Thermodynamic approach for prediction of oxide materials properties at high temperatures

Introduction

Innovations in the field of high-temperature oxide ceramics and refractory materials depend to a great extent on the accuracy and abundance of the thermodynamic information related to the oxide components and systems. Acquisition of the relevant thermodynamic data is usually a starting point in the development and evaluation of performance of oxide materials designed for practical applications. Moreover, the thermodynamic approach is one of the keystones in theoretical analyses of practically all the phenomena related to the properties and thermal behavior of ceramics, glasses, and melts. One of the central issues in the vast program of thermodynamic studies of oxide systems defined by M.M. Shultz [1] was attainment of detailed understanding of all aspects of glass formation. This challenging task required employment of various mutually complementary experimental techniques, such as calorimetric, EMF, and high temperature mass spectrometric methods. For a particular problem of investigation and development of high refractory and super refractory oxide ceramics devised for operation at temperatures higher than 2000 K, Knudsen effusion mass spectrometry (KEMS) is a unique tool [2], [3]. Phase transitions in the oxide components of the condensed phase and their selective vaporization as well as possible interaction with the ambient gasses may lead to a drastic deterioration of the refractory material. Therefore information on the vapor composition over these refractory ceramics at high temperatures is of primary importance. Only the KEMS method can provide quantitative and sufficiently accurate data on the partial pressures of the vapor components. Since this method furnishes also the ample information for theoretical analysis and calculations, M.M. Shultz prompted performing the mass spectrometric investigations as an experimental basis for a large number of thermodynamic studies under his guidance. The results of the KEMS measurements expressed in the form of concentration dependences of the component activities inspired M.M. Shultz and his colleagues, particularly in [2], [3], [4], [5], [6], [7], [8], [9], to develop the unique high temperature thermodynamic approach for the prediction and modeling physicochemical behavior of various types of inorganic materials such as glasses, ceramics, and coatings that may be used up to the temperature 3000 K.

Thus, development and improvement of performance of inorganic oxide materials at high temperatures require reliable and comprehensive information on the vaporization processes and thermodynamic properties of the oxide systems that can serve as a base for glasses, ceramics, and coatings widely used in nuclear industry, metallurgy, aviation and rocket engineering, and for resolving the issues of environmental protection. It has been demonstrated repeatedly that alteration of physicochemical properties of oxide materials at high temperatures results from changes in their chemical or phase composition caused by a selective vaporization of components in the condensed phase. Systematic study of the vaporization processes and thermodynamic properties of oxide systems and materials by the KEMS method was launched in the beginning of the seventies on the initiative and under the supervision of M.M. Shultz [1]. It is worth mentioning that, in the studies carried out in recent years using this method, oxide systems are still the most common and relevant objects of the experimental investigations [2].

The main goal of this invited article is to review the recent data on vaporization processes, thermodynamic properties, and modeling of glasses, melts, and ceramics based on binary and ternary silica- and hafnia-containing systems obtained with the participation of the authors.

Experimental study of oxide materials by Knudsen effusion mass spectrometric method

The fundamentals of application of the KEMS method to the study of the vaporization processes and thermodynamic properties of oxide systems and materials are discussed, for example, in monograph [3]. The vaporization schemes and specific ways of the thermodynamic description of borate, silicate, and zirconate systems revealed by KEMS were summed up in recently published reviews [2], [3], [4], [5], [6], [7], [8]. However, some recently obtained new experimental data on the vapor composition and the thermodynamic properties of the silicate systems containing bismuth oxide, on the one hand, and the systems containing oxides of rare earth elements, zirconium, and hafnium (in addition to [9]), on the other hand, were not considered earlier systematically. For this reason, the present study is devoted to a discussion of these particular systems.

The bismuth-silicate systems attract researchers’ attention in view of their possible use in data storage devices, photoresistors, scintillators [10], and due to the discovered phenomenon of infrared luminescence significant for further development of fiber light guides and fiber lasers [11], [12]. Other attractive features of the bismuth-silicate glasses are their high absorption coefficient for ionizing radiation combined with transparency to visible light [13] and their ability to serve as an environmental-friendly substitute for lead oxide glasses in various components of electronic circuitry and microelectronics [14].

At present, ceramics based on oxides of zirconium and rare earth elements (REE) are widely used for synthesis of super refractory materials required for such products as thermal barrier coatings and casting moulds for gas turbine engine parts [15], [16]. One of the valuable characteristics of the specified systems is low volatility of their components at the temperatures up to 2200 K preventing modification of the physicochemical properties of the high-temperature materials resulting from the selective vaporization of the condensed phase components during cyclic heating-cooling operation. A well-established fact is that REE admixture to zirconia-based ceramics leads to formation of metastable solid solutions, which inhibit phase transitions in the considered systems in a broad temperature range up to 1473 K [17], [18], [19]. At higher temperatures, the metastable solid solution undergoes phase transition resulting in the formation of two stable solid solutions and consequently in the degradation of the high-temperature performance of the material [18], [19], [20]. It is believed that, when ZrO₂ is partially or completely substituted by HfO₂, the operational temperature range of the super refractory ceramics may be expanded due to higher temperatures of the HfO₂ phase transitions and smaller volume effects of these transitions [9], [18], [21]. Hence, it is reasonable to investigate the vaporization processes of ceramics containing HfO₂ or ZrO₂ with HfO₂ mixtures.

Let us consider first the main characteristic features of vaporization processes of pure oxides of the considered binary and multicomponent systems. Vaporization of individual Bi₂O₃ was investigated in a number of studies [22], [23], [24], [25]. It was shown in [22], [23], [24] that at the temperatures 950-1200 K the principal vapor species over Bi₂O₃ vaporized from a platinum effusion cell are О₂, Bi, BiO, Bi₂, Bi₂O, Bi₂O₂, Bi₂O₃, Bi₃O₄, Bi₄O₄, and Bi₄O₆, the most abundant species being the atomic bismuth and molecular oxygen. Oniyama and Wahlbeck [25] came to conclusion that initial stage of the Bi₂O₃ vaporization is characterized by the selective evaporation of oxygen until the O/Bi molar ratio in the condensed phase composition attains the value of 1.23 and, at the next stage, this composition vaporizes congruently. It was established [26], [27] that, in the temperature range 1610–2038 K, the main vapor species over SiO₂ are O, O₂, SiO, and SiO₂, the partial pressure of SiO being higher than that of SiO₂. Vaporization of pure oxides of zirconium and REE was considered in [27], [28]. It was proved that pure ZrO₂ transfers into the gas phase mostly with dissociation to ZrO and O, but concurrent vaporization without dissociation is also observed. The ZrO₂(g) partial pressure (p _i ) over ZrO₂ amounts to less than 50% of p _ZrO at the temperatures 2500–2715 K [27], [28]. Characteristic of the REE oxides transition to the gas phase is the predominantly dissociative vaporization with the formation of the corresponding gaseous monoxide and oxygen [27], [28].

There is a big difference in volatilities of the REE oxides, but even the most volatile of them transfers to the gas phase at temperatures above 2000 K. Vaporization of pure HfO₂ proceeds similarly to the vaporization of ZrO₂, but HfO₂ vapor species were not identified at the temperatures below 3000 K [22], [29], [30], [31], [32], [33].

Analysis of the data obtained in the studies of the vaporization processes and the thermodynamic properties of the Bi₂Sr₂Ca₂Cu₃O_y, Bi₂O₃-SnO₂, K₂O-Bi₂O₃-TiO₂, and Bi₂O₃-Fe₂O₃ systems is given in review [5]. Consider the most recent published research works in this field reporting the studies of the Bi₂O₃-SiO₂ [34], [35], Bi₂O₃-P₂O₅ [36], and Bi₂O₃-P₂O₅-SiO₂ [36] systems. In Refs. [34], [35], it was established that at the temperatures 950–1050 K only oxygen and atomic bismuth can be observed in the vapor over the Bi₂O₃-SiO₂ system. In the temperature range 1050–1200 K Bi₂, BiO, and Bi₄O₄ molecular species were also identified in the vapor over the samples of the Bi₂O₃-SiO₂ system indicating rapid selective vaporization of the Bi₂O₃ component and enrichment of the condensed phase with SiO₂. Transition of SiO₂ to the gas phase in the form of SiO and O was observed at the temperatures exceeding 1800 K after the complete removal of bismuth oxide. The values of the Bi₂O₃ activity in the Bi₂O₃-SiO₂ system obtained at the temperature 1000 K by the differential mass spectrometric method [35] allowed determination of the Gibbs energy of mixing ΔG and the excess Gibbs energy ΔG ^E in the studied system.

The main results of the studies of the vaporization processes and thermodynamic properties of the systems based on the oxides of REE, zirconium, and hafnium by KEMS [29], [30], [31], [32], [33], [37], [38], [39], [40], [41], [42], [43], [44], [45] are summarized in Table 1.

Modeling of oxide systems based on Generalized Lattice Theory of Associated Solutions (GLTAS)

It was shown earlier that GLTAS is a fruitful approach for modeling and finding the correlation between thermodynamic properties of the system under the study and its structural description, which was illustrated on the examples of oxide glasses and melts in the B₂O₃-SiO₂ and B₂O₃-GeO₂-SiO₂ systems [3]. This theory is very useful also for modeling of various physicochemical properties, such as partial molar volumes and viscosity.

The recently obtained values of the thermodynamic functions in the Bi₂O₃-SiO₂ system and the results of modeling on the basis of GLTAS [46] allowed correlation of the thermodynamic properties of the bismuthsilicate glasses with their structure to be examined [36]. In the study of the vaporization processes in the Bi₂O₃-P₂O₅-SiO₂ system, including the binary Bi₂O₃-P₂O₅ system, it was demonstrated that the general character of the vaporization behavior is similar to that of the Bi₂O₃-SiO₂ system [34], [35], [36]. However, at the temperatures 1500–1700 K, the PO and PO₂ vapor species were detected in the vapor over the specified ternary system. Bismuth oxide activities in the Bi₂O₃-P₂O₅-SiO₂ system were determined by the differential mass spectrometric method at the temperature 950 K whereas the Darken method [47] was applied for calculation of the values of the P₂O₅ and SiO₂ activities and excess Gibbs energy. The ΔG ^E values calculated for the temperatures 950 and 1273 K indicated significant negative deviations from the ideal behavior in the Bi₂O₃-P₂O₅-SiO₂ system. Validity of application of the semi-empirical Kohler method [48] to the determination of the ΔG ^E values in the glass-forming melts and glasses in the Bi₂O₃-P₂O₅-SiO₂ system at the temperatures 950 and 1273 K was also illustrated in [36] in addition to the ability of GLTAS. It follows from the analysis presented that the samples of the systems containing Bi₂O₃, P₂O₅, and SiO₂ are characterized by the selective vaporization of Bi₂O₃ and the main vapor species correspond to the vapor composition over the pure oxides composing both binary and ternary systems.

It should be underlined that, using the results of GLTAS-based modeling [46], correlation of the thermodynamic properties with the structural features of solid solutions in the Gd₂O₃-Y₂O₃-HfO₂ [44], [45] and La₂O₃-Y₂O₃-HfO₂ [45] systems was also considered. The results obtained by optimization based on the GLTAS model and the Redlich-Kister approach [49] were compared in these solid solutions mentioned above.

Conclusions

It was convincingly shown that thermodynamic approach to study high temperature behavior of oxide glasses, ceramics, solid solutions, and melts using Knudsen effusion mass spectrometric method and modeling based on the Generalized Lattice Theory of Associated Solutions allows one to obtain the reliable information on thermodynamic properties and vaporization processes for the further development of advanced inorganic materials up to 3000 K. The results discussed in the current review may be considered for the further addition to the thermodynamic databases of oxide systems available nowadays for modeling of phase diagrams at high temperatures and their further improvement in the frame of the CALPHAD approach.