Investigation of the Oxidation Behaviour of Ti and Al in Inconel 718 Superalloy During Electroslag Remelting

In the current study, the thermodynamics of the slag-metal equilibrium reaction between Inconel 718 Ni-based alloy and CaF2-CaO-Al2O3-MgO-TiO2 electroslag remelting (ESR)-type slags were systematically investigated in the temperature range from 1773 to 1973 K (1500 to 1700 °C). The equilibrium Al content increased with increasing temperature, whereas the equilibrium Ti content decreased with increasing temperature at a fixed slag composition. The important factors for controlling the oxidation of Al and Ti in the Inconel 718 superalloy were TiO2 > Al2O3 > CaO > CaF2 > MgO in ESR-type slag and Al > Ti in a consumable electrode. The conventional method of sampling by means of a quartz tube could result in contamination of the molten metal and changes in the size of the “special reaction interface”. Therefore, a novel method was used in the present study to investigate the slag-metal reaction kinetics to accurately obtain the kinetic parameters. The mass transfer coefficient was determined by coupling with the kinetic model derived from the assumption that the reaction rate ([Al] + (TiO2) = [Ti] + (Al2O3)) was controlled by the mass transfer of [Ti], [Al], (TiO2) and (Al2O3) in the boundary layer, respectively.

Inconel 718 is extensively used for aerospace and other components that operate at high temperatures and in corrosive environments, where materials with both high strength and excellent corrosion resistance are required [1][2][3][4][5] . The increasing demand for alloys with remarkable comprehensive performance necessitates the development of alloys with highly uniform microstructures and highly homogeneous composition. Electroslag remelting (ESR) is well known for cleanliness and homogeneity of the solidification structure of the resultant ingot. The poor homogeneity of the ingot's composition, however, illustrates that some problems with the process remain unsolved 6,7 . Strong chemical reactions usually occur at the electrode-slag interface (ESI) or the droplet-slag interface (DSI) as well as at the metal pool-slag interface (MSI), as shown in Fig. 1 8 . Consequently, in some cases, the concentrations of critical elements cannot be maintained within specifications or the elements cannot be uniformly distributed along the height of the ingots during the ESR process 9 .
Numerous studies of the aforementioned issues have been reported. The approaches mainly involve encapsulating a preformed consumable electrode by covering the cap between the electrode and water-cooled mold and blowing inert gases onto the surface of the slag bath [10][11][12] , adding an aluminium shot to the slag bath or an aluminium coating to the electrodes to reduce oxidation of the slag caused by rust on the surface of the consumable electrode and by air above the slag pool [12][13][14] . Furthermore, the oxidation of Ti and Al in Inconel 718 is unlikely to be avoided, as demonstrated by the following equilibrium between Al 2 O 3 and TiO 2 in the CaF 2 -CaO-Al 2 O 3 -based slag 6 Therefore, determining the thermodynamic equilibrium between the reactive elements considered and oxide components in ESR slag is very important to diminish the loss of Al and Ti during the ESR process.
In the present study, the dependence of the equilibrium content of Al in Inconel 718 on each component in CaF 2 -CaO-Al 2 O 3 -MgO-TiO 2 slag in the temperature range from 1773 to 1973 K (1500 to 1700 °C) was investigated. Meanwhile, the effect of the Al content on the equilibrium Ti content in the Ni-based alloy was also studied, through which the appropriate composition of the consumable electrode was obtained.
Under conventional conditions, the melt-quenching method is used to investigate chemical reaction kinetics; that is, slag and metal samples are periodically collected using quartz tubes and quenched in ice water, which is the most commonly used approach 15 . However, the liquid metal containing reactive elements such as Al, Ti, rare-earth elements (REE), etc., can react with the quartz tube, viz., 4[Al] + 3SiO 2 = 2Al 2 O 3 + [Si], resulting in contamination of the molten metal 16 . In addition, the net flux of species i in the slag or the metal phase can be written as , ⁎ C i and C i represent the mass transfer coefficient of component i (m/s), the ratio of the interfacial reaction area to the effective liquid melt volume (we introduce the concept of "specific reaction interface" (SRI) (1 /m) in the present study, and concentrations at the slag-metal interface and in the bulk (mol/m 3 ), respectively. The preceding experimental technique can increase the SRI value, either because of the turbulence of the reaction interface or because of a decrease in the absolute amount of melts during sampling 17 . Consequently, the changes in the value of the SRI cause the integration of Eq. (2) to become more complex and inconvenient 16 .
To solve the aforementioned problems, we investigated the reaction kinetics of Inconel 718 alloy with CaF 2 -CaO-Al 2 O 3 -MgO-TiO 2 slags using laboratory-scale experiments, which we conducted under the same experimental conditions (concentration, temperature, and protective atmosphere) by using several identical crucibles with the same melt contents. Meanwhile, we derived a kinetic model using the fundamental equation of heterogeneous reaction kinetics based on the concept of effective boundary layer proposed by Wagner to obtain kinetic parameters 18 .

Thermodynamic considerations
According to reaction (1), the relationship between the equilibrium content of Al in Inconel 718 and variables such as the activity a i of components i in CaF 2 -CaO-Al 2 O 3 -MgO-TiO 2 slags, chemical constitution of the consumable electrode, and the temperature of the slag can be obtained by simple mathematical derivation. Calculating the equilibrium content of Al requires that the relevant parameters be obtained: (I) The mass action concentration (activity) N i of each component in the slag can be calculated using the reported activity model (for details of the modelling and solution procedure, see Eqs (1) through (3) in ref. 19 ) based on the ion and molecule coexistence theory (IMCT) 20 . The basic meaning of N i is consistent with the traditionally applied activity a i in the slag, in which pure solid matter is chosen as the standard state and mole fraction is selected as a concentration unit. According to the hypothesis of the IMCT 20    activity coefficient f %,i of Al and Ti can be calculated using the Wagner equation 18 ; the interaction coefficients used in the present study are listed in Table 2. The chemical composition of Inconel 718 alloy is listed in Table 3.

(III)
The temperature range investigated during the ESR process was 1773 to 1973 K (1500 to 1700 °C). The relationship between the calculated equilibrium Al content for a given Ti content (1.13) and the slag composition of component i in CaF 2 -CaO-Al 2 O 3 -MgO-TiO 2 slags in the temperature range from 1773 to 1973 K (1500 to 1700 °C) is illustrated in Fig. 2. The equilibrium Al content increases with increasing temperature at a constant slag composition. The dependence of the determined equilibrium Al content on the CaO content in the slag (CaF 2 :X CaO :Al 2 O 3 :MgO:TiO 2 = 37:X CaO :25:3:10) at different temperatures is illustrated in Fig. 2(a). The figure shows a continuous increase in the equilibrium Al content with increasing addition of CaO. The calculated equilibrium Al content is greater than 0.43 (the Al content in the master alloy used in the present study) under appropriate conditions, viz., the temperature is greater than 1923 K (1650 °C) and (% CaO) > 22.68, which indicates that Al is not subject to oxidation. This phenomenon is consistent with the results of Jiang et al. 24 , who reported that the high CaO content in CaF 2 -CaO-Al 2 O 3 -MgO-TiO 2 -SiO 2 slags can prevent the oxidation of Al in GH8825 during the ESR process. Similar results are shown in Fig. 2(b). In Fig. 2(c), the calculated equilibrium Al content in the molten metal at various temperatures is plotted against the TiO 2 content. The equilibrium Al content decreases sharply under conditions of (% TiO 2 ) < 1.1, and the point of intersection of the equilibrium Al content line and the isoconcentration line ([% Al] = 0.43) is shifted to the high-TiO 2 -content side when the temperature is increased. Similarly, Hou et al. 25 found that the slag containing a low CaO content combined with extra TiO 2 constantly added into the molten slag in the first temperature-rising period is suitable for electroslag remelting of 1Cr21Ni5Ti stainless steel.  when the mass percent of MgO is less than 5.83% at 1973 K (1700 °C). A similar behaviour in the dependence of the equilibrium Al content is observed in Fig. 2(e).
The relationship between calculated equilibrium Ti content for a given Al content (0.43) and the slag composition of component i in CaF 2 -CaO-Al 2 O 3 -MgO-TiO 2 slags in the temperature range from 1773 to 1973 K (1500 to 1700 °C) is illustrated in Fig. 3. It can be observed that the equilibrium Ti content shows negative correlation with temperature in the range of 1773 to 1973 K (1500 to 1700 °C) with constant slag composition. Meanwhile, the effect of mass percent for CaO, Al 2 O 3 , TiO 2 , MgO, and CaF 2 as components in CaF 2 -CaO-Al 2 O 3 -MgO-TiO 2 slags on the equilibrium Ti content illustrated in Fig. 3 shows completely opposite trend compared with Fig. 2.
As it is previously discussed, the effects of MgO and CaF 2 on controlling the equilibrium Al content in Ni-based alloy compared that of TiO 2 , CaO, and  To elaborate the Inconel 718 alloy composition design, the influence of slag composition on the calculated equilibrium Al content for five different Ti contents (0.5, 0.7, 0.9, 1.1 and 1.3) at 1873 K (1600 °C) is shown in Fig. 4, from which it can be found that all above mentioned observations in Fig. 2 are consistent with the trend shown in Fig. 4. The equilibrium Al content increases with increasing Ti content for a given slag composition at a constant temperature, which reveals that, on the prerequisite of satisfying the mechanical properties of the alloy, to properly increases Ti content can prevent oxidation of Al in the Inconel 718 superalloy. The influence of slag composition on the calculated equilibrium Ti content is shown in Fig. 5, which shows that the calculated equilibrium Ti content increases with increasing Al content (0.2, 0.4, 0.6 and 0.8). The determined equilibrium Ti content is greater than 1.13 for a fixed Al content at 0.8 in the full composition range of slag composition of component i in CaF 2 -CaO-Al 2 O 3 -MgO-TiO 2 slags ((% TiO 2 ) > 3.23). However, the determined Al content for the upper limit Ti content (1.3) is less than 0.43 over the full composition range of slag composition ((% TiO 2 ) > 6.25) shown in Fig. 4. These results demonstrate that the Al and Ti content in the consumable electrode can be designed to be the upper limit in the case where some mechanical properties are met, which is an effective method of controlling Al and Ti loss during the ESR process. What's more, it can be obtained by comparing Figs 4 and 5 that the importance of factors for preventing oxidation of active elements in Inconel 718 is ordered as Al > Ti in the consumable electrode.

Experimental Materials and Methods
Metal and slag preparation. To begin the experiment, Inconel 718 alloy samples were produced in a MgO crucible in a vacuum-induction melting (VIM) furnace under a high-purity argon atmosphere; the chemical composition is listed in Table 3. Each of the master alloys was cut into a smaller size (1 to 3 cm 3 ) to facilitate weighing. Analar-grade CaF 2 , CaO, MgO, Al 2 O 3 , and TiO 2 were used as raw materials. The thoroughly mixed powders were melted at 1773 K (1500 °C) in a graphite crucible under a high-purity Ar atmosphere to ensure complete melting and homogenization; the liquid sample was then quenched on the cooled copper plate and ground. The chemical composition of the experimental slag is listed in Table 4.  Table 4. Composition of slag used in this study and measured equilibrium content of Ni-based alloy samples at each experimental heat (wt%).  Experimental apparatus and process. The slag-metal equilibrium reaction between CaF 2 -CaO-Al 2 O 3 -MgO-TiO 2 slags and Inconel 718 alloy was conducted in a vertical resistance-heated alumina tube furnace equipped with MoSi 2 heating elements. Figure 6 shows a schematic of the resistance furnace used in the present study. The temperature of the furnace was controlled by a proportional-integral-derivative (PID) controller connected to a B-type reference thermocouple. The temperature was calibrated to 1773 K (1500 °C) using another B-type thermocouple before the experiment. The kinetic experiments were carried out using the double-layer (DL) graphite crucible shown in Fig. 7. The experimental procedure is briefly summarized in steps as follows: (1) Pre-melted slag (12 g

Results and Discussion
Oxidation behaviour of Al and Ti through CaF 2 -CaO-Al 2 O 3 -MgO-TiO 2 slag. According to the calculated results in the section on 'Relationship between equilibrium content of Al or Ti and slag composition at different temperatures' , three laboratory-scale experiments (T1, T2 and T3) with different slag compositions (Fig. 2(c)) were performed at 1773 K (1500 °C). The changes in concentration of Al and Ti in the metal phase are shown in Fig. 9 as a function of time for various slags. Figure 7(a) shows that the Al 2 O 3 in molten slag was rapidly reduced by Ti during the first 3-5 min, after which the Al 2 O 3 remained nearly constant. Similar results are also observed in Fig. 7(c). The Al and Ti contents remained constant as functions of time. Full details of the experimental results are given in Table 4. These results indicate that the calculated equilibrium content of Al and Ti in the metal phase shows reliable agreement with the measured values.
Establishment of the kinetic model. The interface chemical reaction is generally accepted to be rapid at metallurgical temperatures, which gives rise to the fact that the overall reaction rate is controlled only by mass transfer of a species to or from the slag-metal interface through the concentration boundary layer 17 . On the basis of this theory of Wagner 29 , the main assumptions in the developed kinetic model for elucidating the probable reaction mechanism between molten slag and Ni-based alloy can be briefly summarized as follows: (I) Only two phases (liquid slag and Ni-based alloy) are considered. (II) The interface chemical reaction reaches a local equilibrium at metallurgical temperatures, and this equilibrium does not control the overall rate of reaction.
(III) Reactant and product do not accumulate at the slag-metal interface, and the mass transfer resistance occurs mainly at the boundary layer. Therefore, reaction (1) may be divided into the following elementary steps:  According to the fundamental equation of heterogeneous reaction kinetics based on the concept of the effective boundary layer, the flux of component i across unit area J i is defined as Eq. (4). A schematic of the effective boundary layer is shown in Fig. 10. The derivation process of the fundamental equation of heterogeneous reaction kinetics has been presented in detail elsewhere 18 .
If the mass transfer of Ti in liquid metal is the rate-controlling step, the following equation can be deduced by inserting a relationship between the molar concentration and mass concentration terms:   where a %,i and f %,i are the activity and activity coefficient of composition i in a metal referred to the 1% standard state, with mass percentage [% i] as the concentration unit (−) and a R,i and γ i are the activity and activity coefficient of composition i in the slag relative to pure matter as a standard state, with mole fraction x i as the concentration unit (−).
In view of the small change in the composition of the components included in reaction (1) (e.g., Al, Ti, Al 2 O 3 , and TiO 2 ), the activity coefficient for each aforementioned component can be regarded as approximatively constant. In particular, high concentrations of Al 2 O 3 are found in the present study, indicating that the activity a Al O 2 3 of Al 2 O 3 can also be treated as a constant. These constants are hence incorporated into the equilibrium constant K of reaction (1). The collated equilibrium constant K 1 can be expressed as  where (% TiO 2 ) 0 and [% Al] 0 represent the total amounts of TiO 2 in the slag and Al in the molten metal, respectively. Combining Eq. (9) with Eqs (10) and (11), we obtain the following equation after simple mathematical derivation:  . Inspection of Eqs (12)- (15) shows that they can both be represented as a function of mass concentration of Ti in the bulk metal: When the maximum mass transfer rate models for Ti and Al in the metal (Eqs (12) and (14)) and TiO 2 and Al 2 O 3 in the slag (Eqs (13) and (15) Figure 11 shows the data from Fig. 7(c) replotted according to Eqs (12)- (15). Although the experimental data appears to fit the line well, only the linear relationship between F[(%Ti)] and time t does not assure the mass transfer in the metal phase or the slag phase of being RCS. Therefore, the RCS and apparent activation energy of oxidation of Al and Ti in the Ni-based alloy by ESR slags will be carried out in the future. Certainly, the mass transfer rate of Al and Ti in the metal phase is much larger than the mass transfer rate of TiO 2 and Al 2 O 3 in the slag phase, rendering the mass transfer of TiO 2 and/or Al 2 O 3 in the slag phase likely to be the rate-controlling step. These results have been experimentally confirmed by several authors 25,30,31 . Recently, Hou et al. 25 reported on the effect of slag composition on the oxidation kinetics of alloy elements during ESR of stainless steel experimentally using a 50-kg ESR furnace. They concluded that the rate-determining step of the oxidation reaction was the mass transfer of Al 2 O 3 through the molten metal, SiO 2 through the slag and TiO 2 through both the metal and the slag phase.

Conclusions
In the present study, the thermodynamic analysis for the slag-metal equilibrium reaction between Inconel 718 Ni-based alloy and CaF 2 -CaO-Al 2 O 3 -MgO-TiO 2 ESR-type slags at various temperatures was systematically discussed. Meanwhile, the reaction mechanism was also investigated, coupling with the max mass transfer rate model. Our results are summarized as follows.
(1) The equilibrium Al content showed a positive correlation with temperature in the range from 1773 to 1973 K (1500 to 1700 °C) with a constant slag composition, whereas the equilibrium Ti content showed the opposite trend. (2) The equilibrium Al and Ti contents depended weakly on the CaF 2 and MgO contents in the studied slags, irrespective of the temperature, indicating that MgO can be used to tailor the physicochemical properties of the slags. Data availability statement. All data generated or analysed during this study are included in this published article (and its Supplementary Information files).