19. Thermodynamic Modelling in the Frames of the TRIP-Matrix-Composite Development

Knowledge of phase equilibria and the underlying thermodynamics play a crucial role in the understanding of development and application of materials. Thereby, phase diagrams represent a kind of roadmaps for materials development and provide important information for understanding of technological aspects of design and usage of materials. However, the most of the modern materials consist of more than two or three components, what makes the graphical representation of these systems challenging and complex. Moreover, there is only limited information for many multicomponent systems. Method of computational thermodynamics is very powerful tool for prediction and extrapolation helping to fill these gaps of the areas without experimental information [1].

In the frame of a development of an innovative composite material, thermodynamic simulation using the CALPHAD method (Calculation of Phase Diagrams) can be used in order to support an optimization of chemical composition of the alloy and to develop a production process.

The TRIP-Matrix-Composite is an example of innovative material, which is based on high-alloyed austenitic TRIP-steel and reinforcing ceramic particles of zirconia partially stabilized by MgO (Mg-PSZ). Thereby, thermodynamic calculations can provide information about the stable and metastable phase formation in the material as well as the accompanying energetic effects and basic information of the physico-chemical parameters of the manufacturing processes.

Metal Matrix Composites containing highly alloyed TRIP-steel as metallic component and MgO partially stabilized ZrO₂ as ceramic component are considered as promising new construction materials with high energy absorption. Under deformation metastable austenite transforms into martensite, which results in an increasing strength. It should be mentioned that MgO stabilized ZrO₂ also shows stress-induced martensitic transformation from tetragonal into monoclinic phase [2]. The increased toughness of this ceramic phase is attributed to a stress-induced transformation. For a good performance of the composite material a strong adhesion between the metallic and the ceramic components is required in order to transmit stresses between the different phases. The infiltration and powder metallurgy/sintering processes selected in the Collaborative Research Center 799 (CRC799) to produce Fe–ZrO₂ based TRIP matrix composites may cause heterogeneous reactions in the matrix materials, in the ceramic particles and at the interfaces that can significantly influence on the mechanical properties of final composite materials. This information can be used to derive the structure development in the constituent materials and their compatibility and long-term stability. Therefore, the CALPHAD method was applied in the CRC 799 for many years as a valuable tool for materials design as knowledge of the phases that are present in a material and their compositions is essential for modelling the behavior and properties. It was widely applied for optimization of chemical composition of steel matrix with following annealing improving of its microstructure [3], for prediction and understanding of the local deformation mechanisms [4], for modelling of interfacial reaction between steel matrix and ceramic particles [5], as well as for understanding of phase transformations of the metastable austenite into martensite in the Fe–CrMnNi–N–C model alloy [6]. Additionally, the CALPHAD method provided a basement for further modelling method concerning the development of the TRIP-Matrix-Composite i.e. thermo-mechanical modelling [7], simulation of electron beam welding [8] and phase field modelling.

This Chapter will consider a basement of computational thermodynamics, reveal experimental side of thermodynamic modelling and present the latest results concerning the TRIP-Matrix-Composite development.

Since the CALPHAD approach is a phenomenological method, its parametric functions must be assessed using experimental data before any prediction and/or extrapolation can be made. In order to get a maximum of information, all types of experimental measurements that are related to thermodynamic properties must be considered and assessed. Collected experimental data are applied for adjusting of optimized parameters of the Gibbs energy functions.

Thereby, the reliability and accuracy of the experimental data have to be critically evaluated taking into account, which one of the various experimental techniques was used. Measured experimental data can be roughly classified into a few principal types: “thermodynamic data” and “phase-diagram data” [9]. The most of thermodynamic data can be directly applied to describe Gibbs energy functions of individual phases, while experimental data on the phase relations can be used for optimization of those functions for reproducing of phase diagrams of the system and thermodynamic data within their uncertainty. Since the phase diagram is representing equilibrium states of the system corresponding to minimum of its Gibbs energy being the sum of the properties of the individual phases multiplied to their mole amount respectively [10] at various conditions the phase relations are dependent on thermodynamic properties of the individual phases. Optimization of the Gibbs energy functions is a complex procedure, which will be described further (Sect. 19.3.2).

Computational thermodynamics is powerful tool for solution of various problems in materials science, particularly used in the construction of phase diagrams [10]. At the beginning of the previous century, a thermodynamic modelling a phase diagrams of a metal-based system was firstly performed by Johannes van Laar using regular solutions models, what has evolved in more recent years to the CALPHAD (Calculation of Phase Diagrams) [13]. The CALPHAD method has been pioneered by American metallurgist Larry Kaufman since the 1970s [9, 14, 15]. Calculation of phase equilibrium is based on minimization of the Gibbs energy of the system which is the sum of the Gibbs energies of individual phases multiplied respectively to their mole amount or from equality of chemical potential for components in the equilibrated phases. The Gibbs energy of individual phase is described by thermodynamic model representing its dependence on temperature, pressure and composition [14]. Therefore, phase diagrams are related to the thermodynamic properties of individual phases which can be also determined experimentally using calorimetry, vapor pressure measurements and electrochemical data. These different kinds of data are used for optimization of thermodynamic parameters simultaneously to reproduce both phase diagrams and experimental thermodynamic data. The obtained set of thermodynamic descriptions of individual phases can be used to calculate different kinds of phase diagrams.

It should be noted that thermodynamic data of some components are very well determined and they are not optimized, the other parameters such as mixing parameters of solution phases and metastable end-members of solid solutions should be optimized. The thermodynamic properties of intermediate phases usually also need to be optimized. The aim of the CALPHAD method is to obtain a consistent description of all phases in the system reproducing the thermodynamic properties and phase diagrams within uncertainty of measurements. The self-consistent thermodynamic database allows predicting of the phase relations and thermodynamic properties in regions where experimental information is not available as well as calculation of metastable phase diagrams, calculation of diffusion-less transformation and simulations of non-equilibrium processes assuming local equilibration.

Methodology of the CALPHAD method and main principles of thermodynamic databases development are described in many fundamental books [9, 14‐16] and basics research [1, 17]. In this chapter, the main information about CALPHAD will be described very shortly.

In the beginning of the development of the new composite, an extensive thermodynamic database for steel-based materials (Fe, Mn, Cr, Ni, Ti, Mo, W, V, Si, C and N) was created in the frames of CALPHAD method. Therefore the main research point was focused on an optimization of the alloy for the matrix. Afterwards, focus of thermodynamic modelling was shifted to the development of a database for the ceramic materials (ZrO₂, MgO, Al₂O₃, FeO, Fe₂O₃, MnO, Mn₂O₃).

In the beginning of the project, there were currently several thermodynamic databases for Fe-based multicomponent systems that were developed for the modelling of specific processes in the respective steels. They were based on critical assessments of binary and ternary systems available in the literature. For example, the TCFE7 commercial database included 25 elements and many binary and ternary systems (http://​www.​thermocalc.​com/​Products/​Database). Moreover, this database contains descriptions of some solid oxide phases such as spinel, wustite and corundum in order to predict the tendency of different steels to oxidize. Additionally, there was the commercially available database TCOX, which contained 12 elements and descriptions of many oxide phases as well as the ionic melt, which describes both metallic and oxide melting behavior (http://​www.​thermocalc.​com/​Products/​Database). However, all commercial databases have reproduced most of important binary system such as Fe–Mn, Fe–Ni, Zr–Mn, Zr–Fe very poorly, what could not be accepted for deep process of materials design.

A non-commercial steel database, which was under development in group of B. Hallstedt, contained 8 elements Fe, Al, Mn, Nb, Si, V, C and N and was aimed for modelling phase equilibria in Mn-rich steels [21]. However, this database did not include Cr and Ni, which were very important for highly alloyed TRIP-steels. Therefore, the CRC 799 project required to develop a unique multicomponent steel database, which would fit all specific needs of design process in the fames of the TRIP-Matrix-Composite development.

A new thermodynamic database for steels containing eleven elements (Fe, Mn, Mo, Cr, Ni, Ti, Si, V, W, N, C), has been developed by P. Franke within the first period of the CRC project [22]. Thermodynamic description of one of the most important systems Fe–Cr–Ni was developed based on advanced thermodynamic modelling. Obtained thermodynamic description considered magnetic contribution and chemical ordering in the Fe–Cr–Ni system [22]. This thermodynamic dataset for the ternary system Cr–Fe–Ni which has been reported in the literature for the range from medium to high temperatures has been supplemented with datasets from the binary subsystems at lower temperatures. The magnetic and the chemical ordering transitions which are known from the binary Fe–Ni system were extrapolated into the ternary system Cr–Fe–Ni. The phase diagram of Cr–Fe–Ni alloys at temperatures below 773 K was predicted (Fig. 19.2). The magnetic contribution to the Gibbs energy of Ni-rich alloys induces a miscibility gap which appears in the binary phase diagram of Fe–Ni as a small triangle-like field ending in a tricritical point. In the ternary system, Cr–Fe–Ni the miscibility gap is present as a broad two-phase field in the vicinity of the composition FeNi₃. At lower temperatures, this miscibility gap participates in a sequence of changing equilibria when it interferes with the chemically ordered L₁₂ phase.

Several ternary systems in the Fe–Mn–Cr–Ni–Ti–Si–C–N system were accepted from literature data, checked for the consistency and published in LB series [23]. With this element selection calculations of the phase equilibria and modelling of the crystallization process using Scheil simulation for austenitic TRIP-steels became possible and reliable. Among the systems published in LB were Fe–Cr–Mn, Fe–Cr–Ni, Fe–Cr–C, Fe–Mn–C, Fe–Ni–C and others. The developed database covers a wide range of evaluated systems in comparison with other available databases. Thus, it also covers non-iron systems.

The second milestone was the interfacial interaction between Mg-PSZ and steel, which was experimentally studied by Franke et al. [5]. Experimental details (SPS pre-sintering, annealing in Ar etc.) were reported in [5]. SEM/EDX investigations demonstrated the formation of Mg₂SiO₄ at the interface between the ceramic component and steel. It was determined that Mg-PSZ contained SiO₂ impurities around of 2.4 mass%. It was stated, that another possible source for the SiO₂ could be the Si content within the TRIP-steel (~0.5 mass%). Thermodynamic calculations were performed to explain destabilization of Mg-PSZ and formation of Mg₂SiO₄ forsterite. The activity of MgO at the investigated temperature and the composition was calculated using the ZrO₂–MgO thermodynamic database available in literature [24]. The SiO₂ activity necessary for formations of silicates Mg₂SiO₄ and MgSiO₃ was calculated using the thermodynamic data from literature [25]. Experimental studies of an interaction between steel and pure ZrO₂ and between steel and CaO stabilized ZrO₂ showed that silicates did not form at the investigated conditions [5]. Thermodynamic calculations were also performed for the ZrO₂–SiO₂ and ZrO₂–CaO systems and ranges of the SiO₂ activity were determined at which silicates should form. The oxygen partial pressure was calculated at which the SiO₂ starts to form from Si dissolved in the steel. The corresponding limiting activity of Si in the TRIP-steel and the concentration of Si in the steel were calculated.

The ceramic material used in the present project is ZrO₂ stabilized by 3.4 mass% of MgO. A comprehensive thermodynamic assessment of the ZrO₂–MgO system was available in literature. However, all of the data were based on a substitutional model for the solid and liquid phases. Consequently, re-assessment based on the more advanced modelling using the compound energy formalism had to be performed. Additionally, it was experimentally found that an addition of Titanium can improve bonding between ZrO₂ ceramic particles and austenitic steel containing Mn, Cr and Ni [26]. Therefore, ceramic systems containing TiO₂ became one of the important tasks as well. Moreover, during the investigation of the interfacial interaction between Mg-PSZ and steel [5] it was found that the C–ZrO₂ (fluorite) was destabilized due to reaction between MgO and impurities in ceramic material such as Al₂O₃ and SiO₂. Therefore, systems with Al₂O₃ and SiO₂ became one of the main points.

Thermodynamic descriptions of the systems MgO–Al₂O₃ and MnO–Al₂O₃ based on the compound energy formalism for solid phases and partially ionic liquid model were available in literature [27, 28]. However, the model of the spinel phase in the MnO–Al₂O₃ system had to be extended by introducing an interstitial sublattice to be compatible with the model used for the MgO–Al₂O₃ system.

Many thermodynamic assessments for the systems containing TiO₂, Ti₂O₃, MgO, FeO, MnO and other oxides were performed in the group of A. D. Pelton (http://​www.​sgte.​org/​fact/​documentation/​FToxide). Solid phases were modelled by the compound energy formalism, while the liquid phase was described by a modified quasi-chemical model [29]. The database for ZrO₂-based systems was set up with the help of very limited experimental literature data. However, the ZrO₂ containing phases do not contain the chemical element Ti, which makes it impossible to calculate the interaction with titanium oxides, which are very important for the planned work. Commercial steel and oxide databases have been developed by the FactSage group (http://​www.​sgte.​org/​factsage/​fact/​factsage/​FactSage). Although these databases contain descriptions for the TiO₂–Ti₂O₃–MO systems (M = Mg, Fe, Mn), only very limited data are available for ZrO₂-based systems. Model for liquid is not compatible with models used in the present study.

Therefore, the thermodynamic database of the ZrO₂–MgO–MnO–Al₂O₃ system had to be developed for modelling of the interactions between Al₂O₃ impurities, Mg-PSZ and Fe–CrMnNi-TRIP-steels. In a similar way the SiO₂ containing binary descriptions of the MgO–SiO₂, MnO–SiO₂, ZrO₂–SiO₂ systems had to be combined with databases of the ZrO₂–MgO, ZrO₂–MnO systems and the thermodynamic database of the ZrO₂–MgO–MnO–SiO₂ system had to be developed to model phase relations between SiO₂ impurities, Mg-PSZ and the steel phases.

The thermodynamic description for the quasibinary system ZrO₂–MgO (Fig. 19.3) was based on own experimental investigations with XRD, SEM/EDX and DTA as well as existing literature data [30]. The industrial Mg-PSZ ceramic was also tested in the initial state and after heat treatments at 1523 K with DTA. Differences between the calculations in the ZrO₂–MgO and the experimental data could be attributed to the presence of Al₂O₃ additives in the industrially produced samples. The additives cause the formation of the MgAl₂O₄ phase with spinel structure.

As the ZrO₂–MgO–Al₂O₃ quasi-ternary system had only a very limited amount of experimental data available in literature, the phase equilibria were investigated in more detail in the work of Pavlyuchkov et al. [31]. Throughout the composition range, the solid phase equilibria in the ZrO₂–MgO–Al₂O₃ system were investigated using DTA, XRD, and SEM/EDX. Thereby, the isothermal sections at 1523, 1873 and 2023 K have been constructed. Furthermore, the stability of ternary X-phase at 2073 K found by Tassot et al. [32] was confirmed. The temperature limits of the X-phase stability limits were determined in the range between 1894 and 2094 K. In addition, two ternary eutectic reactions and one eutectic maximum could be determined experimentally. The experimental data thus obtained were used to develop a thermodynamic description for this system. Thus, the liquidus and solidus surface projections and the isopleth section ZrO₂–MgAl₂O₄ were calculated [31]. The calculations showed that much more complicated phase relations exist in this system in comparison to the literature data [33, 34]. The calculated liquidus and solidus surface’s projections of the ZrO₂–MgO–Al₂O₃ phase diagram are presented in Fig. 19.4.

As part of a separate work of Fabrichnaya and Pavlyuchkov [35], a thermodynamic description for the ternary Zr–Fe–O system using the CalPhaD approach was developed based on experimental data from literature. Thermodynamic parameters of ZrO₂–FeO and ZrO₂–Fe₃O₄ systems were assessed using literature data [36‐38]. The solubility of FeO and Fe₂O₃ in the ZrO₂ and of ZrO₂ in the Fe₂O₃ and Fe₃O₄ phases were taken into account and described with the compound-energy formalism. The two sublattice model of partially ionic liquid was used for the description of the melt phase. The descriptions obtained for the ZrO₂–FeO and ZrO₂–Fe₃O₄ systems were combined into the description of the ZrO₂–FeO–Fe₂O₃ system. The isothermal section at 1473 K and the liquidus surface projection have been calculated for the system using the complex data set. The calculated isopleth sections ZrO₂–FeO and ZrO₂–Fe₃O₄ are shown in Fig. 19.5a, b together with the experimental data. Figure 19.6 shows the liquidus surface projection of the ZrO₂–FeO–Fe₂O₃ system. The equilibria between the metallic melt and the solid ZrO₂ phase were calculated and compared with the literature values [39, 40]. Similar to other calculations [41], significant differences between the calculated oxygen solubilities in the Fe–Zr melt and the experimental results were found. New experimental study should be performed to resolve this contradiction.

The phase equilibria in the systems ZrO₂–MnO and ZrO₂–MnO–Mn₂O₃ were investigated experimentally with DTA in Ar atmosphere and by heat treatment in air in the temperature range between 1523 and 1873 K [42]. The reaction temperatures were determined with DTA-TG, the phase compositions in the samples with XRD and the chemical compositions of the phases with SEM/EDX. Based on the experimental data, the thermodynamic parameters were optimized and phase diagrams at oxygen partial pressures of 10⁻⁴ bar and in air were calculated. The phase diagrams are shown in Fig. 19.7a, b along with the experimental data.

Phase equilibria in the ZrO₂–MgO–MnO–Mn₂O₃ system were investigated experimentally in air and in Ar atmosphere in the work of Pavlyuchkov et al. [43]. The samples were characterized with XRD and SEM/EDX. The reactions occurring in these systems were determined by DTA-TG experiments under He atmosphere. Isothermal sections constructed at low partial pressure of O₂ are presented in Fig. 19.8.

At the last stage of the TRIP-Matrix-Composite development, the main objective was the further development of the thermodynamic database for ZrO₂-based ceramic materials and their implementation in the existing steel database. The combined database will make complete simulation of interfacial reactions between steel and ceramics in the TRIP metal matrix composite material possible. Therefore, the following partial goals result:

First, high-temperature phase transformations in strongly metastable austenitic-martensitic Fe–CrMnNi–N–C cast steels were studied using SEM/EXD and DTA based on preliminary CALPHAD calculations. Our studies of the Fe–15Cr–3Mn–3Ni–0.1N cast stainless steels with five different carbon contents, in particular the SEM imaging and EDX elemental mapping of the segregation of Cr and Ni, have shown that the solidification mode changes from primary ferritic to primary austenitic with increasing carbon content. This is in contradiction to thermodynamic calculations (Fig. 19.9) of a primary ferritic solidification of all alloys, but can be explained by the experimental conditions, e.g. by the solidification rate, which creates a nonequilibrium state and facilitates therefore the austenitic solidification. Melting temperatures determined by DTA measurements showed no clear trend with respect to the carbon content in the investigated steel compositions, probably due to the influence of local chemical inhomogeneities. The experimental temperature range for melting is narrow and lies above the calculated melting range, probably due to an overheating effect. The transformation temperature for the solid-solid phase transformation fcc(γ) → fcc(γ) + bcc(δ) was also measured by DTA. In agreement with the calculations, it increases with increasing carbon content for steels NC05 to NC15, but above 0.155 wt% C it remains approximately constant regardless of the further increasing carbon content. Again, several effects can explain the deviation from the calculation in alloys with a higher carbon content: local fluctuations of the chemical composition, but also a reduced overheating due to an increased transformation rate at higher temperatures. The transformation fcc(γ) → fcc(γ) + bcc(δ) was found to be fully reversible, that means it occurs during heating and cooling at almost the same temperature, thus the undercooling is very small.

Furthermore, the reversion transformation of a thermal martensite α′ → γ was shown for the steels NC05 and NC10, which contain a significant fraction of martensite formed during quenching. For the other alloys, the effect was below the detection limit of DTA because of the low volume fractions (<5 vol%) of martensite present. The onset temperature of the transformation decreased with the carbon content.

Concerning further thermodynamic modelling of the ceramic systems, thermodynamics of the Mg–Mn–O system has been modeled based on new heat capacity measurements of the MgMn₂O₄ and Mg₆MnO₈ phases [44]. Phase diagram data, structural information, and thermochemical data were used in the assessment. All solid solution phases were modeled using the compound energy formalism. Mg-solubility in the cubic spinel has been modeled according to the findings in a previous study of Pavlyuchkov et al. [43], which suggests that Mg solubility reported by earlier studies was too low. Thus, the older reports on the Mg solubility in the cubic spinel were not considered. In general experimental data found in the literature was well reproduced. The results presented were significant for further thermodynamic modelling of the Mg–Mn–Zr–O system.

Phase relations in the ZrO₂–TiO₂ system were investigated in the temperature range from 1303 to 1903 K using XRD and SEM/EDX. Melting reactions in this system were studied using DTA followed by microstructure investigation [45]. The Liq = β-(Zr_xTi_1−x)₂O₄ + TiO₂ eutectic and the Liq + T-ZrO₂ = β-(Zr_xTi_1−x)₂O₄ peritectic reactions were determined at 2029 K and 2117 K respectively. Composition of eutectic was determined by SEM/EDX to be 83.2 ± 1.0 mol%. First, the drop solution calorimetry method was applied using AlexSys 800 (SETARAM Instrumentation) in order to measure enthalpy of formation of the β-ZrTiO₄ compound from oxides (−18.3 ± 5.3 kJ mol⁻¹). Molar heat capacities of the β-(Zr_xTi_1−x)₂O₄ compound was measured in the range 233–1223 K. Experimental thermodynamic values (i.e. heat capacity and enthalpy of formation of β-ZrTiO₄ compound) determined in [45] were used in order to optimize the description of heat capacity of α-ZrTiO₄ and β-(Zr_xTi_1−x)₂O₄, as well as the contribution of the formation enthalpy of the β-Zr_xTi_1−xO₄ phase, respectively. Using the obtained experimental results together with literature data, the thermodynamic parameters in the ZrO₂–TiO₂ system were derived. Calculated phase diagram is presented in the Fig. 19.10.

Later on, based on the newly obtained results for the ZrO₂–TiO₂ system, the ZrO₂–TiO₂–MgO ternary system was experimentally investigated in the temperature range from 1533 K up to melting temperatures using XRD, SEM/EDX and DTA [46]. Isothermal sections of the system were constructed based on experimental data at 1533, 1683 and 1883 K. It has been determined that TiO₂ doping did not stabilized T-ZrO₂ phase in this system which transformed to monoclinic structure on cooling. Ternary compound described by formula Zr₄TiMg₂O₁₂ has been discovered. Homogeneity range of the compound was not established. However, based on experimental results, it was stated that the homogeneity range was insignificant and this compound was practically stoichiometric. The ternary compound has a trigonal structure of the Pr₇O₁₂-structure type. Nevertheless, further crystallographic investigations are necessary to establish the cations occupancies in the crystal structure of the phase. High temperature limit of the phase stability of the ternary compound has been determined to be 1664 K. Using results obtained by DTA and SEM/EDX, liquidus projection for the ZrO₂–TiO₂–MgO system has been constructed. The eutectic reactions Liq = C-ZrO₂ + β-(Zr_xTi_1−x)₂O₄ + MgTi₂O₅, Liq = TiO₂ + β-(Zr_xTi_1−x)₂O₄ + MgTi₂O₅ and Liq = MgTi₂O₅ + C-ZrO₂ + MgTiO₃ have been determined at 1800 K, 1851 K and 1872 K respectively. Based on the obtained experimental results, thermodynamic description of the ZrO₂–TiO₂–MgO system was developed. Comparison of calculated and experimental results shows a good mutual agreement. Experimental and calculated liquidus projection of the system is shown in the Fig. 19.11.

As it was said above, the integration of Zr into steel database was required for combining of thermodynamic databases for ceramic materials with the steel database. Therefore, experimental differential scanning calorimetry measurements and ab initio simulations were carried out to define the heat capacities of Zr₃Fe and C15–ZrFe₂ compounds from 0 K up to their maximum stability temperatures [47]. Experimental measurements of heat capacity of each compound were performed for the first time in wide range of temperatures. Density functional theory and quasi-harmonic approximation (QHA) were employed to calculate the Gibbs energy of the studied systems as a function of volume and temperature. Using the combination of DFT + QHA approach and experimental DSC analysis the main thermodynamic functions C_P(T) and parameters S²⁹⁸ and ∆H⁰ for Zr₃Fe and ZrFe₂ intermetallic phases were obtained form 0 K up to temperatures of their stability. In addition, experimental measurements of thermal expansion coefficient were performed for verification of DFT calculations. Analysis of theoretical and experimental data on α_V and C_P shows that QHA remarkably underestimates the anharmonic and magnetic effects starting from temperatures ~200 to 300 K. However, for low-temperature regions we observed very good agreement between theory and experiment.

Experimental measurements of heat capacity of Zr₂Fe were performed using DSC in the temperature range from 220 to 450 K for the first time [48]. Obtained results were compared with theoretical calculations of C_P(T) presented by Ali et al. [49]. Using the combination of calculated [49] and experimental results, temperature dependence of heat capacity C_P(T) for Zr₂Fe was described in the temperature range of 0–450 K as well. The standard entropy S²⁹⁸ of Zr₂Fe was evaluated using obtained heat capacity data. Taking into account recent experimental data on heat capacity and ab initio calculations of enthalpy of formation for intermetallic compounds and most reliable data for phase diagram [50, 51] thermodynamic re-assessment of the Fe–Zr system has been performed [48]. Liquid and solid solution phases such as bcc, fcc, and hcp have been described using substitutional model. Compound energy formalism has been used in order to describe homogeneity ranges of the C15- and C36–ZrFe₂ Laves phases. In the results, it has been demonstrated that the set of obtained thermodynamic parameters describes experimental data better than thermodynamic descriptions published earlier. Calculated phase diagram of the Fe–Zr system is presented in Fig. 19.12 along with experimental data.

Afterwards, the Zr–Mn system was studied using XRD, SEM/EDX, DSC and DTA by Flandorfer et al. [53] and in the present study. The heat capacity of the C14–ZrMn₂ phase was measured in the temperature range of 770 to 1320 K. Based on the obtained results, thermodynamic description was developed. The calculated phase diagram is presented in Fig. 19.13.

Newly obtained thermodynamic parameters of the Zr–Mn and Fe–Zr systems were combined together with Fe–Mn parameters [53] into description of Fe–Zr–Mn system based on binary extrapolation. This database was created for calculations of the ternary diagram which was further used for selection of sample compositions. Experimental investigation of Zr–Fe–Mn system included study of quasi-binary C14–ZrMn₂–C15–ZrFe₂ system and ternary phase equilibria. Quasi-binary section of the ternary system was studied by diffusion couple (DC) method. DC was prepared from single phase C14–ZrMn₂ and C15–ZrFe₂ samples by spark plasma sintering (SPS) plating. Obtained samples were heat-treated at 1173 and 1373 K in order to examine phase relation at different temperatures. Microstructure of the DCs was then studied using SEM/EDX with engaging of line-scan for analysis of composition gradient. Samples for ternary phase relations investigation, corresponding to three phase regions, were prepared by arc melting. Samples were heat-treated at 1073 K and quenched into water. They were then studied using XRD and SEM/EDX for phase identification and phase relation and chemical composition analysis.

There was contradiction in literature data for this system connected with the area on the phase diagram corresponding to the two-phase region C15–C14. In the work [54] a two-phase region was reported, while in the work [55] an anomaly change of magnetic moment was observed and XRD results indicated formation of C36 Laves phase structure in the composition range between C15 and C14 Laves phases. In the present work results from SEM/EDX investigation indicated absence of a phase with an intermediate composition. Therefore, it was concluded that two solid solution phases C15 and C14 were present in the system coexisting with each other in the range between 60 and 80 mol% ZrFe₂. Measured solubility ranges of the boundaries of the phases are in good agreement with the literature data [54].

It should be mentioned, that ternary Fe–Zr–Mn system was studied the first time. It was partially constructed based on the results obtained on ternary system and thermodynamic assessments of the composing binary systems. Obtained results are presented in the Fig. 19.14.

Within the present work, substantial amount of results were obtained for thermodynamic modelling of the system related to the TRIP-Matrix-Composite development. Advanced methods of thermodynamic simulations were applied for optimization of chemical composition of steel matrix and ceramic particles, for prediction and understanding of mechanisms occurring in the material, for finding new solutions of technological issues. Additionally, the methods of thermodynamic modelling provided a basement for further development of the TRIP-Matrix-Composite.

Thermodynamic database was developed for 11 elements Fe, Mn, Cr, Ni, Ti, Si, N, C, Mo, W, V. Obtained thermodynamic description reproduces most of the available experimental results. Thereby, it gives more reliable extrapolations in comparison to other commercial or noncommercial thermodynamic descriptions. Concerning development of thermodynamic oxide description, 3 binary, 7 ternary and a quaternary systems were investigated and modeled in cooperation with other projects.

However, the main uncompleted task is the integration of Zr, what requires the thermodynamic modelling of binary systems such as Zr–Ni, Zr–Cr and ternary system of iron, zirconium and main alloying elements of steel matrix. Moreover, the incorporation of oxygen into the data set of the steel database requires the implementation of system descriptions such as Fe–O, Mn–O, Cr–O, Ni–O and the associated ternary systems Fe–Ni–O, Fe–Mn–O, Fe–Cr–O, Ni–Cr–O, etc.