THERMODYNAMIC ASSESSMENT OF THE Al Mo V TERNARY SYSTEM

Transcription

1 J. Min. Metall. Sect. B-Metall. 53 (2) B (217) Jurnal f Mining and Metallurgy, Sectin B Metallurgy THERMODYNAMIC ASSESSMENT OF THE M TERNARY SYSTEM B. Hu a,*, B. Ya a, J. Wang b,*, J.-R. Zha c, F.-F. Min a, Y. Du b a Anhui University f Science and Technlgy, Schl f Materials Science and Engineering, Huainan, China b Central Suth University, State Key abratry f Pwder Metallurgy, Changsha, China c Shandng Academy f Sciences, Advanced Materials Institute, Shandng Key abratry fr High Strength ightweight Metallic Materials (HM), Shandng Engineering Research Center fr ightweight Autmbiles Magnesium ly, Jinan, China Abstract (Received 1 Nvember 216; accepted 19 January 217) Thermdynamic assessment f the M ternary system was perfrmed by means f the CAPHAD (CAculatin f PHAse Diagram) apprach based n the thermdynamic descriptins f three cnstitutive binary systems ( M, and M ) as well as the experimental phase equilibria data available in the literature. The slutin phases, i.e. liquid, bcc (M, ) and fcc (), were described using the substitutinal slutin mdels with the Redlich-Kister equatin. The binary phases in the M and systems with the slubilities f the third element were mdeled using the sublattice mdels. An ptimal set f thermdynamic parameters fr the M system was btained. Six isthermal sectins at 12, 1, 75, 715, 675 and 63 C and liquidus prjectin with istherm were calculated. The reactin scheme fr the entire M system was als cnstructed. Cmparisns between the calculated and measured phase diagrams indicated that almst all the reliable experimental infrmatin was satisfactrily accunted fr by the present mdeling. Keywrds M system; CAPHAD apprach; Isthermal sectin; iquidus prjectin 1. Intrductin M ternary system is f great interest because it is an imprtant sub-system in -based and Ti-based allys. In -based allys, M and as tw f the cmmn additinal elements imprve the perfrmance f the -based allys [1-4]. In Ti-based allys, additins f transitin metal elements such as M and t titanium can stabilize the high temperature β phase t rm temperature fllwing rapid cling. M and are the mst frequently used β ismrphus elements in Ti-based allys [5]. In additin, M can imprve the quenchability f the β phase in Ti-based allys [6, 7] and can imprve the rm-temperature ductility f Ti and Ti 3 allys [8]. The design f cmpsitins f r Ti based nvel allys requires infrmatin abut the phase equilibria f the M ternary system. Therefre, a thrugh thermdynamic assessment f the M system is necessary fr prviding a set f reliable thermdynamic parameters fr thermdynamic extraplatins t related higher rder systems. Thermdynamic descriptin fr the M system is part f ur effrts [9-17] t establish thermdynamic databases f multi-cmpnent and/r Ti based allys. T the best f ur knwledge, thermdynamic descriptin fr the M system is nt available in the literature nr in cmmercial database [18]. The purpses f the present wrk are t critically evaluate the measured phase diagram data available in the literature and t btain a set f selfcnsistent thermdynamic parameters fr the M systems by means f the CAPHAD apprach [19, 2]. 2. Evaluatin f experimental data T facilitate reading, the symbls used t dente the slid phases in the M system are listed in Table 1. The Gibbs energy functins fr the pure elements, M and are taken frm the SGTE (Scientific Grup Thermdata Eurpe) database cmpiled by Dinsdale [21]. The thermdynamic parameters fr M,, and M systems are taken frm Peng et al., Gng et al. and Zheng et al. [24], respectively. In particular, Peng et al. refined the thermdynamic parameters f the M system based n the wrk f Cupid et al.. A * Crrespnding authr wangjinga@csu.edu.cn; hubia54771@163.cm. DOI1.2298/JMMB161115H

2 96 B. Hu et al. / JMM 53 (2) B (217) set f thermdynamic parameters f the M binary system is taken frm Zheng et al. [24] rather than the newer ne frm Bratberg and Frisk [25]. On the ne hand, the thermdynamic parameters f the M system frm Zheng et al. [24] are cnsistent with the multi-cmpnent allys database develped by ur research grup [16]. On the ther hand, the calculated results frm Bratberg and Frisk shw a miscibility gap in the bcc phase belw 116 K withut experimental evidence. Fr the system, the thermdynamic parameters are adpted frm ur wn grup rather than indahl et al.[26] als in rder t be cnsistent with the database f ur grup. The calculated three cnstitutive binary systems are presented in Fig. 1 (a) t (c). Figure 1. Calculated binary phase diagrams (a) M system, (b) system, and (c) M system [24]. Table 1. Summary f crystal structures f slid phases in the M system. Phase/Temperature range ( C) Prttype Pearsn symbl Space grup Phase descriptin (), < 66 Cu cf4 Fm3 m Slid slutin based n fcc_a1 (M), < 2623 W ci2 Im3 m Slid slutin based n bcc_a2 M (), < 191 W ci2 Im3 m Slid slutin based n bcc_a2 12 M, < W ci26 Im3 P Slid slutin based n 12 M 5 M, < W hp12 P6 3 Slid slutin based n 5 M 22 M 5, < M 5 F216 Fdd2 Slid slutin based n 22 M 5 17 M 4, < M 4 mc84 C2 Slid slutin based n 17 M 4 4 M, 941~ W mc3 Cm Slid slutin based n 4 M M, 791~1222 M mc32 C2/m Slid slutin based n M, < 1528 mc22 C2/m Slid slutin based n 63 7, 1489~1569 Binary phase 63 7 M, 147~1721 W ci2 Im3 m Slid slutin based n bcc_a2, < 2148 Cr 3 Si cp8 Pm3 n Slid slutin based n 21, < cf176 Fd3 m Slid slutin based n 21 45, < mc14 C2/m Slid slutin based n 45 23, < hp54 P6 3 /mmc Slid slutin based n 23, < 1222 Ti ti8 I4/mmm Slid slutin based n, < 1413 Cu 5 Zn 8 ci52 I43m Slid slutin based n

3 B. Hu et al. / JMM 53 (2) B (217) The phase equilibria data f the M system were mainly experimentally determined by Sperner [27] and Raman [28]. In 1959, six isthermal sectins at 12, 1, 75, 715, 675 and 63 C were investigated by Sperner [27]. Accrding t these isthermal sectins, n ternary cmpund was fund in the M system. The binary phases,, M, 5 M and 12 M in M binary side and,, 6 (r 23, 45 ) and 21 in binary side were detected in the wrk f Sperner [27]. The slubilities f M in and and in and slightly decrease with temperature ranges frm 12 t 63 C. The slubilities f M in 6, 21, M, 5 M and 12 M are nearly cnstant in temperature ranges. The average slubilities f M in,, 6 and 21 are abut 3, 25, 1 and 6.5 wt.%, respectively, and the nes f in,, M, 5 M and 12 M are abut 2, 11, 6, 3 and 1.5 wt.%, respectively, in temperature ranges frm 12 t 63 C. The slubilities f M in binary phases and in M binary phases decrease with the decreasing f temperature. Nine invariant reactins, i.e. + (M, ) + at abut 16 C, + + at 145 C, + + at 13 C, + + M at 11 C, + M + 5 M at 72 C, M at 7 C, + 5 M M at 69 C, M at 68 C, and 12 M () at 656 C, were reprted and a tentative reactin scheme fr the M system was als cnstructed by Sperner [27] n the basis f the isthermal sectins. The experimental data measured by Sperner [27] are included in the present ptimizatin due t the cnsistency f these isthermal sectins. Twenty ternary allys were prepared and the isthermal sectin at 1 C was detemined by Raman [28]. Accrding t the experimental results [28], the binary phases,, 4 M and 5 M in M binary side and and in binary side were detected. A ternary cmpund 14 M 5 clsing t the binary cmpund was reprted by Raman [28]. ater, irkar and Raman [29] carried ut the crystallgraphic investigatins shwing that the 14 M 5 phase has a similer structure with the phase and believed that the s-called ternary phase 14 M 5 is the slid slutin f the allying element in. Hence, the 14 M 5 phase is nt included in the present ptimizatin. In additin, the phase relatins f the isthermal sectin at 1 C reprted by Raman [28] are incnsistent with the nes frm Sperner [27]. Hence, the experimental phase diagram data reprted by Raman [28] is nt used in the thermdynamic ptimizatin but nly used fr cmparisn. 3. Thermdynamic mdel The phases in the M system t be ptimized in this wrk are as fllws slutin phases, liquid, bcc (M, ) and fcc (); binary phases extending int the ternary system, 12 M, 5 M, 22 M 5, 17 M 4, 4 M, M,,, 21, 45, 23, and. Different mdels were emplyed t describe the abve mentined phases. 3.1 Slutin phases The slutin phases, i.e. liquid, bcc (M, ) and fcc () are described by the substitutinal slutin mdel. The mlar Gibbs energy f slutin phase ( = liquid, bcc r fcc) is expressed by the Redlich- Kister-Muggianu plynmial [3] Gm x G xm GM x RT ( x ln x xm ln xm xln x) x xm, M x x, (1) xm x M, x xm x 1 2 ( x x x ), M, M, M,, M, where R is the gas cnstant, x, x M and x are the mlar fractins f the elements, M and, respectively. The standard element reference (SER) state [21], i.e. the stable structure f the element at 25 C and 1 bar, is used as the reference state f Gibbs energy. The parameters i, j (, i j,m,) are the A interactin parameters frm binary systems. The ternary interactin parameters, 1 and 2, M,,M,,M, are linearly temperature-dependent, which can be expressed as A A. The cefficients A,M, = A+BT and B will be ptimized frm experimental data in the present wrk. G 3.2 Binary phases Accrding t the experimental data frm Sperner [27] and Raman [28], the binary phases 12 M, 5 M, M, and in the M system and 21, 6 (r 23, 45 ), and in the system exhibit sme slubilities fr and M, respectively. Sublattice mdels [31,32] are used t describe these binary phases and listed in Table 2. In view f the experimental results [27, 28], it is assumed that M and substitute each ther in the sublattice mdels. In accrdance with the frmula fr sublattice mdel, the Gibbs energy f 12 M, mdeled as 12 (M, ) 1, taking as an example can be expressed as 12M 12M 12M G y M GM y G (2) RT ( y M ln y M y ln y ) ym y 12M 1 M 1 12 y y M, M, M...

4 98 B. Hu et al. / JMM 53 (2) B (217) where y M and y are the site fractins f M 12M and in the secnd sublattice. The parameters G M 12M and G crrespnd t the Gibbs energies f the 1 end-members 12 M and 12, respectively. The A interactin parameters M and M M, M, are als linearly temperature-dependent, which can be 12M A expressed as, and the cefficients a M, =a+bt and b will be ptimized in the present wrk. It is nted that the and phase are mdeled as (, M, ).75 (, M, ).25 and (, ) 2 (, M, ) 3 (M, ) 2 () 6, respectively. The bldfaces mean the nrmal atms (i.e. majr species) in the sublattices. The 22 M 5, 17 M 4 and 4 M phases were nt determined by Sperner [27]. In view f the slubilities f in ther bianry phases in the M system, these phases were described as () 22 (M, ) 5, () 17 (M, ) 4, and () 4 (M, ) 1, respectively, in the present wrk. Analgus expressins like Eq. (2) are applied t describe the Gibbs energies f the,, 22 M 5, 17 M 4, and 4 M phases. 4. Results and discussins The thermdynamic parameters are evaluated by the ptimizatin mdule PARROT [33] in the prgram Therm-Calc sftware, which wrks by minimizing the square sum f the differences between the measured and calculated values. The step-by-step ptimizatin prcedure described by Du et al. [34] is utilized in the present assessment. The ptimizatin begins with the isthermal sectin at 12 C. Accrding t the slubilities f in the and phases and M in the and phases and the phase relatins at 12 C determined by Sperner [27], the interactin parameters a fr the,, and phases in Eq.(2) are ptimized. Then, the isthermal sectins at 1, 75, 715, 675 and 63 C are cnsidered ne by ne in the ptimizatin. Next, the temperatures f invariant reactins reprted by Sperner [27] are evaluated. The ternary interactin parameters A fr the liquid and bcc_a2 phases in Eq.(1) are btained by fitting the experimental data f invariant reactins. Finally, all the parameters are ptimized simultaneusly. The thermdynamic parameters btained in the present wrk are listed in Table 2. Table 2. Summary f the thermdynamic parameters fr the M system a Phase/Mdel Thermdynamic parameters Reference iquid Mdel (, M, ) 1 Table 2. cntinued n next page [24] [24] fcc_a1 fcc_a1,ma T Mdel (, M, ) 1 a 1 fcc_a T bcc_a2 Mdel (, M, ) 1 a 3 iquid,m 1 iquid,m 2 iquid,m iquid, 1 iquid, iquid M, iquid M, iquid,m,,a bcc_a2,ma 1 bcc_a2,ma 2 bcc_a2,ma T T T T T T T T T bcc_a2,a 1 bcc_a2,a bcc_a2 M,a 1 bcc_a2 M,a bcc_a2,m,a T T T [24] [24]

5 B. Hu et al. / JMM 53 (2) B (217) Table 2. cntinued frm previus page 12 M M 12 M fcc bcc G T 12 G GM Mdel () 12 (M, ) 1 12 M fcc bcc G G 5M fcc bcc 5 M GM T 5 G GM Mdel () 5 (M, ) 1 5M fcc bcc G G 22M5 fcc bcc 22 M 5 GM T 22 G 5 GM Mdel () 22 (M, ) 7 22M5 fcc 5 G G 5 G bcc 17M4 fcc bcc 17 M 4 G M T 17 G 4 GM Mdel () 17 (M, ) 4 17M4 fcc bcc G G 4 4 M GM 4 M fcc bcc.. T G GM 4 Mdel () 4 (M, ) 1 1 4M fcc bcc G 75 4 G 3M fcc bcc M G M T 3 G GM Mdel () 3 (M, ) 1 3M fcc bcc G G 8M3 fcc bcc GM T 8 G 3 GM Mdel () 8 (M, ) 3 8M3 4 fcc bcc G G M37 fcc bcc Mdel () 63 (M) GM T 63 G 37 GM 37 M3 fcc G 1 G M 1 3 fcc bcc GM G. 25 GM fcc bcc GM T 25. G 75. GM M3 bcc GM 1 GM M3 G,M 456. T M3 GM,M T Mdel (, M, ) (, M, ) M3 bcc M3 fcc bcc G 75. G 25. M 3 fcc bcc G. 75 M 3 bcc bcc GM 75. G M 25. M 3 bcc bcc M 25. GM 75. M3 GM, G T 21 Gfcc bcc 2 Mdel () 21 (M, ) fcc bcc G G 2 G G fcc bcc T 45 G 7 Mdel () 45 (M, ) G fcc bcc M G 7 G M Table 2. cntinued n next page M M 234 fcc bcc 23 G T 23 G 4 Mdel () 23 (M, ) fcc bcc GM T 23 G 4 GM G 3

6 1 B. Hu et al. / JMM 53 (2) B (217) Table 2. cntinued frm previus page Mdel () 3 (M, ) 1 Mdel (, ) 2 (, M, ) 3 (M, ) 2 () 6 fcc bcc G T 3 G G 3 fcc M T 3 G G 3 G M, 85 fcc bcc G 1 11 G 2 85 fcc G 8 fcc fcc bcc G 7 85 G, G, G, , fcc bcc GMM 8 G 5 GM 85 fcc bcc G M 11 G 2 GM 85 fcc bcc bcc GM 8 GA l 2 GM 3 85 fcc bcc bcc MM 6 G 5 GM 2 85 fcc bcc b M 6 G 3 GM 4 G cc 85 fcc bcc bcc M 9 G 2 GM 2 85 fcc bcc bcc M 6 G 2 GM 5 85 fcc M.. G 8 M, bcc M G. 26 T 9 G 4 G bcc bcc T 8 G 5 G bcc G T 8 G 3 G 2 G M bcc a l parameters are given in J/(mle-atms); Temperature (T) in K. The Gibbs energies fr the pure elements, M and are taken frm the SGTE database cmpiled by Dinsdale [21]. In figure 2, the calculated isthermal sectin at 12 C f the M system is cmpared with the bserved ne by Sperner [27]. As can be seen frm these figures, the calculated results can accunt fr mst f the experimental data [27] in view f experimental errrs. It is ntewrthy that there is a sharp edge n the phase in the tw-phase regin + bcc (M, ) at 12 C in Fig. 2(b). It can be interpreted by the fllwing tw reasns. On the ne hand, the shape f is determined by the thermdynamic parameters f bth the phase and ther phases arund, which are glbally ptimized based n the phase equilibria data. On the ther hand, a sharp edge n the phase in the tw-phase regin + bcc (M, ) is expected t exist at a temperature abve 1 C. This can be deduced frm the difference between the phase relatins f the isthermal sectins at 12 and 1 C. A miscibility gap f bcc (M) + bcc () appears at 1 C in Fig. 3. Thus, there exists the three-phase regin f + bcc (M) + bcc (). The cmpsitins f fr the tw three-phase regins + bcc (M) + bcc () and + + bcc () at 1 C are nt identical and the miscibility gap f bcc (M) + bcc () disappears abve 1 C. In ther wrds, the three-phase regin f + bcc (M) + bcc () des nt exist abve 1 C. Hence, based n the phase rule, there shuld be a sharp edge n the in the tw-phase regin + bcc (M, ) at the temperatures abve 1 C, which will disappear at higher temperatures. The exact temperature shuld be measured in the future experiments, which is nt the purpse f the present wrk. Figure 3 shws the calculated isthermal sectin at 1 C in cmparisn with the experimental data reprted by Sperner [27] and Raman [28]. The calculatins can reprduce mst f the experimental data frm Sperner [27]. The 4 M phase was nt fund at 1 C in the wrk f Sperner [27], which is incnsistent with the accepted M phase diagram, as shwn in Fig.1 (a). The calculated three-phase regins liquid + 4 M + and 4 M + + M need further experimental verificatins. As

7 B. Hu et al. / JMM 53 (2) B (217) Figure 2. Observed and calculated isthermal sectins at 12 C f the M system (a) bserved sectin by Sperner [27] and (b) calculated sectin accrding t the present wrk alng with the experimental data frm Sperner [27]. mentined abve, the experimental data frm Raman [28] are nt used in the present ptimizatin but nly used fr cmparisn due t the cntradictins f the experimental results between Sperner [27] and Raman [28]. In additin, the present calculatins shw that there exists a miscibility gap f bcc (M) + bcc () clsing t the M binary side belw 1 C. The existence f the miscibility gap als needs t be cnfirmed by further experiments. In figure 4, the calculated isthermal sectin at 75 C is cmpared with the experimental data frm Figure 3. Calculated isthermal sectin at 1 C f the M system, cmpared with the experimental data frm Sperner [27] and Raman [28]. Sperner [27]. In cmparisn with the experimental data, sme discrepancies exist in M binary side. Accrding t the experimental data frm Sperner [27], the binary phase 3M was determined but the 5M, 22M5 and 17M4 phases nt at 75 C. The experimental results are incnsistent with the accepted M binary phase diagram in Fig.1 (a). The 5M, 22M5 and 17M4 phases are stable at 75 C but 3M nt. Thus, the phase relatins liquid + 3M + 3 and 3M + 8M3 + 3 reprted by Sperner [27] are mdified t be liquid + 5M + 3, 5M + 22M5 + 3, 22M5 + 17M4 + 3, and 17M4 + 8M3 + 3 in the present wrk. In additin, due t the existence f the miscibility gap f bcc (M) + bcc (), the calculated cmpsitin (i.e. 1 wt.% M and 7 wt.% ) f the bcc () phase fr the three-phase regin M bcc () deviates frm the experimental ne f 44.7 wt.% M and 47.6 wt.% by Sperner [27]. It leads t three data pints f half-black circle in -rich crner in tw-phase regin f 85 + bcc () measured by Sperner [27] t be in three-phase regin f 85 + bcc () + M3 in the present wrk. Figure 5 presents the calculated isthermal sectin at 715 C alng with the experimental data frm Sperner [27]. Just as the isthermal sectin at 75 C, there are sme discrepancies between the calculated and experimental isthermal sectin at 715 C. Besides the issues f the 22M5 and 17M4 phases and the miscibility gap f bcc (M) + bcc () mentined abve, the calculated phase relatins in rich crner alng the binary side are incnsistent with the experimental data reprted by Sperner [27]. The 6 binary phase was determined

8 12 B. Hu et al. / JMM 53 (2) B (217) Figure 4. Calculated isthermal sectin at 75 C f the M system, cmpared with the experimental data frm Sperner [27]. Figure 5. Calculated isthermal sectin at 715 C f the M system, cmpared with the experimental data frm Sperner [27]. in the isthermal sectin at 715 C by Sperner [27]. Actually, the 6 phase is replaced by the 234 and 457 phases in the accepted phase diagram in Fig.1 (b). Hence, the phase relatins liquid and liquid + 5M + 3 reprted by Sperner [27] are mdified t be liquid + 5M + 457, 5M , and 5M in the present wrk. The calculated isthermal sectins at 675 and 63 C f the M system in cmparisn with the experimental data frm Sperner [27] are shwn in Fig. 6 (a) and (b), respectively. As can be seen frm this figure, mst f the reliable experimental data reprted Figure 6. Calculated isthermal sectins f the M system alng with the experimental data frm Sperner [27] (a) 675 C and (b) 63 C. by Sperner [27] can be reprduced well by the present mdeling except fr the phase relatins f the 22M5, 17M4, 234 and 457 phases and the miscibility gap f bcc (M) + bcc () mentined abve. The calculated phase relatins at 675 C are the same with the nes at 63 C except fr the liquid () at 675 C and fcc () at 63 C. Based n the abve discussin, almst all the reliable experimental phase diagram data are satisfactrily accunted fr by the present mdeling except fr the phase relatins f the 4M, 22M5, 17M4, 234 and 457 phases and the miscibility gap f bcc (M) + bcc (). Accrding t the experimental data frm Sperner [27], the 4M, 22M5 and 17M4 phases were nt determined and

9 B. Hu et al. / JMM 53 (2) B (217) the 23 and 45 phases were replaced by the 6 phase. The results f Sperner [27] d nt agree with the accepted M and binary phase diagrams, as shwn in Fig.1 (a) and (b), respectively. Thus, the calculated and experimental isthermal sectins shw sme differences. Further experiments are needed t cnfirm the accuracy f the calculated phase relatins related t these binary phases 4 M, 22 M 5, 17 M 4, 23 and 45. Furthermre, the calculated isthermal sectins shw there is a miscibility gap f bcc (M) + bcc () clsing t the M binary side belw 1 C. Further experiments are als necessary t verify the existence f the miscibility gap. On the basis f the ptimizatin f the experimental data reprted by Sperner [27], the liquidus prjectin with istherm f the M system is als calculated in the present wrk, as shwn in Fig. 7 (a). Fig.7 (b) is the enlargement f the triangle in Fig. 7 (a) and Fig.7 (c) is the enlargement f the circle in Fig. 7 (b). A cmparisn between the calculated and literature reprted invariant reactins is listed in Table 3. Figure 8 presents the partial reactin scheme fr the M system. A general agreement is btained between the calculatins and the experiments [27]. Fr the type f the invariant reactins, the calculated invariant reactins are + + (M, ), + + Table 3. Calculated temperatures fr the invariant reactins n the liquidus surface in the M system cmpared with the experimental values. Type Invariant Reactin Temperature/ºC Surce U M 152 Calculated () U 2 + M Calculated () U Calculated () E 1 + (M, ) + ~ 16 Measured [27] + + (M, ) 1329 Calculated () P ~ 13 Measured [27] Calculated () U M ~ 11 Measured [27] 112 Calculated () U 5 + M + 4 M 169 Calculated () U M + 17 M Calculated () U M M 5 91 Calculated () P M 5 5 M 94 Calculated () U M 7 Measured [27] M 717 Calculated () U M 715 Calculated () U M M 69 Measured [27] + 5 M M 73 Calculated () U M 68 Measured [27] M 683 Calculated () U M () 656 Measured [27] M + () 664 Calculated ()

10 14 B. Hu et al. / JMM 53 (2) B (217) 95-16, and M + (), whereas the reprted nes [27] are + (M, ) +, + +, and 12 M (), respectively. Fr the temperatures f the invariant reactins, the calculated results are in gd agreement with the reprted nes within the estimated experimental errrs except fr the invariant reactin + + (M, ). The difference between the calculated and the reprted temperature f the invariant reactin + + (M, ) is abut 271 C. Further experiments are needed t verify the type and temperature f the invariant reactins because these invariant reactins reprted by Sperner [27] are tentative and btained by cnsidering the determined isthermal sectins. In additin, Sperner [27] als reprted tw ternary invariant reactins + + and + M + 5 M derived frm binary invariant reactins + at 176 C and + M 5 M at 735 C in the M system. Accrding t the accepted M phase diagram in Fig.1 (a), these binary invariant reactins d nt exist. Thus, the ternary invariant reactins + + and + M + 5 M reprted by Sperner [27] are bviusly wrng. The present wrk demnstrates that the CAPHAD apprach is a pwerful tl t evaluate a ternary system with limited experimental data. It is pssible t describe the cmplicated phase equiliria f a system ver the entire cmpsitin in a wide temperature range based n limited reliable experimental infrmatin. The CAPHAD apprach is highly recmmended in the present wrk. It is expected that this apprach can be applied t ther systems in rder t develp reliable thermdynamic descriptins f multi-cmpnent allys. 5. Cnclusins Figure 7. Calculated liquidus surface prjectin in the M system (a) the whle cmpsitin, (b) enlarged triangle in (a), and (c) enlarged circle in (b). The experimental phase equilibria data fr the M system available in the literature are critically evaluated. Based n these experimental data, the M system is evaluated by means f the CAPHAD apprach. A set f self-cnsistent thermdynamic parameters f the M system is btained. Sme representative isthermal sectins and liquidus surface prjectin are calculated. The calculated results are in gd agreement with the mst f the experimental data. In spite f the fact that the CAPHAD methd is a pwerful tl t ptimize a system based n the limited experimental data, n updated descriptins f the binary phases in the - M and - systems in the wrk f Sperner [27] and

11 B. Hu et al. / JMM 53 (2) B (217) Figure 8. Partial reactin scheme f the M system accrding t the present wrk. 15

12 16 B. Hu et al. / JMM 53 (2) B (217) the absence f the thermdynamic experimental data (such as mixing enthalpy, activity, etc.) in the M system may lead t the btained thermdynamic parameters in the present wrk failing t accunt fr sme new phase equilibria data and thermdynamic data. Therefre, further experiments are necessary t verify the phase relatins related t the binary phases 4 M, 22 M 5, 17 M 4, 23 and 45 and the existence f the miscibility gap f bcc (M) + bcc (). Acknwledgments The financial supprt frm the Natinal Natural Science Fundatin f China (Ns and ), the China Pstdctral Science Fundatin (N. 215M581972), and the Hunan Prvincial Natural Science Fundatin fr Yuth f China (N. 216JJ3152) are greatly acknwledged. Reference [1] M. Eumann, M. Palm, G. Sauthff, Intermetallics, 12 (24) [2] H. Bei, E.P. Gerge, Acta Mater., 53 (25) [3] M. Dudvá, K. Kuchařvá, T. Barták, H. Bei, E.P. Gerge, C. Smsen, A. Dluhý, Scr. Mater., 65 (211) [4] S. Milenkvic, A.A. Celh, R. Caram, J. Cryst. Grwth, 211 (2) [5] G. utjering, J.C. Williams, Titanium, Springer, New Yrk, 27. [6] I.S. Jung, H.S. Jang, M.H. Oh, J.H. ee, D.M. Wee, Mater. Sci. Eng. A, (22) D.M. Cupid, O. Fabrichnaya, F. Ebrahimi, H.J. Seifert, Intermetallics, 18 (21) [8] X.G. u, N. Gui, A.T. Qiu, G.X. Wu, C.H. i, Metall. Mater. Trans. A, 45A (214) [9] J. Wang, H.H. Xu, S.. Shang,.J. Zhang, Y. Du, W.Q. Zhang, S.H. iu, P.S. Wang, Z.-K. iu, Calphad, 35 (211) [1] B. Hu, W.-W. Zhang, Y.B. Peng, Y. Du, S.H. iu, Y.. Zhang, Thermchim. Acta, 561 (213) [11] D. Ha, B. Hu, K. Zhang,.J. Zhang, Y. Du, J. Mater. Sci., 49 (214) [12] B. Hu, Y. Du, J.C. Schuster, W.H. Sun, S.H. iu, C.Y. Tang, Thermchim. Acta, 578 (214) [13] B. Hu, S. Qin, Y. Du, Z.Y. i, Q.P. Wang, J. Phase Equilib. Diff., 36 (215) [14] B. Hu, Y. Du, J.-J. Yuan, Z.-F. iu, Q.-P. Wang, J. Min. Metall. Sect. B-Metall., 51(2) B (215) [15] J. Zha, J. Zhu, S. iu, Y. Du, S. Tang, Y. Yang, J. Min. Metall. Sect. B-Metall., 52(1) B (216) [16] B. Hu, J. Wang, C. Wang, Y. Du, J.B. Zhu, Calphad, 55 (216) [17] B. Hu, X.M. Yuan, Y. Du, J. Wang, Z.-K. iu, J. lys Cmpd., 693 (217) [18] http// [19] Z.-K. iu, Y. Wang, Cmputatinal thermdynamics f materials, Cambridge University Press, Cambridge, 216. [2] H. ukas, S.G. Fries, B. Sundman, Cmputatinal thermdynamics the CAPHAD methd, Cambridge University Press, Cambridge, 27. [21] A.T. Dinsdale, Calphad, 15 (1991) J. Peng, P. Franke, D. Manara, T. Watkins, R.J.M. Knings, H.J. Seifert, J. lys Cmpd., 674 (216) W.P. Gng, Y. Du, B.Y. Huang, R. Schmid-Fetzer, C.F. Zhang, H.H. Xu, Z. Metallkd., 95 (24) [24] F. Zheng, B.B. Argent, J.F. Smith, J. Phase Equilib., 2 (1999) [25] J. Bratberg, K. Frisk, Calphad, 26 (22) [26] B. indahl, X.. iu, Z.-K. iu, M. Selleby, Calphad, 51 (215) [27] F. Sperner, Z. Metallkd., 5 (1959) (in German). [28] A. Raman, Z. Metallkd., 57 (1966) (in German). [29] A.. irkar, A. Raman, Z. Metallkd., 6 (1959) [3] O. Redlich, A.T. Kister, Ind. Eng. Chem., 4 (1948) [31] M. Hillert,.I. Staffanssn, Acta Chem. Scand., 24 (197) [32] B. Sundman, J. Ågren, J. Phys. Chem. Slids, 42 (1981) [33] B. Sundman, B. Janssn, J.-O. Anderssn, CAPHAD, 9 (1985) [34] Y. Du, R. Schmid-Fetzer, H. Ohtani, Z. Metallkd., 88 (1997)