Critical Assessment of the Al-Ti-Zr System

Only within the last couple of years, complete isothermal sections for the Al-Ti-Zr system have been determined. Up to then there had been several investigations, but these were limited to the Ti-Zr and Ti-Al sides and the Ti- and Al corners of the system. Also recently the system has been evaluated by thermodynamic ab initio calculations and CALPHAD-type (CALculation of PHAse Diagrams) modelling. As Al-Ti-Zr alloys are of interest for a variety of applications and as the last assessment has been performed more than 15 years ago, this new critical evaluation of the existing literature about phase equilibria in the Al-Ti-Zr system has been performed.


Introduction
In view of applications, different parts of the Al-Ti-Zr system are of interest and investigation of phase equilibria over the decades reflects these interests. With the development of Ti-base alloys, the extension of the homogeneity ranges of b(Ti,Zr) and a(Ti,Zr) within the ternary system in dependence of temperature have been investigated. [1][2][3] In the Al corner of the system precipitation of (Ti,Zr)Al 3 has been investigated for strengthening Al alloys at higher temperatures [4][5][6][7] and for grain refining. [8][9][10] As ductility may improve if instead of tetragonal TiAl 3 (D0 22 ) or ZrAl 3 (D0 23 ) metastable (Ti,Zr)Al 3 with cubic L1 2 structure forms, quite some effort has been spent on establishing phase stability in the Al-rich part of the system. [11][12][13][14][15][16][17] With the industrialisation of c TiAl based alloys, phase equilibria among the Ti-Al based phases in this system came into focus. [18][19][20][21][22][23] While all these activities were limited to specific parts of the system, studies of full isothermal sections have been performed only very recently. [24,25] Though of some practical importance, experimental difficulties in investigating Ti-Al(-X) systems at high temperatures make the determination of phase equilibria difficult. High susceptibility to impurities, specifically oxygen, which can have a pronounced effect on phase equilibria, reactions of melts with crucibles or preferential evaporation of Al are some of these problems. [26,27] The addition of Zr does not improve things, as it is also highly susceptible to oxygen uptake and because of its high melting point and low diffusivity, quite long annealing times are necessary to attain equilibrium even at high temperatures. [24,25] And the fact that even ''high-purity'' Zr contains comparable high amounts of impurities, [18,28] specifically Hf, is most of the time neglected.
The key for any aimed alloy development is a sound knowledge of phase equilibria in dependence of temperature and composition. In this regard, assessments play an important role as they collect all the available evidence and critically evaluate it. This is specifically true for the Al-Ti-Zr system, where until recently only scattered information had been available. The current work continues previous assessments by Ansara et al. [29] and Tretyachenko, [30] which have been performed in the framework of MSIT [50] Therefore also the recent update of the system [42] shows only the presence of the two polymorphs TiAl 3 (h) and TiAl 3 (l), but no transformation temperature.

Phases
Some of the binary phases show large solid solubility ranges for the third element and two ternary compounds, Ti 2 AlZr [51][52][53] and Zr 2 TiAl, [54] have been reported which actually could be ordered structures within the wide homogeneity range of b(Ti,Zr).
Addition of Zr to Ti or Ti to Zr stabilizes b with respect to a, i.e. in both cases the a/b transformation temperature is lowered. [55,56] Within the Al-Ti-Zr system b(Ti,Zr) encompasses a wide range of compositions. At high temperatures it includes the stoichiometric compositions Ti 2 AlZr and Zr 2 TiAl, for which both specific crystallographic structures have been reported (Table 1).
All phases originating in the binary Ti-Al system show a marked solid solubility for Zr (Table 1). At 1000°C 6 at.% Zr in a(Ti,Zr), 20 at.% Zr in Ti 3 Al, 8 at.% Zr in TiAl, 12 at.% Zr in TiAl 2 and 7.5 at.% Zr in TiAl 3 may dissolve. [24] The solid solubility in all phases seems to increase with increasing temperature, e.g. at 1274°C about 13 at.% Zr may dissolve in TiAl. [18] For the site occupation of Zr in TiAl a strong preference for Ti sites was found. [18,[20][21][22]65,66] Also in Ti 3 Al Zr substitutes for Ti. [22,65,66] It was also found that the temperature of the a(Ti,Zr)/Ti 3 Al phase boundary is only slightly raised by the addition of Zr. [3] The change from TiAl 3 with D0 22 -structure to ZrAl 3 (D0 23 -structure) along (Ti,Zr)Al 3 in dependence of composition and temperature was investigated by high-temperature XRD. [12] Lattice constants for (Ti,Zr)Al 3 with D0 22 -and D0 23 -structure have been determined in (Ref 4,6,12,59) and for metastable L1 2 in ( Ref 7,11,13,15,16). The formation of metastable (Ti,Zr)Al 3 with L2 1 -structure in Al has been investigated in (Ref 17) and transformation to stable D0 23 during aging between 450 and 600°C was studied by transmission electron microscopy (TEM). [14] Also, most phases originating in the binary Zr-Al system show a marked solid solubility for Ti (Table 1). Solid solubilities of about 12 at.% Ti in ZrAl 3 , 9 at.% Ti in ZrAl 2 , and even 32 at.% Ti in Zr 5 Al 3 at 1000°C [24] and about 14 at.% Ti in Zr 4 Al 3 , Zr 3 Al 2 and Zr 2 Al at 800°C have been reported. [25] 4 Isothermal Section at 1000°C Most data are available for 1000°C and the most comprehensive investigation was performed by (Ref 24), who determined a complete isothermal section (Fig. 1). More than 38 alloys of about 5 grams each were produced by arcmelting. As the weight loss during alloy production did not exceed 1%, nominal compositions have been considered as ultimate alloy compositions. Heat-treatments were performed at 1000°C for 1440 h for samples encapsulated in quartz tubes back-filled with Ar followed by water quenching. Samples were examined by metallography, XRD and electron probe microanalysis (EPMA). Compositions of coexisting phases were established by an average of five EPMA measurements. The standard deviations of the measured concentrations are ± 0.6 at.% and the total mass of Al, Zr, and Ti was in the range of 97-103%. Figure 1 shows the established isotherm from ( Ref 24). While no ternary phases were detected, most binary phases show marked solid solubility ranges for the third component. It is noted that phase boundaries do not match those currently accepted for Ti-Al [27] and that some phase boundaries are not in accordance with thermodynamic rules applying to isothermal sections. [67] Extrapolation of the phase boundaries from the ternary system onto the binary Al-Zr system shows that apparently the ''line compounds'' Zr 5 Al 3 and ZrAl 2 have some marked solid solubility ranges in the binary. The phase Zr 3 Al, which should be stable at 1000°C (Table 1), has not been detected in ( Ref 24). As the solid solubility for Ti in this phase could be very small, it may not have been observed, because no alloy of appropriate composition has been investigated. The phase Zr 5 Al 4 , which might be stable at 1000°C, [31] has also not been detected in (Ref 24). This is in line with an investigation of the Fe-Al-Zr system, which showed that this phase may only become stable above * 1120°C. [68] For a discussion, whether Zr 5 Al 3 with the Mn 5 Si 3 -type crystal structure is stable in the binary Al-Zr system or not see (Ref 69). However, it is clear that impurities and third alloying elements stabilise the Mn 5 Si 3 -type structure in favour of W 5 Si 3 -type Zr 5 Al 3 , which might be the stable structure in binary Al-Zr at 1000°C. [31] Therefore, it is plausible that [24] observed the Mn 5 Si 3 -type structure for (Zr,Ti) 5 Al 3 . The phase Ti 2 Al 5 has by now been identified as a one-dimensional antiphase domain structure, which forms from TiAl that becomes supersaturated in Al on cooling. [27] Among other investigations at this temperature, the homogeneity range of TiAl was studied on 24 different arcmelted alloys, heat-treated at 1000°C for 10 h. [70] Phases were identified by XRD but no compositions of coexisting phases were established. The solid solubility for Zr in TiAl was found to be about 15 at.%, which is much higher than that reported in ( Ref 24). Presumably-and as acknowledged by the authors-annealing times in (Ref 70) were too short for equilibrating TiAl. Therefore, alloys may have been supersaturated in Zr from the melting process at high temperatures and therefore the reported solid solubility may be too high. The solid solubility range of TiAl has also been examined on 21 alloys heat treated at 1000°C for 168 h. [71] Phases were analysed by XRD and compositions of phases were established by EPMA, but only lattice constants for TiAl are given and compositions can only be read for TiAl from a figure. According to this study the maximum solid solubility for Zr in TiAl could be about 11 at.% at about 47 at.% Al. Also the presence of the three-phase equilibria TiAl ? Ti 3 Al ? ZrAl and TiAl ? ZrAl 2 ? ZrAl at 1000°C is shown, [71] in contradiction to the results by (Ref 24). The occurrence of phase equilibria between TiAl and ZrAl seems unlikely, because the solid solubility for Ti in ZrAl is very limited compared to that in ZrAl 2 and Zr 5 Al 3 , which makes the presence of three-phase equilibria with the latter two phases more likely, as determined in (Ref 24) ( Fig. 1 and 2 23). Only one tie-line close to the Ti-Al binary system was established at 1000°C, which fits very well with the binary. [27] The composition 50 ± 2 at.% Ti, 25 at.% Zr, 25 ± 2 at.% Al was found to be single-phase D0 19 , the structure of Ti 3 Al, after annealing at 1000°C for 720 h. [51] Whether this means that Ti 3 Al may have a larger solid solubility for Zr than * 20 at.%, as found in (Ref 24) or whether D0 19 forms on cooling at around 1000°C from B2, as discussed before, cannot be settled based on the existing experimental evidence.
Vertical sections along Ti-14.9 at.% Al/Zr, Ti-25.3 at.% Al/Zr, and Ti-33.3 at.% Al/Zr were investigated in the 1960s by metallography, differential thermal analysis (DTA), and XRD and results were published in a series of overlapping papers. [55,64,[72][73][74][75] At 1000°C samples were annealed for 100 h and quenched in water. All values for phase boundaries taken from the figures are unreasonable at 1000°C, as discussed later, except that for the a(Ti,Zr) ? Ti 3 Al/Ti 3 Al phase boundary. [75] 9 diffusion couples prepared for a diffusion study in b.c.c. b(Ti,Zr) were apparently all single-phase b(Ti,Zr) after annealing for 48 h at 1000°C, [63] in accordance with the composition range outlined in (Ref 24).
Finally, a ternary compound Zr 2 TiAl with cubic L2 1structure was identified in an alloy of appropriate composition that had been annealed for 480 h at 1000°C and 720 h at 1050°C. [54] As discussed before, it is assumed that the composition may lie within the extended singlephase region of b(Ti,Zr) and therefore ordering may occur on cooling. Figure 1 shows the diagram established in (Ref 24) together with all other results from investigations at this temperature. Figure 2 shows the isothermal section as assessed from the results discussed above. It is based on the one established by (Ref 24) with the phase boundaries adjusted to match with those of the accepted binaries and to be in accordance with thermodynamic rules. A small phase field for Zr 3 Al and respective tentative multi-phase equilibria have been added to comply with the accepted Al-Zr binary system. As it has not been settled yet, whether the compositions Ti 2 AlZr and Zr 2 TiAl are separate phases, or indicate B2-ordering at this temperature within Al-rich compositions of b(Ti,Zr), [52,57,59] an area where B2ordering may occur has been outlined in Fig. 2.

Isothermal Section at 800°C
A complete isothermal section at 800°C [25] (Fig. 3) was determined by the same group that established the isotherm at 1000°C using the same techniques as in (Ref 24), except that no XRD has been employed in (Ref 25). In addition, they employed a Ti/TiAl 3 /Zr diffusion triple and this, like 12 alloys of fixed composition, was heat-treated for 2400 h at 800°C. Again the isotherm contains some violations concerning thermodynamic rules and determined phase boundaries for the Ti-Al phases are not in good agreement with the accepted binary system, [27] particular in showing a much lower solid solubility of Al in a(Ti). Also at 800°C no ternary phases are observed while all binary phases have considerable solid solubility ranges, with the exception of Zr 2 Al 3 and ZrAl. The latter phase was not detected at all, presumably because of its limited homogeneity range in the ternary system. All ternary homogeneity ranges of the binary Zr-Al phases show a pronounced tendency for substitution of Zr by Ti, except ZrAl 2 , which shows a pronounced tendency for substitution of Al by Ti (Fig. 3). Though a complete isotherm has been established, many three-phase fields have not been experimentally confirmed (dashed triangles in Fig. 3). Therefore it could be theoretically possible that instead of the two-phase equilibrium b(Ti,Zr) ? Zr 4 Al 3 the phases ZrAl 2 and Zr 3 Al 2 are in equilibrium with each other. The solubility for Zr in TiAl 2 is 11.2 at.%, which is about the same value as at 1000°C. [24] The solubility for Ti in Zr 2 Al is 13.8 at.%, somewhat higher than at 1000°C. [24] Solid solubilities of the third element in other binary phases could actually even be higher than indicated in Fig. 3, as the maxima shown there stem either from phase equilibria shown by dashed lines, i.e. experimentally not determined, or from evaluating the diffusion path in the diffusion triple. As the diffusion path will always cross two-phase fields, established compositions can be more or less close to the three-phase equilibrium and therefore do not correspond to a maximum solid solubility in a phase.
Otherwise, there are few other data available for this temperature, mostly for the Ti corner. The effect of Zr addition on the a(Ti,Zr)/a(Ti,Zr) ? Ti 3 Al phase boundary was investigated in (Ref 2) in the composition range Ti-(8-13)Al-(1-2)Zr at.%. Alloys were produced by arcmelting and rolled prior to annealing at 800°C for 200 h under flowing Ar. Chemical analyses after heat treatment were in good agreement with the nominal compositions and the amount of oxygen was assumed to be 0.03 to 0.04 wt.%. By light microscopy it was established that all investigated alloys were single-phase a(Ti,Zr) at 800°C. This shows that a(Ti,Zr) extends to somewhat more Zr-rich and markedly more Al-rich compositions than shown in Fig. 3, in good agreement with the accepted binary Ti-Al system. [27] Quite a couple of vertical sections exist, which include results at 800°C. [64,[72][73][74][75][76] Though, all of them either Fig. 1 (a) Isothermal section at 1000°C according to [24] with additional experimental results from the literature. (b) Enlarged area from this figure showing phase equilibria and experimental results for TiAl in more detail missed out some phases and/or phase equilibria, denote data points to other phase boundaries than those shown in Fig. 3 or are contradictory in itself (for a detailed discussion see section on Vertical Sections). However, as far as the Ti corner has been investigated, they are inline that a(Ti,Zr) extends further into the ternary system than shown in (Ref 25).
Four samples in the Al corner of compositions 0-15Ti-Al-5Zr (at.%) were investigated in ( Ref 77). The samples were prepared by annealing pre-cursors pressed from elemental powders at 800°C for 30 min. Samples were analysed by observations in a scanning electron microscope (SEM), XRD and electron-dispersive X-ray spectroscopy (EDS). All alloys consist of the two phases Al ? (Zr,Ti)Al 3 . According to the isothermal section by Lü et al.,(Ref 25) the two Ti-rich compositions should show the three-phase equilibrium Al ? (Zr,Ti)Al 3 ? TiAl 3 at 800°C (Fig. 3). One explanation for this discrepancy could be that the annealing time of 30 min was too short to attain equilibrium.
The isothermal section assessed here is shown in Fig. 4. It is based on the results by (Ref 25) with an increased solid solubility range for a(Ti,Zr), in agreement with (Ref 2) and the binary Al-Ti system. Phase boundaries have been adjusted to match with those of the accepted binaries and to be in accordance with thermodynamic rules.

Data at Temperatures Below 800°C
As attaining thermodynamic equilibrium in Al-Ti-Zr alloys at low temperatures becomes more and more difficult, data on phase equilibria below 800°C are scarce. The effect of Zr addition on the a(Ti,Zr)/a(Ti,Zr) ? Ti 3 Al phase boundary in the temperature range 500-700°C is shown in (Ref 2), which also shows a partial isothermal section at 700°C. The phase boundary matches well with the accepted binary. [27] From a series of 16 alloys equilibrated for 500 h at 700°C, the phase boundaries of the two-phase field a(Ti,Zr) ? Ti 3 Al with up to 5 wt% Zr were determined. [75] Compared to the binary system, the two phase area widens by the addition of Zr, in line with the observation by (Ref 2). The a(Ti,Zr)/a(Ti,Zr) ? Ti 3 Al phase boundary was also studied at 600°C by equilibrating alloys with 2, 6 and 10 at.% Zr for 400 h. [78] The extrapolated phase boundary matches well with the extrapolated Fig. 2 Critically assessed isothermal section of the Al-Ti-Zr system at 1000°C one in the binary Al-Ti system. [27] A partial isothermal section of the Ti-corner at 500°C showing the a(Ti,Zr) ? Ti 3 Al phase area is included in (Ref 75).

Data at Temperatures Above 1000°C
Information above 1000°C is limited to phase equilibria between the phases a(Ti,Zr), b(Ti,Zr) and TiAl. The phase relations between these phases have been studied by investigating alloys annealed at 1200°C for 168 h and at 1300°C for 24 h. [23] Heat treatments were carried out in quartz capsules, which are usually considered not to be any longer gas-tight at these temperatures. However, oxygen and nitrogen contents were below 400 (wt.) ppm after the heat treatments. Compositions of coexisting phases in the quenched samples were determined by EPMA by averaging data from 10 points. At 1200°C the three-phase equilibrium a(Ti,Zr) ? b(Ti,Zr) ? TiAl could be determined, showing a maximum solid solubility of 5.1 at.% Zr in a(Ti,Zr). Though this tie-triangle was not measured directly at 1300°C, the adjacent tie-lines suggest that the solubility for Zr in a(Ti,Zr) may only slightly increase up to about 5.5 at.% Zr at this temperature.
In the diffusion study of b.c.c. b(Ti,Zr), [63]  An arc melted alloy of the composition Ti-24.8Al-24.9Zr at.% that was solution treated at 1200°C for 30 min and water quenched, was found to be single-phase B2ordered b(Ti,Zr) by TEM. [52] As no anti-phase domains were observed, the authors concluded that the alloy has been B2 at 1200°C and did not undergo ordering at lower temperatures during quenching.
In a couple of early studies, the extension of the TiAl phase field at 1093°C [79] and 1274°C [18,28] was studied by metallography and XRD. At 1093°C, 27 different alloys were heat treated for 36-39 h and air cooled. [79] The maximum solid solubility for Zr in TiAl was found to be about 8 at% at 1093°C. [79] A first partial isothermal section for ''1274°C'' was constructed from 19 alloys, which were actually heat treated between 1246 and 1379°C for 24-39 h. [28] The partial isothermal section for 1274°C was updated by 18 alloys, which were wrapped in Ta foil and encapsulated in quartz ampules for the heat treatments and which were quenched in brine after annealing for 24 h. [18] As the determined composition range for TiAl in the binary system is shifted markedly to higher Al contents compared to the currently accepted one, [27] the established solid solubility limit of about 13 at.% Zr in TiAl at 1274°C [18] could be doubted. For establishing various vertical sections, quite a couple of alloys have been studied, which have been equilibrated at 1100°C. [64,72,73,75] As discussed in more detail in the following section, these results are all considered to be questionable.

Sections Towards the Zr Corner
The vertical section Ti-14.9 at.% Al/Zr was investigated between 500 and 1100°C by metallography of 19 different annealed alloys and thermal analysis. [72] Established phase boundaries do not match at 800°C with the current knowledge of the binary Ti-Zr system or the ternary system ( Fig. 4) with the sole exception of the b(Ti,Zr)/ a(Ti,Zr) ? b(Ti,Zr) phase boundary. Therefore, the location of the minimum in the a(Ti,Zr)/b(Ti,Zr) transformation temperature of about 660°C and 65 wt% Zr may be doubtful. A comparable minimum was found in the vertical section Ti-25.3 at.% Al/Zr at about 515°C and 70 wt% Zr. [55] In this study, the vertical section has been determined between 500 and 1900°C by thermal analysis of 11 alloys and microstructural and XRD investigations of quenched alloys. [55] Beside determination of the solidus temperatures, phase boundaries of the a(Ti,Zr), a(Ti,Zr) ? b(Ti,Zr), and b(Ti,Zr) phase fields were determined. The melting temperature determined for Zr (1850°C) and the solidus temperature of Ti 3 Al with 24.1 at.% Al (* 1650°C) are very close to the currently accepted values 1855°C [80] and 1655°C. [27] Therefore, remaining solidus and liquidus temperatures determined in (Ref 55) may be considered as relevant. Though the existence of the compound Ti 3 Al has been realised in (Ref 55), the phase has not been included in the vertical section. Also, according to the isotherms at 800°C and 1000°C shown in Fig. 2 and 4, this vertical section should include phase equilibria with quite a number of other phases e.g. TiAl or Zr(Al,Ti) 2 . As no other phases than a(Ti,Zr) and b(Ti,Zr) are shown in the section, solid phase equilibria from [55] are not further considered here. One more ''tentative'' section along Ti-33.3 at.% Al/Zr [64] was constructed from 20 samples annealed between 500 and 1100°C, which were analyzed by metallography and partly by XRD, supplemented by data from thermal analysis. The section had been tentative, as many alloys underwent phase transformations during cooling and therefore phase equilibria at the annealing temperature were not clear. Again the section misses out phase equilibria with the phases originating in the Al-Zr binary system, with the exception of Zr 3 Al, which according to this section would coexist over a large composition range with a(Ti,Zr) and b(Ti,Zr). [64] In the vertical sections Ti/Ti-49.4 at.% Zr containing 0, 6.9, and 9.6 at.% Al the phase boundaries for a(Ti,Zr) and b(Ti,Zr) between 600 and *1100°C were determined by metallography of annealed samples and additional dilatometry for the binary section. [76] All phase boundaries show a sharp increase in temperature between 0 and about 1 at.% Zr, e.g. about 45 K for a(Ti,Zr)/a(Ti,Zr) ? b(Ti,Zr), and then temperatures decrease steadily to 49.4 at.% Zr. As far as temperatures can be read from the diagram, they seem not to match phase boundaries shown for 800°C and 1000°C in Fig. 2 and 4 and as a peak in temperature in the a(Ti,Zr) and b(Ti,Zr) phase boundaries is thermodynamically improbable, results of (Ref 76) are not further considered here.

Sections Towards the Al Corner
Based on metallography on heat treated samples quenched from 800, 1000, 1100 and 1200°C, thermal analysis and dilatometry, two vertical sections for Ti-2.7 at.% Zr/Ti-25.3 at.% Al between 700 and 1750°C and for Ti-2.7 at.% Zr/Ti-25.8 at.% Al, 2.4 at.% Zr between 500 and 1200°C were determined. [73] Results of the former section were also published in (Ref 81) and in some more detail in (Ref 74). The latter section showing additional data for 700°C was also published in (Ref 75). Though single data points fit well to data shown in Fig. 2 and 4, the general sequence of phase equilibria is not correct. While the phase equilibrium a(Ti,Zr) ? b(Ti,Zr) ? Ti 3 Al is detected at 1000°C in the former, i.e. more Zr lean section, it does not show up at this temperature in the latter, i.e. the more Zr rich one, which only shows the three-phase equilibrium at higher temperatures. According to Fig. 2, the three phase equilibrium should either be present in both sections or only in the more Zr-rich one, but not vice versa as shown in (Ref 73-75,81).
The a(Ti,Zr)/b(Ti,Zr) phase boundaries in the vertical section Ti-2.3 at.% Al/Ti-20 at.% Al, 2.3 at.% Zr were calculated in the temperature range 850-1000°C and verified by analysing three alloys. [82] Comparison of the a(Ti,Zr)/b(Ti,Zr) phase boundaries at 1000°C shows that they fit quite well to those shown in Fig. 2. The shift of the Fig. 3 Isothermal section at 800°C according to (Ref 25) with additional experimental results from the literature a(Ti,Zr)/a(Ti,Zr) ? Ti 3 Al phase boundary towards higher temperatures and lower Al contents with increasing Zr content is shown for the temperature range 500-700°C in [2] .
According to the modelling, the phase field of a(Ti,Zr) extends much further into the ternary system at 800°C compared to (Ref 25), in line with the discussion of this section above. Also b(Ti,Zr) extends somewhat more into the ternary system at 800°C, i.e. has a bit higher solid solubility for Al than shown in (Ref 25). The major difference between the isothermal sections for 800°C, are that the experimental one shows phase equilibria between b(Ti,Zr) and Zr(Al,Ti) 2 , [25] while the calculations show that TiAl should be in equilibrium with Zr 4 Al 3 . [83] Therefore, multiphase equilibria in a wide range of compositions in the two isotherms are quite different from each other as discussed in (Ref 83). Which of the two versions is correct cannot be decided on the existing evidence.
Modelled [83] and experimentally determined [24] isothermal sections at 1000°C qualitatively match much better. Though, there are some differences in the solid solubility ranges of individual phases, most notably for Ti 3 Al, which has less solid solubility for Zr according to the modelling. Otherwise, all multiphase equilibria in the experimental section are reproduced in the modelling. At higher temperatures there is quite some discrepancy at 1200°C between the modelling [83] and experimental data in the Ti-corner, [23] while the match at 1300°C is somewhat better. Calculated phase boundaries at 800 and 1000°C of the vertical section [83] fit very well with those of the binary accepted here, with the sole exception for the a(Ti)/a(Ti) ? Ti 3 Al phase boundary at 800°C, which according to Fig. 4 should be at a somewhat lower Al content. Fig. 4 Critically assessed isothermal section of the Al-Ti-Zr system at 800°C A vertical section along (Ti,Zr)Al 3 has been calculated for 900-1100°C. [85] In this section the two-phase field D0 22 ? D0 23 is located much closer to the TiAl 3 (D0 22 ) side than in the experimentally determined section at 1000°C (Fig. 1). [24] The relative stability of the L1 2 , D0 22 and D0 23 structures along TiAl 3 -ZrAl 3 was investigated at 0 K by calculating the enthalpy of formation using first principles calculations. [86] The results indicate that the D0 23 structure is the most stable along the complete section. While this finding agrees with experimental evidence for ZrAl 3 , it is in contradiction for TiAl 3 , where D0 23 is known to be the high-temperature polymorph while at lower temperatures D0 22 becomes stable. This discrepancy between ab initio calculations and experiments in case of TiAl 3 is well known and also discussed in ( Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons. org/licenses/by/4.0/.
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