THERMODYNAMIC ASSESSMENT OF THE Al – Mo – V TERNARY SYSTEM

a Anhui University of Science and Technology, School of Materials Science and Engineering, Huainan, China b Central South University, State Key Laboratory of Powder Metallurgy, Changsha, China c Shandong Academy of Sciences, Advanced Materials Institute, Shandong Key Laboratory for High Strength Lightweight Metallic Materials (HLM), Shandong Engineering Research Center for Lightweight Automobiles Magnesium Alloy, Jinan, China


Introduction
Al-Mo-V ternary system is of great interest because it is an important sub-system in Al-based and Ti-based alloys.In Al-based alloys, Mo and V as two of the common additional elements improve the performance of the Al-based alloys [1][2][3][4].In Ti-based alloys, additions of transition metal elements such as Mo and V to titanium can stabilize the high temperature β phase to room temperature following rapid cooling.Mo and V are the most frequently used β isomorphous elements in Ti-based alloys [5].In addition, Mo can improve the quenchability of the β phase in TiAl-based alloys [6,7] and V can improve the room-temperature ductility of TiAl and Ti 3 Al alloys [8].The design of compositions of Al or Ti based novel alloys requires information about the phase equilibria of the Al-Mo-V ternary system.Therefore, a thorough thermodynamic assessment of the Al-Mo-V system is necessary for providing a set of reliable thermodynamic parameters for thermodynamic extrapolations to related higher order systems.
Thermodynamic description for the Al-Mo-V system is part of our efforts [9][10][11][12][13][14][15][16][17] to establish thermodynamic databases of multi-component Al and/or Ti based alloys.To the best of our knowledge, thermodynamic description for the Al-Mo-V system is not available in the literature nor in commercial database [18].The purposes of the present work are to critically evaluate the measured phase diagram data available in the literature and to obtain a set of selfconsistent thermodynamic parameters for the Al-Mo-V systems by means of the CALPHAD approach [19,20].

Evaluation of experimental data
To facilitate reading, the symbols used to denote the solid phases in the Al-Mo-V system are listed in Table 1.The Gibbs energy functions for the pure elements Al, Mo and V are taken from the SGTE (Scientific Group Thermodata Europe) database compiled by Dinsdale [21].The thermodynamic parameters for Al-Mo, Al-V, and Mo-V systems are taken from Peng et al. [22], Gong et al. [23] and Zheng et al. [24], respectively.In particular, Peng et al. [22] refined the thermodynamic parameters of the Al-Mo system based on the work of Cupid et al. [7].A set of thermodynamic parameters of the Mo-V binary system is taken from Zheng et al. [24] rather than the newer one from Bratberg and Frisk [25].On the one hand, the thermodynamic parameters of the Mo-V system from Zheng et al. [24] are consistent with the multi-component alloys database developed by our research group [16].On the other hand, the calculated results from Bratberg and Frisk show a miscibility gap in the bcc phase below 1160 K without experimental evidence.For the Al-V system, the thermodynamic parameters are adopted from our own group [23] rather than Lindahl et al. [26] also in order to be consistent with the database of our group.The calculated three constitutive binary systems are presented in Fig. 1 (a) to (c).
96 Figure 1.Calculated binary phase diagrams: (a) Al-Mo system [22], (b) Al-V system [23], and (c) Mo-V system [24].The phase equilibria data of the Al-Mo-V system were mainly experimentally determined by Sperner [27] and Raman [28].In 1959, six isothermal sections at 1200, 1000, 750, 715, 675 and 630 o C were investigated by Sperner [27].According to these isothermal sections, no ternary compound was found in the Al-Mo-V system.The binary phases AlMo , were reported and a tentative reaction scheme for the Al-Mo-V system was also constructed by Sperner [27] on the basis of the isothermal sections.The experimental data measured by Sperner [27] are included in the present optimization due to the consistency of these isothermal sections.
Twenty ternary alloys were prepared and the isothermal section at 1000 o C was detemined by Raman [28].According to the experimental results [28], the binary phases AlMo 3 , Al 8 Mo 3 , Al 4 Mo and Al 5 Mo in Al-Mo binary side and Al 8 V 5 and Al 3 V in Al-V binary side were detected.A ternary compound Al 14 Mo 5 V closing to the binary compound Al 8 Mo 3 was reported by Raman [28].Later, Virkar and Raman [29] carried out the crystallographic investigations showing that the Al 14 Mo 5 V phase has a similer structure with the Al 8 Mo 3 phase and believed that the so-called ternary phase Al 14 Mo 5 V is the solid solution of the alloying element V in Al 8 Mo 3 .Hence, the Al 14 Mo 5 V phase is not included in the present optimization.In addition, the phase relations of the isothermal section at 1000 o C reported by Raman [28] are inconsistent with the ones from Sperner [27].Hence, the experimental phase diagram data reported by Raman [28] is not used in the thermodynamic optimization but only used for comparison.

Thermodynamic model
The phases in the Al-Mo-V system to be optimized in this work are as follows: solution phases, liquid, bcc (Mo, V) and fcc (Al); binary phases extending into the ternary system, Al

Solution phases
The solution phases, i.e. liquid, bcc (Mo, V) and fcc (Al) are described by the substitutional solution model.The molar Gibbs energy of solution phase  ( = liquid, bcc or fcc) is expressed by the Redlich-Kister-Muggianu polynomial [30]: (1) where R is the gas constant, x Al , x Mo and x V are the molar fractions of the elements Al, Mo and V, respectively.The standard element reference (SER) state [21], i.e. the stable structure of the element at 25 °C and 1 bar, is used as the reference state of Gibbs energy.The parameters are the interaction parameters from binary systems.The ternary interaction parameters , and are linearly temperature-dependent, which can be expressed as .The coefficients A and B will be optimized from experimental data in the present work.

Binary phases
According to the experimental data from Sperner [27] and Raman [28], the binary phases Al 12 Mo, Al 5 Mo, Al 3 Mo, Al 8 Mo 3 and AlMo 3 in the Al-Mo system and Al 21 V 2 , Al 6 V (or Al 23 V 4 , Al 45 V 7 ), Al 3 V and Al 8 V 5 in the Al-V system exhibit some solubilities for V and Mo, respectively.Sublattice models [31,32] are used to describe these binary phases and listed in Table 2.In view of the experimental results [27,28], it is assumed that Mo and V substitute each other in the sublattice models.In accordance with the formula for sublattice model, the Gibbs energy of Al 12 Mo, modeled as Al 12 (Mo, V) 1 , taking as an example can be expressed as: (2)

B. Hu et al. / JMM 53 (2) B (2017) 95 -106
)   where and are the site fractions of Mo and V in the second sublattice.The parameters and correspond to the Gibbs energies of the end-members Al 12 Mo and Al 12 V, respectively.The interaction parameters and are also linearly temperature-dependent, which can be expressed as , and the coefficients a and b will be optimized in the present work.
It is noted that the AlMo 3 and Al 8 V 5 phase are modeled as (Al, Mo, V) 0.75 (Al, Mo, V) 0.25 and (Al, V) 2 (Al, Mo, V) 3 (Mo, V) 2 (Al) 6 , respectively.The boldfaces mean the normal atoms (i.e.major species) in the sublattices.The Al 22 Mo 5 , Al 17 Mo 4 and Al 4 Mo phases were not determined by Sperner [27].In view of the solubilities of V in other bianry phases in the Al-Mo system, these phases were described as (Al) 22

Results and discussions
The thermodynamic parameters are evaluated by the optimization module PARROT [33] in the program Thermo-Calc software, which works by minimizing the square sum of the differences between the measured and calculated values.The step-by-step optimization procedure described by Du et al. [34] is utilized in the present assessment.
The optimization begins with the isothermal section at 1200 o C. According to the solubilities of V in the Al 8 Mo 3 and AlMo 3 phases and Mo in the Al 3 V and Al 8 V 5 phases and the phase relations at 1200 o C determined by Sperner [27], the interaction parameters a for the Al 8 Mo 3 , AlMo 3 , Al 3 V and Al 8 V 5 phases in Eq.( 2) are optimized.Then, the isothermal sections at 1000, 750, 715, 675 and 630 o C are considered one by one in the optimization.Next, the temperatures of invariant reactions reported by Sperner [27] are evaluated.The ternary interaction parameters A for the liquid and bcc_A2 phases in Eq.( 1) are obtained by fitting the experimental data of invariant reactions.Finally, all the parameters are optimized simultaneously.The thermodynamic parameters obtained in the present work are listed in Table 2 Liquid: Model (Al, Mo, V) 1 [22] [22] [22] [23] [23] [24] [24] This work fcc_A1: Model (Al, Mo, V) 1 Va 1 [7] [23] bcc_A2: Model (Al, Mo, V) 1 Va 3 [7] [7] [7]

Table 2. continued on next page
.   .

T G G G
In figure 2, the calculated isothermal section at 1200 o C of the Al-Mo-V system is compared with the observed one by Sperner [27].As can be seen from these figures, the calculated results can account for most of the experimental data [27] in view of experimental errors.It is noteworthy that there is a sharp edge on the AlMo 3 phase in the two-phase region AlMo 3 + bcc (Mo, V) at 1200 o C in Fig. 2(b).It can be interpreted by the following two reasons.On the one hand, the shape of AlMo 3 is determined by the thermodynamic parameters of both the AlMo 3 phase and other phases around AlMo 3 , which are globally optimized based on the phase equilibria data.On the other hand, a sharp edge on the AlMo 3 phase in the two-phase region AlMo 3 + bcc (Mo, V) is expected to exist at a temperature above 1000 o C.This can be deduced from the difference between the phase relations of the isothermal sections at 1200 and 1000 o C. A miscibility gap of bcc (Mo) + bcc (V) appears at 1000 o C in Fig. 3. Thus, there exists the three-phase region of AlMo 3 + bcc (Mo) + bcc (V).The compositions of AlMo 3 for the two three-phase regions AlMo 3 + bcc (Mo) + bcc (V) and AlMo 3 + Al 8 V 5 + bcc (V) at 1000 o C are not identical and the miscibility gap of bcc (Mo) + bcc (V) disappears above 1000 o C. In other words, the three-phase region of AlMo 3 + bcc (Mo) + bcc (V) does not exist above 1000 o C. Hence, based on the phase rule, there should be a sharp edge on the AlMo 3 in the two-phase region AlMo 3 + bcc (Mo, V) at the temperatures above 1000 o C, which will disappear at higher temperatures.The exact temperature should be measured in the future experiments, which is not the purpose of the present work.
Figure 3 shows the calculated isothermal section at 1000 o C in comparison with the experimental data reported by Sperner [27] and Raman [28].The calculations can reproduce most of the experimental data from Sperner [27].The Al 4 Mo phase was not found at 1000 o C in the work of Sperner [27], which is inconsistent with the accepted Al-Mo phase diagram [22], as shown in Fig. 1 2. continued from previous page a All parameters are given in J/(mole-atoms); Temperature (T) in K.The Gibbs energies for the pure elements Al, Mo and V are taken from the SGTE database compiled by Dinsdale [21].

This work
mentioned above, the experimental data from Raman [28] are not used in the present optimization but only used for comparison due to the contradictions of the experimental results between Sperner [27] and Raman [28].In addition, the present calculations show that there exists a miscibility gap of bcc (Mo) + bcc (V) closing to the Mo-V binary side below 1000 o C. The existence of the miscibility gap also needs to be confirmed by further experiments.
In figure 4, the calculated isothermal section at 750 o C is compared with the experimental data from Sperner [27].In comparison with the experimental data, some discrepancies exist in Al-Mo binary side.According to the experimental data from Sperner [27], the binary phase Al In addition, due to the existence of the miscibility gap of bcc (Mo) + bcc (V), the calculated composition (i.e. 10 wt.% Mo and 70 wt.%V) of the bcc (V) phase for the three-phase region AlMo 3 + Al 8 V 5 + bcc (V) deviates from the experimental one of 44.7 wt.% Mo and 47.6 wt.% V by Sperner [27].It leads to three data points of half-black circle in V-rich corner in two-phase region of Al 8 V 5 + bcc (V) measured by Sperner [27] to be in three-phase region of Al 8 V 5 + bcc (V) + AlMo 3 in the present work.
Figure 5 presents the calculated isothermal section at 715 o C along with the experimental data from Sperner [27].Just as the isothermal section at 750 o C, there are some discrepancies between the calculated and experimental isothermal section at 715 o C.Besides the issues of the Al 22 Mo 5 and Al 17 Mo 4 phases and the miscibility gap of bcc (Mo) + bcc (V) mentioned above, the calculated phase relations in Alrich corner along the Al-V binary side are inconsistent with the experimental data reported by Sperner [27].The Al 6 V binary phase was determined Al-Mo-V system, compared with the experimental data from Sperner [27] and Raman [28].the Al 23 V 4 and Al 45 V 7 phases were replaced by the Al 6 V phase.The results of Sperner [27] do not agree with the accepted Al-Mo and Al-V binary phase diagrams, as shown in Fig. 1 (a) and (b), respectively.Thus, the calculated and experimental isothermal sections show some differences.Further experiments are needed to confirm the accuracy of the calculated phase relations related to these binary phases Al On the basis of the optimization of the experimental data reported by Sperner [27], the liquidus projection with isotherm of the Al-Mo-V system is also calculated in the present work, as shown in Fig. 7 (a).Fig. 7 (b) is the enlargement of the triangle in Fig. 7 (a) and Fig. 7 (c) is the enlargement of the circle in Fig. 7 (b).A comparison between the calculated and literature reported invariant reactions is listed in Table 3. Figure 8 presents the partial reaction scheme for the Al-Mo-V system.A general agreement is obtained between the calculations and the experiments [27].For the type of the invariant reactions, the calculated invariant reactions are L ↔ Al 8 V 5 + AlMo  The present work demonstrates that the CALPHAD approach is a powerful tool to evaluate a ternary system with limited experimental data.It is possible to describe the complicated phase equiliria of a system over the entire composition in a wide temperature range based on limited reliable experimental information.The CALPHAD approach is highly recommended in the present work.It is expected that this approach can be applied to other systems in order to develop reliable thermodynamic descriptions of multi-component alloys.

Conclusions
The experimental phase equilibria data for the Al-Mo-V system available in the literature are critically evaluated.Based on these experimental data, the Al-Mo-V system is evaluated by means of the CALPHAD approach.A set of self-consistent thermodynamic parameters of the Al-Mo-V system is obtained.Some representative isothermal sections and liquidus surface projection are calculated.The calculated results are in good agreement with the most of the experimental data.In spite of the fact that the CALPHAD method is a powerful tool to optimize a system based on the limited experimental data, no updated descriptions of the binary phases in the Al-Mo and Al-V systems in the work of Sperner [27] and

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Im m Im Pm n Fd m I m G Im m Im Pm n Fd m I m G Im m Im Pm n Fd m I m G Pm

3 ,
Al 8 Mo 3 , Al 3 Mo, Al 5 Mo and Al 12 Mo in Al-Mo binary side and Al 8 V 5 , Al 3 V, Al 6 V (or Al 23 V 4 , Al 45 V 7 ) and Al 21 V 2 in Al-V binary side were detected in the work of Sperner [27].The solubilities of Mo in Al 8 V 5 and Al 3 V and V in AlMo 3 and Al 8 Mo 3 slightly decrease with temperature ranges from 1200 to 630 o C. The solubilities of Mo in Al 6 V, Al 21 V 2 , Al 3 Mo, Al 5 Mo and Al 12 Mo are nearly constant in temperature ranges.The average solubilities of Mo in Al 8 V 5 , Al 3 V, Al 6 V and Al 21 V 2 are about 30, 25, 10 and 6.5 wt.%, respectively, and the ones of V in AlMo 3 , Al 8 Mo 3 , Al 3 Mo, Al 5 Mo and Al 12 Mo are about 20, 11, 6, 3 and 1.5 wt.%, respectively, in temperature ranges from 1200 to 630 o C. The solubilities of Mo in Al-V binary phases and V in Al-Mo binary phases decrease with the decreasing of temperature.Nine invariant reactions, i.e.L + (Mo, V) ↔ Al 8 V 5 + AlMo 3 at about 1600 o C, L + AlMo 3 ↔ Al 8 V 5 + Al 8 Mo 3 at 1450 o C, L + Al 8 V 5 ↔ Al 3 V + Al 8 Mo 3 at 1300 o C, L + Al 8 Mo 3 ↔ Al 3 V + Al 3 Mo at 1100 o C, L + Al 3 Mo ↔ Al 3 V + Al 5 Mo at 720 o C, L + Al 3 V ↔ Al 6 V + Al 5 Mo at 700 o C, L + Al 5 Mo ↔ Al 6 V + Al 12 Mo at 690 o C, L + Al 6 V ↔ Al 21 V 2 + Al 12 Mo at 680 o C, and L ↔ Al 12 Mo + Al 21 V 2 + (Al) at 656 o C (a).The calculated three-phase regions liquid + Al 4 Mo + Al 3 V and Al 4 Mo + Al 3 V + Al 3 Mo need further experimental verifications.As B. Hu et al. / JMM 53 (2) B (2017) 95 -106 100 Table

3
Mo was determined but the Al 5 Mo, Al 22 Mo 5 and Al 17 Mo 4 phases not at 750 o C. The experimental results are inconsistent with the accepted Al-Mo binary phase diagram in Fig.1 (a).The Al 5 Mo, Al 22 Mo 5 and Al 17 Mo 4 phases are stable at 750 o C but Al 3 Mo not.Thus, the phase relations liquid + Al 3 Mo + Al 3 V and Al 3 Mo + Al 8 Mo 3 + Al 3 V reported by Sperner [27] are modified to be liquid + Al 5 Mo + Al 3 V, Al 5 Mo + Al 22 Mo 5 + Al 3 V, Al 22 Mo 5 + Al 17 Mo 4 + Al 3 V, and Al 17 Mo 4 + Al 8 Mo 3 + Al 3 V in the present work.

Figure 2 .
Figure 2. Observed and calculated isothermal sections at 1200 o C of the Al-Mo-V system: (a) observed section by Sperner [27] and (b) calculated section according to the present work along with the experimental data from Sperner [27].

Figure 4 .
Figure 4. Calculated isothermal section at 750 o C of theAl-Mo-V system, compared with the experimental data from Sperner[27].

Figure 6 .
Figure 6.Calculated isothermal sections of the Al-Mo-V system along with the experimental data from Sperner [27]: (a) 675 °C and (b) 630 °C.

Figure 5 .
Figure 5. Calculated isothermal section at 715 o C of theAl-Mo-V system, compared with the experimental data from Sperner[27].

Al 3 V
, and L + Al 21 V 2 ↔ Al 12 Mo + (Al), whereas the reported ones[27] are L + (Mo, V) ↔ Al 8 V 5 + AlMo 3 , L + Al 8 V 5 ↔ Al 3 V + Al 8 Mo 3 , and L ↔ Al 12 Mo + Al 21 V 2 + (Al), respectively.For the temperatures of the invariant reactions, the calculated results are in good agreement with the reported ones within the estimated experimental errors except for the invariant reaction L ↔ Al 8 V 5 + AlMo 3 + (Mo, V).The difference between the calculated and the reported temperature of the invariant reaction L ↔ Al 8 V 5 + AlMo 3 + (Mo, V) is about 271 o C. Further experiments are needed to verify the type and temperature of the invariant reactions because these invariant reactions reported by Sperner [27] are tentative and obtained by considering the determined isothermal sections.In addition, Sperner [27] also reported two ternary invariant reactions L + AlMo 3 ↔ Al 8 V 5 + Al 8 Mo 3 and L + Al 3 Mo ↔ Al 3 V + Al 5 Mo derived from binary invariant reactions L ↔ AlMo 3 + Al 8 Mo 3 at 1760 o C and L + Al 3 Mo ↔ Al 5 Mo at 735 o C in the Al-Mo system.According to the accepted Al-Mo phase diagram in Fig.1 (a), these binary invariant reactions do not exist.Thus, the ternary invariant reactions L + AlMo 3 ↔ Al 8 V 5 + Al 8 Mo 3 and L + Al 3 Mo ↔ Al 3 V + Al 5 Mo reported by Sperner [27] are obviously wrong.

Figure 7 .
Figure 7. Calculated liquidus surface projection in the Al-Mo-V system: (a) the whole composition, (b) enlarged triangle in (a), and (c) enlarged circle in (b).

Figure 8 .
Figure 8. Partial reaction scheme of the Al-Mo-V system according to the present work.

Table 1 .
Summary of crystal structures of solid phases in the Al-Mo-V system.Phase/Temperature range ( o C) Prototype Pearson symbol Space group 5 , < 1413 Cu 5 Zn 8 cI52 Solid solution based on Al 8 V 5 12 Mo, Al 5 Mo, Al 22 Mo 5 , Al 17 Mo 4 , Al 4 Mo, Al 3 Mo, Al 8 Mo 3 , AlMo 3 , Al 21 V 2 , Al 45 V 7 , Al 23 V 4 , Al 3 V and Al 8 V 5 .Different models were employed to describe the above mentioned phases.

Table 2 .
. Summary of the thermodynamic parameters for the Al-Mo-V system a

Table 2 .
continued on next page

Table 2 .
continued from previous page 4 Mo, Al 22 Mo 5 , Al 17 Mo 4 , Al 23 V 4 and Al 45 V 7 .Furthermore, the calculated isothermal sections show there is a miscibility gap of bcc (Mo) + bcc closing to the Mo-V binary side below 1000 o C. Further experiments are also necessary to verify the existence of the miscibility gap.

Table 3 .
3 + (Mo, V), L + Al 8 V 5 + Al 8 Mo 3 ↔ Calculated temperatures for the invariant reactions on the liquidus surface in the Al-Mo-V system compared with the experimental values.