Thermodynamic Database Development for the ZrO2-MgO-MnOx System

Thermodynamic description of the ZrO2-MgO-MnOx was derived for the first time using available experimental data on phase relations in air and protective gas atmosphere. Solid solution phases were modelled using compound energy formalism. The liquid phase was described by the modified two-sublattice model for ionic liquid. Solubility of ZrO2 was modelled in cubic spinel and MgO-MnO solid solution (halite structure) and therefore the Gibbs energies of Zr-containing endmembers were introduced. Ternary interaction parameters were introduced for halite, cubic spinel and cubic ZrO2 to reproduce the stabilization of cubic ZrO2 at temperatures below its stability in bounding systems and stabilization of cubic spinel at temperatures above its stability limit in the bounding systems. The obtained thermodynamic database was used to interpret results of differential thermal analysis.


Introduction
Phase equilibria in the ZrO 2 -MgO-MnO x system are of interest due to several possible applications. One of them is development of TRIP steel metal matrix composite material strengthened by particles of MgO partially stabilized zirconia (Mg-PSZ). [1] Manganese provides good adhesion bonding between the steel matrix and the Mg-PSZ ceramics. [2,3] On the other hand, manganese is one of the main alloying elements of the steel matrix and can substitute Mg in Mg-PSZ during processing of this metal matrix composite [2,4,5] thus influencing the stability of the Mg-PSZ structure. It was shown that due to Mg diffusion from Mg-PSZ into precipitate sites or the steel matrix the Mg-PSZ was destabilized and transformed into the monoclinic phase, while due to diffusion of Mn into ZrO 2 particles, grains at its boundary remained cubic or tetragonal. [5] Therefore, knowledge of phase relations in the ZrO 2 -MgO-MnO x system is important to improve the stability of Mg-PSZ and its bonding to the steel matrix.
The other possible application of the ZrO 2 -MgO-MnO x system is for directionally solidified eutectic materials since both bounding systems ZrO 2 -MgO and ZrO 2 -MnO x are known to form directionally solidified eutectics. [6,7] The phase relations in the ZrO 2 -MgO-MnO x system were experimentally studied by Pavlyuchkov et al. [8] for the first time. The investigations were carried out in air and inert gas atmosphere. It was shown that relatively small additions of ZrO 2 stabilize cubic spinel in the ternary system in air at temperatures exceeding its stability range in the MgO-MnO x bounding system and compositions substantially enriched by MgO. The addition of ZrO 2 also significantly extends the homogeneity range of halite (MgO-MnO solid solution) toward MnO solubility in air. It should be also noted that cubic ZrO 2 -based solid solutions are stabilized in the ZrO 2 -MgO-MnO x system down to lower temperatures in comparison with the bounding systems both in air and inert gas atmosphere.
The thermodynamic descriptions of the bounding systems are available in literature. [9][10][11] However the description of the ZrO 2 -MnO x system needed to be modified since the description of the Mn-O system accepted by Dilner et al. [11] was from work of Kjellqvist and Selleby [12] while the one accepted by Pavlyuchkov et al. [10] was from work of Grundy et al. [13] Though the phase diagram of the Mn-O system was very similar in both works, the description of Kjellqvist and Selleby [12] is more advanced as it takes into account species distribution in the Mn 3 O 4 tetragonal and cubic spinel. Special attention should be given to the fact that the thermodynamic description of the bounding systems ZrO 2 -MnO x and ZrO 2 -MgO will be modified due to introducing Zr ?4 in spinel and halite models and this should cause only minimal change to the phase diagrams of the bounding systems. It should also be noted that stabilization of spinel and cubic ZrO 2 in the quaternary system outside its stability ranges in the bounding system would require introducing Zr containing end-members in spinel and halite as well as ternary interaction parameters in all above mentioned phases to reproduce experimental data. Though the thermodynamic descriptions of the bounding systems are available, the system ZrO 2 -MgO-MnO x was not modelled so far.
The aim of the present work is to develop thermodynamic description of the ZrO 2 -MgO-MnO x system which reproduces experimental data for the system. Some key DTA experiments are planned to verify the thermodynamic description.

Materials and Methods
Samples were prepared using the co-precipitation method followed by evaporation procedure. The zirconium acetate solution in acetic acid Zr(CH 3 COO) 4  X-ray powder diffraction (XRD) was performed using the URD63 diffractometer (Seifert, FPM, Freiberg, Germany) equipped by graphite monochromator with CuKa radiation (a = 1.5418 Å ). The goniometer of the diffractometer had Bragg-Brentano geometry. Rietveld refinement was applied using the Maud software [14] for the characterization of all measured diffraction patterns in order to obtain the volume fractions of present phases as well as lattice parameters. Microstructural investigations have been carried out using scanning electron microscopy combined with dispersive x-ray spectrometry (SEM/EDX; Leo1530, Carl Zeiss/Bruker AXS Mikroanalysis GmbH). Chemical compositions of samples, phases and eutectic compositions have been determined using an EDX detector with an accuracy of ± 4 mol.%. Differential thermal analysis coupled with thermogravimetry (DTA-TG) was performed using a Setsys Evolution 1750 device with * b-spinel is supposed to have a cubic structure. However, in the work of Pavlyuchkov et al., [8] b-spinel has been identified by a tetragonal structure, which is very close to cubic symmetry PtRh10% crucibles, a heating rate of 10 K min -1 and He atmosphere.

Thermodynamic Modelling
As basis for the thermodynamic description of the ZrO 2 -MgO-MnO x system, the modelling of the MgO-MnO x boundary system was accepted according to the work of Dilner et al. [11] The phase and their models are listed in Table 1. The liquid phase is described by modified twosublattice model for ionic liquid, [15,16] while solid solutions are described by compound energy formalism. [17] Zr ?4 ions were introduced in the liquid phase, cubic spinel and halite phase. The thermodynamic descriptions of the ZrO 2 -MgO [9] and MgO-MnO x [11] systems are compatible. Only due to the introduction of Zr ?4 in the halite phase the boundary system should be checked to avoid noticeable solubility of ZrO 2 in halite. Due to using different species in the ionic liquid in the Mn-O system by Kjellqvist and Selleby [12] (MnO 1.5 neutral species in the anionic sublattice) and by Grundy et al. [13] (Mn ?3 in the cationic sublattice) which were subsequently accepted in the work of Dilner et al. [11] for the MgO-MnO x system and Pavlyuchkov et al. [10] for the ZrO 2 -MnO x system, the liquid phase description appeared to be incompatible. Though there is no experimental evidence, which model is to be preferred the thermodynamic description of the liquid by Kjellqvist and Selleby [12] was accepted because of their advanced modelling of tetragonal and cubic spinel phases along with their good reproduction of the phase diagram and thermodynamic properties in the Mn-O system. Therefore, the description of the liquid phase should be modified in the ZrO 2 -MnO x system. Due to the introduction of Zr ?4 in halite and bSp phases the solubility of ZrO 2 should be very small in the ZrO 2 -MnO x system.
The thermodynamic model assuming two-sublattices was accepted for the three modifications of ZrO 2 solid solutions as in the bounding systems. The solubility of Mg ?2 , Mn ?3 and Mn ?2 in the ZrO 2 solid solutions were first based on extrapolations from bounding systems and then ternary interaction parameters were introduced to the cubic ZrO 2 based solid solution (c-ZrO 2 ). The solubilities of ZrO 2 in cubic spinel (bSp) and halite phases were experimentally established by Pavlyuchkov et al. [8] in the system ZrO 2 -MgO-MnO x . The thermodynamic description of t-ZrO 2 and m-ZrO 2 were combined based on descriptions of bounding systems because solubility of MgO and MnO x was rather small in these phases and no ternary parameters were necessary to reproduce phase relations involving these phases. Thermodynamic descriptions of c-ZrO 2 , bSp and halite were modified in comparison with extrapolations from the bounding systems. Ternary parameters and the Gibbs energy of end-members involving Zr ?4 were necessary to model the solubility of ZrO 2 in bSp and halite and to reproduce phase relations involving c-ZrO 2 , bSp and halite. The description of liquid was based on extrapolations from bounding systems. This was enough to reproduce phase relations involving liquid. The description of other phases such as a-spinel, Mn 2 O 3 , MnO 2 and Mg 6 MnO 8 were accepted from Ref 11 and were not modified further because phase equilibria studied in Ref 8 did not involve only these phases.
It should be noted that phase equilibria were investigated in the field of stability of cubic spinel phase, while it transformed to tetragonal spinel during cooling. For most compositions cubic spinel is not quenchable (except Mgrich compositions). Tetragonal ZrO 2 in the studied system is not quenchable transforming to the monoclinic phase. To get the preserved ZrO 2 with cubic structure also fast cooling was required. Therefore, to interpret experimental results, it was assumed that phases such as cubic spinel, tetragonal and cubic ZrO 2 solid solutions transformed to their low-temperature modifications without composition change.

Liquid
Liquid phase was described using the modified two sublattice model for ionic liquid [15,16] with the formula (Mg ?2 , Mn ?2 , Zr ?4 ) P (O -2 , Va -Q , MnO 1.5 ) Q , where P and Q are stoichiometric parameters changing with composition to keep electro-neutrality.

Cubic Spinel
Cubic spinel was described by the compound energy formalism assuming mixing in tetrahedral and octahedral sites also assuming that Mg ?2 and Mn ?2 can occupy part of octahedral sites which are normally vacant: (Mg ?2 , Mn ?2 ) 1 (Mg ?2 , Mn ?2 , Mn ?3 , Mn ?4 , Zr ?4 , Va) 2 (Mg ?2 , Mn ?2 , Va) 2 (O -2 ) 4 . Therefore the model used in the work of Dilner et al. [11] was expanded by considering Zr ?4 cations occupying the octahedral sites. It was assumed that smaller tetrahedral sites cannot be occupied by large Zr ?4 cations. Therefore, six new end-members appeared. The Gibbs energy of two of them can be derived using the electro-neutrality reactions between end-member compounds: are fictive compounds, both unstable in the boundary systems. The Gibbs energy for these fictive compounds were described as the sum of the Gibbs energy of the oxides G ZrO2_c ? 2ÁG MO ? Vn, where M = Mg ?2 or Mn ?2 and Vn (n = 1, 2) stands values to be optimized in both bounding systems. The calculated phase diagrams should show very limited solubility of ZrO 2 in spinel in the case of the ZrO 2 -MnO x system and avoid the spinel phase appearing in the ZrO 2 -MgO system.
The Gibbs energy of inversed spinel in both systems can be written as following were accepted from Mn-Mg-O system. [11] For other four end-members (in bold) the Gibbs energy can be obtained from reciprocal reactions involving endmembers with known Gibbs energy: The Gibbs energies of reciprocal reactions were assumed to be zero. However, in case of necessity they can be considered as deviating from zero and adjusted to reproduce experimental data.

Halite
Halite is a monoxide solid solution with NaCl structure. The thermodynamic description of the halite phase was accepted from Dilner et al. [11] assuming that the cations Mg ?2 , Mn ?2 and Mn ?3 occupy the cationic sublattice together with vacancies that assure to keep electro-neutrality condition. To take into account the limited solubility of ZrO 2 (up to 4 mol.%) in halite the determined by Pavlyuchkov et al., [8] Zr ?4 was introduced into the cationic sublattice and thus the model for halite phase was presented by the formula (Mg ?2 , Mn ?2 , Mn ?3 , Zr ?4 , Va) 1 The electro-neutrality condition due to the hetero-valent substitution of divalent cation for Zr ?4 was described by following reaction between end-members: The Gibbs energy for VaO -2 fictive end-member was accepted to be equal to zero in accordance with Kjellqvist and Selleby. [12] The compound Zr 0.5 O is therefore the fictive end-member with the NaCl structure and its Gibbs energy is equal to ( G ZrO 2 c þ V3), where V3 is the parameter to describe the very small solubility of ZrO 2 in the halite phase stable in both bounding systems ZrO 2 -MgO and ZrO 2 -MnO x . Therefore, the Gibbs energy of the Zr ?4 O -2 fictive compound can be obtained from Eq 6 as follows: G Zrþ4:OÀ2 ¼G ZrO 2 c þV3À G Va:OÀ2 þ2ÁRÁTÁlnð2Þ; which can be further rearranged to G Zrþ4:OÀ2 ¼G ZrO 2 c þV3þ11:52622ÁT:
Phases present in the system Zr-Mg-Mn-O are listed in Table 1 including crystallographic information and accepted thermodynamic models. It should be mentioned that in the thermodynamic description developed in the present work besides the already mentioned sub-systems like Mn-O, ZrO 2 -MnO x , ZrO 2 -MgO and MgO-MnO x , the binary descriptions for the systems of Zr-O, [18] Mg-O, [19] Zr-Mn, [20] Zr-Mg [21] and Mg-Mn [22] were included.

Optimization Procedure
First of all the thermodynamic description of Grundy et al. [13] was substituted by the thermodynamic description of Kjellqvist and Selleby. [12] It should be noted that this procedure did not substantially influence phase equilibria in sub-solidus region. The liquid phase description was modified by removing Mn ?3 from the first sublattice and introducing the neutral species MnO 1.5 to the second sublattice. Correspondently, the mixing parameter in liquid 0 L(Zr ?4 , Mn ?3 :O -2 ) was substituted by 0 L(Zr ?4 :O -2 , MnO 1.5 ) which was then optimized to reproduce the phase diagram in air and in inert gas atmosphere assuming partial pressure of oxygen equal to 1 9 10 -4 bar.
As mentioned above, introducing Zr ?4 into the halite and spinel phases should result in some solubility of ZrO 2 in halite in the ZrO 2 -MgO system (spinel should not appear as stable phase in this system) and in bSp and halite in the ZrO 2 -MnO x system. Solubility of ZrO 2 in halite and bSp were not modelled in the assessments [8,9] because they were within experimental uncertainty. Therefore, for consistency with experimental data available for the bounding systems the calculated solubility of ZrO 2 in these phases should be small. The next step was the optimization of the end-member parameters in cubic spinel and mixing parameters of the halite phase to reproduce the experimental data [8] for the ZrO 2 -MgO-MnO x system. Optimized thermodynamic parameters are presented in Table 2.

Results and Discussions
The calculated phase diagrams of the ZrO 2 -MgO and ZrO 2 -MnO x systems are presented in Fig. 1(a), (b), (c) and (d) with experimental data. [23][24][25][26][27][28][29] The calculations were performed taking into account the gas phase which thermodynamic description was accepted SGTE Substance Database (SGSUB). [30] The calculated data for invariant reactions are compared with the results from previous descriptions [8,9] in Tables 3 and 4. Due to some uncertainty of oxygen partial pressure in inert gas atmosphere [11] calculations in the ZrO 2 -MnO x system were performed at oxygen partial pressures equal to 1 9 10 -4 and 3.1 9 10 -3 bar. The phase diagrams only slightly deviate from previous descriptions due to the changes introduced in the present work, but the differences are within experimental uncertainty.

Isothermal Sections of Phase Diagrams of the ZrO 2 -MgO-MnO x System
The phase diagrams of the ZrO 2 -MgO-MnO x system calculated in the present study at air oxygen partial pressure and fixed temperatures are compared with ones constructed based on experimental data [8] in Fig. 2 [8] it was assumed that there were two three-phase equilibria c-ZrO 2 ? H?bSp with minimal and maximal content of MnO x in b-spinel. The reason for inconsistency can be limitations in modelling as well as problems of experimental data interpretation due to transformations occurring in samples during cooling.
Phase diagrams calculated at oxygen partial pressures corresponding to protective gas atmosphere (P(O 2 ) = 1 9 10 -4 bar [8] ) and temperatures of 1523 and 1913 K are compared with ones constructed based on experimental data [8] in Fig. 3(a) and (b). The stabilization of c-ZrO 2 below its stability ranges in bounding systems was reproduced by calculations at 1523 K though the homogeneity range of c-ZrO 2 at these conditions was very narrow and substantially shifted towards the ZrO 2 -MnO         indicating small amount of primary c-ZrO 2 along with a wide eutectic area (Fig. 4).

Experimental Investigations
Two samples with compositions ZrO 2 -8.67MgO-61.03MnO x and ZrO 2 -58.33MgO-16.08MnO x (in mol.%) after preliminary heat treatment in He atmosphere were investigated using DTA. The DTA-TG heating curves are presented in Fig. 5(a) and (b) together with calculated phase fraction diagrams. Though there were some inconsistencies between calculated and experimental phase diagrams, as discussed above the calculations help to interpret the obtained DTA results. It should be noted that there was an overheating effect for the m-ZrO 2 to t-ZrO 2 transformation indicated in pure ZrO 2 [31] as well as in the solid solutions. [9] It should be noted that XRD indicated the presence of halite and cubic ZrO 2 in both samples after heat treatment at 1913 K. In both samples exothermic effects were observed at 991 K, indicating the transformations of the initial phase assemblage c-ZrO 2 ? H into the stable assemblage.
According to calculations the stable assemblage for the sample of ZrO 2 -8.67MgO-61.03MnO x (in mol.%) composition at 1000 K should be aSp ? m-ZrO 2 . The first heat effect at 1201 K can be related to the appearance of the halite phase observed in the calculated phase fraction diagram at 1250 K. The formation of halite should be associated with a small mass loss since only a small   Therefore, the second effect in the melting peak can be related to the disappearance of halite. The calculated stable assemblage for the sample with composition ZrO 2 -58.33MgO-16.08MnO x (in mol.%) at 1000 K should be H ? aSp ? m-ZrO 2 . The first effect in the heating curve was observed at 1214 K. It can be related to the transformation of aSp into the halite phase accompanied by mass loss. The mass loss was confirmed by the TG heating curve. The calculations show that a sharp decrease of aSp content starts at * 1200 K and finishes at 1300 K. However, in DTA this process occurs with some overheating due to kinetic reasons and finishes at substantially higher temperatures. Besides this there was an uncertainty concerning the oxygen partial pressure in the DTA. Calculations showed that if the partial pressure was 3.2 9 10 -3 bar as assumed by Dilner et al. [11] the stable phase will be bSp and it will disappear at higher temperatures. Next two heat effects at 1398 and 1575 K can be related to transformation of m-ZrO 2 to t-ZrO 2 which further transforms into c-ZrO 2 . According to the calculations these transformations occurred at 1350 and 1589 K, respectively. The last transformation occurs in some temperature range until all t-ZrO 2 is transformed into c-ZrO 2 at 1594 K. It should be noted that according to the calculations the t-ZrO 2 dissolves a small amount of stabilizer (MnO ? MgO), while c-ZrO 2 dissolved up to 25 mol.% of stabilizer that is also consistent with the experimental data of Pavlyuchkov et al. [8] Therefore, the amount of halite phase decreases due to the dissolution of MgO and MnO in c-ZrO 2 . According to the calculation the dissolution of MgO and MnO occurs simultaneously with formation of c-ZrO 2 . However, in the DTA this process is substantially slower and finish at 1863 K which can be observed as the last heat effect on the heating curve. Calculated mass loss for both compositions ZrO 2 -8.67MgO-61.03MnO x and ZrO 2 -58.33MgO-16.08MnO x (in mol.%) are compared with TG data in Fig. 6(a) and (b). In calculations, components were selected as MgO, MnO and O 2 . Mass% of O 2 presented at the plots show the difference in mass between halite and spinel. Calculated mass loss is in reasonable agreement with TG though the temperature of the beginning and end of mass loss show deviation from experimental data. The reason for these inconsistencies can be explained by the fact that the partial pressure of oxygen was not controlled in the experiments and by influence of kinetics from one side and uncertainty of calculations from another side. It should be noted that calculations show some small mass gain due to higher concentration of Mn ?3 in bSp and in liquid. However, it is not clear if such effects can be observed in DTA/TG experiments.
Though the experiments have some uncertainties, such as oxygen partial pressure and kinetic effects, the derived thermodynamic description helps to relate observed heat effects with phase transformations and chemical reactions. (e) 1913 K in air with experimental data from Pavlyuchkov et al. [8] Open circles-c-ZrO 2 ; closed circles-c-

Conclusions
A thermodynamic database for the ZrO 2 -MgO-MnO x system was derived based on experimental data of Pavlyuchkov et al. [8] Thermodynamic modelling of the current oxide system has been performed for the first time. This work focused on the reproduction of the phase diagrams for oxide systems. The main features described are the stabilization of cubic ZrO 2 based solid solutions at temperatures below their stability limits in the bounding systems both in air and protective gas atmosphere as well as stabilization of cubic spinel (bSp) at temperatures above its stability limits in bounding systems. The thermodynamic description also incorporates all available descriptions of the binary subsystems. The obtained thermodynamic description was verified by interpretation of DTA-TG results obtained for two samples with compositions ZrO 2 -8.67MgO-61.03MnO x and ZrO 2 -58.33MgO-16.08MnO x (in mol.%). Calculated phase fraction diagrams were used to interpret observed heat effects and mass loses. The current database can be used for further thermodynamic modelling of the high-order systems for the development of the TRIP-Matrix-Composites. [3,32] Thus, results of current modelling can be applied for optimization of the coating process of the Mg-PSZ mentioned above. Moreover, the obtained thermodynamic description has