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Phase equilibria and materials in the TiO2-SiO2-ZrO2 system: a review
S. A. Kirillova1'2, V. I. Almjashev1'2'3, V. L. Stolyarova1'4
1I. V. Grebenshchikov Institute of Silicate Chemistry of RAS, Emb. Makarova, 2, St. Petersburg, 199034, Russia
2St. Petersburg Electrotechnical University "LETI", Professor Popov St., 5, St. Petersburg, 197376, Russia
3FSUE "Alexandrov Research Institute of Technology", Koporskoye sh., 72, Sosnovy BorLR, 188540, Russia
4St. Petersburg State University, Universitetskaya nab., 7/9, St. Petersburg, 199034, Russia refractory-sveta@mail.ru, vac@mail.ru, stolyarova.v@iscras.ru
PACS 64.75.-g; 28.52.Fa; 28.52.Nh DOI 10.17586/2220-8054-2021-12-6-711-727
This paper analyzes the available data on phase equilibria in the TiO2-SiO2-ZrO2 system. The advantages of specialized databases and software systems for the analysis of information on phase equilibria are pointed. Phase diagrams are kind of a roadmap for the design of materials. As shown in the review, nanomaterials are no exception to this. Data on phase equilibria, such as eutectic points, solubility limits, binodal and spinodal curves, make it possible to predict the possibility of the formation of nanoscale structures and materials based on them. In its turn during the transition to the nanoscale state, the mutual component solubility, the temperature of phase transformation may change significantly, and other features may become observable. This provides additional variability when choosing compositions and material design based on the phases of a given system. As an example, for design of nuclear fuel assemblies that are tolerant to severe accidents at nuclear power plants, mixed carbides (so-called MAX-phases) are considered as one of the most promising options as nanoscale layers on fuel cladding. It is suggested that the materials of the TiO2-SiO2-ZrO2 system, which are the product of oxidation of some MAX-phases, can serve as an inhibitor of their further corrosion. Ensuring the stability of materials based on MAX-phases expands their prospects in nuclear power. This requires comprehensive information about phase equilibria and formation conditions of nanostructured states in the analyzed system.
Keywords: phase equilibria, zirconia, silica, titania, nanomaterials, MAX-phases, nuclear safety. Received: 3 February 2021 Revised: 25 September 2021
1. Introduction
Nuclear power safety directly depends on the choice of reactor materials. The core materials are especially critical. In particular, the zirconium as a fuel cladding material, which has proven itself well under normal operating conditions, turns out to be extremely dangerous in beyond design basis accidents [1]. For this reason, there is an active search for a safer material to replace zirconium all over the world. One of these options is MAX-phases - a family of ternary layered compounds corresponding to the conditional formula Mn+1AXn (n = 1,2, 3, ...), where M is a transition d-metal (Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta); A - p-element (Si, Ge, Al, Ga, S, P, Sn, As, Cd, I, Tl, Pb); X is carbon or nitrogen. These materials exhibit a unique combination of properties common to both metals and ceramics [2,3]. They are of low density; high thermal and electrical conductivity; high strength; excellent corrosion resistance in aggressive liquid media, resistance to high-temperature oxidation and thermal shock; easily machined; high melting point and are quite stable at temperatures up to 1000 °C and above [2-5]. That is, according to the combination of characteristics, the MAX-phases can be ideal for the fuel cladding material of nuclear reactors. However, the prospects of their use cannot be assessed without a comprehensive study of their stability, especially in the Nuclear Power Plants accident conditions. In this case, their unique features can be used to the full, leading to a decrease in the likelihood of severe accidents or, at least, to mitigate their consequences.
One of the aspects of such investigations is the study of the oxidation products of MAX-phases, in particular, zirconia, silica and titania. Materials based on these components, presenting certain combinations of phases and features of their dimensional parameters and mutual arrangement, can both contribute to the destruction of claddings based on MAX-phases and serve as good protectors against their further corrosion. To assess the boundaries of stability and predict the properties of these materials, it is necessary to know the phase equilibria in the TiO2-SiO2-ZrO2 system, as well as to know the features of the formation of structures that have the physicochemical and mechanical properties necessary to create a protective layer.
So, for example, on the basis of the system under consideration, the formation of nested glass-crystalline structures is possible. Interest in materials with a hierarchically organized spatial distribution of phases, including nanostructured materials, is associated with their unique characteristics. For such materials, it becomes possible to fine-tune their properties in a very wide range [6-9].
The study of the formation of hierarchical structures deserves special attention. One of these processes is phase decay and, in particular, separation in the liquid phase - miscibility gap [10-20]. The structures that appear upon rapid cooling of samples from the miscibility gap can be classified as hierarchical due to the appearance of a number of sublevels with rounded inclusions ranging in size from 0.01 to 10 ^m [11].
Materials with a hierarchical structure arising during the crystallization of immiscible viscous oxide liquids can be classified as nanomaterials containing nanosized blocks (crystallites) at the lowest levels of the hierarchy, included in a glassy or crystalline matrix [7]. In addition to the size factor, the shape and spatial distribution of phases have a significant effect on the properties of such materials. The hierarchical structure formed during the cooling of immiscible melts is associated with the boundaries of phase stability and reflects the history of the decay of primary and formation of secondary phases [21]. This determines, as a rule, the characteristics of the materials thus formed [18,19,22-25].
Thereby, to solve the problem of creating and studying the physicochemical features and stability of materials, it is necessary to analyze the available information on phase equilibria. In the review, we are performed such an analysis for the TiO2-SiO2-ZrO2 system. It also provides information on materials based on the TiO2-SiO2-ZrO2 system and their relationship with data on phase equilibria.
2. TiO2-SiO2 system
The TiO2-SiO2 system is important for interpreting the interaction of titanium and silicon dioxides in the production of ceramics, glass ceramics, and glasses. Based on the components of the system, it is possible to create fundamentally new materials with unique mechanical, optical and catalytic properties [26-37]. In addition, the components of the system themselves have a variety of properties that are promising for modern technology [38-40].
The data given in the literature on the TiO2-SiO2 system are contradictory [4,41-43,45-53]. In particular, the authors of [41-43] carried out experiments in a reducing atmosphere, and in this connection, possibly, in addition to TiO2, the samples contained the oxides Ti2O3 and Ti3O5. The authors of [42] found that this system is characterized by the presence of a region of immiscibility of two liquid phases, which was not noted in [44]. In [45], contrary to previous studies, two series of solid solutions were found in the system, the existence of which was not confirmed later in [46]. The authors of [46] clarified the position of the eutectic point defined in [44]. According to those authors [46], the eutectic in the TiO2-SiO2 system corresponds to a composition of 8.1 mol. % TiO2 and a temperature of 1550±4 °C. In [46], data on the position in the system of the region of immiscibility of two liquid phases arising at 1780±10 °C in the range from 15.0 to 90.9 mol. % TiO2, i.e., significantly different from the data of [42].
Other research [47] shows the calculated diagram of the state of the system obtained on the basis of previously published data on phase equilibria in the system and thermodynamic data on SiO2 and TiO2 [48]. It is noted that the experimental data on the boundaries of the region of immiscibility of two liquid phases are unknown, and the critical point of the miscibility gap is 56.3 mol. % TiO2 and 2618 °C, was obtained only from the data of thermodynamic modeling of the region of immiscibility of liquid phases. In addition, the existence of solid solutions from the side of TiO2 is taken into account. It should be noted that the work [47] used an approach based on combining the available experimental information for phase equilibria and thermodynamic properties of the phases of the system. Then it is describing the properties of each phase by a mathematical model containing a set of tunable parameters, and carrying out the procedure for finding the parameters of the phase models that best suit all available information about the phase equilibria of the system of interest to the researcher. This approach has become widespread and has actually become the standard for thermodynamic optimization of phase diagrams. In the literature, the method has the abbreviation CALPHAD (from the CALculation of PHAse Diagrams) [54].
In works [49,50] on the basis of experimental data [46,51-53] and their own data on the boundaries of the region of immiscibility of two liquid phases, a variant of the thermodynamically optimized diagram of phase equilibria in the TiO2-SiO2 system based on the sub-regular model was proposed. In the case when the thermodynamic parameters of the used model are taken to be independent of temperature, the critical point of the miscibility gap is 50.8 mol. % TiO2 and 2374 °C, and for the linear dependence of the model parameters on temperature - 54.7 mol. % and TiO2 2339 °C.
In [55], the eutectic and monotectic nature of the phase diagram of the TiO2-SiO2 system was confirmed by the Differential Thermal Analysis method (DTA) on an original setup. The temperature of the eutectic (1543±3 °C) and monotectic (1780±7 °C) transformations has been specified. The temperature of the eutectic is somewhat at odds with the previously obtained literature data, however, in general, it can be considered that the experimental data are in good agreement with the previously obtained results in [44,46]. Scanning electron microscopy proved the presence
of a region of two immiscible melts. The data obtained for the temperature of monotectic transformation coincided with the results of [46], and the results for the liquidus line above the monotectic temperature also do not contradict them. Based on the coordinates of the liquidus line and the points of invariant transformations, the parameters of the model of subregular ionic solutions [56] for melts of the TiO2-SiO2 system were determined and a thermodynamically optimized phase diagram was constructed in the temperature range of 1500-1900 °C.
In [57], phase equilibria in the TiO2-SiO2 system in the region of liquid phase separation were experimentally investigated. It is shown that in the experimental study of silicon-containing immiscible melts, an important factor that determines the microstructure and complicates the interpretation of the data is the dynamics of system cooling. Along with the rate of cooling of the melt, it is necessary to take into account such parameters of the system as the viscosity and density of coexisting liquid phases, diffusion of components, etc. Thus, for a melt based on SiO2 at temperatures below monotectic, due to high viscosity, the liquid phase is slowly freed from the solid phase based on TiO2, and at temperatures above monotectic, the release of the liquid phase from TiO2 occurs at a significantly higher rate. Also, the work carried out a critical analysis of the available and obtained experimental data. A thermodynamically optimized phase diagram of the TiO2-SiO2 system based on the model of subregular solutions has been constructed. The phase diagram obtained by optimization by the CALPHAD method differs markedly from the diagram given in [50], which was constructed using experimental data on the composition of liquid phases at the boundary of the miscibility gap at temperatures significantly higher than the monotectic temperature. Apparently, in [50], the microstructure of samples quenched from temperatures of 2185 and 2260 °C was unreasonably interpreted as corresponding to the state of equilibrium immiscibility at these temperatures (Fig. 1a). Such a character of the microstructure may be a consequence of the decomposition of a homogeneous melt during quenching. This assumption is supported by the fact that a uniform pattern of phase decomposition is observed over the entire volume of the sample.
Fig. 1. Phase diagram of the TiO2-SiO2 system: a - 1 - [47], 2 - [49], 3 - [50], 4 - [57]; b - [58]: 1 - binodal curves; 2 - spinodal curves
In [58], on the basis of experimental data obtained in [57], the parameters of the subregular melt model were determined without and taking into account the temperature dependence of the mixing energies of the components. Using the obtained parameter values, as well as thermodynamic data for the pure components [59-61], and taking into account the absence of miscibility of the components in the solid phase, the binodal and liquidus lines in the TiO2-SiO2 system were constructed. On the basis of the obtained thermodynamic model, the curves of spinodal decomposition of the liquid phase were also constructed (Fig. 1b). Comparison of the experimental data with the curves of binodal separation and spinodal phase decomposition showed that, upon rapid cooling of the melt, the phase
decomposition in the liquid-phase region proceeds according to the spinodal mechanism [48] with the formation of materials with a hierarchically organized structure down to the nanometer scale. There are at least three levels of the hierarchy (Fig. 2). Thus, there is a fundamental possibility of experimentally constructing the spinodal of the system from data on the composition, shape, and spatial distribution of the solid regions of the phases over the volume of the material, obtained upon rapid cooling of the melt from the region of existence of two immiscible liquids.
In addition to determining the boundaries of phase equilibria and the features of phase separation and decomposition during cooling of immiscible oxide liquids in the TiO2-SiO2 system, the dependence of the microstructure on heating and cooling conditions was investigated. The results of the studies performed indicate that the parameters of the microstructure can be controlled at all levels of the hierarchy.
The authors of [63] draw attention to the fact that in the phase diagram of TiO2-SiO2 system, there are large discrepancies between the calculated and experimental data (Fig. 3). They suggest that these discrepancies are likely due to inherent difficulties in the system: the need to operate in an inert atmosphere to avoid the formation of Ti2O3 and Ti3O5, and the high temperature problems associated with miscibility gap and high SiO2 content. For example, in [46], it is indicated that difficulties arose with the determination of the eutectic in the SiO2-rich region, since it was impossible to reach equilibrium due to the high viscosity and the steep slope of the liquidus. In [57], the importance of the quenching rate for obtaining equilibrium data is also indicated. In general, it is necessary to implement new approaches for further experimental studies that will allow confirming the equilibrium data. As indicated, the experimental data from [57] are closest to the calculations. The critical temperature of the miscibility gap in the TiO2-SiO2 system is closer to [57]. The melting point of rutile is higher than that taken from [64]. The run of the liquidus curve correlates well with the new values from the Scientific Group Thermodata Europe (SGTE) substance database. Deviations from monotectic and eutectic points have not yet been explained and should be further investigated. The line going from pure rutile to the eutectic at 9 mol. % SiO2 is parallel to that in [46] and the eutectic temperature is also higher than the experimental one. The calculated liquid level decreases towards SiO2 enrichment. The discrepancy can be explained by the experimental difficulty in establishing equilibrium, and the kinetics can be very complex for such viscous compositions. The absence of the SiO^- ion is notable. The SiO4- ion is usually present in most oxide binary systems MOx-SiO2. However, in the case of the TiO2-SiO2 system, according to the experimental phase diagram, there is a wide region of immiscibility between TiO2 and SiO2. This indicates that TiO2 does not participate in the destruction of the SiO2 network, and does not use it together. In the model proposed in [49], liquid TiO2 is described as Ti4+ : O2-, where the addition of TiO2 to SiO2 does not destroy the oxygen bridge of SiO2. Thus, there is a metastable miscibility gap between TiO2 and SiO2.
In [63], calculated data on the activity of SiO2 in the TiO2-SiO2 system at 1527, 1627, and 2527 °C are also presented. Unfortunately, there is only one experimental point at 1627 °C for the TiO2 : SiO2 molar ratio of 1: 1 [65]. A strong positive deviation from ideality and the inflection point of the liquidus arises due to the presence of liquid phase separation (Fig. 3).
The concepts of the nature of immiscibility in the TiO2-SiO2 system, opposite to those of [63], are given in [66]. Thermodynamic/dynamic modeling of liquid immiscibility in silicate systems is seriously hampered by the lack of in situ studies of the structural evolution of the melt. In work [51], the structural evolution at the atomic level of the TiO2-SiO2 system with a miscibility gap is studied by in situ high-energy X-ray diffraction. The authors suspended 10 mg fragments of sintered at 1000 °C ceramics in a stream of pure oxygen and melted with a CO2-laser. Samples were overheated up to 2300 °C, then they were quenched to the target temperature, and the droplet was stabilized for 20-30 s and the diffractometric data were collected for 15 s. In the opinion of the authors, this was sufficient to avoid a strong drift of the composition due to the evaporation of SiO. For a composition of 30 mol. % TiO2, a homogeneous liquid was assumed by the authors at a level of 2220 °C. At 1950 °C, according to their data for a composition of 30 mol. % TiO2, a heterogeneous state was observed. At 1600 °C there was a metastable miscibility gap. Authors did not carry out measurements between these temperature levels. They chose the composition and temperature based on one of the versions of the phase diagram [46]. The authors, taking the work [46] as a basis, did not take into account other data [57,58,63], which can significantly affect the processing of their data and conclusions.
It was found that both the configuration of the [SiO] monomers and the polymerization between them are closely related to the incorporation and extraction of metal cations (Ti4+). The [SiO] monomer undergoes oxygen-deficient polymerization and over-polymerization before liquid-liquid separation and self-healing after liquid-liquid separation, thus challenging the traditional concept of unchanged monomer [SiO4].
Ti4+ cations with tetrahedral oxygen coordination first participate in the formation of the network before liquid separation. The four-fold Ti-O bond breaks during liquid separation, which can facilitate the movement of Ti4+ through the Si-O network to form TiO2-rich nodules. The structural features of the nodules were also investigated and found to be very similar to those of the TiO2 melt, suggesting parallel crystallization behavior in the two cases. The authors [66] hope that their results will allow one to see the structural evolution of immiscible liquid phases on
Fig. 2. Formation of a multilevel hierarchical microstructure in the process of spinodal decomposition of immiscible oxide liquids [58]: a - scheme of the phenomenon: 1 - binodal separation curve and 2 - spinodal decomposition curve; 1, 2, 3 - levels of the structural hierarchy, b - hierarchically organized microstructure in the TiO2-SiO2 system
Fig. 3. Immiscibility thermodynamic analysis in the TiO2-SiO2 system taken from [63]: a - calculated miscibility gap, experimental data and models; b - calculated miscibility gap, liquidus, terminal phases and experimental data; c - SiO2 activity at 1527, 1627 and 2527 0C, experimental point at 1627 0C; d - Yion for SiO2, SiO^-, O2- species at 2727 0C
an atomic scale, which will contribute to the construction of a complete thermodynamic/dynamic structure describing systems of silicate immiscibility in the liquid phase outside of existing models.
Thus, despite a large number of studies on phase equilibria in the TiO2-SiO2 system, there are a number of conflicting information on the position of the phase equilibrium lines that require additional analysis, experimental and calculated refinements.
3. TiO2-ZrO2 system
Phase formation in the TiO2-ZrO2 system was studied in a number of works [67-98], but only the high-temperature region of the phase diagram is described in detail, as a rule, above 1000-1200 0C. There are very few studies of the behavior of this system in the low-temperature region, as well as those taking into account the particle size of the components. At the same time, for the creation of new materials, including those based on TiO2-ZrO2 composites, nanosized compositions can be promising, the reactivity, behavior, structure and properties of which are determined to a large extent by the sizes of their constituent particles [99-105].
The data obtained in [104] show that the nucleation process limits chemical transformations in the low-temperature region in the system under study. The formation of a compound of variable composition (Zr,Ti)2O4 with a fluorite structure at low temperatures is caused by the formation of the hydroxocomplex [Zr(OH)2-4H2O]8+(OH)- in the structure of which Ti4+ ions are dissolved at the stage of precipitation. Moreover, the limiting substitution of Zr4+ ions for Ti4+ ions in the amorphous hydroxocomplex is significantly lower than 45 mol. %. Thus, the results obtained in this work confirm the promise of an approach to the control of solid-phase chemical transformations and phase transformations in nanostructured systems based on the formation of pre-nucleus clusters with a given structure (see, for example, [106,107]).
It was noted in [105] that there are significant inconsistencies between the versions of the TiO2-ZrO2 phase diagrams regarding the structure and phase field of the existence of zirconium titanate, especially at low temperatures. As a result, a detailed study of the formation of zirconium titanate was carried out. ZrTiO4 nanocrystals with a skrutinite structure (a-PbO2) were obtained by coprecipitation followed by calcination in air. Phase formation was studied in the temperature range 25-1100 ° C using simultaneous thermal analysis, high-temperature diffractometry, and scanning electron microscopy. It was found that crystallization of ZrTiO4 occurs at temperatures above 700 °C after complete removal of water. Nanoceramics based on ZrTiO4 were obtained by sintering the nanopowder at 1200 °C for 5 hours. The thermophysical characteristics of the obtained nanodispersed ceramics were measured using laser pulse analysis and thermomechanical analysis. The resulting ceramics exhibit improved thermal insulation properties (a = 0.138-0.187 mm2/s, A = 5.446-11.512 W/(m K)) and a low coefficient of thermal expansion (CTE = (3.45-7.38) x 10-6 K-1) in the temperature range 25-800 °C. This makes the resulting nanoceramics promising as a material for creating thermal barrier coatings.
Fig. 4 shows the known experimental versions of the phase diagrams of the TiO2-ZrO2 system. It is easy to see that the data on phase equilibria are replete with discrepancies, both in the region of the solubility of the components in each other, and in the field of the formation of compounds, their nature and character.
It should be noted that in [67] the liquidus curve is shown with the eutectic in exact accordance with the historically first constructed phase diagram [70] (Fig. 4a, red lines). Compounds formation was not found in [68]. The phase diagram published in [69] shows the absence of compounds and eutectics at 45-50 mass. % TiO2 and 1600 °C.
Fig. 4. Phase diagram of the TiO2-ZrO2 system (experimental study): a - red line [70], black line [71], b - black line [72, 73, 75, 85], red line [88], c - red line [78], black line [79], d - [81, 82], e - [83], f - [96]; ss - solid solution, m-, t-, c- - monoclinic, tetragonal and cubic polymorph, respectively, L - liquid
In [71], fourteen compositions were prepared from zirconium dioxide with impurities less than 1 % and anatase. The samples were mixed, compressed into tablets and heated for two hours in an oxygen-acetylene oven with excess O2 at 1760 °C. After that, they were heated in an electric resistance furnace at 1370 °C for 336 hours and at 980 °C for 1465 hours. The phases were determined using X-ray diffractometry. The plotted phase diagram (Fig. 4a, black lines) does not include the cubic form of the ZrO2 solid solution or the ZrTi2O6 phase.
The system has been extensively researched and the phase diagram (Fig. 4b, black lines) reproduced the results of other studies [72,73,75,85]. In [72], ZrO2 (with 2 mass. % HfO2 and without other spectrographically observed impurities of more than 0.05 %) and TiO2 (with 1.5 mass. % SiO2 and without other spectrographically observed impurities of more than 0.005 %) was used. They investigated the solid solution boundaries between ZrO2 and ZrTiO4, the effect of the TiO2 solid solution on the monoclinic-tetragonal transition of ZrO2, and the TiO2 solid solution boundary. The following analytical methods were used: X-ray diffraction at elevated and room temperatures and electrical conductivity.
In [75,85], using ZrO2 with a purity of 99.8 %, including 1.8 mass. % HfO2 and TiO2 with a purity of 99.7 %, 18 liquidus points were determined from the solar heating and rapid cooling curves. The temperatures measured by the brightness pyrometer were considered with accuracy up to ±20 °C at 2700 °C and ±15 °C at 1700 °C. In addition, 25 compositions quenched in air from the melt, as well as from 1700 °C were studied by X-ray diffractometry. High temperature X-ray diffractometry was also used on the ZrO2 rich side to determine the boundaries of the solid solution below 1200 °C. As for the maximum degree of a tetragonal solid solution, the data [75,85] agree with the data [72-74], but differ somewhat from other studies.
The agreement for the lowest transition temperature between monoclinic and tetragonal ZrO2 is poor. In [75,85], the dependence of the unit cell parameters on the composition for solid solutions based on ZrO2, ZrTiO4 and TiO2 are presented. They also offer a fourth form of ZrO2 that is stable above 2494 °C, but this is doubtful as it is based solely on small kinks in the rapid cooling curves.
Although other studies [72-75,85] agree with the end terms of solid solutions and one solid solution based on an intermediate compound, some details of phase equilibria remain a big question.
In [70], the starting materials were dense ZrO2 with a nominal purity of 99 % and highly purified TiO2 with a purity of >99.9 %. Samples for 16 compositions were mixed with a binder and compressed into tablets, which were then annealed in air for 4 hours at 1200 °C on Pt foil. After cooling, the samples were crushed, pressed, and annealed for 4 h at 1350 °C in air. X-ray examination showed that the solid phase reactions were completely done. The tablets were then ground, mixed again with the binder, compressed into tablets, from which small four-sided pyramids were ground. These pyramid samples were heated in an oven with resistance heaters and thorium oxide lining with an oxidizing atmosphere to determine the solidus and liquidus temperatures. The rounding of the corners of the pyramids was taken as the temperature of the solidus, and the complete melting was taken as the liquidus. Cooled fused samples and others quenched at temperatures up to 1600 °C were studied petrographically and by X-ray diffraction. The X-ray diffraction pattern of ZrTiO4 powder is indexed as a rhombic phase.
In Fig. 4 (b, red lines) show the phase diagram of the TiO2-ZrO2 system according to [88]. The precursors were prepared by the sol-gel method, heated to 800 °C, and held at that temperature for 10 h. The products were studied by X-ray diffraction and DTA. Metastable solid solution based on ZrTiO4 is shown by dash-dotted lines. The main diagram is taken from [76] (Fig. 4b, black lines).
In [78], analytically pure ZrO2 and TiO2 were used as starting materials. The pressed powders were heated in an electric resistance oven for 168 hours. The samples were examined by DTA and X-ray diffractometry. It was found that the ZrO2 tetragonal solid solution undergoes eutectoid decomposition at 1080 ° C. The monoclinic to tetragonal transition of ZrO2 occurs at 1160 °C and the tetragonal to cubic transition at 2300 °C. The data obtained are shown as a refinement on a fragment of the phase diagram (Fig. 4c, red lines).
Twenty-five compositions were prepared from ZrO2 and TiO2 of high-purity qualification, pressed into tablets, and heated in a gas (air) furnace at 1700 °C in corundum crucibles in [79]. Sintering and thermal analysis were carried out on air in a solar oven. DTA in a He atmosphere was used to determine the temperatures of formation of ZrTiO4 and eutectic. The phases were studied by X-ray diffraction and microstructural analysis. At 1700 °C, there is a single-phase region of tetragonal zirconia up to about 17.5 mol. % TiO2, a single-phase solid solution ZrTiO4 from ^40 to 52 mol. % and a rutile-based solid solution TiO2 from about 82.5 mol. %. Cooling curves of pure ZrO2 and ZrO2-based solid solutions show that cubic ZrO2 transfers to the tetragonal form at 2330±25 °C and the transition temperature is reduced to 2190 °C by adding TiO2. The unit cell sizes of various solid solutions are reported. Phase diagrams are constructed (Fig. 4c, black lines).
The subsolidus region of the system has attracted and continues to attract close attention of researchers. In papers [81,82], preliminary data on phase relations are given for the system. The experimental data also are focused around the ZrTiO4 compound. Pure (unalloyed) powders were prepared using alkoxide precursors. It was found that ZrTiO4
solid solutions undergo an order-disorder phase transition, and the phase below ~1125—1150 °C is only metastable (Fig. 4d, dashed lines). The stable phase at temperatures below ~1150 °C is the solid solution Zr1-xTi1+xO4. This phase has an incommensurate superstructure, and its structure based on Zr5Ti7O24 was described in [84]. Evidence for a phase transition in ZrTiO4 was included in [81,82].
The phase relations in the TiO2-ZrO2 system in [83] were investigated near the ZrTiO4 compound by means of an experimental study, including the characterization of both single-crystal and powder samples. Since ZrTiO4 melted incongruently at 1820 °C, it could not be grown directly from the melt of its own composition. Therefore, growth methods using a flux were used [77]. Conventional ceramic powders with particle sizes several orders of magnitude larger than powdered alkoxide precipitates were obtained by solid-phase reaction of high-purity TiO2 (anatase) and low-hafnium ZrO2. Several cycles of prolonged thermal treatment at ^1500 ° C with grinding between heat treatments were necessary for the complete reaction to proceed until a homogeneous solid solution was obtained.
The total number of heat treatments varied from ^3-7 for different compositions. In the case of some compositions, doping with 0.5 mol. % Y2O3 was carried out to accelerate the kinetics of phase transitions in order to achieve phase equilibrium in studies. Some compositions were prepared by coprecipitation of a mixed metal alkoxide solution using zirconium n-butoxide [Zr(OC4H9)4] and titanium isopropoxide [Ti(OC3H7)4] as starting materials and toluene as solvent. The sediment was X-ray amorphous. The average particle size of the agglomerates was from 1.0 to 0.05 ,um, and the BET surface area was 350 m2/g, corresponding to a particle size of 10.5 nm. These powders crystallized at temperatures above 450 °C to a metastable single-phase structure. To achieve true structural equilibrium, prolonged annealing (over 1 month) at temperatures from 500 to 1000 °C was required. Powder X-ray diffraction, neutron powder diffraction, and X-ray diffraction studies on a single-crystal precession chamber were used to characterize the structure of various solid solutions of zirconium titanate prepared and thermally-treated for research.
The presented unit cell parameters were obtained from the refinement of X-ray powder diffraction data using the least squares method [77], with additional refinement using multiple regression analysis to determine the disproportionate vector (intermediate degrees of the a-axis superstructure observed during a continuous phase transition from high to low temperature forms of zirconium titanate) when appropriate. The existence of the new compound ZrTi2O6 as a stable low-temperature phase was confirmed by the recently published discovery of the mineral srilankite [80], which has the same nominal composition and structure. The lattice parameters reported for the new mineral are in good agreement with the results of experiments on low-temperature crystallization at 650 °C using coprecipitated powders. The wide range of solid solution from 35 to 75 mol. % TiO2 was the result of metastable crystallization at low temperature of the high-temperature disordered a-PbO2 polytype, and the single-phase field was much wider than the equilibrium region at high temperatures. It was found that minor impurities play a large role in the kinetics of the order-disorder transition in zirconium titanate compositions. The addition of 0.5 % Y2O3 to compositions for high-temperature synthesis leads to the fact that the cell of tripled phase, leading to a phase with a Zr : Ti ratio of ^5 : 7, is in equilibrium with cubic ZrO2 and Y2 Ti2O7 pyrochlore. The authors revised the earlier phase diagram of the system represented on Fig. 4d to include this new information (Fig. 4e).
Fig. 4f shows the TiO2-ZrO2 phase diagram constructed from experimental data in the range from 800 to 1200 °C (1 atm) [96]. The data above 1200 ° C correspond to the data of [92]. The temperature range under consideration was previously inaccessible for equilibrium experiments due to the kinetic features of crystallization of (Zr,Ti)2O4. The crystallization of the ordered phase from the oxides was facilitated by the addition of a flux (CuO or Li2MoO4/MoO3), and seeds. Note that all phases (tetragonal and monoclinic ZrO2, ordered and disordered (Zr,Ti)2O4, TiO2) are solid solutions, and the phase fields are marked with a predominant end member of the corresponding series. No distinction is made between partially or fully ordered (Zr,Ti)2O4, and the "ordered" label includes both partially and fully ordered (Zr,Ti)2O4 in this study.
The method of synthesis at high pressures with flux and seeds, developed previously [93,94], was successfully applied for synthesis at atmospheric pressure and effectively ensured phase equilibria in the ZrO2-TiO2 system at temperatures below 1200 °C. Thus, the phase diagram extended by 400 °C differs from previously published works in that the composition of ordered (Zr,Ti)2O4 depends more on temperature than is constant [83,89]. Moreover, the authors of [96] did not find evidence of the previously proposed two-phase field of the coexistence of ordered and disordered (Zr,Ti)2O4 [97]. Rather, the onset of the ordered transition was marked by the stability of the (Zr,Ti)2O4 phase with a composition (xTi = 0.495), which differs both from the disordered (Zr,Ti)2O4 above 1160 °C and from the ordered (Zr,Ti)2O4 below 1060 °C. Thus, the two different ordered phases differ in composition. Nevertheless, it was noted in [96] that detailed studies are needed to determine their exact ordering [86].
Many attempts have been made at the thermodynamic optimization of the phase diagram of the TiO2-ZrO2 system (Fig. 5). But since there is a wide variety of experimental material, the calculated versions of the diagram also differ greatly.
Fig. 5. Phase diagram of the TiO2-ZrO2 system (thermodynamic optimization): a - [85, 87], b -[97], c - [91], d - [98], e - [90]; ss - solid solution, m-, t-, c- - monoclinic, tetragonal and cubic polymorph, respectively, R - rutile, L - liquid
Fig. 5a shows a calculated version of the phase diagram based on data from [87]. The diagram was calculated using the known thermodynamic data for ZrO2, various estimates for TiO2 based on correlations between the interaction parameters and ionic radius [85], and other data. To model the mixing of components, a simple subregular model was adopted using only the ideal entropy of mixing and without taking into account any temperature dependence of the mixing parameter coefficients. The thermodynamic properties of the ZrTiO4 and ZrTi2O6 compounds relative to hypothetical "cubic" TiO2 have been determined to comply with the published experimental phase relationships.
Various interaction parameters were used for the crystalline and liquid phases, the solubility of ZrO2 in TiO2 was neglected. The parameter of interaction of the liquid phase was adjusted in such a way as to reproduce the peritectic melting of ZrTiO4 at 1820 ° C, as well as a temperature of 1760 ° C and a composition of 80 mol. % TiO2 corresponding to the eutectic point.
The thermodynamic optimization of the TiO2-ZrO2 phase diagram performed in [97] are in good agreement with the available experimental data (Fig. 5b). The presence of two-phase fields between pyrochlore and ZrTiO4, as well as between pyrochlore and t-ZrO2 at 1300 ° C, which were not considered in earlier versions of the phase diagram, is essential. Two invariant transition-type reactions were found in calculations and then experimentally confirmed in the temperature range between 1300 and 1500 ° C.
The phase diagram of the TiO2-ZrO2 system, calculated on the basis of the available experimental data [7072,74-76,79,83], based on the fact that ZrTiO4 and ZrTi2O6 are taken as peritectically decomposing stoichiometric compounds, is shown in Fig. 5c according to the data of [91].
The phase diagram and thermodynamic data available for the TiO2-ZrO2 system were reviewed. An attempt was made to provide a consistent set of thermodynamic parameters describing the system by combining the CALPHAD
method using Thermo-Calc software and a database system. The set of thermodynamic functions is intended for a simplified version of the TiO2-ZrO2 phase diagram, in which ZrTiO4 and ZrTi2O6 are considered as stoichiometric compounds. Comprehensive comparisons are made with the available experimental data, and it is shown that the set can satisfactorily take into account most of the experimental data, with the exception of the data on the homogeneity of ZrTiO4 andZrTi2O6.
The thermodynamically optimized phase diagram of the TiO2-ZrO2 system according to experimental data [98] and data from other authors is shown in Fig. 5d.
The phase relationships in the TiO2-ZrO2 system were studied in the temperature range from 1000 to 1600 °C using X-ray diffractometry and scanning electron microscopy (SEM) with energy dispersive X-ray spectrometry (EDS). The temperature of peritectic reactions Liquid = e-(ZrxTi1-x)2O4 + TiO2 and Liquid + t-ZrO2 = в-(ZrxTi1_x)2O4 were determined to be 1756 and 1844 °C, respectively.
The compositions of the eutectic were determined by SEM/EDS as 83.2 ± 1.0 mol. % TiO2. The temperature of the eutectic reaction Liquid = в-(ZrxTi1_x)2O4 + TiO2 determined in this work is in good agreement with other data. The eutectic composition measured in this work contains more TiO2 compared to previous results. However, the results obtained are within the uncertainty of experimental methods. The enthalpy of formation of the в-ZrTiO4 compound from oxides was measured to be -18.3 ± 5.3 kJ/mol using capillary calorimetry.
The molar heat capacities of the e-(ZrxTi1-x)2O4 compound were measured in the range -38-950 °C. Experimental data were used for the thermodynamic values (i.e., the heat capacity and enthalpy of formation of the в-ZrTiO4 compound) measured in this work. In order to optimize the description of the heat capacity of a-ZrTiO4 and e-(ZrxTi1-x)2O4, as well as the contribution of the enthalpy of formation of the в-ZrxTi1-xO4 phase, respectively. Using the obtained experimental results together with the literature data, thermodynamic parameters were obtained in the TiO2-ZrO2 system.
In [90], a thermodynamic description of the TiO2-ZrO2 system based on a critical evaluation of limited experimental data from literature is obtained. Non-stoichiometric compound ZrTiO4 is described as (Ti,Zr)1O2 while ZrTi2O6 is treated as a stoichiometric phase. Comparison shows that the calculated phase diagram agrees reasonably with the experimental set selected by authors (Fig. 5e).
So, in this system, there are many contradictions in both experimental and calculated data. In general, we can conclude that this system needs detailed revision, with independent experimental and calculation expertise.
4. SiO2-ZrO2 system
Interest in the phase relationships in the SiO2-ZrO2 system in connection with the need for these data for the technology of baddeleyite and zircon refractories has not weakened since [108]. The known variants of state diagrams are shown in Fig. 6.
The most complete version is presented in the experimental work [109] (Fig. 6b). Subsequent works are only clarifying on the temperature boundaries of the existence of zircon [110] (Fig. 6b), on the region of solid solutions [111] (Fig. 6c), and on the border of metastable miscibility gap and the critical point of the immiscible region [112] (Fig. 6c).
In [113] (Fig. 6d), the Gibbs energies of three solid polymorphic and liquid ZrO2 were again optimized based on a critical assessment of all available experimental data. All data from the experimental phase diagram and thermodynamic properties of the solid and liquid phases in each binary system were simultaneously evaluated and optimized to obtain a set of model parameters. Certain discrepancies in the phase diagram and thermodynamic data in the literature were eliminated with this optimization. Any type of thermodynamic data and phase equilibria can be calculated using models with optimized parameters.
It can be concluded that this system has been studied in sufficient detail and no additional research is required on it. However, if we discuss the nanoscale state of the components of this system, then it is possible for the manifestation of features that appear to contradict the available data on phase equilibria, for example, the phenomenon of phase selection [114].
An example of phase selection, which is a consequence of the fact that for the formation of a critical nucleus, the condition of a minimum distance between nanoparticles of more than half the size of the critical nucleus must be met, can be the nature of the course of solid-phase processes in systems with different reagent particle sizes of. In particular, the study of the interaction between ZrO2 and SiO2 showed that the use of a mixture of ZrO2 nanoparticles (15-20 nm) with amorphous SiO2 nanoparticles (about 5 nm) as a reaction composition does not lead to the formation of ZrSiO4, but crystallization of cristobalite occurs. At the same time, during thermal treatment of a mixture of ZrO2 particles tens of micrometers in size with the same SiO2 nanoparticles, ZrSiO4 is formed in significant amounts. The explanation for this phenomenon, unusual for the kinetics of solid-phase reactions, when a decrease in the particle size of reagents causes a decrease in the rate of the chemical reaction, is that the size of the critical ZrSiO4 nucleus is much
Fig. 6. Phase diagram of the SiO2-ZrO2 system: a - [108]; b - red line [109], black line [110]; c - black line [111], blue line and dots [112], d - [113]; ss - solid solution, m-, t-, c - monoclinic, tetragonal and cubic polymorph, respectively, trid. - tridymite, crist. - cristobalite, L - liquid
larger than the distance between ZrO2 nanoparticles in the reaction composition of ZrO2 and SiO2 nanoparticles [114]. At the same time, crystallization of cristobalite in a composition of ZrO2 and SiO2 nanoparticles is possible, which is explained by the small size of the nuclei of this phase.
It should also be noted that isostructural ZrSiO4 uranium silicate is not formed by high-temperature methods, but is easily synthesized under hydrothermal conditions at relatively low temperatures [115].
5. TiO2-SiO2-ZrO2 system
There are only a few brief works on the study of the TiO2-SiO2-ZrO2 ternary system [51,116,117]. In [116], a projection of the liquidus surface was constructed, on which the dashed line indicates the immiscibility area (Fig. 7a), as well as two isothermal sections at 1400 °C (Fig. 7b) and at 1500 °C (Fig. 7c).
Fig. 7. Phase diagram of the TiO2-SiO2-ZrO2 system [116]: a - liquidus surface projection; b -1400 ° C isothermal section; c - 1500 ° C isothermal section, ss - solid solution
Initial reagents are not described. The original compositions were taken according to previous studies [51,117] to clarify the critical points. The exact compositions are not given, as are the instruments or research methods. However, most likely, the DTA method was used to obtain data of this type in this temperature range.
Fig. 7a is taken from [51] with modification according to the results of study [116] (Fig. 7b,c) present a summary of several experimental studies of the ZrSiO4-TiO2 system [117] and the TiO2-ZrO2 system [70]. Data are summarized as preliminary experimental results. Three peritectics and one eutectic were found. Only a eutectic at 1500 °C has been suggested by earlier studies in this system. The new critical points appear to be consistent with experimental observations of the cooling and crystallization behavior of the respective compositions, as shown in Fig. 7. Thus, the system needs further detailed research.
6. Conclusions
The incompleteness, contradictions of the available data and the arising problems in the interpretation of study results are demonstrated. As an example, the proposed in [116] topology of the liquidus surface in ternary system does not take into account the presence of a miscibility gap in the binary section of the SiO2-ZrO2 system, as well as the character of the liquidus line in the binary TiO2-ZrO2 system.
It should be noted that during the preparation of this review a perfect tool was actively used to search for information on phase diagrams - Phase Equilibria Diagrams Online Search System by NIST ACerS [118], which unfortunately has limited availability for free use. The development of such tools and databases makes it possible to significantly
simplify the search for the necessary information [119] and reduce routine procedures to a possible minimum [120]. It would be beneficial to see more of these tools, not only commercial, but also freely available. This will undoubtedly contribute to progress in materials science and technology.
The analyzed information allows us to conclude that the design of new materials based on the TiO2-SiO2-ZrO2 system with a given set of physicochemical, structural and dimensional parameters without using data on phase equilibria is almost impossible. It should be especially emphasized that the greatest contradictions in the data are observed in the synthesis and analysis of nanoscale substances and nanomaterials. This feature of the nanoscale state leads to the conclusion that, for completeness, it is necessary to add a dimension factor to the analysis of phase equilibria. At the same time, there are still few examples of such an approach [106]. This greatly complicates and constrains the possibilities of directed synthesis and analysis of nanoscale objects. Thus, a wide field for experiments opens in front of us - a new dimension and a new life of classical physicochemical analysis. By combining the acquisition of these data with the development of software tools that make it possible to work with them comfortably and efficiently, it is possible to bring the design of nanoscale substances and nanostructured materials to a brand-new level.
The question is in which field the new approach will be firstly applied. Of course, for a precedent to grab the attention of researchers, it must be a critically important task in a topical area.
Of great concern today is the energy crisis and the ways out of it. The emphasis is shifting towards nuclear energy as the main hope of overcoming energy and resource problems. But the fact is that at the dawn of the century of atomic energy a great leap forward was made. Many options have been tried, out of which a small number of solutions were preferred. At that date and level of knowledge these decisions seemed optimal. But, the experience of nuclear power development has shown that there are serious safety problems for the most popular solution which seemed ideal - for oxide nuclear fuel in a zirconium cladding.
The serious problem is the zirconium reaction with vapor. If this reaction occurs, then it launches a chain of negative events that aggravate each other. As a result, the probability is very high that a nuclear power plant have a severe accident, such as the Chernobyl and Fukushima-1 accidents, could occur. Thus, with the renaissance of nuclear energy for preventing the described problem, began the development new safer options for fuel assemblies -an advanced accident-tolerant fuel.
One of the solutions to improve fuel safety is the use of special coatings to protect the cladding from oxidation. In particular, a promising coating option are MAX-phases, that have a good compatibility with the cladding material, high ductility and, potentially, good resistance to high temperatures.
At the same time, these phases and their combinations with metallic and oxide materials have not practically been studied, and we need experimental and theoretical evidence of their effectiveness. The first and most important step on the way is the study of phase equilibria. In particular, it is necessary to know what happens with that coating under oxidizing conditions at high temperatures. This requires comprehensive physicochemical information not only about MAX-phases, but their oxidation products and possible interactions.
For that, a critical analysis was carried out for the synthetic possibilities, the conditions for high-temperature experiments, the assessment of nonequilibrium phase formation in binary systems and information about the TiO2-SiO2-ZrO2 system which is the currently available. It will allow us to further take into account the features of phase formation and phase equilibria in the TiO2-SiO2-ZrO2 system at high temperatures and in nanoscale to evaluate the stability limits of MAX-phases in conditions at severe accidents on nuclear power plants.
Successful implementation of this or another actual problem must demonstrate the effectiveness of the described approach. We are hope to see this.
Acknowledgement
The authors are grateful to Corresponding Member of the Russian Academy of Sciences Professor Victor V. Gusarov for fruitful discussions and advices on improving the quality of this review.
The reported study was funded by Russian Foundation for Basic Research and ROSATOM (project no. 20-2100056).
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