Thermodynamic assessment of oxide system In2O3-SnO2-ZnO 166 D O I: 1 0. 15 82 6/ ch im te ch .2 01 8. 5. 4. 02 Jantzen T., Hack K., Yazhenskikh E., Müller M. Chimica Techno Acta. 2018. Vol. 5, No. 4. P. 166–188. ISSN 2409–5613 T. Jantzena, K. Hacka, E. Yazhenskikhb, M. Müllerb a GTT-Technologies, Kaiserstraße 103, D-52134 Herzogenrath, Germany b Forschungszentrum Jülich GmbH, IEK-2, D-52425 Jülich, Germany E-mail: tj@gtt-technlogies.de Thermodynamic assessment of oxide system In2O3‑SnO2‑ZnO The In2O3-SnO2-ZnO system is of special interest for applications as transparent conducting oxides and also transparent semiconductors. In the present work, a thermodynamic assessment for this system is discussed using all available experimental data on phase equilibria and thermodynamic properties. All sub- systems including elemental combinations were considered in order to generate a self-consistent Gibbs energy dataset for further calculation and prediction of thermodynamic properties of the system. The modified associate species model was used for the description of the liquid phase. Particular attention was given to two significant solid solution phases: Spinel with the formula Zn(2–x)Sn(1–x)In2xO4 based on Zn2SnO4 and Bixbyite based on In2O3 and extending strongly toward the SnZnO3 composition according to the formula In(2–2x)SnxZnxO3. In addition to the component oxides, nine quasi-binary compounds located in the In2O3-ZnO binary subsystem have also been included in the database as stoichiometric phases. Keywords: phase diagram; thermodynamic modeling; indium oxide; bixbyite; spinel Received: 28.11.2018. Accepted: 14.12.2018. Published: 31.12.2018. © Jantzen T., Hack K., Yazhenskikh E., Müller M., 2018 Introduction Compositions in  the In2O3– SnO2–ZnO ternary oxide system are of in- terest owing to their optical transparency combined with high electrical conductiv- ity [1, 2]. Transparent conducting oxides (TCOs) can be used as electrodes in solar cells, flat panel displays and other com- mercial devices. Although TCOs are ap- plied usually in film form, the study of bulk phase relations and physical properties can be useful for understanding fundamental materials properties. At the present time, ITO (tin-doped indium oxide) is the ma- terial of choice for TCO layers (e.g. in re- view [3]), but the increasing cost of indium metal and the development of new tech- nologies will require alternative TCOs. According to  Palmer [4] both SnO2 and ZnO are good TCOs with conductivities comparable to  ITO. Compositions from the In2O3–ZnO system with high Zn con- centration are attractive due to their high electrical conductivity, optical transpar- ency and excellent chemical stability [5, 6]. The materials from the system ZITO (Zn-In-Sn-O) [2] are promising replace- ments for  ITO as  TCO layers in  many opto-electronic applications. ZITO con- tains less indium than ITO, which low- ers the cost, and it has a  broad window of compositions that allow the TCO layer to be adjusted (conductivity, etc.) for each 167 application. The bulk equilibrium phases of  ZITO have been defined and exhibit two transparent and conductive regions: the bixbyite solid solution In2–2xZnxSnxO3 and the homologous series of compounds In2ZnkOk+3. Thermodynamic modelling on the basis of reliable experimental data and appro- priate Gibbs energy models for solid and liquid phases is a powerful tool for calcula- tion and prediction of the thermodynamic properties and phase equilibria for various systems. Furthermore, such data can be applied for heat balance calculations, i.e. for information on the energetics of pos- sible production processes. The quality and completeness of the thermodynamic data- bases used is a key prerequisite for reliable calculations. According to  CALPHAD- type modelling all available experimental data (phase equilibria, mixing properties, component activities, etc.) are critically an- alyzed in terms of their consistency. Each phase in the system is treated by an appro- priate Gibbs energy model with adjustable parameters (Gibbs energy of constituents, interaction parameters, etc.), which are optimized in accordance with the experi- mental information in order to generate a self-consistent dataset of Gibbs energies of all phases in a system. In the present study the thermody- namic assessment of  the oxide system In2O3–SnO2–ZnO is presented using all available experimental data on phase equi- libria and thermodynamic properties. The calculation of phase equilibria and the pre- diction of thermodynamic properties us- ing the database for the In2O3-SnO2-ZnO system can be helpful for developing and manufacturing TCOs for  optoelectronic devices. The experimental information on the available thermodynamic proper- ties (phase diagram, phase transition etc.) is used for the generation of self-consistent Gibbs energy datasets for all known phases and compounds in this ternary system. The Gibbs energy of the liquid phase has been modelled using a non-ideal as- sociate solution model proposed by Bes- mann and Spear [7]. This model has been successfully applied for  the description of melts containing oxides and sulphides in our previous studies, e.g. in [8–10]. Solu- bilities in the solid state have been treated using the multi-sublattice approach which allows the description of experimentally determined solubilities. In the present study there are two solid solution series with different structure. The spinel phase with formula (Zn+2,In+3)2(Sn +4, Zn+2)1(O –2)4 includes Zn2SnO4, In2SnO4, Zn2ZnO4, In2ZnO4 as  end-members. The model for bixbyite in form of In(2–2x)SnxZnxO3 us- ing the formula (In, Zn, Va)1(In, Sn)1(O)3 allows description of the limited solubility from pure indium oxide extending to SnZn compounds. The present database contains a  gas phase, a multi-component liquid phase, 7 solid solutions and 27 solid stoichiometric compounds. Thermodynamic models The Gibbs energies of the elements were taken from the SGTE unary database [11] while the pure component oxides were taken from the SGTE Pure Substance da- tabase [12], the thermodynamic descrip- tions of  the metallic systems were taken from the SGTE Solution database [13]. The thermodynamic data sources used in the present work are collected in Table 1. The thermodynamic descriptions of the assessed stoichiometric compounds are presented in Table 2. 168 The solid solution phases in  the In2O3-SnO2-ZnO system considered in the present work are given in Table 3 and are described below in more detail. The molten oxide phase The Gibbs energy of the liquid phase in the system is represented by the modi- fied non-ideal associate species model [7]. The basic species In2O3, SnO2 and ZnO along with one (quasi)binary species (Sn- Zn2O4) have been introduced as  liquid components. Although the corresponding metallic species were added for the systems Me-O, the present work will attend to the melt oxide species only; the interactions between these oxides and other oxide spe- cies are responsible for the thermodynamic properties of the liquid phase. To provide equal weighting of each associate species with regard to  its entropic contribution in the ideal mixing term, each species con- tains a total of two cations in its formula based on [7]. In addition, interactions be- tween associate species were introduced in order to fine tune the thermodynamic description. The molar Gibbs energy of  the solu- tion is presented by a three-term expres- sion with contributions of  the reference part, the ideal and the excess part taking into account binary interactions as follows: G x G RT x x x x L x x m i i i i i j i j v ij v i j v � � � � � � �� �� � � � � �� � ln 0 (1) where xi is the mole fraction of phase con- stituent i (including the associate species), °Gi is the molar Gibbs energy of the pure phase constituent i and is an interaction coefficient between components i and j, according to the Redlich — Kister polyno- mial. The Lij v� � with v = 0, 1, 2 and °Gi are temperature dependent in the same way according to: � � � � � � � � �� � � � � � � � � � G L A B T c T T D T E T F T i ij v, ln 2 1 3 (2) Thermodynamic data for  the liquid components are summarized in Table 3. The elemental systems In–O and Zn–O contain one stable oxide, In2O3 and ZnO, respectively, while in the system Sn-O two oxides were considered, Sn2O2 and Sn2O4. The liquid phase of the quasi-binary oxide systems will contain the basic oxides along with one (quasi)binary species (SnZn2O4 · 3 / 2). No ternary species were necessary. The Gibbs energy of the binary species are taken from the SGTE Pure Substance da- tabase [12] without modifications. The G function of the liquid species SnZn2O4 · 3 / 2 was derived using the melting data of the Table 1 Thermodynamic data sources used in present work System Source System Source In-Sn [13] In2O3–SnO2 This work In-Zn [13] In2O3–ZnO This work Sn-Zn [13] SnO2–ZnO This work In-O This work In2O3–SnO2–ZnO This work Sn-O This work – – Zn-O This work – – 169 Table 2 Thermodynamic properties of stoichiometric compounds assessed in this work Compound ∆fH 298, J / mol S298 0 , J / mol · K T (K) Cp, J / mol·K SnO –289853 48.95 298–1250 43.7399+0.01356023·T+ 10·T–2–1.06·10–10·T2 [13] Sn3O4 –1155713 151.23 298–1250 163.5208+0.03448263·T – 2223847·T–2+5.57·10–10·T2 SnIn2O5 –1439306.47 187.51 298–1903 197.5511+0.01742532·T – 4485329·T–2+3.968488·10–10·T2 1903–2186 213.5101 +0.01006315·T – 2261462·T–2–3.721512·10–10·T2 Sn3In4O12 –3458277.2 426.23 298–1903 471.1432+0.04221281·T – 11194525·T–2+3.968488·10–10·T2 1903–2186 213.5101 +0.01006315·T – 2261462·T–2+1.5626976·10–9·T2 Zn3In2O6 –1975291.24 231.8 298–2186 264.2621+0.02177245·T – 4512542·T–2 +3.8375878488·10–6·T2 Zn4In2O7 –2326518.2 274.79 298–2186 311.8461+0.02567555·T – 4512542·T–2 +3.8375878488·10–6·T2 Zn5In2O8 –2678001 317.6 298–2186 359.4301+0.02957865·T – 6013262·T–2 +6.3962278488·10–6·T2 Zn6In2O9 –3028592 360.86 298–2186 407.0141+0.03348175·T – 6763622·T–2 +7.6755478488·10–6·T2 Zn7In2O10 –3379500 403.92 298–2186 454.5981+0.03738485·T – 7513982·T–2 +8.9548678488·10–6·T2 Zn9In2O12 –4080212 490.44 298–2186 549.7661+0.04519105·T – 9014702·T–2 +1.15135078488·10–5·T2 Zn11In2O14 –4781168.4 576.79 298–2186 644.9341+0.05299725·T – 10515422·T–2 +1.40721478488·10–5·T2 Zn13In2O16 –5482137.2 663.13 298–2186 644.9341+0.05299725·T – 10515422·T–2 +1.40721478488·10–5·T2 Zn15In2O18 –6183104.984 749.4702 298–2186 835.2701+0.06860965·T – 13516862·T–2 +1.91894278488·10–5·T2 SnZn2O4 –1282630 151 298–1903 171.209+0.01516837·T – 3724587·T–2 +2.55940900002·10–6·T2 1903–2250 187.168+0.0078062·T – 1500720·T–2 +2.55864·10–6·T2 170 corresponding constituent oxides. The in- teractions between liquid species are listed in Table 3. Spinel Normal Spinels can be described using the formula AB2O4, where A is a divalent metallic cation and B represents a trivalent cation placed on the second sublattice. For example, zinc aluminate (ZnAl2O4) and zinc ferrite (ZnFe2O4) are normal spinels. On the other hand, zinc stannate Zn2SnO4 is an inverse spinel and has the chemi- cal formula A2BO4 where A are divalent zinc cations and B tetravalent tin cations, as in (Zn2+)2(Sn 4+)(O2–)4. The inverse Spi- nel Zn2SnO4 has the cubic spinel structure (space group ) and Pearson symbol cF56 [14]. This inverse spinel structure is pre- sent in  many systems, e.g. as  Ülvöspinel Fe2TiO4, manganese titanate Mn2TiO4 and gandilite Mg2TiO4. All of them can be treated with the same common formula Table 3 Thermodynamic descriptions of the liquid and solid solution phases Parameter value, J / mol Reference Liquid: (In, In2O3, Sn, Sn2O2, Sn2O4, Zn, Zn2O2, SnZn2O4 / 1.5) � � � �G GIn Liq In SGPS � � � �G GIn O Liq Ti O SGPS 2 3 2 3 � � � �G GSn Liq Sn SGPS � � � �G GSn O Liq SnO SGPS 2 2 2 � � � �G GSn O Liq SnO SGPS 2 4 2 2 � � � �G GZn Liq Zn SGPS � � � � �G G TSnZn O SnZn O Spinel 2 4 2 4 163400 80 81806. • � �LIn In O liq , � 2 3 +27600 � �LSn SnO liq , � +39000 1LSn SnO liq , = +11200 � �LSn SnO liq , � 2 +44000 � �LIn O SnO liq 2 3 2, � –11000 � �LIn O ZnO liq 2 3 , � –11000 � �LIn O SnO Sn liq 2 3 2, , –187000 * [11] [12] [11] [12] [12] [11] * * * * * * * * Spinel: (Zn2+, Sn4+)1(Zn 2+, In3+)2(O 2–)4 � � �� � �� �� � �G G GZn Zn O SnZn O Spinel ZnIn O Spinel 2 2 2 2 4 2 4 0 5 0 5 95 : : . . 000 � � � � � �� �� � �G G G G Spinel Zn In O ZnIn O ZnO SGPS In O SGPS 2 3 2 2 4 2 3 2700 : : 00 � � �� � �G GSn Zn O SnZn O Spinel 4 2 2 2 4: � � �� � �� �� � �G G GSn In O SnZn O Spinel ZnIn O Spinel 4 3 2 2 4 2 4 0 5 0 5 95 : : . . 000 * * * * * 171 (A2+)2(B 4+)(O2–)4. In the In2O3–SnO2–ZnO ternary system the spinel phase Zn2SnO4 dissolves a significant amount of indium and extends toward the fictive ZnO·In2O3 composition, having constant Zn:Sn ratio [1] according to the formula Zn(2–x)Sn(1–x) In2xO4. The proposed multi sublattice for- mula reads (Zn2+, In3+)2(Sn 4+, Zn2+)1(O 2–)4 and allows to describe the deviation from the stoichiometric composition towards higher In2O3-contents keeping the Zn:Sn ratio to 2:1. The molar Gibbs energy of the phase Spinel was expressed using the compound energy formalism derived by Hillert and Staffansson [15] and generalized by Sund- man and Ågren [16] under the condition y O III � �2 1 as follows: G y y G y y G y m o o � � � � � � � � � �� � Zn I Sn II Zn SnO Zn I Zn II Zn ZnO In 2 4 2 4 2 2 2 4 2 33 4 2 4 3 2 2 4 2 2 2 � � � � � �� � � �� � I Sn II In SnO In I Zn II In ZnO Zn y G y y G RT y o o II Zn I In I In I Sn II Sn II Zn II ln ln ln ln y y y RT y y y y 2 3 3 4 4 2 � � � � � � �� �� � � ZZn II 2�� �� Gmex G y y G y y G y m o o � � � � � � � � � �� � Zn I Sn II Zn SnO Zn I Zn II Zn ZnO In 2 4 2 4 2 2 2 4 2 33 4 2 4 3 2 2 4 2 2 2 � � � � � �� � � �� � I Sn II In SnO In I Zn II In ZnO Zn y G y y G RT y o o II Zn I In I In I Sn II Sn II Zn II ln ln ln ln y y y RT y y y y 2 3 3 4 4 2 � � � � � � �� �� � � ZZn II 2�� �� Gmex (3) where yi s represents the site fractions of sublattice component i on sublattice s. � �Gi j O: : 2 are the Gibbs energy of real (Zn2S- nO4) or hypothetical compounds where the first and second sublattices are occupied by appropriate components i and j, is the excess Gibbs energy which depends on the site fractions yi N and on temperature. Bixbyite Indium oxide In2O3 exists in  form of two crystalline phases, the cubic form (Bixbyite type like Mn2O3) with Pearson symbol cI80, and the rhombohedral form (Corundum type like Cr2O3) with Pear- son symbol hR30. The rhombohedral modification is metastable under normal Parameter value, J / mol Reference Bixbyite: (In, Zn, Va)(In, Sn)(O)3 � � �G GIn In O In O SGPS : : 2 3 � � �� � �� � � �G G G TIn Sn O In O SGPS ZnSnO Bixbyite : : . .0 5 0 5 20000 112 3 3 � � �� � �� � � �G G G TZn In O In O SGPS ZnSnO Bixbyite : : . .0 5 0 5 119044 32 3 3 � � � � � �� �G G G GZn Sn O ZnSnO Bixbyite ZnO SGPS SnO SGPS : : 3 2 10800 � � ��G GVa In O In O SGPS : : .0 5 2 3 � � � � �G GVa Sn O SnO SGPS : : 2 12000 0 46403 13L TIn In Sn O Bixbyite : , : •� � � 0 10 52L TIn Zn In O Bixbyite , : : . •� � 0 1700LIn Zn Sn O Bixbyite , : : � � 0 318000LIn Zn In Sn O Bixbyite , : , : � � 1 97000LIn Zn In Sn O Bixbyite , : , : � � * [12] * * * * * * * * * * — This work. Сontinuation of table 3 172 conditions, but can be produced at high temperatures and pressures [17]. In the present work this modification has been ignored. The solubility of tin in the stable form of In2O3 (Bixbyite) was investigated by  Gonzalez and Mason [18], Ohya and Ito [19], Enoki and Echigoya [20], as well as  Heward and Swenson [21] using dif- ferent methods. All investigations are in general agreement and confirm a sig- nificant solubility of SnO2 in Bixbyite. In contrast, the solubility of  zinc in  Bixby- ite appears to  be relatively small. In the ternary In2O3-SnO2-ZnO system Bixby- ite is enriched with tin and zinc extend- ing toward to  the composition ZnSnO3 and can be described as  In(2–2x)SnxZnxO3 (0 < x < 0.40) [1]. Bixbyite is described in this work as sol- id solution phase based on In2O3 using the atomic sublattice model (In, Zn, Va)1(In, Sn)1(O)3 assuming that the first and second sublattices can be occupied by  metal at- oms while the third contains oxygen atoms only. The atomic model is chosen, because the use of ions would require more addi- tional unknown Gibbs energies to describe the solubility of tin oxide in Bixbyite. The molar Gibbs energy of this phase was ex- pressed using the compound energy for- malism [15, 16] as follows: G y y G y y G y y G y m o o o � � � � �In I In II In O In I Sn II InSnO Zn I In II ZnInO 2 3 3 3 ZZn I Sn II ZnSnO Va I In II InO Va I Sn II SnO In y G y y G y y G RT y o o o 3 3 3 � � � � � ( II In I Zn I Zn I Va I Va I In II In II Va II V lnln ln ) ( ln ln y y y y y RT y y y y � � � � � aa II ) � Gm ex (4) where yi I and yi II represent the site frac- tions of the component i and j in the first respectively second sublattices. oGIn O2 3 cor- responds to the Gibbs energy of the indium oxide and is taken from the SGPS database [12], the Gibbs energy oGInO3 is estimated to be one half of the Gibbs energy of the appropriate oxide In2O3. oGZnSnO3 is the Gibbs energy of the hy- pothetical compound ZnSnO3, while the Gibbs energies for  the also hypothetical compounds oGInSnO3 and oGZnInO3 could be estimated using the following reciprocal equation o o o o G G G G In O ZnSnO InSnO ZnInO 2 3 3 3 3 � � � � (5) and accepting that the species on the right- hand side have identical Gibbs energies o o o o G G G G InSnO ZnInO In O ZnSnO 3 3 2 3 3 0 5 0 5 � � � � � �. . (6) Assessments Thermodynamic descriptions for  the binary metal systems are taken from the SGTE Solution database [13], the thermo- dynamic descriptions of binary metal-oxy- gen systems are proposed in this work. The data for the binary oxide systems In2O3– SnO2, In2O3–ZnO and SnO2–ZnO as well as the ternary system In2O3-SnO2-ZnO are optimized using available experimental in- formation. The calculated phase diagrams are in good agreement with the experimen- tal data. The thermodynamic data for the ternary compounds assessed in this work are given in  Table 2. The Gibbs energies of  (Me1Ox)A(Me2Oy)B have been based on stoichiometric combinations of Me1Ox and Me2Oy using a  Neumann-Kopp ap- proach. The values for  ∆H298 0 and S298 0 have been assessed according to available experimental data. The end-member Gibbs-energies G° as well as the various binary and ternary 173 interaction parameters between species both in the liquid and solid solutions have been assessed in  order to  obtain correct representations of  the solubility regions. The optimization of  the chosen solution parameters based on the available experi- mental data was performed using the op- timizer module OptiSage included in the FactSage software [22, 23]. Results and discussion The metallic subsystems As indicated above, the data for  the three metallic subsystems have been tak- en from the SGTE Solution database [13]. The resulting binary phase diagrams as well as the ternary liquidus surface are given below for reasons of completeness. The In–O system The binary In-O system contains one stoichiometric compound, In2O3. The crys- tal structure of stable Indium oxide is the cubic form (Bixbyite type), whereas the rhombohedral modification (Corundum type) is metastable. According to Schneider [24], the melting point of Bixbyite In2O3 is 1910 ± 10 °C. The solubility of oxygen in liquid in- dium was investigated first by Fitzner and Jacob [25] in the temperature range 650– 820 °C using a phase equilibration tech- nique. Later investigations using different techniques [26, 27] did not confirm these results [25]. Otsuka, Sano and Kozuka [26] determined the solubility of oxygen using coulometric titrations and later Otsuka, Kozuka and Chang [27] have used an isopi- estic equilibration technique. Both meas- urements are in good agreement and show lower solubility of oxygen in liquid indium than determined by Fitzner and Jacob [25]. Isomäki, Hämäläinen et al. [28] in their assessment of the In-O binary system used the experimental data Fitzner and Jacob [25] applying the ionic liquid model. Figure 5 shows the calculated phase diagram of the In-O binary system calcu- lated from the present database compared with the experimental melting temperature of In2O3 [24]. Figure 6 shows the Indium- rich part of the phase diagram compared Fig. 1. Calculated In-Sn phase diagram Fig. 2. Calculated In-Zn phase diagram Fig. 3. Calculated Sn-Zn phase diagram TE TR AG O N AL _A 6 TET_ALPHA1 TET_ALPHA1 + INSN_GAMMA IN SN _G AM M A BC T_ A5 LIQUID mole fraction Sn 0 0.2 0.4 0.6 0.8 1 0 50 100 150 200 250 300 T( C) LIQUID + HCP_Zn LIQUID HCP_Zn + TETRAGONAL_A6 TETRAGONAL_A6 HCP_Zn mole fraction Zn 0 0.2 0.4 0.6 0.8 1 0 100 200 300 400 500 T( C) HCP_Zn + BCT_A5 LIQUID + HCP_Zn LIQUID BCT_A5 HCP_Zn mole fraction Zn 0 0.2 0.4 0.6 0.8 1 0 100 200 300 400 500 T( C) 174 with the experiments [25–27], the agree- ment is very good. The Sn-O system The Sn-O phase diagram used for the optimization was taken from Massalski [17], which is based on the experimental data reported by McPherson, Hansen [29] and Spandau, Kohlmeyer [30]. The system is characterized by a large region of liquid immiscibility between pure tin and “tin ox- ide” — rich compositions. The monotectic reaction between metal-rich and tin oxide- rich liquid is assumed to have a tempera- ture of 1040 °C and liquid compositions of 3.3 and 50.3 at. % O according to [17]. It was confirmed by later investigations car- ried out by Cahen, David et al. [31] using DSC and XRD experiments. The Sn-O binary system contains three intermediate compounds SnO, SnO2 and Sn3O4. Although the experimentally de- termined melting temperatures of  SnO2 vary enormously, all investigations agree that this compound melts congruently. Ac- Fig. 5. Calculated In-O phase diagram Fig. 6. Calculated phase equilibria in the In-rich part of the In–O diagram compared with experimental data [25–27] Fig. 4. Calculated liquidus surface in the In-Sn-Zn system 0.1 0 .2 0.3 0.4 0.5 0.6 0.7 0.8 0. 9 0.10.20.30.40.50.60.70.80.9 0.1 0.2 0. 3 0.4 0.5 0 .6 0.7 0.8 0. 9 Zn In Sn mole fraction T(min) = 379.19 K, T(max) = 692.67 K 456.70 395.76 379.19 1 3 300 400 500 600 700 800 900 1000 1100 1200 T(K) HCP_Zn BCT_A5 INSN_GAMMA TET_ALPHA1TETRAGONAL_A6 620 600 580 640 560 540 520 Liquid + In 2 O 3 (s) In(s) + In 2 O 3 (s) Liquid gas_ideal + + In 2 O 3 (s) gas_ideal + In 2 O 3 (s) gas_ideal Liquid gas_ideal + Liquid gas_ideal + Liquidgas_ideal + Liquid [24] mole fraction O 0 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 T( C) In 2 O 3 (s) Liquid Liquid + In 2 O 3 In(s) + In 2 O 3 [25] [27] [26] mole fraction O 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0 200 400 600 800 1000 1200 1400 T( C) 175 cording to [31] this compound melts con- gruently at 2000 °C in contradiction to the SGPS database [12] which gives a melting temperature of 1630 °C. In the present work the thermodynamic properties of  pure SnO2 were taken from [12]. Moh [32] have reported the existence of the compound SnO which is formed by a peritectoid reac- tion at 270 °C (βSn) +Sn3O4→SnO. Sn3O4 is not stable at room temperature and decom- poses at 450 °C [32]. A first thermodynamic assessment of the binary Sn-O system was given by Ca- hen, David et al. [31]. They assumed the melting temperature of SnO2 to be 2000 °C and have modelled also the stoichiometric compounds SnO and Sn3O4 using the ther- mal stabilities experimentally determined by  Moh [32]. Later, a  thermodynamic assessment was carried out by  Isomäki, Hämäläinen et al. [28] where the thermo- dynamic data for SnO2 were taken from the SGPS database [12] with the lower melt- ing temperature of 1630 °C. The other two compounds were not considered in  this work. In both assessments, the liquid phase was described using the ionic liquid model. In the assessment by Cahen [31], the entropies of  formation for  the com- pounds SnO and SnO2 were determined to be 96.347 J / mol·K and 183.114 J / mol·K, respectively, which is in contradiction with the values published by Barin [33] (56.48 and 52.34 J / mol·K) and also the SGPS da- tabase [12] (57.17 and 49.01 J / mol·K). In the present work the thermody- namic data for SnO2 were taken from the SGPS database [12]. Also, the heat capacity of the compound SnO was taken from this source. The heat of formation of SnO deter- mined by Li-Zi et al. [34] (–285920 J / mol) was used for the optimization combined together with the phase diagram data [32]. The assessed value is –289853 J / mol, the difference to  the measured value being about 1.37 %. Sn3O4 is modeled to be stable till 450 °C according to the experimental value of 450 °C [32]. The calculated Sn–O phase diagram is presented in Figure 7 compared with avail- able experimental information; the agree- ment is good. The Zn-O system For the binary Zn–O system no phase diagram is available. The information on this system including thermodynam- ics and structure of ZnO has been summa- rized by Wriedt [35]. The system contains one stoichiometric compound ZnO with known melting temperature (1972 °C) [17] but unknown melting behavior. No solu- bility of oxygen in pure zinc was reported. The binary Zn-O phase diagram resulting from the present dataset is shown in Figure 8 compared with the experimental data given in [17]. Zinc monoxide decomposes congru- ently by  sublimation to  the gaseous ele- ments according to the following reaction: ZnO(s)  Zn(g) + 0.5O2(g). The sublimation / vaporization of zinc oxide has been investigated by  Knudsen Effusion Mass-spectroscopy (KEMS) [36– 39]. At temperatures below 1500 K the va- por above ZnO consists almost exclusively gas_ideal + SnO 2 (s) gas_ideal gas_ideal + Liquid [29] Sn 3 O 4 (s) SnO(s)Sn(s) + SnO(s) [32] Liquid + SnO(s) Liquid + Liquid#2 gas_ideal + Liquid Liquid Liquid Liquid + SnO 2 (s) gas_ideal + Liquid mole fraction O 0 0.2 0.4 0.6 0.8 1 0 500 1000 1500 2000 2500 3000 T( C) SnO 2 (s) Fig. 7. Calculated Sn-O phase diagram compared with experimental data [29, 32] 176 of Zn atoms and O2 molecules, which con- firms the congruent vaporization of ZnO. The oxygen partial pressure, which could not be measured correctly in the experi- ment, was estimated in agreement with the congruent sublimation condition by  the above reaction as  P(O2)  =  1 / 2  ·  P(Zn). Under the conditions of  gas phase ef- fusion from the cell, this relation takes the form P(O2)= 1 / 2[M(O2) / M(Zn)] 1 / 2 · P(Zn), where M(O2) and M(Zn) designate the oxygen and zinc molar masses. The sub- limation enthalpy can be obtained from the temperature dependence of P(Zn) [38, 39] or calculated using the third-law [39]. The latter value is considered as more exact. The selected data on the partial pres- sure of atomic Zn from the literature [37– 41] are presented in Figure 9 (points and dashed lines) compared with the present equilibrium calculations (solid lines). The deviation between the experimen- tal datasets is notable especially in  case of  oxygen. It should be noted that the thermodynamic data for  pure Zn, ZnO, O2 were taken from the SGTE databases [11, 12] without changes. Therefore, the discrepancy can be explained by  differ- ences with respect to both the thermody- namic data of individual gaseous species and the sublimation enthalpy of ZnO. For this, a value of 465.66 kJ / mol is used in the SGPS database. It is, however, in  good agreement with the literature, i.e. 461.9 (via third-law calculations in [39]) or 467.66 in [37, 38]. The Me1-Me2-O systems Predicted isothermal sections at 500 °C for  the ternary In–Sn–O, In–Zn–O and Sn–Zn–O systems are given in  Figures 10–12. The pseudo-binary systems In2O3– SnO2, SnO2–ZnO and In2O3–ZnO are considered as a part of the corresponding systems Me1–Me2–O. It should be noted Liquid + ZnO(s) Zn(s) + ZnO(s) gas_ideal + ZnO(s) gas_ideal + ZnO(s) gas_ideal ZnO(s) [17] a) mole fraction O 0 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 T( C) Fig. 8. Calculated Zn–O phase diagram: a — with participation of the gas phase, b — without Liquid + ZnO(s) Zn(s) + ZnO(s) gas_ideal + ZnO(s) ZnO(s) [17] Liquid b) mole fraction O 0 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 T( C) O 2 (g) O 2 (g) Zn(g) Zn(g) partial pressure of O 2 (g) over ZnO in different systems [39-41] temperature dependence of partial pressure of Zn(g) [39] partial pressure of Zn(g) over ZnO in different systems [39-41] partial pressure of Zn(g) via Kp [37] partial pressure of Zn(g) and O 2 (g) calculated in present work partial pressure of Zn(g), O 2 (g) from [37] cited in [38] Zn(g) partial pressure of Zn(g), O 2 (g) [38] T(K) 1200 1250 1300 1350 1400 1450 1500 –8 –7 –6 –5 –4 –3 –2 lo g 1 0( pa rt ia l p re ss ur e) , at m Fig. 9. Partial pressure of Zn and O2 over ZnO: comparison of literature data (points, dashed, dotted lines) with calculations solid (lines) 177 that the data for the ternary metallic system In-Sn-Zn and its binary subsystems were taken from the SGTE alloy database [13] and are not given in this paper. Only in the liquid metal phase a small solubility of O is calculated from the present data. The behaviour of the respective systems along the oxide pseudo-binary systems is discussed below. The In2O3–SnO2 system The pseudo binary system In2O3–SnO2 is characterized by  the presence of  two intermediate phases stable at  high tem- peratures, a  significant solubility of  tin in  indium oxide and a  eutectic reaction close to the tin-rich side. The system was investigated by Enoki and Echigoya [20] between 1200 and 1600 °C by TEM obser- vations. Heward and Swenson [21] stud- ied the phase diagram in the temperature range 1000–1650 °C using electron probe microanalysis (EPMA) and X-Ray diffrac- tion (XRD) analysis of solid-state sintered samples. The solubility ranges of tin oxide in Bixbyite solid solution were investigat- ed by Ohya, Ito et al. [19], Gonzales and Mason [18] and Harvey [1]. The experi- mentally determined solubility limits and phase boundaries for  the Bixbyite solid solution contradict each other. According to Heward and Swenson [21], the maximal solubility of SnO2 in In2O3 was found to be 13.1 mol.% at 1650 °C, whereas Ohya [19] reported 5 % at 1500 °C. In contrast, the solubility of indium in SnO2 appears to be negligibly small [18, 21], which differs from the phase diagram obtained by Enoki [20]. In the In2O3-SnO2 system two intermediate compounds, Sn3In4O12 and SnIn2O5, were observed. Both are stable at high tempera- tures and decompose eutectoidally at 1325 and 1575 °C, respectively [21]. The stoichi- ometric compound Sn3In4O12 was reported to be stable at temperatures above 1300 °C [18, 20] but was not observed by Harvey [3] at 1275 °C. The data on the experimentally determined thermal stability of the com- pound In4Sn3O12 are collected in Table 4. The In-Sn-O system has been ther- modynamically modelled by  Isomäki, Fig. 10. The calculated In-Sn-O isothermal section at 500 °C 0.1 0 .2 0.3 0.4 0.5 0.6 0.7 0.8 0. 9 0.10.20.30.40.50.60.70.80.9 0.1 0.2 0. 3 0.4 0.5 0 .6 0.7 0.8 0. 9 Bixbyite SnO 2 Liquid + Bixbyite O Sn mole fraction In 178 Hämäläinen et al. [28] who applied an ionic liquid two-sublattice model for the description of the liquid phase (Sn+2, In+3) (SnO2,O –2,Va). Only one compound (Sn3I- n4O12) was modeled in this work, the solu- bility of tin in In2O3 were optimized using the data of Enoki [20] which are signifi- cantly higher than those reported by Ohya Fig. 11. The calculated In-Zn-O isothermal section at 500 °C 0. 1 0.2 0.3 0. 4 0.5 0.6 0 .7 0.8 0.9 0.10.20.30.40.50.60.70.80.9 0 .1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 O In mole fraction Bixbyite ZnO In 2 Zn 7 O 10 In 2 Zn 5 O 8 Liquid + ZnO Zn Fig. 12. The calculated Sn-Zn-O isothermal section at 500 °C O Sn mole fraction 0.1 0 .2 0.3 0.4 0.5 0.6 0.7 0.8 0. 9 0.10.20.30.40.50.60.70.80.9 0.1 0.2 0. 3 0.4 0.5 0 .6 0.7 0.8 0. 9 Liquid + ZnO ZnO SnZn 2 O 4 SnO 2 Zn 179 [19], Harvey [1] and Gonzalez [18]. The values by Enoki [20] were not used for the optimization in the present work. The cal- culated In2O3-SnO2 binary system in air is presented in Figure 13 compared with the experimentally determined phase bounda- ries. The tin solubility in In2O3 increases with temperature and reaches 4.6 at. % at 1730 °C. The system contains further- more two intermediate high-temperature compounds Sn3In4O12 and SnIn2O5, the transition temperatures of which could be taken from the literature [20, 21, 42]. The calculated decomposing temper- ature of  Sn3In4O12 is 1333  °C, very close to the experimental values 1325 [21] and 1335 °C [18] while the calculated T2-tem- perature (1646  °C) agrees well with the experimental data by [21] and [42]. The In2O3-ZnO system In the pseudo-binary system In2O3-ZnO Kasper [43] found that zinc oxide and in- dium oxides reacted at 1100 °C with for- mation of a series of homologous oxides In2ZnkOk+3 where k = 2–5 and 7. Based on  high-resolution electron microscopy results, Cannard and Tilley [44] proposed that the structures consist of k ZnO layers separated by two InO1.5 layers. ZnO has the wurtzite structure, In2O3 crystallizes in the cubic bixbyite structure, and these two structures intergrow along the hexagonal c-axis direction. According to [44], at high ZnO concentrations In2ZnkOk+3 form com- positions with k = 4–11 at 1100 °C. Later, Nakamura [45] and Kimizuka [46] sug- gested that the compounds are isostruc- tural with LuFeO3(ZnO)k. Although the two models are not identical, both exhibit wurtzite-type layers perpendicular to the c-axis of the In2ZnkOk+3 structures. Com- pounds with k = 3–11, 13, 15, 17, 19 were characterized by Nakamura [45, 47] using XRD and scanning electron microscopy (SEM). Moriga et al. [6] presented the sub-solidus phase diagram for the system In2O3-ZnO over the temperature range 1100–1400 °C. Homologous compounds In2ZnkOk+3 with k = 3–7, 9, 11, 13, and 15 were reported based on XRD. At 1100 °C, In2Zn5O8 and In2Zn7O10 only were found to  be stable along with ZnO and In2O3, whereas the number of stable compounds increased as  the temperature increased. Table 4 Thermal stability of ternary stoichiometric compound Sn3In4O12 T1, oC T2, oC T1, °C in this work T2, °C in this work 1300 Enoki [20] – 1333 1646 1365 Ohya [19] – 1335 Gonzalez [18] – 1325 Heward [21] 1650 Heward [21] – 1652 Bates [42] Fig. 13. The calculated In2O3-SnO2 phase diagram in air compared with experimental data [1, 18–21, 42] Slag + Bixbyite [21] [42] Bixbyite Liquid Bixbyite + SnO 2 (s) [19] [20] [18] [1] mole fraction SnO 2 0 0.2 0.4 0.6 0.8 1 0 500 1000 1500 2000 2500 T( C) SnIn 2 O 5 (s) Sn 3 In 4 O 12 (s) Sn 3 In 4 O 12 (s) + SnO 2 (s) 180 The temperature ranges of  stability de- termined in [6] agree with the previously reported information [43, 45, 46]. The dif- ference was that the compounds with k = 4 and 8 were not observed by Moriga [6] over the temperature range studied. Moreover, the presence of  the compound with k = 15 of the In2ZnkOk+3 series was almost im- possible to detect with the XRD technique used in [6]. The formation of homologues series In2ZnkOk+3 (where k = 3–7, 9, 11) was confirmed at  1275  °C in  the study on the ternary system In2O3–SnO2–ZnO [1], while the compounds with k = 6, 13, 15 became stable at higher temperatures. The lattice constant, microstructure and electrical characteristics of In2O3 ceramic doped by ZnO were investigated by Park et al. [48]. The solubility limit of ZnO in In2O3 was reported to  be close to  1 at.% when IZO (indium zinc oxide) was sintered in oxygen atmosphere. Sintering in nitro- gen decreased the solubility limit to below 1 at.%. No previous assessments on  the sys- tem In2O3–ZnO were found in the litera- ture. The present description of the system In2O3–ZnO is based on the data reported by Moriga [6]. The series of phases with the general formula In2ZnkOk+3 with k = 3–7, 9, 11, 13, 15 was modelled in form of stoichi- ometric oxides. The thermodynamic data of these compounds are given in Table 2. Heat capacities of these compounds were generated according to Neumann — Kopps rule based on the component oxides; the enthalpies and entropies of formation were optimized in accordance with the stability ranges of  the phases. The formation en- thalpy for the compounds with k = 5 and 7 optimized in the present work are in very good agreement with those reported in [41] as shown in Figure 14. The literature data have been derived from a vaporization study of the system In2O3–ZnO with the KEMS technique. It is worth noting that all compounds show a very consistent trend with increasing content of Sn. The solubility limit of  ZnO in  In2O3 ( bi x by it e p h a s e ) w a s c a l c u l at e d at 1.56 mol.% and 1698 °C using the fol- lowing atom-based model description of  the phase: (In, Zn, Va)1(In, Sn)1(O)3. The liquid phase is assumed to  consist of the component oxides, Zn2O2 and In2O3, i.e. following the rule of two cations per molecule. The Gibbs energies of the stoi- chiometric homologous compounds are summarized in  Table 2. The calculated phase diagram for the system In2O3–ZnO [41] amounts of Zn atoms 2 4 6 8 10 12 14 16 300 400 500 600 700 Zn 3 In 2 O 6 –∆ fH 29 8 , k J/ g – at om Zn 4 In 2 O 7 Zn 5 In 2 O 8 Zn 6 In 2 O 9 Zn 7 In 2 O 10 Zn 9 In 2 O 12 Zn 11 In 2 O 14 Zn 13 In 2 O 16 Zn 15 In 2 O 18 [6]Liquid Liquid + Bixbyite Bixbyite Liquid + ZnO 1 mole fraction ZnO 0 0.2 0.4 0.6 0.8 1 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 T( C) Bixbyite + Zn 3 In 2 O 6 Bixbyite + Zn 4 In 2 O 7 Bixbyite + Zn 5 In 2 O 8 Zn 3 In 2 O 6 Zn 4 In 2 O 7 Zn 6 In 2 O 9 Zn 5 In 2 O 8 Zn 7 In 2 O 10 Zn 15 In 2 O 18 Zn 13 In 2 O 16 Zn 11 In 2 O 14Zn 9 In 2 O 12 Fig. 14. Heat of formation of the stoichiometric compounds in the In2O3–ZnO system Fig. 15. The calculated In2O3–ZnO phase diagram in air compared with experimental data [6] 181 is presented in Fig. 15 compared with the experimental data [6]. The SnO2-ZnO system Enoki [49] proposed a  preliminary phase diagram for the system SnO2–ZnO with the spinel phase only. The oxide mix- tures were equilibrated at 1200 and 1400 °C and characterized by XRD. Most of the ex- perimental studies [4, 49, 50] on this sys- tem agreed that there is one stable com- pound with the composition SnZn2O4. This compound has inverse spinel structure and can be obtained by solid state reaction from the component oxides or by decomposition of the salts zinc acetate (Zn(CH3COO)2 and tin tetrachloride (SnCl4). In contrast, the information on the second phase, ZnSnO3, is contradictory. Shen and Zhang [51] re- ported that this compound has a perovskite structure, whereas Inagaki [52] proposed an ilmenite structure which is more rea- sonable due to the fact that the ionic radius of Zn2+ radius is too small to form a stable perovskite structure as has been confirmed later by Kovacheva and Petrov [53]. Palmer and Poeppelmeier [4] studied sub-solidus phase equilibria in the system Ga2O3–SnO2–ZnO at 1250 °C using solid state synthesis and XRD. The ZnO–SnO2 binary system contains one intermediate compound, SnZn2O4 with two-phase re- gions between the end-members and the spinel. According to [4], the lattice parame- ters of SnZn2O4 were unchanged (from the nominal value) in two-phase mixtures with ZnO or SnO2, indicating minimal solubil- ity of  either oxide into the spinel phase. Hansson et al. [50] investigated phase equilibria for  SnO2-ZnO system in  air in the temperature range 1200 to 1400 °C using high-temperature equilibration and quenching techniques followed by electron probe X-ray microanalysis (EPMA). The maximum solubility of ZnO in SnO2 was found to be approximately 1.5 mol.% in the range of conditions investigated. The con- centration of tin oxide in zincite (ZnO) is negligible between 1300 and 1400 °C in air within the limits of experimental uncer- tainty. A slight solubility of ZnO in the stoi- chiometric SnZn2O4 spinel can be observed at all temperatures. Later Harvey et al. [1] did not observe a change of lattice param- eter between pure ZnO or pure SnO2 and doped compositions. Mihaiu et al. [54] un- dertook a systematic study of the phase for- mation over the whole compositional range of  the ZnO-SnO2 binary system in  the temperature range 500–1500 °C. Starting with 900 °C, the formation of the SnZn2O4 with inverse spinel type structure was found in all samples. The formation of the ZnSnO3 was not observed under the ex- perimental conditions used. In the tem- perature ranges 1000–1500 °C, no change in the phase composition was observed. Vaporization processes in  the ZnO– SnO2 system have been studied by  the Knudsen effusion technique in  combi- nation with mass spectrometric analysis (KEMS) of the vapor phase in the tempera- ture range 1360 K to 1460 K [39]. Complete isothermal sublimation experiments have been performed to determine the partial pressures of  vapor components over the whole system. The elemental composition of samples was quantified using laser mass spectrometry. By isothermal sublimation, the change of partial pressure of Zn over the system is caused by  phase transfor- mations in the solid state from pure ZnO through two heterogeneous fields (ZnO + Zn2SnO4 and Zn2SnO4 + SnO2) to pure tin oxide. It has been found that the gas phase mainly consists of Zn(g), O2 and SnO(g). The partial pressures of the vapor species were determined at 1450 K. 182 In the present work, the compound Sn- Zn2O4 is treated as stoichiometric accord- ing to [3, 6] and calculated to be stable up to its melting point of 1675 °C. This com- pound is considered as the end-member constituent in the Spinel phase for the ter- nary system. The heat capacity of SnZn2O4 was based on the data of the component oxides according to Neumann-Kopp (Table 2), the standard enthalpy of formation was optimized based on the experimental value from Gribchenkova [39]. The entropy was adjusted in order to represent the melting point of  spinel. The compound ZnSnO3 was omitted from consideration accord- ing to literature data on its instability [39]. The liquid phase in the system SnO2– ZnO includes the associate SnZn2O4 / 1.5 along with the basic oxides according to the modified associate species model. The melting properties of the spinel com- pound were based on those for liquid ox- ides. The two eutectics (Spinel and ZnO as well as Spinel and SnO2) are calculated at  1647 and 1425  °C, respectively. The calculated phase diagram of  the system SnO2-ZnO is given in Figure 16. The calculated activities across the sys- tem SnO2–ZnO at 1450 K are compared in Figure 17 with those measured in [39] using KEMS. The thermodynamic data on the gas phase are taken from the SGPS database [12]. The following main gas spe- cies are found by calculation of equilibrium between the condensed phases and gas – Zn, SnO and O2. The ratio between these species agreed with the measurements [39]; however, the absolute values of  the partial pressures (especially for Zn) differ from the experi- mental data due to scattering of experimen- tal data on P(Zn) obtained by using such a complicated method as KEMS. Moreover, the disagreement can be explained by pos- sible small inconsistencies concerning the thermodynamic data of the gas components in the SGTE database, as was already men- tioned above regarding the Zn–O system. The In2O3-SnO2-ZnO system The ternary In2O3-SnO2-ZnO system does not exhibit any ternary compounds, but presents two significant solid solu- tion phases, the SnZn2O4 Spinel phase enriched with indium with the formula Zn(2–x)Sn(1–x)In2xO4 and the Bixbyite solid solution based on  In2O3 and extending far toward the SnZnO3 composition with the formula In(2–2x)SnxZnxO3. Palmer, Po- eppelmeier and Mason [55] studied the solid solubility of ZnO and SnO2 in Bixby- ite at 1100 and 1250 °C using X-ray diffrac- tion and determined a very strong coupled SnZn 2 O 4 (s) + SnO 2 (s) ZnO(s) + SnZn 2 O 4 (s) SnZn 2 O 4 (s) Liquid Liquid + ZnO(s) Liquid + SnZn 2 O 4 (s) Liquid + SnO2(s) mole fraction SnO 2 0 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 1200 1400 1600 1800 2000 T( C) exp. KEMS: Zn(gas), P in Pa [39] exp. KEMS: SnO(gas), P in Pa [39] exp. KEMS: O 2 (gas), P in Pa [39] exp. Zn in gas exp. SnO in gas solid lines are calculated 1450 K, total pressure 101325 Pa Zn(g) SnO(g) 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ac ti vi ty ( pa rt ia l p re ss ur e) , Pa exp. O 2 in gas O 2 (g) Fig. 16. Calculated SnO2–ZnO phase diagram in air Fig. 17. Calculated and experimental activities in SnO2–ZnO system at 1450 K 183 solubility of SnO2 and ZnO. The maximum combined solubility of Zn and Sn can reach 40 cation %, the resulting material at this point can be described as In1.2Sn0.4Zn0.4O3. Later investigations by Kammler et al. [56] using X-ray powder diffraction confirmed high solubility of  zinc and tin in  In2O3 at 1250 °C. Kammler reported also a wide spinel solution range, Zn2–xSn1–xIn2xO4 (0 < x < 0.45) and also a significant solubility of tin in Zn3In2O6 which was, however, not confirmed by later investigations [1, 2]. The phase diagram data published in [56] are constructed schematically and were not used for the present optimization work. The present assessment of the ternary system is mainly based on the phase equi- libria data published in [1]. Harvey, Poep- pelmeier and Mason [3] investigated the subsolidus phase relationships at 1275 °C using X-ray diffraction. They reported the existence of two extended solid solutions and preliminary phase relations between them and other coexisting compounds. Both solid solution phases exhibit con- stant Zn:Sn ratio and appear on the phase diagram as  long vertical lines. The one significant solid solution phase is Bixbyite In2O3, enriched by tin and zinc, where up to 40 % of indium can be replaced by tin and zinc. According to  Harvey [1], the Bixbyite phase can be described using the formula In(2–2x)SnxZnxO3, where x can reach a maximum of 0.4. At 1275 °C, Bixbyite is in general in equilibrium with the Spinel phase, compound (ZnO)k(In2O3), where k = 3, and also with the tin oxide SnO2. The other important solid solution phase reported by Harvey [1] is the Spinel phase, which extends from the binary composi- tion SnZn2O4 towards the In2ZnO4 com- position. Harvey confirmed Spinel phase boundaries and formula experimentally found by Kammler [56] to describe this in- dium-doped Spinel as Zn(2–x)Sn(1–x)In2xO4,(0 < x ≤ 0.45), whereby at x = 0.45 the Spinel composition corresponds to the formula Zn1.55Sn0.55In0.90O4. Harvey investigated also very intensively a zinc-oxide-rich re- gion at 1275 °C and corresponding phase equilibria. As mentioned before, along the binary ZnO-In2O3 edge at 1275 °C there is a  series of  homologous compounds (ZnO)k(In2O3) (where k = 3–5, 7, 9, 11), all of  which are in  equilibrium with the phase Spinel, starting with the first one (ZnO)11(In2O3) and finishing with the last (ZnO)3(In2O3) which is in equilibrium with Spinel maximally enriched in indium. The compounds with k > 11 were not found in equilibrium with spinel at 1275 °C due to sluggish kinetics in the ZnO-rich com- position range [1]. Figure 18 shows the calculated iso- thermal section at 1275 °C in the InO1.5– SnO2–ZnO system in air compared with experimental data [1]. The experimentally determined extensions of the solid solution phases Bixbyite and Spinel, the two-phase regions and also the compatibility triangles could be reproduced satisfactorily by the calculations. Conclusions A thermodynamic dataset containing all phases in the system In2O3-SnO2-ZnO has been generated using the available ex- perimental information (phase diagrams, phase transitions, structure, enthalpies of formation). The liquid and solid phases have been introduced into the thermody- namic description, solid solution phases such as Spinel and Bixbyite have been mod- elled using the multi-sublattice approach. Fourteen stoichiometric compounds have also been thermodynamically assessed. The 184 liquid species tin (II, IV) oxides, indium and zinc oxides and the binary associate species (SnZn2O4) have been introduced to  the non-ideal associate solution. The general agreement between the calculated phase equilibria as well as thermodynamic properties and the respective experimental data is good. The dataset can be applied to studies on the formation of ZITO-based TCOs. References 1. Harvey SP, Poeppelmeier KR, Mason TO. Subsolidus Phase Relationships in the ZnO– In2O3–SnO2 System. 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