The Al–B–Nb–Ti system

Journal of Alloys and Compounds 472 (2009) 133–161

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The Al–B–Nb–Ti system IV. Experimental study and thermodynamic re-evaluation of the binary Al–Nb and ternary Al–Nb–Ti systems V.T. Witusiewicz a,∗ , A.A. Bondar b , U. Hecht a , T.Ya. Velikanova b a b

ACCESS e.V., Intzestr. 5, D-52072 Aachen, Germany Frantsevich Institute for Problems of Materials Science, Krzhyzhanovsky Str. 3, 03680 Kyiv, Ukraine

a r t i c l e

i n f o

Article history: Received 7 March 2008 Accepted 2 May 2008 Available online 30 June 2008 Keywords: Al–Nb Al–Nb–Ti Phase diagram Thermodynamic description CALPHAD approach

a b s t r a c t The thermodynamic description of the entire ternary Al–Nb–Ti system is obtained by CALPHAD modelling of the Gibbs energy of all individual phases, taking into account experimental data on phase equilibria and thermodynamic properties published and complemented by own experiments. The description includes a re-evaluation of the constituent binary Al–Nb system. Selected equilibrium calculations were performed with the Thermo-Calc software using the proposed description. They are shown to well reproduce experimental data on both, phase equilibria and thermodynamic properties in the entire Al–Nb–Ti system. © 2008 Elsevier B.V. All rights reserved.

1. Introduction The present paper continues our series of publications on the development of a thermodynamic database for the quaternary Al–B–Nb–Ti system [1–3] and focuses on the thermodynamic description of the core constituent ternary system Al–Nb–Ti. The thermodynamic description was performed on the basis of the Al–Ti description [3], the re-evaluated binary description for Al–Nb, and the description of Ti–Nb used in Ref. [2]. A large number of experimental data on phase equilibria and thermodynamic properties for ternary alloys were selected from literature and complemented by own experiments in critical composition–temperature ranges. A thorough analysis of earlier thermodynamic descriptions for the Al–Nb–Ti system [4–7] as well as for the constituent binary Al–Nb system [8–10] shows that they are not able to correctly reflect the present status of experimental knowledge in these systems. Especially the previous thermodynamic descriptions proposed for the Al–Nb–Ti system are contradicted by recent experimental information on liquid–solid equilibria, i.e. liquidus and solidus temperatures, fields of primary solidification, invariant reactions, etc. To some degree this mismatch can be traced back to inex-

∗ Corresponding author. Tel.: +49 241 8098007; fax: +49 241 38578. E-mail address: [email protected] (V.T. Witusiewicz). 0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.05.008

act descriptions of the constituent binary systems Al–Ti [8,11] and Al–Nb [8–10,12], but the more influential factor is the lack of experimental data on liquid–solid equilibria in the ternary system. The work presented here aimed to close this lack and lead to an improved thermodynamic description of the entire Al–Nb–Ti system that is of major interest for the alloy development and process engineering perspective. A good, reliable thermodynamic description of the ternary system Al–Nb–Ti is most relevant for alloy design and processing of titanium aluminides but also for a number of aluminium- and titanium-based alloys. Of special interest for aluminides are equilibria involving the liquid phase for casting, the surfaces that correspond to beta- and alpha-transus for heat treatment, and certainly low temperature equilibria for the analysis of phase stability in the expected conditions of service. The present paper is structured as follows: in Section 2 experimental data are summarized with main emphasis on the measurements performed within the frame of this work. Section 3 contains a brief description of the thermodynamic models used for describing the Gibbs free energy of the individual phases of the alloy system and of the optimization procedure applied for energy minimisation in the entire system. The resulting thermodynamic database is given in Appendix A. Section 4 contains a large number of calculations performed with the elaborated database, including the liquidus, solidus, and ␤ solvus projections, isothermal sections and selected isopleths as well as thermodynamic properties. The

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Table 1 The phase designations most often used in literature for the Al–Nb–Ti system along with crystal structure data [3,16] and thermodynamic models used in the present description Phase (designation)

Pearson symbol

Space group

Strukturbericht designation

Prototype

Model used in the present description/remark

cF4 hP2 hP8 cI2 cI2 tP4 cP8 tI8 tI32 tP28 tI24 tP30 tP32 oC16 oC16 hP6 tP16

¯ Fm3m P63 /mmc P63 /mmc ¯ Im3m ¯ Pm3m

A1 A3 D019 A2 B2 L10 A15 D022 – – – D8b – – – B82 –

Cu Mg Ni3 Sn W CsCl AuCu Cr3 Si TiAl3 (h) TiAl3 (l) Ti2 Al5 HfGa2 ␴CrFe Ti3 Al5 NaHg NaHg Ni2 In ␥1 -Ti4 Nb3 Al9

[Al,Nb,Ti] [(Al,Ti)1 :(Va)1 ] [(Al,Nb,Ti)1 :(Va)0.5 ] [(Al,Nb,Ti)3 :(Al,Nb,Ti)1 ] [(Al,Nb,Ti)1 :(Va)3 ] [(Al,Nb,Ti)1 :(Va)3 ] + [(Al,Nb,Ti)0.5 :(Al,Nb,Ti)0.5 :(Va)3 ] [(Al%,Nb,Ti)1 :(Al,Nb,Ti%)1 ] [(Al,Nb,Ti)0.75 :(Al,Nb,Ti)0.25 ] [(Al,Ti)3 :(Al,Ti)1 ] [(Al,Ti)3 :(Al,Ti)1 ] [(Al,Nb,Ti)5 :(Al,Nb,Ti)2 ] [(Al,Nb,Ti)2 :(Al,Nb,Ti)1 ] [(Al,Nb,Ti)0.533 :(Al,Nb,Ti)0.333 :(Nb,Ti)0.134 ] [(Al)5 :(Ti)3 ] [(Al,Nb,Ti)0.75 :(Al,Nb,Ti)0.25 ] [(Al,Nb,Ti)0.50 :(Al,Nb,Ti)0.25 :(Al,Nb,Ti)0.25 ] [(Al)3 :(Nb)1 (Ti)4 ] Not considered in this work

La ,

liquid (Al) (␣Al), fcc A1 ␣, (␣Ti), hcp A3 ␣2 , Ti3 Al ␤, (␤Ti), bcc A2 ␤0 , ␤ , bcc B2 ␥, ␥TiAl, TiAl ␦, Nb3 Al ␧, (Ti1-x Nbx )Al3 , TiAl3 (h), NbAl3 ␧(l), TiAl3 (l) ␨, Ti2+x Al5-x ␩, TiAl2 ␴, Nb2 Al Ti3 Al5 O1 b , O, O1 (h), Ti2 NbAl O2 b , O2 (r), Ti2 NbAl ␶b , Ti4 NbAl3 ␥1 -Ti4 Nb3 Al9 b , c a b c

P4/mmm ¯ Pm3n I4/mmm I4/mmm P4/mmm I41 /amd P42 /mnm P4/mbm Cmcm Cmcm P63 /mmc P4/mmm

Designations given in bold letters are used throughout the present work. Ternary phase. New intermetallic compound [26].

calculations are discussed in comparison to experimental data regarding phase equilibria of major interest. 2. Experimental data 2.1. Literature data The status of investigations available for the Al–Nb–Ti system was summarized in recent critical assessments by Raghvan [15] and Tretyachenko [16] where the

majority of all literature data up to 2003 were comprised. In the ternary system three ternary phases were found, of which O1 and O2 have near composition (Ti2 NbAl) and crystal structure (Table 1). In the constituent binary Al–Nb system the key experimental information was reviewed by Zhu et al. [12]. Important experimental data were published later than 2003 [12–14,17–26], or were recently shared within the IMPRESS project [27,28]. The data pool was further enlarged with our own measurements, described below. These measurements were meant to provide data in critical composition–temperature regions for both, the Al–Nb and the Al–Nb–Ti systems, with main focus on solid–liquid phase transitions.

Table 2 Composition and phase identification for as-cast and annealed samples No.

Composition (at.%) Nominal

XRD and metallographic phase identification EDX analysis

As-cast alloy

Annealed alloy

Ti

Nb

Al

Ti

Nb

Al

Primary phase

Phase constituents

Annealing conditions, T (K)/t (h)/quench

Phase constituents

1 2 3 4 5 6 7 8 9 10 11

0 0 0 0 0 0 0 0 0 0 46

5.0 24.5 24.7 24.9 25.2 25.6 45.0 70.0 77.0 79.0 8

95.0 75.5 75.3 75.1 74.8 74.4 55.0 30.0 23.0 21.0 46

0 0 0 0 0 0 0 0 0 0 46.1

5.1 24.9 25.1 25.3 25.5 25.9 45.6 70.9 77.8 81.2 8.1

94.9 75.1 74.9 74.5 74.5 74.1 54.4 29.1 22.2 18.8 45.8

␧ ␧ ␧ ␧ ␧ ␧ ␴ ı ␤ ␤ ␤

␧ + (␣Al) ␧ + (␣Al) ␧ ␧ ␧ ␧+␴ ␧+␴ ␴+ı ␤+ı ␤+ı ␣2 + ␥

12 13 14 15

45 44 38 65

8 8 8 11

48 50 55 24

44.5 43.1 38.3 67.3

7.7 7.3 7.6 10.6

47.8 49.6 54.1 22.1

␤ ␤ ␣ ␤

␣2 + ␥ ␣2 + ␥ ␣2 + ␥ ␣ + ␣2 + ␤

16

58

17

25

57.7

17.1

25.2

␤

␣2 + ␤+O

17

50.0

12.5

37.5

50.4

12.6

37.0

␤

␣2 + ␤

18 19 20 21 22

25 55 51 47 43

19 0 4 8 12

56 45 45 45 45

25.3 55.8 51.0 47.0 43.8

19.0 0 4.2 8.2 11.9

55.7 44.2 44.8 44.9 44.3

␥ ␤ ␤ ␤ ␤

␥ ␣2 + ␥ ␣2 + ␥ ␣2 + ␥ ␤+␥

23 24 25 26

53 49 45 41

0 4 8 12

47 47 47 47

53.2 48.8 45.0 41.5

0 4.1 8.1 11.7

46.8 47.1 46.9 46.8

␤ ␤ ␤ ␤

␣2 + ␥ ␣2 + ␥ ␣2 + ␥ ␤+␥

– Ar, 1823/5/fca Ar, 1823/5/fc Ar, 1823/5/fc Ar, 1823/5/fc Ar, 1823/5/fc – – – – Ar, 1703/10/fc Ar, 1633/2/H2 O Ar, 1633/2 + 1200/15/H2 O Ar, 1673/10/fc Ar, 1673/10/fc Ar, 1673/10/fc Vac., 1673/4.5/fc Vac., 1673/4.5 + Ar, 973/625/fc Vac., 1673/4.5/fc Vac.,1673/4.5 + Ar, 973/625/fc Vac., 1673/4.5/fc Vac., 1673/4.5 + Ar, 973/625/fc Ar, 1673/8/H2 O Ar, 1703/10/fc Ar, 1703/10/fc Ar, 1703/10/fc Ar, 1703/10/fc Ar, 1473/3/H2 O Ar, 1703/10/fc Ar, 1703/10/fc Ar, 1703/10/fc Ar, 1473/3/H2 O

– ␧ + (␣Al) ␧ ␧ ␧ ␧+␴ – – – – ␣2 ␣ ␣+␥ ␣2 + ␥ ␣2 + ␥ ␥ ␣ + ␣2 + ␤ ␣ + ␣2 ␣ + ␣2 + ␤ ␣2 + O ␣2 + ␥ ␣2 + ␥+␶ ␥ ␣2 + ␥ ␣2 + ␥ ␣2 + ␥ ␤+␣2 + ␥ ␤+␣+␥ ␣2 + ␥ (␣2 ?) + ␥ ␣2 + ␥ ␤ + ␣+ ␥

a

fc denotes cooling in a furnace with rate of 180 K min−1 .

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Fig. 1. XRD spectra of selected samples with 12 at.% Nb (taken from metallographic sections): Ti41.5 Nb11.7 Al46.8 as-cast (a); the same annealed at 1703 K for 10 h, cooled in furnace with a rate of 180 K min−1 (b); Ti43.8 Nb11.9 Al44.3 as-cast (c); the same annealed at 1703 K for 10 h (d).

Fig. 2. Examples of microstructure of as-cast samples: (a) ␤ primary solidification in sample Ti44.5 Nb7.7 Al47.8 ; (b) ␣ primary solidification in sample Ti43 Al52 Nb5 ; (c) ␣ primary dendrites enveloped by ␥-dendrites in sample Ti38.3 Al54.1 Nb7.6 .

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Fig. 3. The left hand column shows the microstructure of samples with 45 at.% Al and different Nb content after annealing for 8 h at 1703 K followed by cooling with a rate of 180 K min−1 : (a) 4 at.% Nb, (c) 8 at.% Nb and (e) 12 at.% Nb (samples nos. 20–22). The right hand column shows the corresponding microstructures for samples with 47 at.% Al and (b) 4 at.% Nb, (d) 8 at.% Nb and (f) 12 at.% Nb (samples nos. 24–26).

2.2. Experimental results 2.2.1. Preparation of alloys In order to verify phase equilibria in the Al–Nb and Al–Nb–Ti systems a number of 26 different samples, with a mass of 15 or 20 g each, were prepared (Table 2) by arc melting with a non-consumable tungsten electrode on a water-cooled copper hearth under purified Ar (cooling rates of about 100 K s−1 ). The initial materials were metallic Al (99.99 wt.% Al), Nb (99.9 wt.% Nb) and Ti (99.9 wt.% Ti) obtained from the iodide titanium process. As shown by reducing extraction in a Ni bath followed by chromatography, the oxygen content in the samples ranged from 0.01 to 0.04 wt.% (100–400 wt. ppm) and the contamination by N and H was lower than the threshold of sensitivity (about 0.001 wt.% N and 0.003 wt.% H). The samples were chemically characterized and studied in the as-cast state and after annealing at selected temperatures (see

Table 2) by DTA, XRD and optical microscopy. The microstructure of selected samples was also analyzed in SEM. Annealing was performed in a resistance furnace with a tungsten heater in argon gettered by Ti cuttings. The cooling rate was estimated as approximately 180 K min−1 .

2.2.2. XRD and SEM analysis of the samples XRD was carried out in a DRON-3 diffractometer on metallographic sections for ductile samples and on powders for brittle samples, respectively. Scanning electron microscopy (SEM) was carried out in a JEOL Superprobe 733. The integral chemical composition of the samples was measured by EDS in a Gemini 1550 scanning electron microscope equipped with an INCA analysis system. Quantitative analysis of EDS spectra was done against own Ti–Al–Nb standard, previously characterized by elastic recoil detection analysis (ERDA) at the Hahn-Meitner Institute in Berlin.

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The majority of the XRD spectra of as-cast and annealed ternary alloys contained the diffraction peaks of the ␥-phase and the ␣2 -phase (see Table 2), including the (2 0 1) reflection of the latter (Fig. 1). The primary solidification phase of the samples was identified from the morphology of the dendritic patterns observed in SEM. Examples are shown in Fig. 2. The XRD spectra of samples with more than 10 at.% Nb (samples nos. 15–17, 22 and 26) contained one or two strong reflections of the bcc ␤-phase, labelled (␤Ti,Nb,Al). In samples with 8 and 12 at.% Nb, the ␥-phase solidified from the last crops of melt (see Fig. 2, black constituent). The weak XRD peaks in some as-cast samples were found at 2 equal to 34.1◦ (see Fig. 1a and c) and 39.8◦ but disappeared after annealing. Therefore, they are thought to originate from metastable phases, which were not investigated further. After annealing in the single ␣-phase field prominent texture was observed in the XRD spectra taken from metallographic sections, being due to gigantic ␣-grains that transformed to lamellar structure upon cooling (e.g. Fig. 3b and d). The lattice parameters of the identified phases remained almost unaffected by the alloy composition; for the ␥-phase they were a = 400–403 pm and c = 407–409 pm; for the ␣2 -phase they were a = 575–577 pm and c = 462–463.5 pm; for the ␤-phase they were a = 322–323 pm. For the binary NbAl3 (␧-phase) they were a = 384.0–384.1 pm and c = 860.8–861.5 pm. Concerning the ␤-phase, no distinct reflex of the CsCl (B2) crystal structure was identified, perhaps due to its small phase fraction (see the (1 1 0) peak in Fig. 1). From the point of view of ␥TiAl-based materials, of special interest is the microstructure evolution in the samples with 45 at.% Al (samples nos. 19–22) and with 47 at.% Al (samples nos. 23–26) as function of their Nb content, at different annealing temperatures. At the annealing temperature of 1703 K the samples with 45 at.% Al and Nb lower than 12 at.% were in two-phase ␣ + ␤ field (Fig. 3, left column), while the samples with 47 at.% Al and Nb lower than 12 at.% were in the single ␣ field that resulted in their pronounced coarsening (Fig. 3, right column). The sample with 47 at.% Al and 12 at.% Nb displayed a small amount of ␤-phase at 1703 K (see Fig. 3f) that significantly reduced the coarsening of ␣-grains. Fig. 4a and b displays the microstructure of the samples with 12 at.% Nb after annealing at 1473 K followed by water quenching. For both 45 and 47 at.% Al, the microstructure at 1473 K consists of a three-phase mixture of ␥, ␤ and ␣, however the fractions of these phases differ considerably: in sample no. 26 (47 at.% Al, 12 at.% Nb) large ␥-grains are decorated

Fig. 4. Microstructure of sample no. 22 Ti43.8 Nb11.9 Al44.3 (a) and no. 26 Ti41.5 Nb11.7 Al46.8 (b) annealed for 3 h at 1473 K and quenched in water as well as sample no.11 Ti46.1 Nb8.1 Al45.8 annealed as follows: Ar, 1633 K/2 h/H2 O (c) and Ar,1633 K/2 h + 1473 K/15 h/H2 O (d).

Fig. 5. DTA curves of Al–Nb and Al–Nb–Ti alloys processed in Sc2 O3 crucibles along with temperatures of incipient melting determined by pyrometry: (a) Nb25.9 Al74.1 annealed at 1823 K for 5 h (20 K min−1 ); (b) Nb25.1 Al74.9 annealed at 1823 K for 5 h (20 K min−1 ); (c) Ti46.1 Nb8.1 Al45.8 annealed at 1703 K/2 h + 1743 K/8 h + 1623 K/10 h processed at 20 K min−1 ); (d) the same as (c) processed at 40 K min−1 . For clarity, the DTA curves have been shifted vertically.

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V.T. Witusiewicz et al. / Journal of Alloys and Compounds 472 (2009) 133–161 2.2.3. DTA analysis and incipient melting of the alloys Temperatures of solid-state and solid–liquid phase transformations were determined by DTA using Sc2 O3 crucibles and W/W-20Re string thermocouples designed by Kocherzhinsky et al. [29,30]. The DTA measurements were performed under high purity He with heating and cooling rates of 20 or 40 K min−1 . The thermocouple was calibrated using the IPTS-90 reference points of Al, Au, Pd, Pt, Rd and also additional reference points of Fe and Al2 O3 . The solidus temperature for the samples nos. 2, 3, 7 and 11 (incipient melting) were also determined using the method devised by Pirani and Alterthum [31]. Bar-shaped specimens, which were clamped between two water-cooled copper electrodes through tungsten inserts (tips of electrodes and plate washers), were resistively heated under high purity Ar (slightly higher than the atmospheric pressure). The temperature was measured optically on the background of a black body hole (the diameter to depth ratios were about 1–4) with a disappearing filament-type pyrometer “EOP-68” of standard quality level. Its maximum instrumental errors amount to ±2.8 K for the temperature region 1200–1700 K and ±4 K for 1700–2300 K. It was calibrated and certificated by the National Scientific Centre “Institute of metrol-

Fig. 6. The DTA curves upon heating with 20 K min−1 for samples with nominal Nb content of 8 at.% and Al content from 45 to 48 at.% show how the peritectic reaction is approached: (a) Ti46.9 Nb8.2 Al44.9 , (b) Ti46.1 Nb8.1 Al45.8 , (c) Ti45.0 Nb8.1 Al46.9 and (d) Ti44.5 Nb7.7 Al47.8 . Like in Fig. 5 the curves are shifted vertically.

with few ␤ and ␣ at grain boundaries, while in sample no. 22 (45 at.% Al and 12 at.% Nb) medium sized ␣-grains are heavily decorated with ␤ inter-dispersed with small ␥-grains. The existence of all three phases is well reproduced with the proposed thermodynamic description see Fig. 17. Fig. 4c and d show the microstructure of sample no. 11 with about 46 at.% Al and 8 at.% Nb: after annealing for 2 h at 1633 K the sample displays single phase ␣-grains (Fig. 4c), whereas the double annealing 1633 K/2 h + 1473 K/15 h resulted in a lamellar two-phase structure composed of ␣ and ␥ (Fig. 4d).

¯ i ) of the pure components Al, Nb, Fig. 7. The partial enthalpy of dissolution (diss H Ti and of the single-phase ␥-alloy Ti25.3 Nb19.0 Al55.7 (sample no. 18) in pure Ni at temperature 1773 ± 5 K.

Fig. 8. Calculated Al–Nb phase diagram (lines) along with experimental data from Refs. [12,44,45] and from the present work (points): (a) entire diagram; (b) enlarged part in the vicinity of NbAl3 (␧-phase).

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Fig. 9. Activity of components in the Al–Nb system at 1078 K referred to fcc Al and bcc Nb: points are experimental data from Refs. [14,46], lines resulted from the present thermodynamic description.

ogy” (http://www.metrology.kharkov.ua/eng/centres/NC-1.htm). The temperature of incipient melting was read in the moment of formation of a spot on the background of the black body hole. This moment also corresponds to a change of the sample shape at the bottom (which becomes half-spherical) and (or) to a change of the reflection at the sample surface [32]. The latter turns smooth due to filling the surface roughness by melt. A number of five measurements were carried out for each sample and afterwards the average value as well as standard deviation was determined. DTA and the Pirani–Alterthum methods give similar values for the solidus temperatures. As an example, the DTA curves and solidus temperatures measured by the pyrometer are shown in Fig. 5. Fig. 6 depicts selected heating curves obtained by DTA for a series of samples with the nominal Nb content of 8 at.% and Al contents of 45, 46, 47 and 48 at.%, respectively. These samples were given an annealing treatment prior to DTA processing, in order to make sure that the measured phase transition temperatures would not be affected by segregation inherited from casting. The DTA curves show how the temperature interval corresponding to the presence of single ␤-phase narrows as the alloy composition approaches the onset of the peritectic reaction “␣ ↔ ␤ + liquid”. This reaction is revealed in Fig. 6c and d. The shape of the DTA peaks associated to melting of the ␤-phase reflects the evolution of the liquid fraction with temperature, but may be disturbed by side effects related to the change of sample geometry to droplet upon melting and wetting of the crucible. Table 3 contains the phase transformation temperatures detected by DTA and by the Pirani–Alterthum method in all investigated samples, together with the values calculated with the proposed thermodynamic description of the Al–Nb–Ti system. 2.2.4. Standard enthalpy of formation Within the frame of the present work the standard enthalpy of formation at 298 K was experimentally determined for the ␥ single-phase sample Ti25.3 Nb19.0 Al55.7 (no. 18 in Table 2) annealed for 8 h at 1673 K. The method is well described in Refs. [33,34] and involves the determination of the enthalpy of dissolution of pure solid Al, Nb, Ti as well as that of the alloy in liquid Ni at 1773 ± 5 K by drop isoperibolic calorimetry. Using these data the partial enthalpy of dissolution of cold samples ¯ ◦ ) were evaluated by (298 K) in liquid Ni (1673 K) at infinite dilution (diss H i means of linear extrapolation to xNi = 1. The results are given in Fig. 7 and Table 4. The standard enthalpy of formation (298 H◦ ) and its error (2) for this alloy, referred to bcc Nb, hcp Ti and fcc Al at 298 K, was determined using the values from Table 4 and following expressions: ◦

◦

◦

◦

◦

298 H = 0.557diss HAl + 0.190diss HNb + 0.253diss HTi − diss Halloy 2 =

 i

(ni 2i )2

(1)

(2)

Fig. 10. Enthalpy of formation of alloys in the Al–Nb system: (a) standard enthalpy at 298 K referred to fcc Al and bcc Nb; (b) standard enthalpy at 1620 K referred to liquid Al and bcc Nb; points are experimental [14,46,48,49] and calculated ab initio [50] data, lines resulted from the present thermodynamic description.

This procedure gives the following value for the enthalpy of formation of one mole of formula unit Ti0.253 Al0.557 Nb0.190 : 298 H◦ = −36.8 ± 2.2 kJ mol−1 .

3. Thermodynamic models and optimization procedure In the present work we used the thermodynamic models of the individual phases stemming from the established descriptions of the constituent binary systems Al–Ti [3], Al–Nb [9], Nb–Ti [35] and for the O1 -, O2 - and ␶-phase, those proposed in Ref. [5] for the ternary system Al–Nb–Ti. The designation of individual phases,

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Table 3 DTA and pyrometric data for the Al–Nb–Ti samples in comparison with transformation temperatures calculated using the present thermodynamic description Alloy number

Composition and conditions

Rate (K min−1 )

Phase transformation

Temperature (K) Measured

1 2

Nb5.1 Al94.9 , as-cast Nb24.9 Al75.1 , ann. Ar, 1823/5/fc

20 20

(␣Al) + ␧ ↔ L + ␧ L + ␧ ↔ L incipient melting

3

Nb25.1 Al74.9 , ann. Ar, 1823/5/fc

20

␧↔L+␧ L + ␧ ↔ L incipient melting

4

Nb25.3 Al74.7 , ann. Ar, 1823/5/fc

20

5

Nb25.5 Al74.5 , ann. Ar, 1823/5/fc

20

6

Nb25.9 Al74.1 , ann. Ar, 1823/5/fc

20

7

Nb45.6 Al54.4 , ann. Ar, 1823/5/fc

20

␧↔L+␧ L+␧↔L ␧↔L+␧ L+␧↔L ␧+␴ ↔ L + ␧ – L+␧↔L ␧+␴ ↔ L + ␧ incipient melting

8 9 10 11

Nb70.9 Al29.1 , as-cast Nb77.8 Al22.2 , as-cast Nb81.2 Al18.8 , as-cast Ti46.1 Nb8.1 Al45.8 , ann. Ar, 1703/10/fc

20 20 20 20

12

Ti44.5 Nb7.7 Al47.8 , ann. Ar, 1673/10/fc

20

13

Ti43.1 Nb7.3 Al49.6 , ann. Ar, 1673/10/fc

20

14

Ti38.3 Nb7.6 Al54.1 , ann. Ar, 1673/10/fc

20

15

Ti67.3 Nb10.6 Al22.1 , ann. Vac., 1673/4.5/fc

40

16

Ti57.7 Nb17.1 Al25.2 , as-cast

40

17

Ti50.4 Nb12.6 Al37.0 , ann. Vac.,1673/4.5 + Ar, 973/625/fc

40

18

Ti25.3 Nb19.0 Al55.7 , ann. Ar,1673/8/H2 O

15

19

Ti55.8 Al44.2 , ann. Ar, 1703/10/fc

20

20

Ti51.0 Nb4.2 Al44.8 , ann. Ar, 1703/10/fc

20

L+␧↔L ı++␧↔L+ı ı+␤↔L+␤+ı ␤ ↔ L + ␤ incipient melting ␤0 + ␥ ↔ ␣ + ␤0 + ␥ ␤0 + ␥ ↔ ␣ + ␥ ␣+␥↔␣ ␣↔␣+␤ ␣+␤↔␤ ␤↔␤+L incipient melting ␤+L↔L ␣2 + ␥ ↔ ␥ ␥↔␣+␥ ␣+␥↔␣ ␣↔␣+␤ ␣+␤↔␣+␤+L ␣+␤+L↔␤+L ␤+L↔L ␥↔␣+␥ ␣+␥↔␣ ␣↔␣+L ␣+L↔␣+␤+L ␤+L↔L ␥↔␣+␥ ␣+␥↔␣+␥+L ␣+␥+L↔␣+L ␣+L↔L ␣2 + O2 ↔ ␣2 + ␤0 + O2 ␣2 + ␤0 + O2 ↔ ␣2 + ␤0 ␣2 + ␤0 ↔ ␤0 ␤0 ↔ ␤ ␤↔␤+L ␤+L↔L ␣2 + O1 ↔ ␣2 + ␤0 + O1 ␣2 + ␤0 + O1 ↔ ␣2 + ␤0 ␣2 + ␤0 ↔ ␤0 ␤0 ↔ ␤ ␤↔␤+L ␤+L↔L ␣2 + ␥ + ␶ ↔ ␣2 + ␥ ␣ 2 + ␥ ↔ ␣2 + ␤0 + ␥ ␣ 2 + ␤ 0 + ␥ ↔ ␣2 + ␤ 0 ␣2 + ␤0 ↔ ␤0 ␤0 ↔ ␤ ␤↔␤+L ␤+L↔L ␥↔␥+L ␥+L↔L ␣2 + ␥ ↔ ␣ + ␥ ␣+␥↔␣ ␣↔␣+␤ ␣+␤↔␤ ␤↔␤+L ␤+L↔L ␣2 + ␣ + ␥ ↔ ␣ + ␥ ␣+␥↔␣

Calculated

Heating

Cooling

930a 1994 1987 ± 6b 1983 1994 1988 ± 6b 1949 1987 1935 1982 1844 1953 1983 1857 1833 ± 6b 1916 2208 ± 7b 2336 ± 15b –2387 ± 15b – 1448 1625 1703 1752 1785 1773 ± 83 1859 1380 1507 1661 1763 1781 1803 1831 1578 1697 1753 1787 1801 1728 1761 – 1771 1184 – 1387 – 1968 1998 1208 – 1348 – 1998 2023 1093 1218 1413 1503 – 1913 1948 1834 1871 1381 1572 1702 1745 1778 1835 1429 1590

928a 1973

934.6 1987

1899 1914

1982 1987

1820 1910 1882 1930 1824 – 1924 1854

1960 1987 1904 1987 1844 – 1986 1844

1911 – – – – 1413 1557 1663 1745 1778

1893 2213 2335 2347–2421c 1443 1445 1596 1687 1761 1794

1839 – 1465 1622 1732 1759 1775 1808 1485 1676 1725 1769 1784 1718 1731 – 1744 – 1128 1418 – 1958 – 1183 – 1308 – 1978 – 1023 1198 1313 1488 – 1908 – 1815 1847 1369 1492 1688 1744 1770 1823 1385 1498

1846 1269 1477 1653 1754 1781 1782 1824 1574 1698 1774 1782 1801 1725 1754 1766 1770 1119 1126 1373 1399 1975 1984 1226 1248 1342 1479 1993 2008 1084 1296 1347 1415 1681 1913 1937 1830 1863 1391 1561 1703 1754 1768 1819 1438 1555

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141

Table 3 (Continued ) Alloy number

Composition and conditions

Rate (K min−1 )

Phase transformation

Temperature (K) Measured

21

T46.9 Nb8.2 Al44.9 , ann. Ar, 1703/10/fc

40

22

Ti43.8 Nb11.9 Al44.3 , ann. Ar, 1703/10/fc

20

23

Ti53.2 Al46.8 , ann. Ar, 1703/10/fc

20

24

Ti48.8 Nb4.1 Al47.1 , ann. Ar, 1703/10/fc

20

25

Ti45.0 Nb8.1 Al46.9 , ann. Ar, 1703/10/fc

20

26

Ti41.5 Nb11.7 Al46.8 , ann. Ar, 1673/10/fc

20

␣↔␣+␤ ␣+␤↔␤ ␤↔␤+L ␤+L↔L ␣2 + ␥ ↔ ␤0 + ␣2 + ␥ ␤0 + ␣2 + ␥ ↔ ␤0 + ␥ ␤0 + ␥ ↔ ␣ + ␤0 + ␥ ␣ + ␤0 + ␥ ↔ ␣ + ␥ ␣+␥↔␣ ␣ ↔ ␣ + ␤0 ␣ + ␤0 ↔ ␣ + ␤ ␣+␤↔␤ ␤↔␤+L ␤+L↔L ␣ + ␤0 + ␥ ↔ ␣2 + ␤0 + ␥ ␣ 2 + ␤ 0 + ␥ ↔ ␤0 + ␥ ␤ 0 + ␥ ↔ ␣ + ␤0 + ␥ ␣ + ␤0 + ␥ ↔ ␣ + ␥ ␣+␥↔␣ ␣ ↔ ␣ + ␤0 ␣ + ␤0 ↔ ␣ + ␤ ␣+␤↔␤ ␤↔␤+L ␤+L↔L ␣2 + ␥ ↔ ␥ ␥↔␣+␥ ␣+␥↔␣ ␣↔␣+L ␣+L↔␤+L ␤+L↔L ␣2 + ␥ ↔ ␣ + ␥ ␣+␥↔␣ ␣↔␣+␤ ␣+␤↔␣+␤+L ␣+␤+L↔␤+L ␤+L↔L ␣2 + ␥ ↔ ␤0 + ␣2 + ␥ ␤ 0 + ␣ 2 + ␥ ↔ ␤0 + ␥ ␤0 + ␥ ↔ ␣ + ␤0 + ␥ ␣ + ␤0 + ␥ ↔ ␣ + ␥ ␣+␥↔␣ ␣↔␣+␤ ␣+␤↔␣+␤+L ␣+␤+L↔␤+L ␤+L↔L ␤0 + ␥ ↔ ␣ + ␤0 + ␥ ␣ + ␤0 + ␥ ↔ ␣ + ␥ ␣+␥↔␣ ␣↔␣+␤ ␣+␤↔␤ ␤↔␤+L ␤+L↔L

Calculated

Heating

Cooling

1684 1749 1785 1835 – – 1436 – 1585 1666 1706 1744 1803 1866 – 1427 1501 – 1587 1663 – 1736 1820 1876 1275 1463 1632 1761 1763 1800 1454 1626 1756 1778 1787 1824 1445 – – – 1635 1738 1766 1788 1841 1531 – 1696 1731 1789 1820 1858

1705 1749 1756 1819 1402 – 1424 – 1526 1651 – 1718 1790 1844 – – 1418 – 1511 1674 – 1729 1814 1869 – 1412 1610 – 1755 1793 1433 1615 1738 – 1764 1810 1385 – – 1455 1632 1713 1754 1772 1826 1508 – 1666 1703 1777 – 1845

1684 1741 1785 1834 1429 1432 1445 1447 1567 1653 1708 1735 1807 1855 1369 1381 1480 1481 1579 1628 1702 1716 1836 1881 1294 1455 1627 1760 1762 1792 1437 1616 1740 1769 1770 1811 1432 1433 1443 1444 1631 1725 1782 1783 1835 1478 1478 1689 1722 1778 1799 1857

a

Uncertainty of temperature measurement at T < 950 K ranges at ±5 K. Pyrometric measurement on incipient melting temperature. c According to EDS of the cooled samples the composition of melted surface was leaner in Al by 4.2 at.%. Due to this the calculated values comprise the composition interval 18.8–14.6 at.% Al. b

their crystal structure data and the models employed in the present thermodynamic description are summarized in Table 1. The expressions for the molar Gibbs energy as function of temperature and composition for these models are given in Refs. [5,12,36]. The Gibbs energy descriptions for the stable and metastable structures of the pure elements are adopted from the SGTE database compiled by Dinsdale [37]. The model parameters of the phases listed in Table 1 were evaluated by searching for the best fit to available experimental data, e.g. to phase equilibria and thermodynamic properties of various alloys, using the PARROT optimizer of the software Thermo-Calc [36]. During the process of optimization the present DTA data as

well as the data reported by Hellwig et al. [40] on tie-lines and tietriangles at 1273 and 1473 K were accorded weight of 1.5. A weight of 2 was assigned to all data obtained by DSC [20–23]. All other data from literature [25,27,28,38,42,43,49,51–80] were assigned a weight equal 1. The experimental data are rich: they not only cover a large temperature range from 873 K [41] up to 2277 K [42,43] but also include data on the activity of components, heat capacity and enthalpy of formation of different solid alloys. On this basis, the enthalpic and the entropic terms for all phases could be modelled independently. No excess heat capacity terms were introduced. The gas phase was included in order to allow extrapolation up to temperatures

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Table 4 The partial enthalpy of dissolution of the pure metals and the single ␥-alloy Ti25.3 Nb19.0 Al55.7 in pure Ni at infinite dilution at the temperature 1773 ± 5 K ◦

Material

¯ (kJ mol−1 ) diss H

Error (2 i , kJ mol−1 )

Nb Ti Al Ti0.253 Nb0.190 Al0.557

−81.3 −88.8 −98.3 −55.9

1.7 1.9 1.9 1.8

i

parameters measured by XRD for the annealed samples. Fig. 8b also allows concluding that the melting temperature of NbAl3 measured by levitation thermal analysis [45] rather corresponds to the solidus temperature instead of the liquidus temperature. Thus, in agreement with our own measurements and with the present thermodynamic description, the congruent melting temperature of NbAl3 amount to 1987 K. This value is about 40 K higher than previously reported [9,10,12], whereas the temperature of the eutectic reaction L ↔ ␧ + ␴ at 1844 K is about 16 K lower. The Nb-rich part of the Al–Nb phase diagram closely corresponds to that of the most recent description by Zhu et al. [12]. In Table 5 the temperature and the composition of coexisting phases are listed for each invariant reaction in the Al–Nb system and compared with available experimental and assessed data.

of 6000 K. The complete thermodynamic database in Thermo-Calc format [36] is included in Appendix A. 4. Results and discussion for the binary Al–Nb system The phase equilibria and thermodynamic properties presented in this section were calculated using the computer program Thermo-Calc [36] on the basis of the thermodynamic description obtained from the above optimization.

4.2. Thermodynamic properties Experimental data for thermodynamic properties of binary Al–Nb alloys were reported in literature were based on the Knudsen effusion method [46], calorimetry [47–49] and electromotive forces (EMF) method [14]. Figs. 9 and 10 display the majority of these data along with the corresponding values being calculated with the present description. The agreement is quite good and also the values for the standard enthalpy of formation at 298 K correspond well to the those reported by Colinet et al. [50] based on ab initio calculations using the linear-muffin-tin-orbital method in the full potential approach.

4.1. Phase equilibria Fig. 8a shows the calculated phase diagram along with experimental data published in Refs. [12,44,45] and those determined in the present work. An enlarged view of the phase diagram in the vicinity of the intermetallic compound NbAl3 is presented in Fig. 8b. The solubility range of NbAl3 (␧-phase) at 1823 K (temperature of sample annealing) extends from 74.3 to 74.9 at.% Al. This is consistent with composition variations of the lattice

Table 5 Invariant equilibria in the Al–Nb system; results given in bold stem from the present work (PW) Invariant equilibrium, 1 + 2 + 3

Type

L+␤↔␦

p

L+␦↔␴

p1 a p

L↔␧

p2 c

L↔␧+␴

c1 e

L ↔ (␣Al) + ␧ L + ␧ ↔ (␣Al)

e2 e p

p8 a

T (K)

2333 ± 10 2336 ± 15 2324 2334 2333 2335 2213 ± 10 2208 ± 7 2209 2238 2209 2213 1953 ± 5 1986 ± 4 1968 1956 1961 1987 1863 ± 5 1845 ± 7 1869 1832 1861 1844 933 934.6 ± 0.5 934.6 ± 0.5 934.6 ± 0.5 930 ± 5 934.2 934.2 934.5 934.5

Composition of Al in phases (at.%) 1

2

3

28.0 – 28.8 28.2 26.1 26.5 36.0 – 36.8 35.3 34.9 35.2 75.0 – 74.86 75.0 75.0 74.86 55.0 – 58.1 58.8 58.0 56.2 – 99.96 – – – 99.999 100.0 99.999 99.998

21.5 – 18.0 16.9 19.8 19.5 25.0 – 25.4 22.8 23.8 24.9 75.0 – 74.86 75.0 75.0 74.86 – – 74.5 75.0 75.0 74.3 – – – – – 75.0 75.0 75.0 75.0

22.5 – 21.7 21.8 22.2 22.5 32.0 – 30.6 31.7 31.1 30.2 – – – – –

The reactions are labelled according to a reaction scheme presented below in Fig. 11.

42.0 – 40.4 40.4 40.6 38.6 – 99.94 – – – 99.90 99.9 99.85 99.85

Comment/reference

Experiment [81] Experiment [PW] Description [5,9] Description [10] Description [12] Description [PW] Experiment [81] Experiment [PW] Description [5,9] Description [10] Description [12] Description [PW] Experiment [81] Experiment [PW] Description [5,9] Description [10] Description [12] Description [PW] Experiment [81] Experiment [PW] Description [5,9] Description [10] Description [12] Description [PW] Experiment [82] Experiment [81] Experiment [83] Experiment [12] Experiment [PW] Description [5,9] Description [10] Description [12] Description [PW]

Table 6 Invariant equilibria involving the liquid phase in the Al–Nb–Ti system; results given in bold stem from the present work (PW) Invariant equilibrium 1 + 2 + 3 + 4

Type

T (K)

Composition of phases (at.%) 1

a b c

U U U U U U U1 U P U U U U P1 e e e e e e1 U U E E U U E E U U U U P2 U U U U2 P3

– ∼2073 2223 ∼2073 – 2102 2203 – 2023 ∼1623 ∼1739 – 1945 2012 – – ∼1773 1871 1858 – ∼1742 ∼1523 1743 ∼1742 – 1856 1831 – ∼1736 1941 – 1791 – ∼1573 1645 1679 938.7

2

3

4

Al

Nb

Al

Nb

Al

Nb

Al

Nb

– 30a 30a – 27a 29.5 32.2 – 49a 45a – 39a 39.5 41.5 – 66a – 62a 61.3 60.2 – ∼52 57a 59a – 51a 57.7 56.4 – – 39.0 40a 51.9 – 67a 71.0 70.5 99.9

– 41a 51a – 34a 40.9 58.9 – 20a 24a – 26a 25.7 33.8 – 17a – 8a 27.6 28.2 – ∼39 29a 22a – 31a 38.5 38.7 – – 16.3 21a 10.4 – 3a 0.3 1.2 5 × 10−5

– – – – – 22.6 26.2 – – – – – 32.5 37.8 – – – – 55.3 55.5 – – – – – – 53.0 52.9 – – 33.5 – 47.5 – – 62.8 64.8 76.5

– – – – – 50.4 66.1 – – – – – 30.9 37.4 – – – – 29.8 29.9 – – – – – – 40.9 38.5 – – 19.3 – 12.1 – – 1.4 1.7 0.6

– – – – – 21.7 23.7 – – – – – 37.5 36.0 – – – – 74.6 72.8 – – – – – – 74.5 73.3 – – 35.3 – 51.7 – – 74.9 73.6 75.7

– – – – – 56.1 70.5 – – – – – 26.0 43.8 – – – – 22.6 23.9 – – – – – – 24.6 25.2 – – 20.1 – 13.7 – – 2.9 2.5 2 × 10−6

– – – – – 28.1 30.0 – – – – – 32.7 39.6 – – – – – – – – – – – – 40.3 40.0 – – 36.0 – 49.4 – – 68.0 67.5 99.2

– – – – – 51.6 63.5 – – – – – 42.8 35.5 – – – – – – – – – – – – 55.8 51.5 – – 14.4 – 11.5 – – 0.0 0.7 3 × 10−3

[52–54] [51] [43] [15] b [8] [5] c [PW] c [52–54] [43] [51] [15] b [8] [5] c [PW] c [53] [52] [15] b [8] [5] c [PW]c [53,54] [52] [51] [43] [15] b [8] [5] c [PW]c [52–54] [15] b [5] c [8] [PW]c ␨ = Ti9 Al23 [52] ␨ = Ti5 Al11 [51] ␨ = Ti5 Al11 [5] c ␨ = Ti2 Al5 [PW]c [PW]c

V.T. Witusiewicz et al. / Journal of Alloys and Compounds 472 (2009) 133–161

L+␦↔␤+␴ L+␦↔␤+␴ L+␦↔␤+␴ L+␦↔␤+␴ L+␦↔␤+␴ L+␦↔␤+␴ L+␦↔␤+␴ L+␴↔␤+␥ L+␤+␥↔␴ L+␤↔␥+␴ L+␴↔␤+␥ L+␤↔␥+␴ L+␤↔␥+␴ L+␤+␴↔␥ L↔␥+␧ L↔␥+␧ L↔␥+␧ L↔␥+␧ L↔↔␥+␧ L↔␥+␧ L+␧↔␥+␴ L+␧↔␥+␴ L↔␥+␧+␴ L↔␥+␧+␴ L+␧↔␥+␴ L+␧↔␥+␴ L↔␥+␧+␴ L↔␥+␧+␴ L+␤↔␥+␣ L+␤↔␥+␣ L+␤↔␥+␣ L+␣↔␤+␥ L+␤+␥↔␣ – L+␨↔␥+␧ L+␥↔␧+␨ L+␥↔␧+␨ L + ␧ + ␧(l) ↔ (␣Al)

Reference/remark

Values are taken from diagrams. Tentative values based on a critical assessment of literature data. The present calculations using corresponding databases.

143

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5. Results and discussion for the ternary Al–Nb–Ti system 5.1. Reaction sequence The reaction scheme calculated with the present thermodynamic description down to 800 K is presented in Fig. 11, including

the binary constituent systems Al–Nb from the present work [PW] and Al–Ti reported earlier in Ref. [3]. The ternary system Al–Nb–Ti contains six invariant fourphase equilibria involving the liquid phase (compare Table 6). As reported by Tretyachenko [16], only one of the invariant reactions L + ␦ ↔ ␤ + ␴, marked as U1 in the reaction scheme (Fig. 11) and in

Fig. 11. The reaction scheme calculated down to 800 K in the Al–Nb–Ti system.

V.T. Witusiewicz et al. / Journal of Alloys and Compounds 472 (2009) 133–161

145

Fig. 12. The liquidus surface of the Al–Nb–Ti system showing (a) primary phase fields (points are experimental data of [25,27,38,51–54] and present work (PW) and (b) projection of isotherms (in K) and univariant lines on the Gibbs triangle.

the liquidus projection (Fig. 12), respectively, was distinctly estab¨ lished. It is the U-type (transition) reaction (Ubergangsreaktion), which sometimes is named as quasi-peritectic. The temperature of this reaction was calculated to be 2203 K, a value that agrees fairly well with the experimental value of T = 2223 K, reported by Pavlov and Zakharov [43]. The nature of the other invariant equilibria is not definitely established and various types have been proposed in literature. Our calculations show that the reaction L + ␤ + ␴ ↔ ␥ is peritectic labelled P1 , being at a temperature of 2012 K, which is in good agreement with experimental data of Pavlov and Zakharov (T = 2023 K) [43]. The occurrence of this ternary eutectic was confirmed by Kaltenbach et al. [51] and Pavlov and Zakharov [43], but the reported temperature of the eutectic

melting was underestimated, being 300 K [51] and 88 K [43] lower than the calculated temperature. The following invariant reactions are peritectic at 1791 K (P2 : L + ␤ + ␥ ↔ ␣), peritectic at 938.7 K (P3 : L + ␧ + ␧(l) ↔ (␣Al)) and transition at 1679 K (U2 : L + ␥ ↔ (␣Al) + ␧). The existence of a three-phase invariant equilibrium L ↔ ␥ + ␧ (e1 ) was revealed by [52,53], though its temperature was not established and the composition of phases was given only tentatively. According to the present description, this reaction occurs at 1858 K with the composition of the liquid being Ti11.6 Nb28.2 Al60.2 (see Figs. 11 and 12). The composition of the solid phases is presented in Table 6. According to the present description, a number of 13 fourphase invariant reactions and 5 quasi-binary invariant reactions

146

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Fig. 13. The solidus surface of the Al–Nb–Ti system projected on the Gibbs triangle, with isotherms given in K.

take place in solid state down to 800 K. They are given explicitly in the reaction scheme and some of them will be discussed here: the existence of the invariant equilibrium ␥ + ␨ ↔ ␧ + ␩ (Ud1 ) at 1530 K was reported by Kaltenbach et al. [51], but at lower temperature (∼1373 K). Leonard et al. [64] has suggested that the four-phase equilibrium ␤ + ␦ + ␴ + O occurs at ∼1173 K from a convergence of the ␤ + ␦ + ␴ and ␤ + ␴ + O phase fields in the Ti37.5 Nb37.5 Al25.0 alloy. This invariant equilibrium corresponds to the U-type reaction ␤0 + ␴ ↔ ␦ + O at 1244 K, labelled Ud3 in the present scheme. As calculated, a congruent transformation ␣2 ↔ ␤0 occurs at 1524 K.

5.2. Liquidus, solidus and ˇ-transus surfaces The calculated liquidus surface is displayed in Fig. 12a and b as projection on the Gibbs triangle, along with a large number of experimental data on primary phase solidification. Compared to the thermodynamic descriptions by Kattner [4] and Servant and Ansara [6] the primary ␤ field extends further towards the Al-rich corner, while correspondingly the fields of primary ␣, ␴ and ␦ are less extended. The limit of the primary ␴-phase field proposed by [54] to be at 20 at.% Ti is not fully confirmed by

Fig. 14. The ␤-transus surface of the Al–Nb–Ti system projected on the Gibbs triangle, with isotherms given in K: within the shadowed area the ␤-phase is ordered, i.e. ␤0 .

V.T. Witusiewicz et al. / Journal of Alloys and Compounds 472 (2009) 133–161

147

Fig. 15. Isothermal sections at elevated temperatures: points are experimental data of [4,18,40,43,52,53,58,59,63,64,70–75].

the present calculations: this field extends up to 26 at.% Ti and this limit fairly well corresponds to experimental data of three independent investigations [51–53]. The present description can well reproduce the boundary between ␣ and ␤ primary solidification fields evaluated by Johnson et al. [25] (see enlarged insert

in Fig. 12a) and Shuleshova et al. [27]. In general, except for the nature of invariant reactions, the liquidus surface is similar to a tentative construction proposed by Perepezko et al. [52]. The liquidus surface is characterized by three peritectic (P), two transition (U) and one eutectic (E) invariant reactions. The L − ␥ − ␧ univari-

148

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Fig. 16. Isothermal sections at moderate temperatures and room temperature: points are experimental data of [40,43,58,61,63,67,71,72,74,76–78].

ant line exhibits a maximum point e1 that corresponds to the three-phase L ↔ ␥ + ␧(h) quasi-binary eutectic reaction. This is in agreement with the experimental analysis by Perepezko et al. [52] and Zdziobek et al. [53]. The calculated solidus surface is shown in Fig. 13. It includes 6 tie-triangles corresponding to the four-phase invariant reactions given in Table 5. On the solidus surface 9 phases show considerable homogeneity ranges, with the largest homogeneity range

being that of ␤. The homogeneity ranges for ␧(l) and (␣Al) are very narrow and practically invisible at the given scale. The liquidus surface is also characterized by 14 univariant lines corresponding to two-phase fields in the solidus. Only the L + ␧ + ␥ univariant line exhibits a maximum point e1 , corresponding to a saddle point on the liquidus surface and to quasi-binary eutectic L ↔ ␧ + ␥ at 1858 K. It also corresponds to a maximal fold in the ruled solidus surface of ␧ + ␥ two-phase field.

V.T. Witusiewicz et al. / Journal of Alloys and Compounds 472 (2009) 133–161

The calculated ␤-transus surface is shown in Fig. 14. The invariant reactions are given the same labels as in the reaction scheme (compare Fig. 11). The calculated isotherms are limited at the lower side to 800 K (see dashed isotherm in Fig. 14) and at the upper side to the sequence of univariant reactions connecting p1 − U1 − P1 − P2 − p3 . Along this limiting line the ␤-transus surface connects to the solidus surface. Besides of four- and three-phase invariant reactions, the ␤-transus surface contains a congruent transformation labelled “C”, ␤0 ↔ ␣2 at the composition Ti61.3 Nb6.3 Al32.4 and temperature 1524 K. In 3D space the univariant lines between P1 − P2 and P1 − Ed2 do not intersect, the former being higher than the latter. 5.3. Isothermal sections A number of full and partial isothermal sections were constructed for this ternary system on the basis of experimental investigations published in Refs. [40,41,43,51–78]. Figs. 15 and 16 show the comparison of calculated isothermal sections with experimental data from the mentioned references. It is worthwhile to notice that tie lines measured by different authors

149

for nominally the same alloy composition and temperature sometimes differ for more than 10 at.% (compare, for example, the tie-lines of [40,63] for the 1273 K isothermal section in Fig. 16a). The calculated isothermal section at 1923 K in Fig. 15a shows that experimental ␤ − ␦ tie-line data of [58,59] are in good agreement with calculated boundaries. At 1673 K this is no longer the case: though experimental data on ␴ − ı and ␴ − ␧ boundaries as well as on ␤-ordering are well represented, the experimental ␤ − ␦ tie line data from Ref. [52] differ significantly form calculated values. Efforts to reproduce these specific data within the frame of this description were abandoned, since other equilibria turned incorrect. The calculated isothermal sections at 1473, 1423, 1373, 1333 and 1273 K agree well to experimental data, as may be concluded from Figs. 15d–f and Fig. 6a. The calculations also reproduced correctly the small island-like region of single ␤0 -phase at 1273 K in the range of 35–37 at.% Al and 43 to 45 at.% Ti that was observed experimentally by Hellwig et al. [40] (see Fig. 16a). This “island” becomes broader with increasing temperature and merges with the ␤0 -“bulk” phase field at about 1346 K (see Fig. 15e as well as

Fig. 17. Calculated vertical sections close to the Al–Ti side of Al–Nb–Ti system compared with experimental data from the present work [PW] and selected references [17,20–23,28,52] (points): (a) isopleth for 45 at.% Al, with the dashed lines corresponding to the shift of phase boundaries when the contribution of B2 ordering is eliminated; (b) isopleth for 47 at.% Al; (c) through Ti87.2 Nb12.8 and Nb2.2 Al97.8 and (d) isopleth for 8at.% Nb. The dotted lines show the order–disorder transformation of the ␤-phase.

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Fig. 14, the ed5 point). The formation of this island-like region of ␤0 is due to the strong contribution of ordering and bears no feature of a miscibility gap, as lately proposed by Raghvan in the critical assessment of the Al–Nb–Ti system [15]. According to the present description the Gibbs energy of the ␤-phase increases by about 800 J mol−1 due to B2 ordering in the range of 35–40 at.% Al and temperature 1250–1350 K, such that the three-phase field ␣2 + ␥ + ␴ that is present in the absence of ordering is subdivided into three three-phase fields, each with participation of the ␤0 phase (see Fig. 15f). This ␤0 -phase decomposes at 1197 K following the eutectoid invariant reaction ␤0 ↔ ␣2 + ␥ + ␴, labelled Ed3 in Figs. 11 and 14. A consequence of this ordering behaviour is the presence of the quasi-binary reaction labelled ed5 in the same figures. The occurrence of the ternary O1 -, O2 - and ␶-phases and the evolution of the phase fields with temperature are shown in the calculated isothermal sections at 1173, 1073, 973 and 873 K (see Fig. 16b–e). The O1 - and O2 -phases have the same orthorhombic oC16 crystal structure, space group Cmcm (see Table 1), but different site occupations [65]. A weak first order reversible trans-

formation between these two forms was predicted using the Bragg–Williams model [66]. Experimental investigations show that the O1 -phase forms at a temperature equal or somewhat lower than 1273 K and transforms to the O2 -phase at about 1173 K [67]. This is consistent with the present calculations, giving 1260 K and 1160 K, respectively. The ␶-phase was reported by Bendersky et al. [68] in the Ti50 Nb30 Al20 alloy annealed at 1173 K. Sadi and Servant [69] revealed it by in situ neutron diffraction in the sample Ti50.6 Nb12.9 Al36.5 at 1073 K or somewhat below. According to the thermodynamic description of the Al–Nb–Ti system by Servant and Ansara [5] the temperature of formation of the ␶-phase is 1233 K. Own experiments, summarized in Tables 2 and 3, showed that in the sample no. 17 with composition Ti50.4 Nb12.6 Al37.0 the ␶-phase decomposed upon heating at 1093 K and formed upon cooling at 1023 K. Moreover XRD and Rietveld analysis of the sample annealed at 973 K for 625 h showed that the ␶-phase was present at fractions higher than 95%, the lattice parameters were determined to be a = 456.8 and c = 551.5 pm. The calculation performed with the proposed thermodynamic description gives 1084 K for the decomposition of the ␶-phase upon heating, following a quasi-binary

Fig. 18. Calculated vertical sections (solid lines) in the Al–Nb–Ti system compared with experimental data from the present work (PW) and Refs. [24,42,52,53,65,72,79] (points): (a) through Ti72.8 Nb27.2 and Ti31.6 Al68.4 binary alloys; (b) through Ti70 Al30 and Ti51 Nb49 binary alloys, (c) isopleth for 27.5 at.% Al and (d) isopleth for 74.8 at.% Al, with the dashed lines showing solidus for small variations of Al, e.g. +0.5 and −0.2 at.% Al. The dotted lines show the order–disorder transformation of the ␤-phase.

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reaction ␶ ↔ ␣2 + ␥ (see pd5 in Fig. 11). This is in good agreement with our own measurements as well as with the result of [69]. From Fig. 16d–f it should be expected ␶-phase to be formed in most gamma titanium aluminide materials alloyed with Nb, during long time exposure to typical service temperatures. At present any experimental evidence for this is reported in literature, though it may be significant. The isothermal section at 873 K in Fig. 16e shows that the calculated single-phase fields for ␤ and ␴ are somewhat narrower than observed by [43]. However we believe that the experimental conditions were not adequate to reach equilibrium at such low temperature. The last isothermal section in Fig. 16f represents the calculated isothermal section at room temperature. It shows that all phases, except ␥-phase, are stoichiometric or line compounds. The ␥-phase is modelled such that it becomes a line compound at temperatures close to 100 K with a maximum solubility for Nb of 5 at.%. 5.4. Selected isopleths Selected isopleths were calculated and compared with experimental data from literature and data obtained in the present work. The temperatures of phase transitions obtained by DTA in the present work and by DSC [20–23] are shown in isopleths along 45 at.% Al (Fig. 17a), 47 at.% Al (Fig. 17b), and 8 at.% Nb (Fig. 17d) as well as along a vertical section through the Ti0.872 Nb0.128 and Nb0.022 Al0.978 (Fig. 17c). Note that the composition of alloys used for the experimental measurements, especially of those from literature, are not always precisely in the plane of isopleths calculated, deviating to maximum ±1 at.%. Some differences between measured and calculated phase transition temperatures are possibly related to the A2/B2 ordering phenomena of the ␤-phase. The ordering state of the ␤-phase is hardly ever discussed in the context of DTA or DSC experiments: our own XRD investigations with different samples that contained 12 at.% Nb and that were cooled at 180 K min−1 (see Section 2.2.2) showed no distinct reflex of the B2 (CsCl) crystal structure, meaning that ordering was suppressed. The shift of phase boundaries that results when suppressing the ordering is shown by dashed lines in Fig. 17a. It seems clear that

Fig. 19. Comparison of calculated (lines) and experimental data [74,80] (points) for the activity of Al and Ti at 1473 K with the reference state being bcc Ti and bcc Al.

Fig. 20. Calculated (lines) values for the partial enthalpies of mixing of Al and Ti at 1435 K and 1550 K in comparison with the experimental data measured in the temperature range 1425–1550 K [74,80], the reference state being bcc Ti and bcc Al.

the DTA data on the phase transition temperature associated to ␣2 + ␥ ↔ ␤0 + ␥ for the sample with 12 at.% Nb correspond to the disordered ␤-phase, rather than to the ordered ␤0 . Disregarding this, the majority of literature data are fairly well reproduced within the limit of experimental errors. Fig. 18a through c shows a series of selected sections with focus on low temperature equilibria, mainly including O1 -, O2 - and the ␶-

Fig. 21. Influence of Nb on the standard enthalpy of formation of the ␥-phase at 298 K (reference state is bcc Nb, hcp Ti and fcc Al): the solid line results from the calculation using the thermodynamic description proposed here; the solid circle stems from calorimetry measurements for the Ti25.3 Nb19.0 Al55.7 alloy; the dashed line corresponds to ideal mixing.

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Fig. 22. Specific heat capacity (a) and molar enthalpy upon heating from 673 K and (b) for the alloy Ti46 Nb8 Al46 according to calculations (dashed lines) and DSC measurements (solid lines and solid squares) with a heating rate of 20 K min−1 [28]. The ␶-phase was suspended for the calculations.

phase. Experimental data are rather scarce and the rate dependency of DTA data [24] is more pronounced than at higher temperatures. For the isopleth with 27.5 at.% Al the experimental results of Muraleedharam et al. [65] are selected for comparison in Fig. 18c: the experimental data points do not represent phase transition temperatures but only make distinction between phase equilibria involving the ␤0 , O1 and O2 phases. A detailed investigation of the section NbAl3 –TiAl3 was reported by Perepezko et al. [52] based on DTA measurements and metallographic analysis. The DTA results from Ref. [52] were therefore selected for comparison to the calculated isopleth at a constant Al content of 74.8 at.% and displayed in Fig. 18d. The comparison is good, if one takes into account the fact that small variations of Al in the range 74.3–75.0 at.% drastically affects solidus, with the liquidus remains virtually unaffected (see dashed lines in Fig. 18d). The existence of a congruent melting point for (Nb,Ti)Al3 near the NbAl3 end, as suggested by Perepezko et al. [52] was however not confirmed. The calculated 74.8 at.% Al isopleth closely agrees to the assessment of Raghvan [15].

5.5. Thermodynamic properties Comprehensive work was performed by Eckert et al. [74,80] on measuring the thermodynamic activities of the components in solid Al–Nb–Ti alloys using the Knudsen effusion mass spectrometry (KEMS) at temperatures between 1435 and 1550 K. This method involves the direct measurement of the partial pressure of Al and Ti and also allows evaluating the partial enthalpies and entropies of mixing for the solid alloys. Unfortunately, as discussed in Ref. [3], it is unclear from these publications to what reference state the obtained data were referred to. Our calculations described in Ref. [3], but also the ones described here show that the experimentally measured activities of Ti are reproduced within the limit of experimental errors, when selecting the reference state for the component Ti to be bcc A2 at 1473 K (Fig. 19). The correspondence between the calculated activity of Al and the experimental data is less good, independent of the reference state. This was already discussed in Ref. [3] being related with the inadequate equation used in Refs. [74,80] to calculate the equilibrium partial pressure of pure Al.

Fig. 20 compares the calculated values for the enthalpy of formation of solid phases with the experimental results of Eckert et al. [74,80] in the temperature interval 1435–1550 K. The correspondence is reasonably good, if one takes into account the variation of this thermodynamic property with temperature, the selected reference state and the phases stable in the given temperature interval. Fig. 21 shows the standard integral enthalpy of formation of ␥alloys at 298 K as function of the Nb content: the value measured for the composition Ti25.3 Nb19.0 Al55.7 is in good agreement with the calculation. From the plot it can also be inferred that Nb stabilizes the ␥-phase. The maximum deviation from ideal behaviour (dashed line) is obtained in the vicinity of 20 at.% Nb, being possibly associated to continuous ordering and superstructure formation at the composition Ti4 Nb3 Al9 , as was experimentally observed in Ref. [26] and further discussed in Ref. [39]. The variation of heat capacity and heat with temperature was measured by DSC in alloy Ti46 Nb8 Al46 in the temperature interval from 673 to 1850 K, using a heating rate of 20 K min−1 [28]. With these data we have evaluated the molar enthalpy referred to 673 K. The evolution of heat capacity and molar enthalpy with temperature are presented in Fig. 22a and b, respectively, in comparison with calculated values. The agreement is acceptable, when considering that the DSC data are rate-dependent, while the calculated values represent thermodynamic equilibrium at each temperature. 6. Summary and conclusions A thermodynamic re-evaluation of the entire ternary system Al–Nb–Ti has been elaborated, involving: • experimental analysis of 26 distinct alloys in both, as-cast and annealed conditions using XRD, SEM, EDS, DTA and Pirani–Alterthum techniques for determination of phase constituents, composition of coexisting phases and phase transition temperatures; • experimental determination of the standard enthalpy of formation of the ␥-phase at 298 K by means of dissolution drop calorimetry; • the thermodynamic description of the constituent binary Al–Nb and the ternary Al–Nb–Ti system by CALPHAD modelling, taking into account relevant experimental information for binary Al–Nb

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and ternary Al–Nb–Ti alloys from literature and from the abovementioned measurements; • thermodynamic equilibrium calculations of liquidus, solidus and ␤-transus surfaces, isothermal sections, isopleths and selected thermodynamic properties in comparison to experimental data. Summarizing, one may conclude that the present thermodynamic description of the entire Al–Nb–Ti system is more reliable than earlier descriptions [4–7]. It may serve as a good basis for addressing not only phase equilibria, but also phase transformation kinetics during solidification and heat treatment processes. The advantage of the present description relates to the simplicity of the selected models which involve sig-

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nificantly less parameters than previous descriptions. This is convenient when attempting its integration into high-order systems. Acknowledgements The authors thank L.V. Artyukh, L.A. Duma, O.S. Fomichov, V.V. Garbuz, V.M. Petyukh, N.I. Tsyganenko and V.V. Voblikov for technical assistance and would like to express their gratitude for financial support from the Integrated Project IMPRESS, “Intermetallic Materials Processing in Relation to Earth and Space Solidification” (Contract NMP3-CT-2004-500635) co-funded by the European Commission in the Sixth Framework Programme and the European Space Agency.

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Appendix A. Thermodynamic database for the Al–Nb–Ti system

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