Thermodynamic databases of Ti-Al-Fe-V quaternary alloy systems and its application

Pandat software based on Calculations of phase diagram (CALPHAD) was used in this study. Six binary systems and four ternary systems in the Ti-Al-Fe-V system were evaluated, compared, and optimized. A thermodynamic database of Ti-Al-Fe-V titanium alloys was established by selecting the most recent, accurate, and self-consistent thermodynamic parameters. The database was used to simulate the organization of equilibrium solidification and non-equilibrium solidification alloys of Ti-10V-2Fe-3Al, Ti-10V-3Al-1Fe and Ti-10V-3Al. The precipitated phase fractions of Ti-10V-2Fe-3Al at different temperatures were calculated using the database. The effect of different Fe contents and aging temperatures on the phase composition of the Ti-10V-2Fe-3Al alloy is given in conjunction with the calculated results. There is good agreement with the experimental results for the heat treatment regimens given by the calculations. The above results show that thermodynamic calculations based on phase diagrams can guide the formulation of process parameters for alloy casting and heat treatment. The established thermodynamic database for Ti-Al-Fe-V titanium alloys is accurate and reliable.


Introduction
Metastable β titanium alloys [1][2][3][4] have been widely used in the aerospace, biomedical, and military industries owing to their low density, outstanding mechanical properties, and excellent corrosion resistance.With the aerospace sector continually advancing, the demand for improved titanium alloy performance has surged.Among these alloys, Ti-10V-2Fe-3Al [5] is chosen as a typical representative due to its outstanding overall performance.Nevertheless, the issue of β-flecks during the melting process of Ti-10V-2Fe-3Al alloy has posed a significant challenge to the titanium alloy industry for an extended period.The presence of the β-flecks in Ti-10V-2Fe-3Al substantially diminishes its ductility.In recent years, scholars have been actively engaged in research aimed at mitigating the presence of the betaphase through adjustments to iron content and modifications in heat treatment methodologies [6].Researchers have turned to solution annealing and aging heat treatments to enhance its mechanical attributes.However, conventional research methodologies predominantly rely on the trial-and-error approach, entailing laborious and time-intensive processes of conducting numerous experiments to develop suitable heat treatment protocols.Concurrently, in step with advancements in computer technology, materials science researchers have introduced calculation of phase diagram.This method involves establishing a thermodynamic model, integrating available experimental thermodynamic data extracted from phase diagrams, and incorporating data derived from first-principal calculations.It further optimizes the Gibbs free energy expressions for individual phases and subsequently establishes a comprehensive thermodynamic phase diagram database.Numerous researchers have made significant contributions to the development of thermodynamic databases.For instance, Du et, al. [7] undertook the establishment of a comprehensive thermodynamic and thermophysical properties database for multicomponent aluminum alloys.Their work involved simulating microstructure evolution during solidification.Sundman et, al. [8] provided a concise review encompassing thermodynamic and kinetic models, databases, and computational software.Their efforts included the computation of phase equilibria and phase transformations through software applications.Meanwhile, Li et, al. [9] conducted a comprehensive systematic review of phase diagram calculation techniques, thermodynamic models, and software.They performed calculations to determine equilibrium distribution coefficients and predict second-phase precipitation within the Fe-Mn-Ni system, offering the range of aging temperatures.It's noteworthy that their computational findings closely align with experimental data, demonstrating the reliability and accuracy of their calculations.In this study, we systematically constructed an accurate and self-consistent thermodynamic database for the Ti-Al-V-Fe phase diagram using the CALPHAD method.Utilizing the thermodynamic database, we conducted simulations to investigate the impact of varying iron concentrations on both equilibrium and non-equilibrium solidification processes.Moreover, we calculated the precipitation phase fractions of Ti-10V-2Fe-3Al at different temperatures and conducted a comprehensive analysis of the factors contributing to β-flecks formation in Ti-10V-2Fe-3Al titanium alloys.

Establishment of the Thermodynamic Database for the Ti-Al-Fe-V System
In the pursuit of constructing a precise thermodynamic database for Ti-Al-V-Fe system, it is imperative to conduct a thorough assessment of the experimentally measured and optimally computed binary systems as documented in the existing literature.The establishment of a precise and well-justified thermodynamic database for ternary and multicomponent systems in titanium alloys critically depends on the accurate determination of thermodynamic parameters for these binary systems.Therefore, the primary task in this undertaking involves a meticulous evaluation of the binary systems that govern the fundamental parameters necessary for constructing the Ti-Al-V-Fe thermodynamic database.

Binary Systems within the Ti-Al-Fe-V System
To construct a thermodynamic database for the Ti-Al-V-Fe system, it is imperative to evaluate the thermodynamic parameters of six distinct binary systems: Ti-Al, Fe-Ti, Ti-V, Fe-Al, Al-V, and Fe-V, respectively.The substantial solubility of Al in the α phase, serving as a vital stabilizing element and contributing to an elevated alloy transformation temperature, has made Ti-Al [10,11] system titanium alloys a central research focus for scholars.There has been substantial research on the thermodynamics of phase diagrams in this system.Notably, the thermodynamic parameters given by Witusiewicz [12] et, al. exhibit a alignment with experimental data within the Ti-Al binary system.Consequently, these parameters have gained widespread acceptance and application in the context of Ti-Al-X ternary systems.In the development of the present thermodynamic database, we have incorporated and utilized the phase diagram thermodynamic parameters contributed by Witusiewicz et, al.Previous studies by Jonsson et, al. [13] and Keyzer et, al. [14] have explored the Ti-Fe binary system.Notably, Bo et, al. [15] have made significant advancements in thermodynamic modeling, with particular emphasis on the Fe2Ti and FeTi phases, resulting in a notable enhancement of phase boundary representations within the Ti-Fe system.Consequently, these thermodynamic parameters, as presented by Bo et, al. have been adopted for use in this database.Within the Ti-V system, three phases coexist: the liquid phase, HCP_A3, and BCC_A2 phases.It is noteworthy that the assessments conducted by Ghosh [16] et, al. closely with experimental observations.Consequently, for this thermodynamic database, we have applied the thermodynamic parameters for the Ti-V system proposed by Ghosh et, al.The Al-Fe system presents a structural complexity characterized by the coexistence of the body-centred cubic phase BCC_A2, the BCC_B2 ordered phase, and the D03 ordered phase.However, for the sake of maintaining internal consistency in our integrated database, our study only focuses on the transformations from ordered to disordered states within the BCC_A2 and BCC_B2 phases.Hence, we opted to utilize the thermodynamic model for the Ti-Fe system as proposed by Sundman et, al. [17].As for the Al-V and Fe-V systems, we have integrated the thermodynamic data compiled by Gong [18] et, al. and Kumar [19] et, al. respectively, into our comprehensive database.To provide a visual representation, Figure 1 illustrates the calculated phase diagrams for the six sub-binary systems in the Ti-Al-V-Fe system.

Ternary Subsystems within the Ti-Al-Fe-V System
The Ti-Al-Fe-V system encompasses four distinct ternary subsystems: Ti-Al-V, Ti-Fe-V, Al-Fe-V, and Ti-Fe-Al.Ti-6Al-4V [20], the most frequently utilized alloy in the Ti-Al-V system and among titanium alloys, finds extensive applications in aerospace components and materials.This alloy was successfully developed in the United States as early as the 1960s.Scholars have consistently focused their research on composition design involving the Ti-6Al-4V alloy and its corresponding heat treatment processes.However, with the continuous development of Calculations of phase diagram, an increasing number of scholars [21] are using thermodynamic databases to guide the composition design and heat treatment processes of titanium alloys.For the Ti-Al-V system, numerous scholars have employed analytical techniques such as XRD, SEM, and EPMA to systematically determine the phase diagrams, yet no new ternary compound has been found.Lu [22] et, al. integrating previous experimental data, optimized the thermodynamic parameter of this system.They provided thermodynamic parameters for each phase and calculated isothermal sections at 800°C, 900°C, 1000°C, 1100°C, and 1200°C based on this database.The results indicate excellent consistency between the thermodynamic assessment from this database and experimental results.The thermodynamic parameters obtained from this study are self-consistent, and Figure 2(a) illustrates the calculated isothermal section at 800°C.Due to its cost-effectiveness and significant solid solution strengthening effect, Fe commonly added in certain amounts to titanium alloys.As for the phase diagrams of titanium alloys containing iron (Fe), research in this area has been conducted quite early.Since the 1950s, several scholars have investigated the phase diagrams of the Ti-Fe-V system to varying degrees.In recent years, Massicot [23] et, al. investigated 33 alloys within this system using the equilibrium alloy method.They confirmed the absence of ternary compounds by determining the isothermal sections at 1000°C and 1200°C through XRD, SEM, and EPMA.Initially, Guo [24] et, al. optimized the system's thermodynamics, defining the sigma phase as (Fe, Ti, V)10(Fe, Ti, V)20.Later, Feng [25] and et, al. re-optimized the system, redefining the sigma phase as (Fe)8(V)4(Fe, Ti, V)18.The calculated phase diagram aligns with the experimental data from Massicot et, al. figure 2(b) illustrates the calculated isothermal section at 1000°C.Subsequently, Wang et, al. [26] conducted a thermodynamic optimization using experimental data provided by Maebashi et, al. [27] for the Al-Fe-V system.To address the ordered-disordered transition within this system, they utilized the L21 phase model (Al,Fe,V)0.5(Al,Fe,V)0.5(Fe)1to describe the second-order ordered D03 structure.Figure 2(c) displays the calculated isothermal section at 500°C.Previous studies suggested the presence of three ternary compounds in the Ti-Al-Fe system.However, Plam et al. [28] performed experimental investigations utilizing metallography, XRD, and EPMA techniques, confirming the existence of two ternary compounds: Al2FeTi and Al8FeTi3.Additionally, they also plotted the isothermal sections at 800°C and 1000°C.In subsequent years, a series of studies [29,30] have refined the phase diagram of this system, with a significant emphasis on ordereddisordered transitions.Notably, due to the presence of ordered-disordered transitions in the binary systems Ti-Fe, Al-Fe, and Ti-Al, and the existence of ordered phases on the Ti-Fe and Al-Fe sides in the ternary system, it is remarkable that the Al-Fe side incorporates AlFe (B2) and AlFe3 (D03) ordered phases, representing the first and second-order ordered phases of the disordered phase BCC_A2, respectively.Following this, Plam et, al. [31] conducted a comprehensive evaluation of the Ti-Al-Fe system, combining previous experimental data.They summarized the system's magnetic, electrical, thermochemical, atomic, and diffusion data, and outlined research on phase equilibrium and phase transformation modeling.Furthermore, they provided extensive research pertaining to phase equilibrium and phase transformation modeling.Based on the analysis above, the authors of this paper investigated the ordered-disordered transitions between BCC_A2 and BCC_B2 phases.We optimized the system's thermodynamic parameters, and the calculated isothermal section at 800°C is shown in Figure 2(d).Due to the complexity of the optimization process, it will be detailed in a separate article to be published.The data selection for all binary and ternary subsystems is presented in Table 1.Utilizing the thermodynamic parameters of these systems, we constructed a thermodynamic database for the Ti-Al-V-Fe quaternary phase diagram.Table 1.Thermodynamic information of binary and ternary phase diagrams for the Ti-Al-Fe-V system.

Binary systems
Ternary systems

Application of the Ti-Al-Fe-V System Thermodynamic Database
To validate the accuracy of the constructed Ti-Al-V-Fe quaternary thermodynamic database and elucidate the mechanism governing β-fleck formation in the Ti-10V-2Fe-3Al alloy, this study performed calculations on the equilibrium and non-equilibrium solidification of Ti-10V-3Al-xFe (x=0, 1, 2).Simultaneously, the temperature variation of the precipitate phases in Ti-10V-2Fe-3Al was also calculated.

Influence of Iron Content on Equilibrium and Non-Equilibrium Solidification
Figures 3a-c illustrate the equilibrium and non-equilibrium solidification pathways of Ti-10V-xFe (x=0,1,2)-3Al, respectively.It is evident from these figures that during equilibrium solidification, irrespective of the Fe content variation, the system comprises Liquid+BCC_A2 (β solid solution phase) until the solidification process is complete, transforming entirely into BCC_A2.However, in the case of non-equilibrium solidification, with Fe content at 1% and 2%, the solidification process initiates the formation of Liquid+BCC_A2, followed by the solidification precipitation of BCC_A2.In the final stages of solidification, there is a slight emergence of the BCC_B2, which is the FeTi compound phase.
In cases where the FeTi compound phase does not dissolve uniformly during subsequent homogenization annealing and thermal processing, the formation of β-fleck occurs.The calculations presented above demonstrate that, even with a reduction in iron content to 1%, under rapid cooling conditions, the severe segregation of Fe during the solidification process remains unavoidable.Consequently, this segregation results in the formation of the BCC_B2 phase (FeTi).

Phase Fraction Calculation in Ti-10V-2Fe-3Al
Figure 4 provides a graphical representation of the phase fraction variations in the Ti-10V-3Al-2Fe alloy, as calculated using the database developed in this study, across different temperatures.As illustrated in the figure 4, at temperatures exceeding 800°C, the alloy predominantly comprises the disordered BCC_A2 phase with a body-centred cubic structure.Upon decreasing the temperature to 765°C , a substantial quantity of the HCP_A3 phase (α solid solution phase) with a hexagonal close packed structure form.This transformation is accompanied by a decrease in the BCC_A2 phase, signifying a phase transition from β to α.At a further reduced temperature of 520°C , the transformation BCC_A2(β) →HCP_A3(α)+BCC_B2(FeTi) takes place.During this process, the ordered BCC_B2(FeTi) phase with a body-centred cubic structure initiates its formation in regions abundant in both Fe and Ti elements, such as within the β-fleck.It is important to note that the FeTi phase, being a rigid and brittle compound, does not precipitate coherently with the matrix.While its precipitation enhances the strength of the Ti-10V-3Al-2Fe alloy, but at the expense of reducing the alloy's plasticity, toughness, and fatigue resistance.Hence, according to the computational findings, it is advisable to set the aging temperature higher than the point at which the FeTi phase emerges, above 520°C, during the solution heat treatment of the Ti-10V-3Al-2Fe alloy.
Wang et, al. [32] delved into the impact of different heat treatment regimens on the microstructure and properties of the Ti-10V-2Fe-3Al alloy.Their study involved an exploration of diverse solution heat treatment and aging processes.The outcomes revealed that the material showcased optimal performance when subjected to an aging process at 520°C for 8 hours.Under these conditions, the alloy achieved a yield strength of up to 1100 MPa.In a study conducted by Shang et al. [33], the impact of aging processes on the microstructure and mechanical properties of Ti-10V-2Fe-3Al was investigated.The material underwent hot rolling at 780°C with a deformation of 45%, followed by an aging treatment at 500°C for 8 hours.The results demonstrated a notable yield strength of 1120 MPa.Their findings indicated that the strength observed after the aging process was primarily attributed to the presence of the secondary α phase.Qi et al. [5] discovered that subjecting samples to a short aging treatment at 550°C in the coldrolled state led to the precipitation of a substantial quantity of fine α phase, resulting in exceptional mechanical properties.A comprehensive comparison with experimental data gathered by previous researchers revealed the accuracy and reliability of the computational results obtained from this database.

Conclusion
Utilizing the CALPHAD method, a thorough evaluation, comparison, and optimization of six binary systems and four ternary systems within the Ti-Al-V-Fe system hsve been conducted.This process involved the selection of the most recent, precise, and internally consistent thermodynamic parameters.Ultimately, this effort leads to the establishment of a comprehensive thermodynamic database for Ti-Al-V-Fe titanium alloys.This study also delves into the impact of iron content on both equilibrium and non-equilibrium solidification processes.Even with a reduced iron content of 1%, the research reveals that the severe segregation of iron during solidification remains unavoidable.Consequently, this led to the formation of the BCC_B2 (FeTi phase).The study further explores the precipitation phase fractions of Ti-10V-3Al-2Fe at various temperatures.Notably, it is observed that maintaining the aging temperature above 520°C effectively prevent the precipitation of the BCC_B2 (FeTi phase), thereby improving the overall mechanical properties of the alloy.

Figure 4 .
Figure 4. Precipitation phase fraction of Ti-10V-3Al-2Fe at different temperatures.Hence, according to the computational findings, it is advisable to set the aging temperature higher than the point at which the FeTi phase emerges, above 520°C, during the solution heat treatment of the Ti-10V-3Al-2Fe alloy.