO1.5 –AlO1.5 system Invariant equilibrium, type

T (K)

Liquid composition x(AlO1.5 ) x(ZrO2 ) x(YO1.5 )

Source

L = YAM + F e1 (max)

2225 2213

0.306 0.311

0.029 0.036

0.665 0.653

Calculated Experimental [11]

L = YAM + F + C E1

2224 2183

0.302 0.268

0.028 0.031

0.670 0.701

Calculated Experimental [11]

L = YAP + F e2 (max)

2146 2143

0.453 0.434

0.052 0.058

0.494 0.508

Calculated Experimental [11]

L = YAP + YAM + F E2

2146 2123

0.448 0.389

0.050 0.053

0.502 0.558

Calculated Experimental [11]

L = YAG + F e3 (max)

2124 2138

0.550 0.535

0.082 0.081

0.368 0.384

Calculated Experimental [11]

L = YAG + YAP + F E3

2123 2103

0.532 0.500

0.074 0.064

0.394 0.436

Calculated Experimental [11]

L = AL + YAG + F E4

1984 1988

0.746 0.718

0.095 0.105

0.159 0.177

Calculated Experimental [11]

L + T = F + AL U1

2058 2018

0.763 0.720

0.151 0.143

0.086 0.137

Calculated Experimental [11]

S. Lakiza et al. / Journal of Alloys and Compounds 420 (2006) 237–245

Fig. 6. Calculated projection of liquidus surface of the ZrO2 –YO1.5 –AlO1.5 system.

the description [2] do not exist, it is accepted in present study. The ternary interaction parameter of liquid phase 0 L(Y+3 , +4 Zr :O−2 , AlO3/2 ) = 89311 + 8.7914T has been assessed for a better reproduction of experimental data on liquidus surface

243

[11]. The comparison of calculated temperatures and liquid composition for invariant reactions with experimental data of Lakiza and Lopato [11] is presented in Table 6. The calculated liquidus surface is presented in Fig. 6. The isoplethal sections for x(ZrO2 ) = 0.081, YO1.5 – (1/3)ZrAl2 O5 and ZrO2 –Al0.5 Y0.5 O1.5 are presented in Fig. 7a–c along with the experimental points from work [11]. The calculations mostly reproduce the topology of experimental phase diagrams. Quantitatively they are in reasonable agreement with experiments except for the high temperature liquidus data, where experimental determination of final melting is difficult. The comparison of calculated in the present study and experimental data [11] for the isopleth ZrO2 –Al0.5 Y0.5 O1.5 (Fig. 7c) indicates differences in ZrO2 -rich composition similar to ones observed Fabrichnaya and Aldinger [2]. Both calculations indicate the field of stability of the fluorite phase, which separates into fluorite and tetragonal phase assemblage with the increase of ZrO2 content at 2273–2650 K. However, according to work [11] phase assemblage of liquid + fluorite transforms directly to liquid + tetragonal. It should be mentioned that ZrO2 -rich compositions were not studied in details in work of Lakiza and Lopato [11] and there is not enough experimental evidence to deduce this consequence of phase transformations. The calculated T0 -lines of the diffusionless transformations F ⇔ T and T⇔ M in the ZrO2 –AlO1.5 , ZrO2 –Al0.5 Y0.5 O1.5 and ZrO2 –YO1.5 systems are presented in Fig. 8a–c along with enlarged parts of the phase diagrams of the systems mentioned

Fig. 7. Calculated isoplethal sections: x(ZrO2 ) = 0.081 (a), YO1.5 –(1/3)ZrAl2 O5 (b) and ZrO2 –Al0.5 Y0.5 O1.5 (c).

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Fig. 8. (a–c) T0 -lines for F⇔T and T⇔M diffusionless transformations at Y/(Y + Al) = 0, 0.5 and 1.

above. The isothermal T0 -lines restricting composition range towards ZrO2 at each temperature, where metastable tetragonal phase can be obtained, are given in Fig. 9.

5. Conclusions

Fig. 9. T0 -lines of F⇔T transition in the ZrO2 –YO1.5 –AlO1.5 system.

1. The experimental investigation of phase equilibria at 1523 K confirmed tie-lines derived by Calphad calculations. The change of tie lines due to invariant reaction YAM + F = YAP + ␦ was obtained in the temperature range 1573–1513 K. 2. The thermodynamic description of the ZrO2 –YO1.5 –AlO1.5 system obtained in this study is consistent with the ones obtained in studies of [14,15] based on more realistic modelling of fluorite phase than in previous description [2]. 3. Different kinds of phase diagrams are calculated for the ZrO2 –YO1.5 –AlO1.5 system (isothermal, isoplethal sections and liquidus surface) and compared with available experimental data revealing reasonable mutual agreement. 4. The T0 -lines for fluorite ⇔ tetragonal and tetragonal ⇔ monoclinic transformations are calculated.

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Acknowledgments Support for this investigation was provided by the program of international research collaboration between European Commission (GRD1-2000–30211) and National Science foundation (DMR-0099695). The authors would like to thank S. Geupel for assistance in the XRD analysis. References [1] M. Chen, B. Hallstedt, L.J. Gauckler, Solid State Ionics 170 (2004) 255–274. [2] O. Fabrichnaya, F. Aldinger, Z. Metallkd. 95 (2004) 27–39. [3] N.Q. Minh, J. Am. Ceram. Soc. 76 (1993) 563–588. [4] C.G. Levi, Curr. Opin. Solid State Mater. Sci. 8 (2004) 77–91. [5] X.Q. Cao, R. Vassen, D. Stoever, J. Eur. Ceram. Soc. 24 (2004) 1–10. [6] Y.J. Su, R.W. Trice, K.T. Faber, H. Wang, W.D. Porter, Oxid. Met. 61 (2004) 253–271. [7] M.J. Bannister, J. Aust. Ceram. Soc. 18 (1982) 6–9. [8] L.M. Lopato, L.V. Nazarenko, G.V. Gerasimjuk, A.V. Shevchenko, Izv. Akad. Nauk SSSR, Inorg. Mater. 26 (1990) 701–704. [9] S.G. Popov, S.F. Pashin, M.V. Paromova, Z.U. Kulikova, O.N. Rozanova, A.N. Klimenko, V.M. Ionov, Izv. Akad. Nauk SSSR, Inorg. Mater. 26 (1990) 91–95.

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[10] L.M. Lopato, L.V. Nazarenko, G.V. Gerasimjuk, A.V. Shevchenko, Inorg. Mater. 28 (1992) 644–647. [11] S.M. Lakiza, L.M. Lopato, J. Am. Ceram. Soc. 80 (1997) 893–902. [12] J.M. Calderon-Moreno, M. Yoshimura, Solid State Ionics 154–155 (2002) 311–317. [13] N.S. Jacobson, Z.-K. Liu, L. Kaufman, F. Zhang, J. Am. Ceram. Soc. 87 (2004) 1559–1566. [14] S. Lakiza, O. Fabrichnaya, Ch. Wang, M. Zinkevich, F. Aldinger, J. Eur. Ceram. Soc. 26 (2006) 233–246. [15] O. Fabrichnaya, Ch. Wang, M. Zinkevich, C.G. Levi, F. Aldinger, J. Phase Equilib. Diffus. 26 (2005), in press. [16] N. Saunders, P. Miodovnik, Calphad (Calculation of Phase Diagrams): A Comprehensive Guide, Pergamon, Oxford, 1998. [17] B. Sundman, B. Jansson, J.O. Andresson, Calphad 9 (1985) 153–196. [18] M. Hillert, J. Alloys Compd. 320 (2001) 161–176. [19] D.A. Jerebtsov, G.G. Mikhailov, S.V. Sverdina, Ceram. Int. 26 (2000) 821–823. [20] M.A. Stough, J.R. Hellmann Jr., J. Am. Ceram. Soc. 85 (2002) 2895–2902. [21] G.R. Fischer, L.J. Manfredo, R.N. McNally, R.C. Doman, J. Mater. Sci. 16 (1981) 3447–3451. [22] F. Schmid, D. Viechnicki, J. Mater. Sci. 5 (1970) 470–473. [23] A.M. Alper, R.C. Doman, R.M. McNally, H.C. Yeh, in: A.M. Alper (Ed.), Phase Diagrams, Acad. Press, London, New York, 1970, p. 117.