Critical data evaluation of the aluminium–nickel–titanium system

Intermetallics 14 (2006) 1304e1311 www.elsevier.com/locate/intermet

Critical data evaluation of the aluminiumenickeletitanium system Julius C. Schuster Innovative Materials Group, Universita¨t Wien, A-1090 Wien, Wa¨hringer Str. 42, Austria Received 5 September 2005; accepted 21 November 2005 Available online 27 April 2006

Abstract The literature on data of the system AleNieTi is reviewed. A critical judgement regarding the reliably established facts vs. educated guesses is made. As a result the data, which are found consistent, are presented. A recommendation is given as to which data need to be verified or newly investigated. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: A. Ternary alloy systems; B. Phase diagrams

1. Introduction (applications, previous reviews) Within the system AleNieTi, several alloy systems of interest in high-temperature structural applications occur. Nibased g/g0 superalloys are currently the workhorse for hightemperature/high-strength turbine applications due to their low density, as well as low creep rate and high oxidation resistance at temperatures up to 80% of their melting points. The high-temperature strength is derived from precipitates of the coherent, ordered g0 -Ni3Al phase within the disordered solid solution g-(Ni). Titanium, which has an extended solubility in Ni3Al, will precipitate large amounts of that phase when used in conjunction with Al. Due to their higher melting temperatures as well as lower densities, NiAl-based alloys are considered very attractive for turbine applications, too. Additions of Ti to NiAl-alloys increase the creep strength due to atomic mismatch within the (limited) solubility range [1], as well as due to semicoherent precipitation of t4-Ni2TiAl beyond the solubility limit [2e4]. Similarly, TieAl-alloys of even lower density having a duplex (a2-Ti3Al þ g-TiAl) lamellar microstructure show improved room temperature ductility while maintaining adequate high-temperature creep rates and oxidation resistance.

E-mail address: [email protected] 0966-9795/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2005.11.027

Ni additions to lamellar TiAl are beneficial to the steady state flow behavior, strain rate sensitivity, as well as improving substantially the hot deformability [5]. Furthermore, diffusion barrier designs employing the NiAl phase are widely used for high-temperature oxidation protection of Ni-based superalloy components in gas turbines and aero engines in the form of coatings [6,7], or for electrical contacts to metallize n-GaN [8]. Another application of interest is the shape memory effect exhibited by NiTi-based alloys. It is reported that even small amounts of Al are detrimental to this effect [9]. Prior reviews published on the AleNieTi phase diagram [10e12] tended to extrapolate the available incomplete experimental information by employing educated guesses for unavailable data. Contrary to these, it is the explicit intention of the present paper to line out which data are reliably known and which are inconsistent, controversial, or not corroborated.

2. Phase diagram data 2.1. Binary boundary systems In the present paper binary systems’ evaluations of NieTi by Bellen et al. [13], of AleTi by Schuster and Palm [14], and of AleNi by Schuster [15] are used for the binary

J.C. Schuster / Intermetallics 14 (2006) 1304e1311

boundary systems. The data shown in Table 1 for the AleNi system are corroborated independently by Eleno et al. [16]. 2.2. Solid phases (crystal structures, homogeneity ranges, site preferences) The following substantial ternary solubilities in the binary boundary phases and corresponding lattice parameter changes are reported. Ni3Al dissolves up to 15 at% Ti [22] (more details in Table 3). Ti substitutes for Al. The lattice parameter increases with Ti content to a ¼ 0.3592 nm for Ni75Ti18Al7 [22] or a ¼ 0.35954(5) nm for Ni74Ti17Al9 [23]. The lattice parameter misfit between (Ni) and Ni3Al vs. Ti content was determined by Maniar and Bridge [24] as well as by Mishima et al. [25]; Maniar and Bridge also measured the thermal expansion of Ni3(Al0.5Ti0.5) for 100 < T
C < 900 as well as the lattice parameter mismatch vs. temperature between (Ni) and Ni3(Al0.5Ti0.5). Ni3Ti dissolves up to 5.5 at% Al [26]. Al substitutes for Ti. The lattice parameters decrease with Al content to a ¼ 0.5102(1) nm and c ¼ 0.8307(2) nm for Ni74Ti22Al4 [23]. NiAl coexisting with t4-AlNi2Ti dissolves 11.5 at% Ti at 1400
C [21]. Additional solubility data are given in Table 3. Ti substitutes for Al. The lattice parameter varies with Ti content to a ¼ 0.28969(6) nm for Ni50Ti2.5Al47.5 [1], a ¼ 0.28925(5) nm for Ni50Ti3Al47 [23], a ¼ 0.290 nm for Ni50Ti5Al45 [27], and a ¼ 0.28823 nm for Ni56Ti8Al36 [23], respectively. NiTi dissolves up to 6 at% Al [23]. Al substitutes for Ti. The lattice parameter decreases with Ti content. Lattice parameter values of a ¼ 0.301 nm for 5 at% Al [27] and a ¼ 0.29903(3) nm for Ni52Ti42Al6 [23] were reported. The lattice parameter mismatch vs. temperature between NiAl and t4-AlNi2Ti, as well as between NiTi and t4-AlNi2Ti were reported by Oh-ishi et al. [19,27]. Ti3Al in equilibrium with TiAl dissolves 0.9 at% Ni at 900
C [28]; TiAl dissolves 0.8 at% Ni at 1000
C [29,30], which according to these authors substitutes for Ti þ Al, but according to Hao et al. [31] as well as Nakajima et al. [32] substitutes for Al; NiTi2 dissolves up to 14 at% Al at 900
C [23]. Al substitutes for Ti in the site (48f ), but not in the site (16c) as determined by profile analysis and EPMA [33]. The lattice parameter decreases to a ¼ 1.12367(6) nm for Ni32Ti54Al14 [23]. Four ternary equilibrium phases are reported for this system (Table 2). As all phases were found to occur at all Table 1 Invariant reactions in NieAl assessed from experimental data [15] L ¼ Ni L ¼ Ni þ Ni3Al L ¼ Ni3Al þ NiAl Ni3Al þ NiAl ¼ Ni5Al3 L ¼ NiAl L þ NiAl ¼ Ni2Al3 NiAl þ Ni2Al3 ¼ Ni3Al4 L þ Ni2Al3 ¼ NiAl3 L ¼ NiAl3 þ (Al)

at 1455
C and 0 at% Al or 1465
C and 2 at% Al at 1371  2
C and 24.2  0.1/21.3  0.1/23.8  0.2 at% Al, respectively at 1369  3
C and 24.5  0.2/23.8  0.2/28.1 at% Al, respectively at w700
C and 27.2/39.5/37.5 at% Al, respectively at 1680  5
C and 50 at% Al at 1133
C and 73/58/69 at% Al, respectively at 702
C and 55/59/57.1 at% Al, respectively at 862
C and 85/63/75 at% Al, respectively at 640
C and 97.3/75/99.98 at% Al, respectively

1305

temperatures investigated, there are no experimental data regarding the decomposition of any of these phases in an allsolid phase reaction. Furthermore, there are no melting data for any of these ternary phases, except for t4-Ni2TiAl, which generally is assumed to have a congruent melting point maximum [10,17e19]. This temperature was shown to be at 1490
C or higher [20]. A melting point minimum for t4-Ni2TiAl reported earlier by Field et al. [21] to occur along the isopleth t4-Ni2TiAleNiAl was not confirmed by later works by Simonsson [20] or accepted in the review by Raghavan [12]. The substantial deviations from the ideal stoichiometry of the ternary phases are due to the following site occupancies. In t1 Ni shares the Al site as determined by peak profile analysis [34]. This was confirmed by Grytsiv et al. [35]. Antisite mixing between Al and Ti, as claimed by Ding et al. [36], was not corroborated. In t2 some Ti substitutes for Al on one of the (32f ) sites and Al, in turn, partially fills the site (4b), which is empty in the Th6Mn23 structure type [37]. This results in a phase field for t2, which has a considerable homogeneity range regarding Al, but a rather fixed Ni/Ti ratio. In t3 the homogeneity range of this phase does not include the ‘‘ideal’’ composition Ni33Ti33Al33 [23]. Rather it extends from a Ti-rich limit near Ti42Ni27.5Al30.5 to an Al-rich limit near Ni16Ti34Al50. In Al poor compositions (up to about 40 at% Al) Ti substitutes for Al, but in more Al-rich compositions Al substitutes for Ni [23]. The resulting ‘‘banana like’’ shape of the t3 phase field (Fig. 1) needs verification, however [38]. In the case of t4 the shape of the phase field (Fig. 1) clearly indicates that there is substantial substitution of Ti on the Al site, as well as of Al on the Ti site, but almost no substitution of either metal on the Ni site. 2.3. Phase equilibria In the Ni-rich (>50 at% Ni) section, four all-solid threephase equilibria are reported to exist (Fig. 1) at all temperatures investigated between 750
C and the melt [22,23,26,39e44]. Table 3 lists the compositions of the vertices reported for various temperatures. Additionally, EPMA data on selected two-phase equilibria in this region were given by the above-cited references, as well as in Refs. [45e48]. Furthermore, the liquidus and solidus for (Ni) vs. Ti and Al contents were measured by Miura et al. [49]. Vertical sections were proposed for 75 at% Ni [50,51] and 50 at% Ni [12,18,20,21,52,53]. Based on the data from Ref. [20] it is not clear, whether the latter section is pseudobinary or not. In any case, the eutectic between the NiTi and t4-Ni2TiAl is reported to be extremely shallow [20]. There is a qualitative agreement on three of the invariant equilibria involving the liquid phase plus three solid phases [20,21,41,50,51,54e57] (Table 4). For the ternary eutectic, the data by Thompson and Lemkey [54] seem to be the most reliable. The invariant equilibrium L þ Ni3Ti þ NiTi þ t4-Ni2TiAl was proposed to be either a transition reaction L þ Ni3Ti 4 NiTi þ t4 (tentative [17,41]), or the peritectic L þ NiTi þ t4 4 Ni3Ti [20]. In combination with the generally agreed existence of a melting point maximum for

J.C. Schuster / Intermetallics 14 (2006) 1304e1311

1306 Table 2 Solid phases Phase

Pearson symbol, Space group Prototype

Lattice parameters (nm)

Comments

(Al) <665

cF4, Fm3m Cu

a ¼ 0.40496

[109] in bin. Ti-Al [14]

(Ni), g <1455

cF4, Fm3m Cu

a ¼ 0.35240

[109]

a(Ti) 1491-1120 and <1170

hP2, P63/mmc Mg

a ¼ 0.29506 b ¼ 0.46835

[109] in bin.Ti-Al [14]

b(Ti) 1690-882

cI2, Im3m W

a ¼ 0.33065

[109] in bin.Ti-Al [14]

NiAl3 <862

oP16, Pnma NiAl3-type

a ¼ 0.6114 b ¼ 0.73662 c ¼ 0.48117 a ¼ 0.6618(1) b ¼ 0.7368(1) c ¼ 0.4814(1)

[37Bra1] [82Ell]

Ni2Al3 <1133

hP5, P3m1 Ni2Al3-type

a ¼ 0.40363 c ¼ 0.49004 a ¼ 0.4049(1) c ¼ 0.4900(1) a ¼ 0.4042(1) c ¼ 0.4915(1)

[110] [111] at 62 at%Al [111] at 57 at%Al

Ni3Al4 <702

cI112, Ia3d Ni3Ga4-type

a ¼ 1.1408(1)

[112]

NiAl <1680

cP2, Pm3m CsCl (B2)-type

a ¼ 0.28871(1)

[113] max. at 50.5 at%Al

Ni5Al3
oC16, Cmmm Pt5Ga3-type

a ¼ 0.7475 b ¼ 0.6727 c ¼ 0.3732

[114]

Ni3Al <1371

cP4, Pm3m Cu3Au (L12)-type

a ¼ 0.35764(1) a ¼ 0.35680(2)

[115] at 27at%Al [115] at 24at%Al

TiAl3(h) 1412-?

tI8, I4/mmm TiAl3(DO22)-type

a ¼ 0.3849 c ¼ 0.8610

[116] [117]

TiAl3(r)
tI32 structure not det.

a ¼ 0.3875 c ¼ 3.3835

[116] [117]

tI16, I4/mmn ZrAl3 (DO23)-type tP28, P4/mmm Ti2Al5-type

a ¼ 0.39230 c ¼ 1.6532

[61] [118]

a ¼ 0.39053 c ¼ 2.9192

[119] [118]

1d-APS Ti5Al11 Ti2Al5 TiAl2 <1215

tI24, I41/amd HfGa2-type

a ¼ 0.3971 c ¼ 2.4312

[120] [117]

TiAl <1456

tP4, P4/mmm CuAu (L10)-type

a ¼ 0.3982 c ¼ 0.4078 a ¼ 0.4000(1) c ¼ 0.4075(1)

[121] 38at%Al [122] at 50at%Al

Ti3Al, a2 <1200

hP8, P63/mmc Ni3Sn (DO19)-type

a ¼ 0.5765 c ¼ 0.4625 a ¼ 0.5809 c ¼ 0.4644

[123] at 25at%Al [123] at 21at%Al

Ni3Ti <1118

hP16, P63/mmc TiNi3 (DO24)-type

a ¼ 0.51088 c ¼ 0.83187

[109]

NiTi <1311

cP2, Pm3m CsCl (B2)-type

a ¼ 0.301

[109]

NiTi2 <984

cF96, Fd3m NiTi2-type

a ¼ 1.13193

[109] 33-34at%Ni

t1-Ti(Al1-xNix)3

cP4, Pm3m Cu3Au or L12-type

a ¼ 0.393

[61] for x ¼ 0.12

t2-Niw1Tiw1Alw2 m-phase

cF116, Fm3m filled Cu16Mg6Si7 (G-phase) resp. Th6Mn23-type

a ¼ 1.190 a ¼ 1.18933(4) a ¼ 1.18903(8) a ¼ 1.19128

[61] [37] for Al9(Al0.89Ti0.11)8Ti6Ni7 [23] Ni23.5Ti21.5Al55(coex. with t1) [23] Ni25Ti26Al49(coex. with t3+t4)

t3-Ni1-xTi1+yAl1+x-y l-phase

hP12, P63/mmc MgZn2 (Laves phase) or C14-type

a ¼ 0.4999(3), c ¼ 0.8049(5) a ¼ 0.4994 c ¼ 0.805 a ¼ 0.5018 c ¼ 0.823 a ¼ 0.50006(2) c ¼ 0.80446(4) a ¼ 0.50150(1) c ¼ 0.82249(1)

[124] [62] at 41at%Al(coex. with t4) [62] at 51at%Al(coex. with t1) [23] Ni27Ti39Al34 [23] Ni17Ti35Al48

t4-Ni2TiAl b-phase H-phase

cF16, Fm3m MnCu2Al (Heusler-phase) BiF3 or L21-type

[22] a ¼ 0.58763 a ¼ 0.59098(4)

[23] Ni53Ti14Al33(coex. with b1NiAl) [23] Ni49Ti29Al22

J.C. Schuster / Intermetallics 14 (2006) 1304e1311

1307

Fig. 1. Isothermal section for 900
C [23].

the monovariant equilibrium L þ Ni3Ti þ t4 [17,20,41,57], the latter proposal requires an additional melting point minimum for this monovariant equilibrium, which is highly unlikely. Equilibria involving solid or liquid aluminium are reported by Kamei et al. [58] as well as by Omarov et al. [59,60].

All experimental data reports concur on tie lines to exist between TiAl3 and NiAl3, Ni2Al3 as well as t1 up to the respective melting temperatures of these phases [23,36,58e60]. Consistent with these tie lines, two invariant U-type transition reactions involving the liquid phase are reported ([58,59], Table 4).

Table 3 Compositions (at%) of the 3-phase field vertices in the Ni-rich section Temperature (
C)

Ni

1250 1150 1000 900 850 750

(Ni) þ Ni3Al þ Ni3Ti 85.2 13 87.2 10.4 88 9.8 81.5 16 89.4 9.4 90.5 9.2

1250 1150 1000 927 900 900 850 750

Ni3Al þ NiAl þ t4-Ni2TiAl w73.5 13 13.5 w72 10 18 w72 10 18 71.6 14.3 14.1 72.7 14.4 12.9 73.2 14.9 11.9 w72 10 18 72 9 19

1250 1100 927 900 900 750

Ni3Al þ Ni3Ti þ t4-Ni2TiAl 76 16 8 71.5 15.5 13 73.2 17.6 9.2 73 17 10 74.0 16.8 9.2 74 15 11

Ti

Al 2.8 2.4 2.2 2.5 1.2 0.3

Ni

Ti

80.5 76.5 76.5 79 76.5 76.5

15.5 15 15 15 15 15

Al 4 8.5 8.5 6 8.5 8.5

Ni

Ti

77 75.5 75.5 77 75.5 75.5

20 24.5 24.5 20 24.5 24.5

Al 3 0 0 3 0 0

Comment [57] [22] [22] [41] [22] [22]

EDX metallogr. metallogr. EDX metallogr. metallogr.

56.4 56.5 55.9

9.2 7.6 8.0

34.2 35.9 36.1

52.3 53.2 52.6

19.5 21.7 21.9

28.2 25.1 25.5

56

7

37

55

20

25

[57] EDX [22] metallogr. [22] metallogr. [65] diff. couples [42,43] [23] EPMA [22] metallogr. [39] metallogr.

60 54.5 52.5 54 53.0 55

21 22 25.9 22.5 22.8 22

19 23.5 21.6 23.5 24.2 23

[57] [26] [65] [41] [23] [39]

EDX diff. couple diff.couples EPMA EPMA metallogr.

53.3 52.5 50.6 54

29.3 29.5 28.6 24.7

17.4 18 20.8 21.3

[57] [65] [41] [23] [39]

EDX diff. couples EPMA EPMA metallogr.

75 70 72.3 75 74.3 75.5

20 24.5 23.1 21 21.5 24.5

5 5.5 4.6 4 4.2 0

73 74.0 74.5

26 25.8 25.5

1 0.2 0

74.7

25.3

0

NiTi þ Ni3Ti þ t4-Ni2TiAl 1250 927 900 900 750

53.2 53 52.0 52

41.5 41.5 42.0 45.3

5.3 5.5 5.9 2.7

J.C. Schuster / Intermetallics 14 (2006) 1304e1311

1308

Table 4 Quantitative data on invariant equilibria involving the liquid phase Reaction T (
C)

Ni-rich region L þ (Ni) ¼ Ni3Al þ Ni3Ti

Type

Phase

Composition (at%) Ni

Ti

Comments Al

U

L

77.5

17.5

5

U E

L L

64 67.4 66 67.5

19 11.2 12 13

60 75 75

1300 < T
C < 1310 L þ NiAl ¼ Ni3Al þ t4 L ¼ Ni3Al þ Ni3Ti þ t4

Ni3Al Ni3Ti

75

17 21.4 22 19.5 16.8 25

L Ni2Al3 NiAl3 TiAl3

40 25 0

0 0 25

2.1 0 25

0.6 25 0

0

1288 1270 Al-rich corner L þ Ni2Al3 ¼ NiAl3 þ TiAl3 w820

L þ TiAl3 ¼ NiAl3 þ (Al) 645

U

U

L TiAl3 NiAl3 (Al)

[57] read from Fig. 1; note: composition of L violates mass balance for the reaction proposed [51] [57] read from Fig. 1 [54] EDX [55] EDX [57] read from Fig. 1 [54] EDX [54] EDX [54] determined from heating and cooling curves; quoted as 1277 by [10], quoted as 1304 by [11] [57] DTA on cooling [59]

w650

In the composition region adjacent to the central part of the TieAl binary, no agreement exists for the tie lines between the phases TiAl3, TiAl2, TiAl, t1, t2, and t3. For temperatures ranging from 600
C up to 1200
C tie lines for every geometrically possible triangulation were reported [23,28,36,44, 60e65]. No systematic variation can be seen in these data, however. Even ignoring data, which were only tentative [28,60,61], as well as diagrams explicitly showing that no samples were made in the composition region of dispute [36], does not clarify the issue. Thus e.g., results for 800
C by Markiv et al. [62] (t1 coexisting with TiAl and t3) agree with the data for 1200
C by Mazdyasni et al. [63], but contradict data for 900
C by Huneau et al. [23] (TiAl2 coexisting with t2 and t3), which in turn confirms the report for 1000
C by Biswas and Varin [64]. Equilibria in the Ti-rich section and involving Ti3Al þ TiAl þ X were investigated by Wu and Zamotorin (isotherms at 550
C, 700
C, 800
C, and 900
C; X ¼ NiTi2 [66]), Markiv et al. (800
C, X ¼ t3 [62]), Nash and Liang (900
C, X ¼ t2; dotted tie line only [41]), Bauer et al. (900
C, X ¼ t2; tentative [28]), Xu and Jin (927
C, X ¼ t2 [65]; no XRD was employed; the composition given by these authors for t2 corresponds to t3 according to the data given in Ref. [23]. Thus, it is inferred, that the ternary phase coexisting with Ti3Al þ TiAl was t3, too), Huneau et al. (900
C, X ¼ t3 [23]), as well as Kainuma et al. (1000
C, t not specified [67], but judged to be t3 from the measured composition). For 1200
C and 1300
C (¼ above the decomposition temperature of Ti3Al) Kainuma et al. [67] reported the coexistence of a(Ti) þ b(Ti) þ TiAl as well as b(Ti) þ TiAl þ t3. The

97.3 75 75 >99

[58]

[59]

eutectoid decomposition of b(Ti) into a(Ti) þ NiTi2 is raised by alloying with Al to temperatures above 800
C [66]. Over the entire composition range, the isothermal section at 900
C was most thoroughly investigated by Nash and Liang [41] as well as by Huneau et al. [23] using XRD and EPMA. Complimentary data can be found in Refs. [36,42,43,66]. At slightly higher temperature of 927
C Xu and Jin determined the compositions of coexisting phases for all but the Al-rich region [65]. Fig. 1 shows the version reported by Huneau et al. [23], which deviates from the results of Nash and Liang [41] by showing a tie line between t4-Ni2TiAl (formerly labeled H) and Ti3Al rather than between t3 (formerly labeled l) and TiNi2. Since (t4 þ Ti3Al) was found at 800
C by Markiv et al. [62] which was confirmed by Huneau et al. [23], and (t3 þ TiNi2) was observed at 927
C by Xu and Jin [65], an all-solid phase transition reaction between these four phases might be assumed to occur at/near 900
C. As can be seen from Fig. 1, all ternary phases have substantial homogeneity ranges, the largest one observed for t3 and t4. It should be noted that the large Ni-solubility in a(Ti) assumed in Refs. [23,41,65] is unlikely, because Kainuma et al. determined a b(Ti) þ a(Ti) þ TiAl phase field for 1200
C and 1300
C, where the solubility of Ni in a(Ti) is only 0.6 at% [67]. Additional experimental isothermal sections covering the entire composition range are reported for 800
C [61,62]. Phase field triangulation was based on XRD data only, thus no reliable data on phase homogeneities were given. The compositions given for t3 and t4 agree, however, with the compositions measured by Huneau et al. [23] using EPMA. There is agreement on the phase field triangulation in Refs. [61,62],

J.C. Schuster / Intermetallics 14 (2006) 1304e1311

and the experimental data reported in Ref. [23], except for the tie lines just dotted in Ref. [61]. As already mentioned above, the tie lines among TiAl2, TiAl, t1, t2, and t3 given by Markiv et al. [62] for 800
C differ from the results of Huneau et al. [23] for 900
C, but outside this phase region, these two isothermal sections show the same three-phase equilibria. A ‘‘speculative’’ reaction sequence was proposed by Nash et al. [17]. Based on microprobe data Nash and coworkers [10,41] (reproduced by Budberg [11]) refined and extended it into the Al-rich corner by incorporating the results of Refs. [58,59]. However, except for the above-mentioned reactions in the Ni-rich segment (>50 at% Ni) as well as in the Al corner of the system, none of the invariant temperatures was determined. Thus the Scheil diagrams presented, still must be considered as being speculative. 3. Thermochemical data Thermodynamic data were measured by Kubaschewski [68] (isenthalpic lines from heats of formation in 49 ternary alloys by reaction calorimetry), Kovalev et al. [69] (heat capacity at 50 < T
C < 1000 of g0 -Ni3Al containing 5.3 at% Ti), and Kapala et al. [70] (activities of Ni and Al in Ni3Al1xTix at 1327
C using Knudsen method). 4. Diffusion data Interdiffusion coefficients were reported for Ni and Ti in (Al) (for a review see Du et al. [71]), Al and Ti in (Ni) (at 900 < T
C < 1200 [48]), as well as Al in a(Ti) [72], Al in b(Ti) (1000 < T
C < 1350 [73]), and for Ni in b(Ti) (950 < T
C < 1300 [73], 0.1 < p MPa < 3200 at 950
C [74]). Furthermore, data can be found for 63Ni in Ti3Al at 571 < T
C < 1044 [75] as well as in TiAl at 780 < T
C < 1005 [32,76], and for Ti in Ni3Al [77e82] and NiAl (1150 < T
C < 1375 [83]). 5. Modeling (thermodynamic, ab initio) Thermodynamic modeling of phase equilibria was performed by Kaufman and Nesor (isotherms at 1300, 1400, 1500 and 1600 K [84]), Ansara et al. (isotherm at 1600 K [85]), Yang et al. (vertical section Ni3AleNi3Ti up to 1250
C, isothermal sections for >50 at% Ni at 1150
C and 900
C [42]), Dupin (isotherms at 900
C and 1250
C for >50 at% Ni; vertical section NiAleTiNi; isopleth at 6 at% Ti for 0e40 at% Al; liquidus surface [86]), and Zeng et al. (isotherms at 800, 900 and 1200
C; liquidus surface [23]). None of these descriptions reproduces the experimentally confirmed parts of the liquidus surface. With the exception of the 900
C section all other results must be considered as speculative/tentative/predictive considering the current state of experimental knowledge. Using a thermodynamic model, Kao et al. [87] found that Ti preferentially substitutes for Al in NiAl. Ab initio calculations were made for (Ni) þ Ni3Al phase equilibria ([88,89] CVM), site occupancies in Ni3Al: Ti shares

1309

Al site (pseudopotential model [90]); heat of formation for t4 (81.46 kJ/g at, LMTO [91]; 133.9 kJ/g at, respectively. 137.2 kJ/g at, LMTO, respectively. FLAPW [92]; 0.64 eV/ atom, FLASTO [93]); lattice parameter for t4 (LMTO [91]), FLASTO [93]); lattice parameter for t4 and misfit between NiAl and t4 (LMTO [94]); lattice parameter for t4 and misfit between NiTi and t4 (CVM [46,95]); phase equilibria in the vertical section NiAleNiTi (LMTO [91], BWG approximation [53]); metastable phase diagram NiAl/t4 (CVM [96]); site occupancies in t4: Ti shares the Al site and vice versa (CVM [46]); site occupancies in NiAl: Ti shares Al site (BFS [97e100]; FLAPW [101], LMTO [102], DVM [103], mean field first nearest neighbor interaction [104]); site occupancies in NiTi: Al shares Ti site in NiTi (CVM [46]); site occupancies in Ti3Al: [105e107]; site occupancies in TiAl: Ni likes Al site (Bragg-Williams[31,108]); as well as site occupancies in TiAl: Ni likes Ti site (FLAPW [28]). 6. Conclusions From the above assessment it is clear that outside the Ni-rich section and the very Al-rich corner only solid state data at 900
C are known with reasonable completeness and confidence. There is a particular lack of data regarding the melting behavior and temperatures for the ternary phases. The reliable determination of one additional isothermal section above 900
C over the entire composition range (e.g. 1000
C or 1100
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