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 subsystems 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.


Introduction
Compositions in the In 2 O 3 -SnO 2 -ZnO ternary oxide system are of interest owing to their optical transparency combined with high electrical conductivity [1,2]. Transparent conducting oxides (TCOs) can be used as electrodes in solar cells, flat panel displays and other commercial devices. Although TCOs are applied 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 material of choice for TCO layers (e.g. in review [3]), but the increasing cost of indium metal and the development of new tech-nologies will require alternative TCOs. According to Palmer [4] both SnO 2 and ZnO are good TCOs with conductivities comparable to ITO. Compositions from the In 2 O 3 -ZnO system with high Zn concentration are attractive due to their high electrical conductivity, optical transparency and excellent chemical stability [5,6].
The materials from the system ZITO (Zn-In-Sn-O) [2] are promising replacements for ITO as TCO layers in many opto-electronic applications. ZITO contains less indium than ITO, which lowers the cost, and it has a broad window of compositions that allow the TCO layer to be adjusted (conductivity, etc.) for each application. The bulk equilibrium phases of ZITO have been defined and exhibit two transparent and conductive regions: the bixbyite solid solution In 2-2x Zn x Sn x O 3 and the homologous series of compounds In 2 Zn k O k+3 .
Thermodynamic modelling on the basis of reliable experimental data and appropriate Gibbs energy models for solid and liquid phases is a powerful tool for calculation 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 possible production processes. The quality and completeness of the thermodynamic databases used is a key prerequisite for reliable calculations. According to CALPHADtype modelling all available experimental data (phase equilibria, mixing properties, component activities, etc.) are critically analyzed in terms of their consistency. Each phase in the system is treated by an appropriate Gibbs energy model with adjustable parameters (Gibbs energy of constituents, interaction parameters, etc.), which are optimized in accordance with the experimental information in order to generate a self-consistent dataset of Gibbs energies of all phases in a system.
In the present study the thermodynamic assessment of the oxide system In 2 O 3 -SnO 2 -ZnO is presented using all available experimental data on phase equilibria and thermodynamic properties. The calculation of phase equilibria and the prediction of thermodynamic properties using the database for the In 2 O 3 -SnO 2 -ZnO system can be helpful for developing and manufacturing TCOs for optoelectronic devices. The experimental information on the available thermodynamic properties (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 associate solution model proposed by Besmann 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][9][10]. Solubilities 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 Zn 2 SnO 4 , In 2 SnO 4 , Zn 2 ZnO 4 , In 2 ZnO 4 as end-members. The model for bixbyite in form of In (2-2x) Sn x Zn x O 3 using 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 database [12], the thermodynamic descriptions 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.
The solid solution phases in the In 2 O 3 -SnO 2 -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 modified non-ideal associate species model [7]. The basic species In 2 O 3 , SnO 2 and ZnO along with one (quasi)binary species (Sn-Zn 2 O 4 ) 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 species 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 contains a total of two cations in its formula based on [7]. In addition, interactions between associate species were introduced in order to fine tune the thermodynamic description.
The molar Gibbs energy of the solution is presented by a three-term expression with contributions of the reference part, the ideal and the excess part taking into account binary interactions as follows: where x i is the mole fraction of phase constituent i (including the associate species), °G i 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 polynomial. The L ij v with v = 0, 1, 2 and °G i are temperature dependent in the same way according to: Thermodynamic data for the liquid components are summarized in Table 3. The elemental systems In-O and Zn-O contain one stable oxide, In 2 O 3 and ZnO, respectively, while in the system Sn-O two oxides were considered, Sn 2 O 2 and Sn 2 O 4 . The liquid phase of the quasi-binary oxide systems will contain the basic oxides along with one (quasi)binary species (SnZn 2 O 4 · 3 / 2). No ternary species were necessary. The Gibbs energy of the binary species are taken from the SGTE Pure Substance database [12] without modifications. The G function of the liquid species SnZn 2 O 4 · 3 / 2 was derived using the melting data of the   4 . The inverse Spinel Zn 2 SnO 4 has the cubic spinel structure (space group ) and Pearson symbol cF56 [14]. This inverse spinel structure is present in many systems, e.g. as Ülvöspinel Fe 2 TiO 4 , manganese titanate Mn 2 TiO 4 and gandilite Mg 2 TiO 4. All of them can be treated with the same common formula  . .
. 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 In 2 O 3 (Bixbyite) was investigated by Gonzalez and Mason [18], Ohya and Ito [19], Enoki and Echigoya [20], as well as Heward and Swenson [21] using different methods. All investigations are in general agreement and confirm a significant solubility of SnO 2 in Bixbyite. In contrast, the solubility of zinc in Bixbyite appears to be relatively small. In the ternary In 2 O 3 -SnO 2 -ZnO system Bixbyite is enriched with tin and zinc extending toward to the composition ZnSnO 3 and can be described as In ( Bixbyite is described in this work as solid solution phase based on In 2 O 3 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 atoms while the third contains oxygen atoms only. The atomic model is chosen, because the use of ions would require more additional unknown Gibbs energies to describe the solubility of tin oxide in Bixbyite. The molar Gibbs energy of this phase was expressed using the compound energy formalism [15,16] (4) where y i I and y i II represent the site fractions of the component i and j in the first respectively second sublattices. o G In O 2 3 corresponds to the Gibbs energy of the indium oxide and is taken from the SGPS database [12], the Gibbs energy o G InO 3 is estimated to be one half of the Gibbs energy of the appropriate oxide In 2 O 3 . o G ZnSnO 3 is the Gibbs energy of the hypothetical compound ZnSnO 3 , while the Gibbs energies for the also hypothetical compounds o G InSnO 3 and o G ZnInO 3 could be estimated using the following reciprocal equation and accepting that the species on the righthand side have identical Gibbs energies

Assessments
Thermodynamic descriptions for the binary metal systems are taken from the SGTE Solution database [13], the thermodynamic descriptions of binary metal-oxygen systems are proposed in this work. The data for the binary oxide systems In 2 O 3 -SnO 2 , In 2 O 3 -ZnO and SnO 2 -ZnO as well as the ternary system In 2 O 3 -SnO 2 -ZnO are optimized using available experimental information. 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 The end-member Gibbs-energies G° as well as the various binary and ternary 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 experimental data was performed using the optimizer 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 taken 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, In 2 O 3 . The crystal 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 In 2 O 3 is 1910 ± 10 °C.
The solubility of oxygen in liquid indium was investigated first by Fitzner and Jacob [25] in the temperature range 650-820 °C using a phase equilibration technique. 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 measurements 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 calculated from the present database compared with the experimental melting temperature of In 2 O 3 [24]. Figure 6 shows the Indiumrich part of the phase diagram compared  with the experiments [25][26][27], the agreement 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 oxide" -rich compositions. The monotectic reaction between metal-rich and tin oxiderich liquid is assumed to have a temperature of 1040 °C and liquid compositions of 3.3 and 50.3 at. % O according to [17]  cording to [31] this compound melts congruently 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 SnO 2 were taken from [12]. Moh [32] have reported the existence of the compound SnO which is formed by a peritectoid reaction at 270 °C (βSn) +Sn 3 O 4 →SnO. Sn 3 O 4 is not stable at room temperature and decomposes at 450 °C [32].
A first thermodynamic assessment of the binary Sn-O system was given by Cahen, David et al. [31]. They assumed the melting temperature of SnO 2 to be 2000 °C and have modelled also the stoichiometric compounds SnO and Sn 3 O 4 using the thermal stabilities experimentally determined by Moh [32]. Later, a thermodynamic assessment was carried out by Isomäki, Hämäläinen et al. [28] where the thermodynamic data for SnO 2 were taken from the SGPS database [12] with the lower melting 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 compounds SnO and SnO 2 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 database [12] (57.17 and 49.01 J / mol·K).
In the present work the thermodynamic data for SnO 2 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 determined 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 %. Sn 3 O 4 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 available experimental information; the agreement is good.
The Zn-O system For the binary Zn-O system no phase diagram is available. The information on this system including thermodynamics and structure of ZnO has been summarized by Wriedt [35]. The system contains one stoichiometric compound ZnO with known melting temperature (1972 °C) [17] but unknown melting behavior. No solubility 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 congruently by sublimation to the gaseous elements according to the following reaction: ZnO(s)  Zn(g) + 0.5O 2 (g).
The sublimation / vaporization of zinc oxide has been investigated by Knudsen Effusion Mass-spectroscopy (KEMS) [36][37][38][39]. At temperatures below 1500 K the vapor above ZnO consists almost exclusively  [29,32] of Zn atoms and O 2 molecules, which confirms the congruent vaporization of ZnO. The oxygen partial pressure, which could not be measured correctly in the experiment, was estimated in agreement with the congruent sublimation condition by the above reaction as P(O 2 ) = 1 / 2 · P(Zn). Under the conditions of gas phase effusion from the cell, this relation takes the form P( and M(Zn) designate the oxygen and zinc molar masses. The sublimation 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 pressure of atomic Zn from the literature [37][38][39][40][41] are presented in Figure 9 (points and dashed lines) compared with the present equilibrium calculations (solid lines).
The deviation between the experimental datasets is notable especially in case of oxygen. It should be noted that the thermodynamic data for pure Zn, ZnO, O 2 were taken from the SGTE databases [11,12] without changes. Therefore, the discrepancy can be explained by differences with respect to both the thermodynamic 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]. Zn(g) Zn(g) partial pressure of O 2 (g) over ZnO in different systems [39][40][41] temperature dependence of partial pressure of Zn(g) [39] partial pressure of Zn(g) over ZnO in different systems [39][40][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)  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 In 2 O 3 -SnO 2 system The pseudo binary system In 2 O 3 -SnO 2 is characterized by the presence of two intermediate phases stable at high temperatures, 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 observations. Heward and Swenson [21] studied the phase diagram in the temperature range 1000-1650 °C using electron probe microanalysis (EPMA) and X-Ray diffraction (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 experimentally determined solubility limits and phase boundaries for the Bixbyite solid solution contradict each other. According to Heward and Swenson [21], the maximal solubility of SnO 2 in In 2 O 3 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 SnO 2 appears to be negligibly small [18,21], which differs from the phase diagram obtained by Enoki [20]. In the In 2 O 3 -SnO 2 system two intermediate compounds, Sn 3 In 4 O 12 and SnIn 2 O 5 , were observed. Both are stable at high temperatures and decompose eutectoidally at 1325 and 1575 °C, respectively [21]. The stoichiometric compound Sn 3 In 4 O 12 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 compound In 4 Sn 3 O 12 are collected in Table 4.
The In-Sn-O system has been thermodynamically modelled by Isomäki, In Hämäläinen et al. [28] who applied an ionic liquid two-sublattice model for the description of the liquid phase (Sn +2 , In +3 ) (SnO 2 ,O -2 ,Va). Only one compound (Sn 3 I-n 4 O 12 ) was modeled in this work, the solubility of tin in In 2 O 3 were optimized using the data of Enoki [20] which are significantly higher than those reported by Ohya [19], Harvey [1] and Gonzalez [18]. The values by Enoki [20] were not used for the optimization in the present work. The calculated In 2 O 3 -SnO 2 binary system in air is presented in Figure 13 compared with the experimentally determined phase boundaries. The tin solubility in In 2 O 3 increases with temperature and reaches 4.6 at. % at 1730 °C. The system contains furthermore two intermediate high-temperature compounds Sn 3 In 4 O 12 and SnIn 2 O 5 , the transition temperatures of which could be taken from the literature [20,21,42].
The calculated decomposing temperature of Sn 3 In 4 O 12 is 1333 °C, very close to the experimental values 1325 [21] and 1335 °C [18] while the calculated T 2 -temperature (1646 °C) agrees well with the experimental data by [21] and [42].

The In 2 O 3 -ZnO system
In the pseudo-binary system In 2 O 3 -ZnO Kasper [43] found that zinc oxide and indium oxides reacted at 1100 °C with formation of a series of homologous oxides In 2 Zn k O k+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 InO 1.5 layers. ZnO has the wurtzite structure, In 2 O 3 crystallizes in the cubic bixbyite structure, and these two structures intergrow along the hexagonal c-axis direction. According to [44], at high ZnO concentrations In 2 Zn k O k+3 form com-positions with k = 4-11 at 1100 °C. Later, Nakamura [45] and Kimizuka [46] suggested that the compounds are isostructural with LuFeO 3 (ZnO) k . Although the two models are not identical, both exhibit wurtzite-type layers perpendicular to the c-axis of the In 2 Zn k O k+3 structures. Compounds 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 In 2 O 3 -ZnO over the temperature range 1100-1400 °C. Homologous compounds In 2 Zn k O k+3 with k = 3-7, 9, 11, 13, and 15 were reported based on XRD. At 1100 °C, In 2 Zn 5 O 8 and In 2 Zn 7 O 10 only were found to be stable along with ZnO and In 2 O 3 , whereas the number of stable compounds increased as the temperature increased. The temperature ranges of stability determined in [6] agree with the previously reported information [43,45,46]. The difference 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 In 2 Zn k O k+3 series was almost impossible to detect with the XRD technique used in [6]. The formation of homologues series In 2 Zn k O k+3 (where k = 3-7, 9,11) was confirmed at 1275 °C in the study on the ternary system In 2 O 3 -SnO 2 -ZnO [1], while the compounds with k = 6, 13, 15 became stable at higher temperatures. The lattice constant, microstructure and electrical characteristics of In 2 O 3 ceramic doped by ZnO were investigated by Park et al. [48]. The solubility limit of ZnO in In 2 O 3 was reported to be close to 1 at.% when IZO (indium zinc oxide) was sintered in oxygen atmosphere. Sintering in nitrogen decreased the solubility limit to below 1 at.%. No previous assessments on the system In 2 O 3 -ZnO were found in the literature. The present description of the system In 2 O 3 -ZnO is based on the data reported by Moriga [6]. The series of phases with the general formula In 2 Zn k O k+3 with k = 3-7, 9, 11, 13, 15 was modelled in form of stoichiometric 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 enthalpy 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 In 2 O 3 -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 In 2 O 3 (bixbyite phase) was calculated at 1.56 mol.% and 1698 °C using the following atom-based model description of the phase: (In, Zn, Va) 1 (In, Sn) 1 (O) 3 [6] is presented in Fig. 15 compared with the experimental data [6]. The SnO 2 -ZnO system Enoki [49] proposed a preliminary phase diagram for the system SnO 2 -ZnO with the spinel phase only. The oxide mixtures were equilibrated at 1200 and 1400 °C and characterized by XRD. Most of the experimental studies [4,49,50] on this system agreed that there is one stable compound with the composition SnZn 2 O 4 . 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(CH 3 COO) 2 and tin tetrachloride (SnCl 4 ). In contrast, the information on the second phase, ZnSnO 3 , is contradictory. Shen and Zhang [51] reported that this compound has a perovskite structure, whereas Inagaki [52] proposed an ilmenite structure which is more reasonable due to the fact that the ionic radius of Zn 2+ 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 Ga 2 O 3 -SnO 2 -ZnO at 1250 °C using solid state synthesis and XRD. The ZnO-SnO 2 binary system contains one intermediate compound, SnZn 2 O 4 with two-phase regions between the end-members and the spinel. According to [4], the lattice parameters of SnZn 2 O 4 were unchanged (from the nominal value) in two-phase mixtures with ZnO or SnO 2 , indicating minimal solubility of either oxide into the spinel phase. Hansson et al. [50] investigated phase equilibria for SnO 2 -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 SnO 2 was found to be approximately 1.5 mol.% in the range of conditions investigated. The concentration of tin oxide in zincite (ZnO) is negligible between 1300 and 1400 °C in air within the limits of experimental uncertainty. A slight solubility of ZnO in the stoichiometric SnZn 2 O 4 spinel can be observed at all temperatures. Later Harvey et al. [1] did not observe a change of lattice parameter between pure ZnO or pure SnO 2 and doped compositions. Mihaiu et al. [54] undertook a systematic study of the phase formation over the whole compositional range of the ZnO-SnO 2 binary system in the temperature range 500-1500 °C. Starting with 900 °C, the formation of the SnZn 2 O 4 with inverse spinel type structure was found in all samples. The formation of the ZnSnO 3 was not observed under the experimental conditions used. In the temperature ranges 1000-1500 °C, no change in the phase composition was observed.
Vaporization processes in the ZnO-SnO 2 system have been studied by the Knudsen effusion technique in combination with mass spectrometric analysis (KEMS) of the vapor phase in the temperature 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 transformations in the solid state from pure ZnO through two heterogeneous fields (ZnO + Zn 2 SnO 4 and Zn 2 SnO 4 + SnO 2 ) to pure tin oxide. It has been found that the gas phase mainly consists of Zn(g), O 2 and SnO(g). The partial pressures of the vapor species were determined at 1450 K.
In the present work, the compound Sn-Zn 2 O 4 is treated as stoichiometric according to [3,6] and calculated to be stable up to its melting point of 1675 °C. This compound is considered as the end-member constituent in the Spinel phase for the ternary system. The heat capacity of SnZn 2 O 4 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 ZnSnO 3 was omitted from consideration according to literature data on its instability [39].
The liquid phase in the system SnO 2 -ZnO includes the associate SnZn 2 O 4 / 1.5 along with the basic oxides according to the modified associate species model. The melting properties of the spinel compound were based on those for liquid oxides. The two eutectics (Spinel and ZnO as well as Spinel and SnO 2 ) are calculated at 1647 and 1425 °C, respectively. The calculated phase diagram of the system SnO 2 -ZnO is given in Figure 16.
The calculated activities across the system SnO 2 -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 species are found by calculation of equilibrium between the condensed phases and gas -Zn, SnO and O 2 .
The ratio between these species agreed with the measurements [39]; however, the absolute values of the partial pressures (especially for Zn) differ from the experimental data due to scattering of experimental data on P(Zn) obtained by using such a complicated method as KEMS. Moreover, the disagreement can be explained by possible small inconsistencies concerning the thermodynamic data of the gas components in the SGTE database, as was already mentioned above regarding the Zn-O system.

The In 2 O 3 -SnO 2 -ZnO system
The ternary In 2 O 3 -SnO 2 -ZnO system does not exhibit any ternary compounds, but presents two significant solid solution phases, the SnZn 2 O 4 Spinel phase enriched with indium with the formula Zn (2-x) Sn (1-x) In 2x O 4 and the Bixbyite solid solution based on In 2 O 3 and extending far toward the SnZnO 3 composition with the formula In (2-2x) Sn x Zn x O 3 . Palmer, Poeppelmeier and Mason [55] studied the solid solubility of ZnO and SnO 2 in Bixbyite at 1100 and 1250 °C using X-ray diffraction and determined a very strong coupled Later investigations by Kammler et al. [56] using X-ray powder diffraction confirmed high solubility of zinc and tin in In 2 O 3 at 1250 °C. Kammler reported also a wide spinel solution range, Zn 2-x Sn 1-x In 2x O 4 (0 < x < 0.45) and also a significant solubility of tin in Zn 3 In 2 O 6 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 equilibria data published in [1]. Harvey, Poeppelmeier 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 constant Zn:Sn ratio and appear on the phase diagram as long vertical lines. The one significant solid solution phase is Bixbyite In 2 O 3 , 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) Sn x Zn x O 3 , 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 (In 2 O 3 ), where k = 3, and also with the tin oxide SnO 2 . The other important solid solution phase reported by Harvey [1] is the Spinel phase, which extends from the binary composition SnZn 2 O 4 towards the In 2 ZnO 4 composition. Harvey confirmed Spinel phase boundaries and formula experimentally found by Kammler [56] to describe this indium-doped Spinel as Zn (2-x) Sn (1-x) In 2x O 4 ,(0 < x ≤ 0.45), whereby at x = 0.45 the Spinel composition corresponds to the formula Zn 1.55 Sn 0.55 In 0.90 O 4 . Harvey investigated also very intensively a zinc-oxide-rich region at 1275 °C and corresponding phase equilibria. As mentioned before, along the binary ZnO-In 2 O 3 edge at 1275 °C there is a series of homologous compounds (ZnO) k (In 2 O 3 ) (where k = 3-5, 7, 9, 11), all of which are in equilibrium with the phase Spinel, starting with the first one (ZnO) 11 (In 2 O 3 ) and finishing with the last (ZnO) 3

(In 2 O 3 ) 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 composition range [1]. Figure 18 shows the calculated isothermal section at 1275 °C in the InO 1.5 -SnO 2 -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 In 2 O 3 -SnO 2 -ZnO has been generated using the available experimental information (phase diagrams, phase transitions, structure, enthalpies of formation). The liquid and solid phases have been introduced into the thermodynamic description, solid solution phases such as Spinel and Bixbyite have been modelled using the multi-sublattice approach. Fourteen stoichiometric compounds have also been thermodynamically assessed. The liquid species tin (II, IV) oxides, indium and zinc oxides and the binary associate species (SnZn 2 O 4 ) 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.