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Open Access 2024 | OriginalPaper | Buchkapitel

4. Thermodynamic Assessment as a Tool for Modeling Interactions at the Interface Between Ceramic Filter and Melt

verfasst von : Mariia Ilatovskaia, Olga Fabrichnaya

Erschienen in: Multifunctional Ceramic Filter Systems for Metal Melt Filtration

Verlag: Springer International Publishing

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Abstract

The chapter will focus on the thermodynamic database development relevant to modeling the interactions between filter materials, coatings, and inclusions in steel and Al-alloy. The CALPHAD approach is applied to develop thermodynamic databases, i.e. the available phase diagram data and experimental thermodynamic values are used to optimize the parameters describing the Gibbs energy of phases which can exist in the system. Thermodynamic description of multicomponent systems is the basis for more advance simulation of technological processes. In the chapter, the fundamentals and theory of thermodynamic modeling will be discussed in detail, and the most important results obtained will be presented. Examples of the thermodynamic calculations applied for solution of technological problems will be discussed.

4.1 Introduction

Phase diagrams are widely used in materials research and engineering to understand the interrelationship of composition, microstructure, and process conditions. However, most industrial materials are complex, consisting of more than two or three components. In this case, the direct application of phase diagrams is less representative. On the other hand, only limited data (on phase diagrams) are available for many multicomponent systems. Computational methods such as CALPHAD (CALculation of PHAse Diagrams) are therefore employed as a powerful tool to model thermodynamic properties for each phase and simulate multicomponent multi-phase relations in complex systems [1, 2].

In the context of the Collaborative Research Center 920 (CRC 920), which deals with creating a new generation of metal having improved qualities (e.g. superior mechanical properties) through melt filtration, computational thermodynamics can provide valuable information on the phase behavior in the filter material over a wide temperature range. The formation of stable and metastable phases during the interaction of filter material, coatings, as well as inclusions in molten steel or aluminum alloy can be predicted. Moreover, relevant energy effects and basic information about the physical and chemical parameters of industrial processes can be provided.

As long as two filtration processes have been proposed, for steel and aluminum melt, two main independent complex filter systems can be distinguished and considered separately. For the steel melt filtration, Al₂O₃ filters with different coatings including carbon-bonded ceramics such as Al₂O₃ or spinel MgAl₂O₄ have been suggested [3, 4]. Interaction of coatings with 42CrMo4 steel and its purification were indicated [5, 6]. Therefore, thermodynamic modeling of the complex spinel (Fe,Mg,Mn)Al₂O₄ system is necessary. A modification of Al₂O₃ filter surface using TiO₂ and ZrO₂ additives have also been suggested for the steel filtration [7, 8]. Besides this, different metastable Al₂O₃ phases have been suggested as coatings for the filtration process and therefore the description of the metastable Al₂O₃ phases should be also implemented. Thus, the first main focus of this work is the development of thermodynamic database for the ceramic filter materials consisting of α-Al₂O₃, metastable γ-, δ-, k-, and θ-Al₂O₃, oxides originating from steel oxidation, i.e. FeO, Fe₂O₃, MnO, Mn₂O₃, and oxides used for filter surface modification MgO, TiO₂, and ZrO₂.

For the aluminum melt filtration, carbon-free Al₂O₃ have been suggested as filter materials. The influence of different filter surface chemistries (Al₂O₃, spinel MgAl₂O₄, mullite 3Al₂O₃·2SiO₂, SiO₂, and TiO₂) has been discussed [9, 10]. Moreover, the thermodynamic description of the aluminum alloy itself is of interest to control and modify the morphology of Fe-containing intermetallic phases. Therefore, the focuses in this case are on development of thermodynamic databases for the ceramic filter materials (Al₂O₃, MgO, SiO₂, TiO₂) and aluminum alloy (Al, Fe, Mg, Si).

It is clear that thermodynamic descriptions of some systems are important for both processes, whether it is the filtration of steel or aluminum melt. These are, for example, the binary Al₂O₃–MgO and Al₂O₃–TiO₂ systems and the ternary Al₂O₃–MgO–TiO₂ system. Since the CALPHAD method provides a structured and block approach, the derived thermodynamic description of any binary or ternary system can be easily implemented into a complex database. The only limitation is the consistence of the merged databases.

In the beginning of the project, there were very few related thermodynamic descriptions available. They were mainly based on critical assessment of binary and ternary systems available in literature. Phase relations and melting behavior in the FeO–Fe₂O₃–MgO–SiO₂ [11] and MgO–Al₂O₃–SiO₂ [12] systems were described thermodynamically at 1 bar. However, different models were used in Refs. [11] and [12] to describe the liquid phase. Other related systems were available and should be considered within the project, they are MgO–Al₂O₃ [13, 14], Fe–Mn–O [15], Al₂O₃–SiO₂ [16] etc. The liquid phases in these cases were described by the ionic two-sublattice model, so the descriptions could be easily implemented into the derived datasets in case of consistency. The opposite situation is applied to the FeO–Fe₂O₃–MgO–SiO₂ [17], MnO–Al₂O₃ [18], MgO–Al₂O₃–SiO₂ [19] systems where modified quasi-chemical model was applied for the liquid phase and due to inconsistency it cannot be implemented into database utilizing two-sublattice partially ionic liquid model. However, descriptions of the solid phases based on the compound energy formalism in the form of sublattice model could be used. Moreover, commercial databases (e.g. FactSage, Thermo-Calc) were also available, however not all required ternary oxide systems were described at the beginning of the project. Commercial databases have been expanded over the years, but further development of these databases for the aims of the present work is not possible because the thermodynamic parameters are not available to users. Since there was a great gap in describing many related systems (even binaries) in commercial databases and in literature, precise material design was not possible. Moreover, besides to the existing datasets, consideration of new experimental data on phase relations and thermodynamics is essential. Therefore, the CRC 920 required the development of self-consistent multicomponent multi-phase oxide database that would provide necessary information for simulation of the metal melt filtration process.

4.2 The CALPHAD Approach

The total Gibbs free energy is minimized to determine a state of chemical equilibrium. The CALPHAD (CALculation of PHAse Diagrams) method [1, 20, 21] has been originated as an algorithm utilizing models developed for the Gibbs energy, G, of phases in low-order systems as a function of temperature, pressure and composition, starting from pure compounds and binaries. These models describe the Gibbs energy of each phase in a system, including stable and metastable temperature and composition ranges. By fitting a set of critically evaluated and selected experimental data (for example phase diagram information, thermodynamic values) and theoretical predictions, it is possible to calculate optimal model parameters reproducing experimental data within uncertainty limits, followed by storage in a database. Thus, the CALPHAD method is a hierarchy method that requires to develop thermodynamic descriptions from unary to higher-order systems. Then the derived thermodynamic databases can be used to solve, among other things, practical issues of many technological processes. The algorithm of the CALPHAD approach is shown schematically in Fig. 4.1.

Although the CALPHAD method is convenient and efficient for predicting and estimating thermodynamic properties and phase equilibrium data, it is unable to predict the existence of a phase unless it was experimentally confirmed and included in the thermodynamic assessment. The latter highlights the need for accurate experimental data, because optimized parameters in a thermodynamic assessment are dependent on experimental data.

4.2.1 Experimental Data

The quality of a thermodynamic description is determined by how well nature of phases corresponds to the applied models, e.g. how the crystal structure, short range order, species present in the phase, site occupancies etc. are accounted and how well the description can reproduce experimental data. Consequently, high quality experimental data are essential to develop advanced CALPHAD descriptions. Their availability and critical assessment make the thermodynamic description of the system more efficient and invaluable in describing real processes and in the design of new materials. In general, the experimental data used to optimize thermodynamic parameters can be distinguished as phase diagram data and thermodynamic data [1]. A summary of the methods applied to ensure the reliable experimental data and their evaluation criteria can be found elsewhere [2], while in-detailed information on many methods used for the determination of phase diagram data is provided by Zhao [22]. Only the techniques directly applied within the current project are discussed in detail below. The corresponding methods are differential thermal analysis, X-ray diffraction, and scanning electron microscopy (phase diagram data) and scanning differential calorimetry (heat capacity and enthalpy of transformation data).

Sample Preparation

Samples of the Al–Fe system were prepared by levitation melting followed by casting in a cold copper mold [23] and arc melting of pure metals. The arc melting furnace (AM furnace, Edmund Bühler GmbH, Hechingen, Germany) was three times evacuated to 1·10^–5 atm and backfilled with argon prior melting to prevent oxidation of the samples. The as-cast samples were encapsulated in fused silica glass tubes under Ar. The argon atmosphere was adjusted to normal pressure at target temperature. The samples were then annealed under specified temperature–time conditions and either cooled in a furnace to room temperature to get a homogeneous microstructure applicable for the heat capacity measurement or quenched (RHTV 120/300/18, Nabertherm, Germany) into cold water to get the phase diagram data.

Samples of the oxide systems were prepared by three different methods: solid-state reaction, co-precipitation routine, and co-hydrolysis. Al₂O₃–MgO and TiO₂–SiO₂ samples were prepared by solid-state reaction from high-purity oxide powders. To reduce the time to reach equilibrium at a target temperature, co-precipitation routine and co-hydrolysis (for SiO₂-containing samples) [24] followed by thermal decomposition of aqueous solutions were mainly used. When the samples were prepared by co-precipitation, the initial chemicals dissolved in distilled water were mixed at predetermined ratios and then added dropwise to an aqueous solution of ammonia NH₄OH with the pH value maintained above 9.0 during the process. To grow the precipitated particles and divide the working solutions into two parts, filtrate and filtride, the suspensions were heated up and held at 333 K for 1–2 h followed by filtration. To check composition of the obtained samples, filtrates (to check completeness of the co-precipitation) and precipitates dissolved in diluted solution of H₂SO₄ were controlled by inductively coupled plasma optical emission spectrometry (ICP-OES). In case of a significant deviation of the sample composition from the nominal detected by ICP-OES (mostly in case of TiO₂-containing samples), the filtration stage was replaced by evaporation. The precipitates after filtration or substances after evaporation were dried at 353 K for 1–3 days. By grinding, the powder samples were then subjected to one- or two-stage calcination at 673–1073 K for 2–5 h in air. The powders obtained were ball-milled, pressed into tablets at 300 MPa (tablet size is 5 or 8 mm in diameter and about 2–3 mm in height), and annealed under specified temperature–time conditions in air in Pt-crucibles in a muffle furnace (NABERTHERM, Germany) in order to achieve a pseudo-equilibrium state followed by furnace-cooling. The annealing duration varied depending on the sintering temperature and microstructure development suitable for SEM/EDX quantification. The MnO-containing sample tablets were placed in sealed (under Ar) quartz tubes together with a solid piece of graphite and then annealed. Graphite is required to maintain a reducing atmosphere inside the tube so that the low oxygen potential keeps manganese in its + 2 state.

The SiO₂-containing samples were prepared by co-hydrolysis as follows. The metal–organic precursors of every desired metal were first separately dissolved in isopropyl alcohol and then mixed and stirred for 2 h with preliminary prepared solutions of (H₂O + (CH₃)₂CHOH + NH₄OH) at a fixed concentration of the components. After, the ready solutions were slowly mixed together in the presence of NH₄OH to maintain the pH above 9.0 during the process and to ensure complete precipitation of the corresponding hydroxides. The precipitate was visible as a cloudy white solution. The precipitate was sequentially decanted, evaporated, dried, and calcined to obtain the desired mixed oxide powders. The further procedure is similar to that described above for samples prepared by co-precipitation.

Phase Diagram Data

Structural Investigation

Powder-X-ray diffraction (P-XRD) was carried out to determine relative phase fractions in the powder samples obtained after prolonged annealing at target temperatures. The lattice parameters and crystal structures of the phases were also verified. The powdered samples were investigated at room temperature using an URD63 X-ray diffractometer (Seifert, FPM, Freiberg, Germany) working in Bragg–Brentano reflection geometry and equipped with a graphite monochromator at CuKα radiation (λ = 1.5418 Å). Thin layers of powder samples were sedimented with a drop of ethanol on monocrystalline silicon substrate with (510) orientation which gives a “zero-background” at 2θ of 15°–110°.

Qualitative and quantitative analyses of the P-XRD patterns were performed by Rietveld analysis using MAUD software [25, 26]. ICSD (Inorganic Crystal Structure Database, 2017, Karlsruhe, Germany) [27] was used for interpretation of the powder diffraction patterns. The method makes it possible to determine the site occupancy parameters by analyzing the polycrystalline samples. Each solid phase has its own characteristic diffraction pattern as a function of intensity depending on the diffraction angle 2θ.

Quantitative analysis of the P-XRD patterns of the SiO₂-rich samples subjected to melting can be complicated by a broad background peak in the range of 2θ between 18 and 25° due to the non-crystalline glass formation.

Microstructural Investigation

Microstructural investigations by scanning electron microscopy (SEM) including secondary (SE) and backscattered electrons (BSE) imaging, energy dispersive X-ray spectrometry (EDX), and electron backscatter diffraction (EBSD) were carried out on polished cross-sections of the solidified/quenched samples after prolonged annealing at the target temperatures. The sample microstructures were analyzed using LEO 1530 Gemini (Zeiss, Germany) equipped with an EDX detector (Bruker AXS Mikroanalysis GmbH, Germany) or/and JEOL JSM 7800F (Tokyo, Japan) equipped with an EDX/WDX detector and with an EDAX Hikari Super EBSD system (Octane Elite, EDAX Inc., Berwyn, PA, USA). Both microscopes were equipped with a field emission cathode, used at the acceleration voltage of 20 kV and working distance of 8.0–11.3 mm.

EDX was used to check the chemical compositions of the samples, to determine the compositions of solid phases which also means phase identification, and to estimate the composition of the liquid resulting from partial melting at a given temperature or after melting during an invariant reaction. An experimental uncertainty of EDX measurement is around 2–4 at.%. For SEM/BSE imaging, specimens (cross-sections) must be electrically conductive, at least at the surface, and electrically grounded to prevent the accumulation of electrostatic charge at the surface when scanned by the electron beam. Therefore, specimens (especially less- or nonconductive oxide samples) were well ground and polished followed by sputter coating with an ultrathin graphite layer. In some cases, metal coatings (a thin film of copper or silver paint on the specimen surface) were additionally used.

Thermal Analysis

Temperatures of the solid-state transformations and melting behavior were investigated by differential thermal analysis (DTA). DTA is a technique in which the temperature difference between a substance and a thermally inert reference material is measured as a function of the temperature (or time), while the substance and reference material are subjected to a controlled temperature program. During identical thermal cycles (i.e. same cooling or heating program), any temperature difference between sample and reference is registered so that any changes in the sample, either exothermic or endothermic, relative to the inert reference in terms of thermal voltage (in µV) can be detected. Note that an empty crucible is often used as a reference. DTA can be accompanied by thermogravimetric analysis (TG) which makes it possible to record the mass change of a sample as a function of the temperature (or time) during thermal cycles.

DTA measurements were performed on (i) TG–DTA SETSYS Evolution-1750 (SETARAM Instrumentation, France) in air or inert atmosphere (Ar, He) using B-type tri-couple DTA rod (PtRh 6%/30% thermocouple) and open Pt crucibles (Pt/Rh 10%) and (ii) TG–DTA SETSYS Evolution-2400 (SETARAM Instrumentation, France) using W5-type DTA rod (WRe 5%/26% thermocouple) and open W crucibles and employing a permanent inert He flow. The heating and cooling curves were recorded at the rates of 10 and 30 K·min⁻¹, respectively. In case of the metallic sample investigation, ceramic crucibles (mostly Al₂O₃) were used for SETSYS Evolution-1750.

Temperature calibration of both devices was regularly done using well-known melting points of pure reference substances. Temperature calibration of SETSYS Evolution-1750 (in case of ceramic crucibles application) was performed using Al, Ag, Au, Cu and Ni. Temperature calibration of SETSYS Evolution-2400 was carried out using melting points of Al, Al₂O₃, and temperature of solid-state transformation in LaYO₃ previously measured using SETSYS Evolution-1750.

The temperatures of the phase transformations were recorded on DTA curve in heating mode and were determined as an onset point, i.e. the intersection of the baseline with the linear extrapolation (tangent) from the largest slope of the DTA curve.

Thermodynamic Data

Heat Capacity Measurement

Differential scanning calorimetry (DSC) is widely applied for the heat capacity (${C}_{P}$) measurements. The heat capacities of individual phases and compounds were measured (i) by an instrument DSC 8000 (Perkin Elmer, Inc., USA; inert Ar or He flow; heating rate of 10 K/min; Pt/Rh crucible, with an alumina inlay in case of metallic samples) in the temperature range from 235 to 675 K (the whole temperature range was divided into short intervals of 100–150 K) and (ii) by a DSC device Pegasus 404C (NETZSCH, Germany; inert Ar flow; heating rate of 10 K/min; Pt/Rh crucible, with an alumina inlay in case of metallic samples) in the temperature range from 623 to 1400 K. The classical three-step method [28] using a continuous heating mode of 10 K·min⁻¹ was applied to measure specific heat capacity as follows:

Baseline measurement taking empty both sample and reference crucibles to prevent any negative effects during DSC experiments,

Standard material measurement to account for the calibration factor caused by the difference in heat transfer, and

Unknown sample measurement.

For ceramic samples, both measurement systems were calibrated using a certified sapphire (Alfa Aesar, Karlsruhe, Germany) as a standard; the mass (84.1 mg) and the radius (5 mm) of the sample pellets were the same as for the standard material. For metallic samples, the calibration substances were selected according to the temperature range of interest: copper for the range of 100–320 K, molybdenum for the range of 300–673 K, and platinum for the range 573–1473 K. Each calibration measurement with a preceding measurement with empty crucibles and the sample pellets measurement were carried out three times with an average uncertainty of 3%. Note that the C_p measurements at temperature above 1200 K (by described DSC instrument) could be less reliable because of the increase in heat radiation that decreases the registered signal. This limitation was considered for fitting of experimental data using the Maier–Kelley equation [29] in the form as

$${C}_{P}=a+bT+c{T}^{-2}$$

(4.1)

where a, b, and c are the parameters and T is temperature in K.

Apart from obtaining experimental ${C}_{P}$ data, an algorithm predicting the trend of heat capacity with temperature based on zero-Kelvin properties was derived by Zienert and Fabrichnaya [30]. The algorithm was also implemented as a set of Python classes scripts called cp-tools, which is described elsewhere [31]. Given the available thermophysical data at low temperature (T > 0 K), the developed algorithm can also be used for prediction the melting point of substances.

4.2.2 Models and Gibbs Free Energies

Since the Gibbs energy is described as a function of temperature, pressure, and composition, the Gibbs energy of a stoichiometric compound (or a stable end-member of a phase) is defined as follows

$$\begin{aligned}G\left( {N,P,T} \right) &= {\Delta _f}H_{298.15}^ \circ + \int\limits_{298.15}^T {{C_p}dT} - T\left( {S_{298.15}^ \circ + \int\limits_{298.15}^T {\frac{{{C_p}}}{T}dT} } \right) \\& \quad+ \int\limits_1^P {VdP}\\ \end{aligned}$$

(4.2)

where ${\Delta }_{f}{H}_{298.15}^{^\circ }$ is the enthalpy of formation of the compound at a standard state of 298.15 K and 1 bar, ${S}_{298.15}^{^\circ }$ is the standard entropy of the compound at 298.15 K and 1 bar, $T$ is temperature in K, and ${C}_{P}$ is the heat capacity at constant pressure.

For isobaric conditions, the pressure contribution ${\int }_{1}^{P}VdP$ can be omitted from Eq. (4.2) and it is not considered in thermodynamic assessments within the current project.

According to the NIST database [32], specific heat capacity at constant pressure is often expressed as a power series expansion in T of the type

$${C}_{P}=a+bT+c{T}^{-2}+d{T}^{2}+e{T}^{-3}+\dots$$

(4.3)

where a, b, c, d, and e are the parameters.

Solid solutions and stoichiometric phases with homogeneity ranges are assumed to be substitutional and the compound energy formalism (CEF) [33] is suggested in this case to model thermodynamic properties and to describe the composition and temperature dependences of the Gibbs energy. This means that a mathematical expression such as the CEF is more general than the actual physical model and can be applied to various constituents with different behavior in a phase. It has been shown that the CEF is well suited to model solid solutions with two or more distinct sub-lattices. Furthermore, it allows for cations and anions of different valances to mix in different sub-lattices, corresponding to the structure of a solid solution [1].

The simplest substitutional model presents the case when species are mixing in one possible site as ${(A,B)}_{1}$. This model is applied for the disordered solid solution phases bcc_A2 and fcc_A1 and for the liquid phase of the Al–Fe system as ${({\text{Al}},{\text{Fe}})}_{1}$. The Gibbs energy is then

$${G}_{m}=\sum_{i}^{n}{x}_{i}{^\circ G}_{i}+RT\sum_{i}^{n}{x}_{i}{\text{ln}}({x}_{i})+{}^{{\text{E}}}{G}_{m}+{}^{mag}{G}_{m}$$

(4.4)

where ${x}_{i}$ is the mole fraction of component i, ${^\circ G}_{i}$ is the Gibbs energy of end-member, R is the ideal gas constant, ${}^{{\text{E}}}{G}_{m}$ is the excess Gibbs energy, and ${}^{mag}{G}_{m}$ is the magnetic contribution to the Gibbs energy due to the magnetic ordering. The first term in Eq. (4.4) corresponds to the mechanical mixture, the second term is the contribution from the configurational entropy of mixing for the solution.

The binary excess energy can be expressed by

$${}^{{\text{E}}}{G}_{m}=\sum \limits_{i=1}^{n-1}\sum \limits_{j>i}^{n}{x}_{i}{x}_{j}{L}_{ij}$$

(4.5)

where i and j are the components and ${L}_{ij}$ is the regular-solution parameter representing the interaction energy between i and j. The regular-solution parameter can be expressed by Redlich–Kister equation [34]

$${L}_{ij}=\sum \limits_{v=0}^{k}{({x}_{i}-{x}_{j})}^{v}\cdot {{}^{v}L}_{ij}$$

(4.6)

where ${{}^{v}L}_{ij}$ can be temperature-dependent.

For element or compound having magnetic ordering, an additional term ${}^{mag}{G}_{m}$ accounting magnetic contribution to the Gibbs energy is included in Eq. (4.4) according to Ingen [35] and Hillert and Jarl [36]

$${}^{mag}{G}_{m}=RT{\text{ln}}\left(\beta +1\right)f(\tau ),$$

(4.7)

where $\beta$ is the average magnetic moment, and $\tau$ is the ratio $T/{T}_{cr}$ where ${T}_{cr}$ is the critical temperature (the Curie temperature for ferromagnetic materials or the Neel temperature for antiferromagnetic materials). For the binary Al–Fe system, for example, the concentration dependencies of ${T}_{cr}$ and $\beta$ are expressed as

$${T}_{cr}={x}_{{\text{Al}}}{T}_{{\text{Al}}}^{0}+{x}_{{\text{Fe}}}{T}_{{\text{Fe}}}^{0}+{x}_{{\text{Al}}}{x}_{{\text{Fe}}}{T}_{cr,i}^{{\text{Al}},{\text{Fe}}},$$

(4.8)

$$\beta ={x}_{{\text{Al}}}{\beta }_{{\text{Al}}}^{0}+{x}_{{\text{Fe}}}{\beta }_{{\text{Fe}}}^{0}+{x}_{{\text{Al}}}{x}_{{\text{Fe}}}{\beta }_{i}^{{\text{Al}},{\text{Fe}}},$$

(4.9)

where ${T}_{cr,i}^{{\text{Al}},{\text{Fe}}}$ and ${\beta }_{i}^{{\text{Al}},{\text{Fe}}}$ are the parameters to be optimized.

For phases where species can mix on two sublattices, a two-sublattices model in the form of compound energy formalism should be used to describe the Gibbs energy of the phase. This is also applicable to describe the liquid phase using a partially ionic two-sublattice model [37, 38]. The model can be written as ${({i}_{1},{i}_{2},\dots )}_{{a}_{1}}{({j}_{1},{j}_{2},\dots )}_{{a}_{2}}$, where i and j are the constituents on the first and the second sublattices, respectively. The Gibbs energy is then expressed using the site fraction of the constituents ${y}_{i}$ instead of the mole fraction as

$$\begin{aligned}{G}_{m}&=\sum \limits_{i}\sum \limits_{j}{y}_{i}^{{a}_{1}}{y}_{j}^{{a}_{2}}\cdot {^\circ G}_{i:j}+RT({a}_{1}\cdot \sum \limits_{i}{y}_{i}{\text{ln}}\left({y}_{i}\right)+{a}_{2}\cdot \sum \limits_{j}{y}_{j}{\text{ln}}\left({y}_{j}\right))\\& \quad+{}^{{\text{E}}}{G}_{m}\\ \end{aligned}$$

(4.10)

The excess Gibbs energy is derived in a similar way as for the substitutional model

$${}^{{\text{E}}}{G}_{m}={y}_{{i}_{1}}{y}_{{i}_{2}}{y}_{{j}_{1}}\cdot {L}_{{i}_{1},{i}_{2}:{j}_{1}}$$

(4.11)

with

$${L}_{{i}_{1},{i}_{2}:{j}_{1}}=\sum \limits_{v=0}^{n}{({y}_{{i}_{1}}-{y}_{{i}_{2}})}^{v}\cdot {{}^{v}L}_{{i}_{1},{i}_{2}:{j}_{1}}$$

(4.12)

The Gibbs energy for models with three and more sublattices can be described in a similar way giving more complicated the excess Gibbs energy terms.

Note that if the Neumann–Kopp rule applies (the heat capacity data of a compound is unavailable and it is an average of the heat capacity of the constituting elements), the Gibbs energy, ${G}_{{A}_{a}{B}_{b}}$, of a stoichiometric phase ${A}_{a}{B}_{b}$ is modeled as follows

$${G}_{{A}_{a}{B}_{b}}=a{GHSER}_{A}+b{G}{H}{S}{E}{R}_{B}+{{\text{v}}}_{1}+{{\text{v}}}_{2}T$$

(4.13)

where ${GHSER}_{i}$ is the Gibbs energy of the component $i$ given relative to the enthalpy of $i$ in its stable structure, ${H}_{i}^{SER}$; ${{\text{v}}}_{1}$ and ${{\text{v}}}_{2}$ are parameters to be optimized.

4.2.3 Optimization

The optimization methodology of the CALPHAD method can be simplified to the following steps:

Collection and critical evaluation of all available experimental data (crystallographic data for phases, phase equilibria data, thermodynamic data),

Selection of thermodynamic model for phase description considering its crystallographic information on Wyckoff positions and constituent distribution,

Determination of the parameters to be optimized. Accounting for the temperature dependence of the parameters for the end-members and the introduction of mixing parameters for the Gibbs energy description of the solution phases,

Optimization of the thermodynamic parameters considering all available experimental and theoretical data and setting their weights of influence,

Saving the derived Gibbs energy expressions with the optimized parameters into thermodynamic databases,

Calculation of phase diagrams and various phase equilibria using the thermodynamic databases.

4.3 Databases Development and Their Application

The main objective of the research from the very beginning was a development of thermodynamic databases which may be used as a tool for modeling interactions at the interface between the ceramic filter and the melt. As long as two filtration processes were proposed, for steel and aluminum melt, two independent complex filter systems had to be investigated followed by their thermodynamic description. The following filter systems to be developed can be highlighted:

Database development for Al-melt processing
- Database development for oxide systems MgO–Al₂O₃, TiO₂–Al₂O₃, SiO₂–Al₂O₃ [12], MgO–Al₂O₃–SiO₂ [12], Al₂O₃–MgO–TiO₂ to model interactions between coatings and inclusions in Al-melt,
- Oxide systems TiO₂–SiO₂, Al₂O₃–TiO₂–SiO₂, MgO–TiO₂–SiO₂ to develop databases serving as bridges linking important sub-systems,
- Complex Al–Ti–Mg–Si–O database with an emphasis on oxide system Al₂O₃–MgO–TiO₂–SiO₂ to predict phase relations between complex functional filter system, coatings, and inclusions,
- Complex metallic Al–Fe–Mg–Si database to predict phase relations between complex functional filter system, coatings, inclusions and molten Al-based alloy.
Database development for steel processing
- Database development for oxide systems MgO–Al₂O₃, FeO_x–Al₂O₃, MnO_x–Al₂O₃ to model interactions between spinel MgAl₂O₄ and Al₂O₃ coating system and nonmetal inclusions. Thermodynamic database for steel is available. Therefore, development of thermodynamic description of oxide system makes it possible to simulate interaction between coatings and steel.
- Introduction of carbon and oxycarbides into the systems for accounting influence of carbon on phase relations in carbon containing coatings.
- Database development for the TiO₂–Al₂O₃, TiO₂–ZrO₂ [39], Al₂O₃–TiO₂–ZrO₂ systems to model interactions with inclusions and between coating and filter in case of Al₂O₃ + TiO₂/ZrO₂ filter system.

Below the systems and the corresponding thermodynamic databases are discussed in detail. Note that some of the binaries that are key sub-systems for both filter systems are discussed once in the order they are mentioned. In case of the aluminum melt filtration process, thermodynamic description of the Al-based metallic systems is also discussed. Possible applications of the derived thermodynamic databases are also discussed in line with the experimental observations within the whole project.

4.3.1 Database Development for Al-Melt Processing

In context of the project, spinel MgAl₂O₄ was suggested as one of the possible coatings for Al₂O₃–C active filter for steel and for Al₂O₃ filter for Al purification processes [83]. Therefore, thermodynamic properties of spinel and phase relations in the MgO–Al₂O₃ system had to be considered. The thermodynamic parameters for the MgO–Al₂O₃ system from the description of Hallstedt [13] were reassessed by Zienert and Fabrichnaya [41] based on new evaluation of literature data and own experimental investigation using XRD, SEM/EDX, and DTA. Available experimental data on inversion degree for stoichiometric spinel MgAl₂O₄ were critically analyzed and considered for the parameters optimization. Melting of spinel was investigated using high temperature DTA. The calculated phase diagram of the MgO–Al₂O₃ system and the temperature dependence of degree of inversion for spinel are shown in Fig. 4.2a and b, respectively, along with the literature data.

Later, the influence of different filter surface chemistries (Al₂O₃, spinel MgAl₂O₄, mullite 3Al₂O₃⋅2SiO₂, SiO₂, and TiO₂) on the properties of foam filters were discussed [9] and the corresponding filtration efficiency was evaluated [40]. All investigated filter coatings exhibited quite high filtration efficiency. It was shown that the TiO₂ coatings reacted with Al alloy melt [40]. The wettability of AlSi7Mg alloy on oxide ceramics (Al₂O₃, MgAl₂O₄, mullite, and TiO₂) was measured by Fankhänel et al. [10] and contact angles were found higher than 90° for all investigated ceramics. In case of TiO₂, it was found that the contact angle was quickly decreasing with the time and then leveled out at 101°. The investigation of reaction zone indicated reduction of TiO₂, presence of Ti and Si, and formation of Al₂O₃ layer. Moreover, rutile coatings deposited on corundum were supposed to filtrate actively and reactively spinel MgAl₂O₄ and Al₂O₃ inclusions present in Al alloy melt. Therefore, the thermodynamic database had to be developed for the Al–Ti–O system for modelling interaction between Al melt and TiO₂ coatings on Al₂O₃ filters.

A thermodynamic assessment of the Al–Ti–O system was done by Ilatovskaia et al. [42, 43] using available binary databases and new experimental data regarding the Al₂O₃–TiO₂ system. It should be noted that the thermodynamic description of the Ti–O system by Hampl and Schmid-Fetzer [44] was accepted for solid phases, but two-sublattice partially ionic model was used for the liquid phase and therefore the parameters for liquid were assessed, as well as the parameters for Magneli phase Ti₂₀O₃₉ were slightly modified [42]. The thermodynamic descriptions for the Ti–Al [45] and Al–O [47] were accepted without modifications. Available experimental data on cation disordering (degree of inversion) for pseudobrookite Al₂TiO₅ were critically analyzed and accounted in the parameters optimization [50]. The phase relations in the Al₂O₃–TiO₂ system were verified experimentally. The stability range of Al₂TiO₅ was experimentally studied by Ilatovskaia et al. [42]. The Al₂TiO₅ formation was determined at 1553 K as low phase stability limit. Peritectic character of Al₂TiO₅ melting was established in the Al₂O₃–TiO₂ system at 2123 K by the high-temperature DTA experiments followed by SEM/EDX investigation of the obtained microstructures. The calculated phase diagram of the Al₂O₃–TiO₂ system and the temperature dependence of degree of inversion for stoichiometric pseudobrookite Al₂TiO₅ are shown in Fig. 4.3a and b, respectively, along with the literature data.

The derived database for the Al–Ti–O system [42] was used to predict phase relations between functional rutile coatings and molten Al alloy. By thermodynamic simulations, it was shown that TiO₂ should be reduced by molten aluminum forming Al₂O₃, while the reduced titanium should react with Al to form Al₃Ti. The results were presented and compared with annealing experiments of Salomon et al. [48] confirming formation of Al₃Ti and Al₂O₃. Presence of small amount of Ti₂O₃ was indicated experimentally and it was shown to decrease with the time of annealing. Therefore, Ti₂O₃ was intermediate product forming during TiO₂ reduction.

The experiments performed using Al alloy containing Mg and Si indicated formation of MgTiO₃ phase and absence of Al₃Ti phase [48]. However, Ti₅(Si,Al)₃, Ti(Al,Si)₃ and ternary phases could form. Therefore, thermodynamic database of the complex Al–Ti–Mg–Si–O system is necessary to elucidate influence of Mg content in Al alloys to interface reactions between TiO₂ coating and Al-based alloy melt. By step-by-step approach, the thermodynamic descriptions for the oxide parts of the Al₂O₃–MgO–TiO₂, Al₂O₃–TiO₂–SiO₂, and MgO–TiO₂–SiO₂ systems had to be derived for further joint usage. The thermodynamic description of the forth key oxide ternary MgO–Al₂O₃–SiO₂ sub-system was carried out by Fabrichnaya et al. [12], however the liquid phase model should be changed and the parameters need to be optimized.

Moreover, the thermal shock tests of the Al₂O₃-rich MgAl₂O₄-spinel ceramics were done [49]. It was found that the addition or in situ formation of Al₂TiO₅ could enhance the performance of the Al₂O₃-rich spinel refractories by improving their thermal shock resistance.

Preliminarily, as a key binary sub-system, thermodynamic assessment of the MgO–TiO₂ system was carried out based on own phase diagram data and experimental thermodynamic data [43]. Available data on the cation disordering of the intermediate compounds Mg₂TiO₄ and MgTi₂O₅ as well as the measured heat capacities data of the intermediate phases (Mg₂TiO₄, MgTiO₃, and MgTi₂O₅) were also took into account during optimization of the thermodynamic parameters.

Phase relations in the Al₂O₃–MgO–TiO₂ system were investigated in detail using DTA followed by SEM/EDX and XRD investigations [43]. The solid-state reaction, Al₂O₃ + TiO₂ + Spinel s.s. = Pseudobrookite s.s., was indicated at 1433 K by XRD study of the stepwise annealed samples. Two series of continuous solid solutions in the Al₂O₃–MgO–TiO₂ system were found: MgAl₂O₄–Mg₂TiO₄ (spinel s.s.) and Al₂TiO₅–MgTi₂O₅ (pseudobrookite s.s.) that agrees with the literature data [46]. A miscibility gap for the spinel join with maximum at 1648 ± 20 K [46] was confirmed. Two invariant reactions on the liquidus projection, eutectic L = MgTiO₃ + Psbk + Sp and transitional-type L + Al₂O₃ = Sp + Psbk, were found at 1875 K and 2006 K, respectively, using DTA followed by SEM/EDX microstructure investigations. The experimental data were then used to develop the thermodynamic description of the Al₂O₃–MgO–TiO₂ system [50]. The calculated liquidus projection and sub-solidus isothermal section at 1550 K of the Al₂O₃–MgO–TiO₂ system are shown in Fig. 4.4a and b, respectively.

The thermodynamic description of the pseudo binary TiO₂–SiO₂ system was derived based on own experimental study using XRD, SEM/EDX, and DTA as well as available literature data [51]. The reactions occurring in the system including liquid immiscibility were investigated by DTA experiments in air or under He atmosphere. The calculated phase diagram of the TiO₂–SiO₂ system under normal and reduced oxygen conditions is shown in Fig. 4.5a.

Later on, considering the newly obtained results for the TiO₂–SiO₂ system, phase equilibria in the Al₂O₃–TiO₂–SiO₂ system were investigated experimentally in air by Ilatovskaia et al. [52]. Solid-state phase relations were characterized using XRD and SEM/EDX and the solid-state invariant reaction SiO₂ + Al₂TiO₅ ↔ Al₆Si₂O₁₃ + TiO₂ at 1743 K was observed. The invariant reactions occurring on the liquidus projection of the system were determined by DTA followed by SEM/EDX examination of the obtained microstructures. Consequently, the experimentally observed data were considered for thermodynamic assessment of the system [51]. The calculated liquidus projection is shown in Fig. 4.5b.

Phase relations in the MgO–TiO₂–SiO₂ system were investigated in air in the range of 1500–1900 K using XRD, SEM/EDX, and DTA [85]. Similar to the ternary oxide systems described above, solid-state reaction occurring at 1625 K was observed, MgSiO₃ + TiO₂ = SiO₂ + MgTi₂O₅. Moreover, among seven invariant reactions occurring on the liquidus projection, three of eutectic type were verified experimentally: L = Mg₂SiO₄ + MgTiO₃ + MgTi₂O₅ (E₁) at 1822 K, L = MgSiO₃ + Mg₂SiO₄ + MgTi₂O₅ (E₂) at 1704 K, and L = MgSiO₃ + SiO₂ + MgTi₂O₅ (E₃) at 1690 K. During the thermodynamic optimization of the system, the Gibbs energy of the MgTi₂O₅ phase was deliberately adjusted by considering SiO₂ solubility to make it more stable than MgSiO₃ in order to keep the solid-state reaction. Therefore, the extension of MgTi₂O₅ into the ternary system is more pronounced compared to the experimental observation of an insignificant solubility of SiO₂ in MgTi₂O₅. Note that similar approach was applied for the Gibbs energy of Al₂TiO₅ against Al₆Si₂O₁₃ in the Al₂O₃–TiO₂–SiO₂ system due to the solid-state reaction. The calculated isothermal section at 1673 K and liquidus projection of the MgO–TiO₂–SiO₂ system are shown in Fig. 4.6.

To model the interactions between ceramic filter material and Al melt in a proper way, the thermodynamic assessment of the Al-based alloy itself had to be also undertaken. The Fe content in Al-based alloys is low, but the intermetallic compounds forming in the Al–Fe and Al–Fe–Si systems substantially influence mechanical properties of alloys. Despite a number of thermodynamic assessments for the Al–Fe system [53], thermodynamic functions of intermetallic compounds were simplistically modelled using the Neumann–Kopp rule as sum of heat capacities for elements. Therefore, the thermodynamic reassessment of the Al–Fe system was undertaken using newly obtained experimental data. Heat capacity of Fe₂Al₅ (η) phase was experimentally measured between 235 and 1073 K using differential scanning calorimetry (DSC) [54]. It was found that at temperatures between 523 and 553 K phase transformation occurred in the Fe₂Al₅ phase. It was assumed that the low temperature modification of this phase has an ordered structure. The heat capacity of Fe₂Al₅ was measured at high temperatures up to 1390 K and at low temperatures between 120 and 823 K [55]. The other intermetallic phases Fe₂Al (ζ) and Fe₄Al₁₃ (θ) were studied from 210 K to melting points as well as B2 ordered phase [55]. The measurements for B2 phase were compared with high temperature adiabatic calorimetry data and good agreement confirmed reliability of C_p measurements at high temperatures. Based on the measured data for heat capacity of intermetallic compounds and their homogeneity ranges together with experimental information from literature thermodynamic parameters of the Al–Fe system were assessed [56]. Later on, the thermodynamic description of the Fe₂Al₅ (η) phase was reconsidered accounting newly reported data on the crystal structure of the phase [57]. Moreover, in the assessment [56], the model inconsistent with the crystal structure was used to describe the Fe₅Al₈ (ε) phase structure which led to the stabilization of Fe₅Al₈ at temperatures above 2300 K. Therefore, the thermodynamic parameters of the η, ε, and θ phases in the Al–Fe system were reassessed [86]. The calculated phase diagram of the Al–Fe system is presented in Fig. 4.7.

A thermodynamic dataset for the description of the Al–Fe–Si system for the temperature range below 1073 K was derived by Zienert and Fabrichnaya [58]. The system includes at least 11 known ternary compounds which descriptions were combined from several resources, i.e. Al₁₃Fe₄ [59], τ₂, τ₄, τ₅, and τ₆ [60], τ₁, τ₃, τ₇, τ₈, τ₁₀, and the liquid phase [61]. Thermodynamic parameters of these phases were optimized to reproduce available experimental data. The Al₆₄Fe₂₆Si₁₀-τ₁₁ phase was modelled for the first time in Ref. [58]. With the derived dataset, two reactions were predicted, (i) τ₁₁ + τ₂ + τ₃ = τ₁₀ at 795.2 °C and (ii) τ₁₁ = τ₁ + τ₁₀ + Al₁₃Fe₄ at 683.7 °C. However, the real nature of these transitions between τ₁₀ and τ₁₁ are still unclear and further experimental investigations are necessary. The calculated isothermal section of the Al–Fe–Si system at 727 °C is shown in Fig. 4.8a. The thermodynamic descriptions of pure element were accepted from SGTE Unary Database [62]. Note that the heat capacities of intermediate phases were described using the Neumann–Kopp rule and therefore heat capacities based on more realistic assumption or based on experimental data are desirable. Regarding this, a single-phase sample of AlFeSi-τ₄ was produced and the heat capacity was measured in the single-phase region between 640 and 760 °C. It was shown that use of the Neumann–Kopp rule results in unphysical kink in the temperature dependence of heat capacity of compounds containing a low melting element, i.e. Al. Besides, the heat capacity of the investigated ternary AlFeSi-τ₄ phase was calculated using DFT method [63]. The calculated results are in a very good agreement with the experimental findings and the reasons for deviation from the Neumann–Kopp rule were discussed.

The description of the Al–Mg–Si system is accepted from Ref. [64]. Two other ternary systems Al–Mg–Fe and Si–Mg–Fe were not assessed due to the lack of data and simply combined from the binary descriptions [58]. It should be noted that no ternary phases were found in these systems. Ternary descriptions were then combined into the quaternary description of Al–Mg–Fe–Si.

In the frame of thermodynamic database development for metallic Al-based alloy the solidification behavior of the A356 alloy was investigated experimentally (DTA, XRD, SEM/EDX, SEM/EBSD) and theoretically [58]. It was found experimentally that the AlFeMgSi-π phase solidifies in A356 alloy, however the thermodynamic description of the phase was not included into the dataset for the Al–Fe–Mg–Si system due to the lack of experimental data on the phase. The derived dataset was then used to model phase relations in Al-alloy A356. The calculated phase fraction diagram of the A356 alloy composition is presented in Fig. 4.8b.

As an application issue, the combined datasets of the MgO–Al₂O₃ and of the Al–Fe–Mg–Si systems were used to predict phase relations at the interface between AlSi7Mg0.6 alloy (A356) and alumina filters. The formation of magnesia-alumina-spinel was indicated by thermodynamic calculations. The results were shown and compared with SPS melting experiments provided by Salomon et al. [65]. Moreover, the interaction of molten AlSi7Mg0.6 alloy with mullite and amorphous silica were investigated using SPS [66]. It was found that amorphous SiO₂ as well as SiO₂ originating from mullite decomposition were reduced by Al and Mg. The combined datasets of the Al₂O₃–Fe₂O₃–FeO and Al–Fe–Si–Mg systems were used to predict interactions during contact of molten AlSi7Mg0.6 alloy with mullite and amorphous silica. The formation of Al₂O₃, MgAl₂O₄ spinel and metallic Si were predicted by thermodynamic modelling. The results of calculation were in good agreement with experimental data of SPS melting [66]. In detail description of the Al₂O₃–Fe₂O₃–FeO system is given in the next section.

This advanced thermodynamic description could be introduced into already published description of the Al–Mg–Si–Fe–Mn system [67]. The thermodynamic description of this system (including also Cr) could be used for modeling support of experimental study of Dietrich et al. [68] who investigated influence of Mn and Cr additives to microstructures formed during solidification of Al-alloy melt.

4.3.2 Database Development for Steel Processing

Since the carbon-bonded alumina materials have been proposed as a promising next generation ceramic filter material for steel melt filtration [3], the possibility of a carbothermic reaction between alumina and carbon was discussed by means of thermodynamic calculations considering the Fe–Al₂O₃–Al corner of the Al–Fe–O system [69]. It was also observed experimentally that the equilibrium between alumina and liquid iron is unstable due to the constant formation of CO, and alumina dissolves in liquid iron, increasing the concentration of aluminum in the melt.

A further detailed thermodynamic description of the Al₂O₃–Fe₂O₃–FeO system was developed by Dreval et al. [70] taking into account all available literature data. Available experimental data on phase equilibria at different temperatures and oxygen partial pressures, calorimetric and vapor pressure data, the degree of inversion of the spinel phase as well as an extension of homogeneity range in spinel phase by the dissolution of Al₂O₃ and Fe₂O₃ were critically reviewed. Thermodynamic modelling of spinel phase based on compound energy formalism allowed taking into account inversion degree in the FeAl₂O₄–Fe₃O₄ solid solution and deviation from stoichiometry in the direction of Al₂O₃ and Fe₂O₃. The calculated isothermal section at 1523 K and phase relations as dependence of ${\text{log}}{p}_{{{\text{O}}}_{2}}$ on metal ration Fe/(Fe + Al) at 1553 K in the Al₂O₃–Fe₂O₃–FeO system are shown in Fig. 4.9.

An excellent example of the implementation of these databases is thermodynamic simulation of the interaction between carbon-free and carbon-bonded Al₂O₃ and Armco iron [71]. With the combined use of the databases for Fe–Al₂O₃–Al [69], Al₂O₃–Fe₂O₃–FeO [70], and Al₂O₃–Al₄C₃–AlN [72], an increase in Al-containing species in the gas phase with a decrease in oxygen partial pressure and the formation of solid Al₄C₃ and Al₄O₄C at a low oxygen partial pressure were predicted. Those were also discussed considering experimental data, and in this case, further whiskers formation was observed [71]. In another work, the combined database for the Al–Mg–Fe–O system [23, 70, 73] was used to simulate the interaction of Al₂O₃–MgAl₂O₄ substrate and Armco iron. The results of calculations showed that liquid Fe is enriched mainly in aluminum and Fe is negligible dissolved in MgAl₂O₄ at a low oxygen partial pressure which was subsequently confirmed experimentally [74].

Subsequently, carbon-bonded alumina filters with active or reactive coatings for steel melt filtration were discussed. In the case of reactive filters based on carbon bonded MgO, the assumption of gaseous Mg particles was supported by experimental findings of produced secondary MgO fibers on the filter surface [4]. Moreover, the combination of alumina and magnesia in carbon-bonded filters results in the in situ formation of spinel MgAl₂O₄ which acts as an active coating and is suitable to remove inclusions with the same crystal structure. Also, the formation of spinel leads to volumetric expansion that would counteract the shrinkage phenomenon [75, 76]. The thermodynamic description of the Mg–Al–O–C system would be particularly useful in this context. As an important part, the thermodynamic description of the oxide MgO–Al₂O₃ system was discussed above.

To optimize the reactions taking place during filtration and their effects on the steel melt purification in more detail, the spinel (Fe,Mn,Mg)Al₂O₄ coating system applied on Al₂O₃–C filters was further investigated [77]. It was shown that the subsequent interaction of coating with molten steel leads to the development of multicrystal structures on the filter surface, which stem from interfacial reactions between coating materials, molten steel, and inclusions. Therefore, the thermodynamic database had to be developed by combining data on spinel phases of MgAl₂O₄ [41], FeAl₂O₄ [70], and MnAl₂O₄. The thermodynamic description of the Al₂O₃–MnO system was developed by Ilatovskaia and Fabrichnaya [78] to collect the remaining information requested. Phase relations were investigated experimentally in the range of 1373–2053 K using XRD, SEM/EDX, and DTA and the heat capacity measurements of stoichiometric MnAl₂O₄ were carried out at 250–873 K using DSC. The results obtained were considered along with the available literature data on the degree of inversion of stoichiometric spinel MnAl₂O₄, standard entropy, and its Gibbs energy of formation from oxides. The calculated phase diagram of the Al₂O₃–MnO system and the temperature dependence of degree of inversion for stoichiometric spinel MnAl₂O₄ are shown in Fig. 4.10a and b, respectively, along with the literature data.

Gehre et al. [7] found that TiO₂ and ZrO₂ additions to the alumina-based refractories improve the thermal shock resistance of alumina and increase its corrosion resistance against molten coal slags. The formation of a protective spinel MgAl₂O₄ layer, which stops the slag penetration and the corrosion process, was shown to occur due to the reaction of alumina matrix with MgO of the slag in the presence of titania and zirconia.

Moreover, a modification of Al₂O₃ surface using TiO₂ and ZrO₂ additives was suggested for the steel filtration [79]. Enhanced thermal stability of Al₂TiO₅ provided by ZrTiO₄ phase was indicated [80]. Therefore, the thermodynamic database of the Al₂O₃–TiO₂ system had to be extended by including ZrO₂. As a separate work, a thermodynamic description of the TiO₂–ZrO₂ system using the CALPHAD approach was developed based on own experimental data and from the literature [39]. Experimental and theoretical work on the system Al₂O₃–ZrO₂ was available after Fabrichnaya et al. [81] and Lakiza et al. [82]. The derived thermodynamic descriptions of the pseudo binary TiO₂–ZrO₂ and Al₂O₃–ZrO₂ systems were further accepted for thermodynamic assessment of the high-order system.

The CALPHAD assessment of the Al₂O₃–TiO₂–ZrO₂ system was done by Ilatovskaia et al. [84]. The formation of t-ZrO₂–ZrTiO₄–Al₂TiO₅ and ZrTiO₄–Al₂TiO₅–TiO₂ assemblages was indicated by thermodynamic calculations. Isothermal sections were calculated and the results of calculations for the system were checked experimentally by phase equilibration in the temperature range of 1530–1893 K. Using DTA and equilibration experiments two solid-state reactions at 1593 K and 1648 K were found. Three invariant eutectics were found on the liquidus surface in the range of 1909–1978 K using DTA followed by SEM/EDX microstructure investigation. Obtained experimental results were used for assessment of thermodynamic parameters. The calculated isothermal section at 1703 K as well as the liquidus projection of the Al₂O₃–TiO₂–ZrO₂ system are shown in Fig. 4.11.

The corrosion of carbon containing refractories based on titania-zirconia doped alumina for steel casting was investigated [79]. It was shown that 9 vol.% carbon content is enough to form a functioning matrix material for which the wetting was reduced and corrosion reactions inhibited from the beginning. The calculations using expanded thermodynamic database of the Al₂O₃–TiO₂–ZrO₂–C system could provide new information for a final evaluation of refractories for steel ingot casting considering the oxygen content of the melt.

4.4 Conclusion

Since its launch the project has achieved remarkable results on thermodynamic modeling of the systems related to the metal melt filtration process. Advanced methods of computational thermodynamics were applied for development of a complex databases used to predict and understand mechanisms of chemical reactions occurring in the filter material, coatings, inclusions, molten metal and in-between. Moreover, control and optimization as well as pondering new solutions of technological issues could be suggested.

Considering two independent metal melt filter processes, for steel and aluminum melt, two complex datasets were developed. For Al-melt filtration process, the complex Al–Ti–Mg–Si–O database with an emphasis on oxide part of Al₂O₃–MgO–TiO₂–SiO₂ in order to predict phase relations between complex functional filter system, coatings, and inclusions was developed. Furthermore, the thermodynamic database for metallic Al–Fe–Mg–Si system used in combination with oxide database make it possible to simulate phase relations between filter system and molten Al-based alloy. For the steel filtration process, the complex dataset related to the Al₂O₃–MgO coating system applied on Al₂O₃–C filters was developed. Iron oxides were included into the database to account their presence as inclusions and interactions with coatings. An independent database for the Al₂O₃–TiO₂–ZrO₂ system was also developed for the modeling of interaction in the Al₂O₃ coatings modified by Ti and Zr oxides. Regarding development of thermodynamic datasets for oxides, five binary and four ternary systems were investigated experimentally and assessed thermodynamically using the CALPHAD approach for applications in cooperation with other sub-projects.

Acknowledgements

The authors gratefully acknowledge the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) for financial support of the investigations, which were part of the Collaborative Research Center Multi-Functional Filters for Metal Melt Filtration–A Contribution towards Zero Defect Materials (Project-ID 169148856–SFB 920, subproject A03). Furthermore, the authors would like to thank Dr. Peter Franke, Dr. Liya Dreval, and Dr. Tilo Zienert for scientific support and co-working in the sub-project A03 in the frame of CRC 920.

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Vorheriges Kapitel Ceramic Filter Materials and Filter Structures with Active and Reactive Functional Pores for the Aluminum Melt Filtration

Nächstes Kapitel Structural and Thermodynamic Properties of Filter Materials: A Raman and DFT Investigation

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Titel: Thermodynamic Assessment as a Tool for Modeling Interactions at the Interface Between Ceramic Filter and Melt
verfasst von: Mariia Ilatovskaia
Olga Fabrichnaya
Verlag: Springer International Publishing
Buch: Multifunctional Ceramic Filter Systems for Metal Melt Filtration
Print ISBN: 978-3-031-40929-5

Electronic ISBN: 978-3-031-40930-1

Copyright-Jahr: 2024
DOI: https://doi.org/10.1007/978-3-031-40930-1_4

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