A thermodynamic evaluation of the Ta–V system

Journal of Alloys and Compounds 366 (2004) 191–200

A thermodynamic evaluation of the Ta–V system C.A. Danon, C. Servant∗ Laboratoire de Physico-Chimie de l’Etat Solide, Faculté des Sciences d’Orsay, Université de Paris-Sud, Bˆat. 410, F-91405 Orsay, France Received 7 July 2003; received in revised form 21 July 2003; accepted 21 July 2003

Abstract We present a thermodynamic study of the Ta–V system based on the Calphad–Thermocalc approach. This work is part of a broader project concerning the thermodynamic description of Ta-containing low activation steels, which were developed in the past decade for applications in fusion technology. In the binary system Ta–V, the Gibbs energy functions of the liquid, the bcc solid solution and the Laves phases were determined. Conflicting information exists in the literature concerning the possible polymorphism of the Laves phase at high temperature; a preliminary assessment of the phase diagram was made without taking into account this phenomenon. Then, the C14–C15 transition was introduced for the Laves phase. The calculated phase equilibria were compared with experimental data. © 2003 Elsevier B.V. All rights reserved. Keywords: Thermodynamic modeling; Phase diagrams; Phase transitions; Metals and alloys

1. Introduction The purpose of the present work is to continue the development of a consistent thermodynamic database that allows for a description of phase equilibria of the so-called low activation martensitic steels—namely, the TCFe2000 steel database—within the framework of the Calphad–Thermocalc approach. Reduced activation steels are variations of conventional CrMoVNb ferritic/martensitic steels, with molybdenum replaced by tungsten and niobium replaced by tantalum. These CrWVTa martensitic steels were developed for specific applications to internal components of fusion reactors, owing to an attractive combination of properties such as good stability and lower induced activity under neutron irradiation [1,2]. The most common alloying elements in low activation steels include V, Mn, Si, N, W and Ta. The role of Ta in the evolution of microstructure and its effect on mechanical properties of these materials has been object of study, either for tempering or aging [3,4] as well as for austenitization treatments [2,5,6]. In a previous work [7], we have reassessed the Fe–Ta binary system taking into account solubility data for the ∗

Corresponding author. Tel.: +33-1-69157021; fax: +33-1-69157833. E-mail address: [email protected] (C. Servant).

0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0925-8388(03)00728-X

Fe–Ta–C and Fe–Ta–N ternary systems. The obtained results were essentially applied to model the behavior of low activation steels in the austenite region. In this work, we will focus on the binary system Ta–V as a previous step to model the ternary system C–Ta–V. This ternary system could play a role in describing unmixing phenomena that are likely to occur at lower temperatures, that is, unmixing of complex (Ta, V) carbides or carbonitrides that are present in low activation steels. Experimental studies in some ternary alloy systems such as Hf–Ta–V [8], which exhibits interesting mechanical properties at room temperature, provide an additional motivation for the thermodynamic modeling of the Ta–V system.

2. Literature review 2.1. Experimental information for the Ta–V binary system There is a general agreement that Ta and V form a continuous bcc solid solution at high temperature and that an intermediate phase forms from this solid solution at lower temperatures. This agreement comes from many experimental studies such as those of Carlson et al. [9], Eremenko et al. [10,11], Nefedov et al. [12,13] and Savitskii and Efimov [14]. On the other hand, two features of the Ta–V phase dia-

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gram have produced conflicting reports in the literature: the existence of an azeotropic melting minimum at ∼12 at.% Ta and the nature and range of existence of the intermediate phase. With respect to the first point, Eremenko et al. [10] and Rudy [15] showed an experimental solidus curve with no minimum; Eremenko et al. [10] having pointed out that their alloys were contaminated with Al, Fe and O. On the contrary, the experimental solidus curve of [13] displays an azeotropic minimum. The same result has been obtained by Carlson et al. [9] and Koltygin et al. [16] and reproduced again by Smith and Carlson [17]. Thus, most of the experimental evidence led us to include such a minimum in our model. The second point must be examined with more attention. Even if some early reports identified the intermediate phase as a ␴-phase [11,18], it is now well established that its crystalline structure at low temperature corresponds to a Laves C15 phase of stoichiometry TaV2 and structure MgCu2 [19,20]. Furthermore, this phase has deserved a broad interest that included studies on its superconducting behavior [21,22], ability for hydrogen solution [23–25] and elastic properties [26,27]. All these studies dealt precisely with the properties of the C15 structure at low temperatures; however, the crystal structure of the TaV2 phase at high temperature seems to remain still unclear. In effect, a controversy exists on the possible polymorphic transformation of this C15 structure to a C14 (MgZn2 ) one in going from low to high temperatures. This type of transformation (or transformations including an intermediate C36 (MgNi2 ) Laves phase) has been effectively observed in binary systems formed with transition metals like Cr–Ta [28], Cr–Nb [29], Cr–Ti [30,31], and Cr–Zr [32] and reported for the Ta–V system in [14,33,34]. Some ternary systems of transition metals based on the composition TaV2 can be also quoted in order to complete a picture of the behavior of this phase. In the systems Nb–Ta–V and Mo–Ta–V with constant ratio (at.%) Ta:V = 1:2, the MgZn2 polymorph has been reported to be the equilibrium phase up to the temperature of formation of the bcc solid solution [35]. However, similar experiments in the Ta–V–W system [36] showed the MgCu2 structure to be the stable one; finally, in the system Ta–V–Zr a complete solid solution between the cubic MgCu2 binary structures of V–Zr and Ta–V was observed at 1423 K and a limited solid solution was reported for the hexagonal MgZn2 form [37]. These results suggest that besides temperature, the addition of a third substitutional alloying element could modify the stability of the TaV2 Laves phase, as is the case in other systems containing Laves phases. It is also worth to mention that the Laves C14 phase has been observed at low temperature in presence of hydrogen [25]. The ensemble of information in [9–16] gives rise to essentially two experimental versions of the Ta–V phase diagram. In the first one [9–12], a TaV2 phase transforms

congruently to a bcc solid solution around 1573 K. In Carlson et al.’s proposed diagram [9] the intermediate phase has no homogeneity range although a series of increasing lattice parameters measured as a function of Ta composition is shown, which differ significantly taking into account the given error bar and which seem to correspond to the single-phase field. On the other hand, Nefedov et al. [12] assign a width of ∼6 at.% at 1173 K to the intermediate single-phase field. It should be noted that in both papers the intermediate phase is erroneously identified from the crystallographic point of view, as hexagonal in Carlson et al.’s paper and as tetragonal in Nefedov et al.’s one. In the second version [14], the congruent transformation still exists, but two polymorphs of the Laves phase are included: the MgZn2 structure at high temperature and the MgCu2 structure at low temperature. The phase diagram displays an eutectoid decomposition of the C14 phase in the V-rich side at 1398 K, a (C15 + C14) two-phase field from 1398 up to 1553 K, a peritectoid decomposition in the Ta-rich side at 1553 K and the congruent transformation of the high-temperature C14 structure at 1693 K, this last value being taken directly from [11]. Although Savitskii and Efimov [14] mention the experimental techniques they used, the results of their experiments are not explained in detail. On the other hand [13] (a later version of Nefedov et al.’s phase diagram), accounts for a MgZn2 structure at high temperature, although it does not explain the nature of the C15–C14 transition: even if the high-temperature C14 polymorph is quoted (and its lattice parameters given), the presented phase diagram displays only one intermediate phase. A summary of the previously reported experimental work can be found in Table 1, and the ensemble of the (contradictory) observations on Laves phase stability is collected in Table 2 ordered by decreasing temperature. In the last critical assessment of the Ta–V system [17], the authors decided not to include the high-temperature Laves C14 phase as an equilibrium binary phase, assuming that its presence as a stable phase in the alloys of [14] was due to oxygen contamination; [13,33–37] were not quoted. As a matter of fact, [13] does account for the problem of contamination, pointing out that results obtained from control alloys of higher purity confirmed the presence of the C14 structure at high temperature. With respect to previously reported thermochemical information, the only experimental data for Ta–V alloys are low-temperature heat capacity measurements (see [21,22]), which were not considered in this work. 2.2. Selected previous work on phases modeling To our knowledge, the only report produced so far on the Ta–V binary system within the Calphad approach is that published by Kaufman [38]. In that work, the liquid displays no azeotropic minimum. The Laves phase was considered as a stoichiometric compound, without any polymorphic trans-

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Table 1 Selected experimental information on the Ta–V system Experimental method

Phase boundaries

Temperature (K)

Composition (at.% Ta)

Reference

A, A, A, A,

HTXRD, MPM, M, XRD ␮H, MPM, M, XRD M, XRD ER, H, ␮H, M, TA, XRD

Solidus bcc-TaV2 Solidus bcc rangea bcc-TaV2 bcc-TaV2

1073, 1673, 1273, 1173,

[9] [10] [11] [12]

A, H, MS, MPM, M, TA, XRD

Solidus bcc-TaV2

1073, 1523, 1673, 1823, 1923, 70–1200 (MS)

A, DTA, M, ␮H, EPMA, XRD EPMA, M, ␮H, TA MPM

bcc-TaV2 Azeotropic melting Azeotropic melting

1073, 1398, 1473, 1553, 1673, 1773

0–66 0–100 0–100 0–100 (T ≤ 1523 K), 0–50 (T > 1523 K) 0–100 (T ≤ 1523 K), 0–50 (T > 1523 K) 0–100 0–33 11

1173, 1873, 1423, 1523,

1273, 1373, 1473 2073 1473, 1573, 1673, 1873, 2073 1673, 1823, 1923

2153

[13] [14] [16] [17]

A: annealing; DTA: differential thermal analysis; ER: electric resistivity; EPMA: electron probe microanalysis; H: hardness; HTXRD: high-temperature X-ray diffraction; MS: magnetic susceptibility; MPM: melting point measurement; M: metallography; ␮H: microhardness; TA: thermal analysis; XRD: X-ray diffraction. a The separation of a low-temperature phase was observed at 1673 K.

formation. The width of the (bcc + Laves) two-phase field extended practically over the whole range of composition, which seems to be somewhat broad taking into account the experimental information. On the other hand, the above mentioned binary systems including both the C14 and C15 Laves phases with a C14 → C15 phase transition have been already modeled: Cr–Ta [39], Cr–Nb [40], Cr–Ti [41,42] and Cr–Zr [43,44]. In [42,43], an intermediate phase Laves C36 (Ni2 Mg) was also included in thermodynamic calculations, which gives a C14 → C36 → C15 transition from high to low temperature. A two-sublattice description of the form (A, B)(A, B)2 was adopted for the low-temperature Laves C15 phase in all of the cited references. For the high-temperature Laves C14 phase, both two- and three-sublattice models of the form (A, B)6 (B, A)4 A2 have been proposed [39–43]. In the last case, as shown later, the second and third sublattice can be merged into a single one when the coordination number of the A atom is the same in both sublattices.

3. Thermodynamic modeling of the binary phases The thermodynamic descriptions of elements were taken from the SGTE database [45]. As far as only phase diagram experimental data were available in the literature, thermodynamic constraints and estimated thermochemical data were introduced to model the different phases. 3.1. Solution phases The solution phases (liquid and bcc A2) were modeled as a substitutional solution according to the polynomial Redlich–Kister model [46]. The concentration dependence of the Gibbs energy G of a phase φ is given by Gφ = ref Gφ + id Gφ + E Gφ

(1)

with

id

φ

φ

Gφ = xTa 0 GTa + xV 0 GV

(2)

Gφ = RT(xTa ln xTa + xV ln xV )

(3)

ref

Table 2 Selected values for the observed lattice parameters of Laves phases in different regimes of temperature and time Experimental method

Observed phase

Composition

Temperature (K)

Time (h)

Lattice parameters (Å)

XRD XRD XRD XRD, ED XRD XRD ND XRD XRD XRD XRD XRD

C15a

TaV2 TaV2 Ta0.32 V0.68 TaV2 TaV2 TaV2 TaV2 Ta:V = 1:2 (10 at.% Nb) Ta:V = 1:2 (5 at.% Mo) TaV2 TaV2 TaV2

1523 1523 1473 1373 1273 1193 1173 1173 1173 Not given Not given Not given

96 + 240 10 100 100–150 840 120 1000 >1300 >1300 Not given Not given Not given

a a a a a a a a a a a a

C14 C15 C15 C15 C15 C15b C14 C14 C14 C14 C15

XRD: X-ray diffraction; ED: electron diffraction; ND: neutron diffraction. a The bcc solid solution was observed after 7 h at 1973 K. b The bcc solid solution was observed after 150 h at 1273 K.

= 7.1597 = 5.058, c = 8.250, c/a = 1.631 = 7.163 = 7.14 = 7.153 = 7.155 = 7.16 = 5.058, c = 8.250, c/a = 1.631 = 5.090, c = 8.322, c/a = 1.635 = 4.96, c = 8.11, c/a = 1.63 = 4.96, c = 8.11, c/a = 1.63 = 7.14

Reference [23] [13] [9] [19] [21] [22] [20] [35] [35] [33] [14] [33]

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is the excess Gibbs energy, expressed by the polynomial

Gφ = xTa xV

n


ν φ LTa,V (xTa

− x V )ν

(4)

ν=0

with ν φ LTa,V

= aν + bν T

(5)

νL

are interaction parameters, aν corresponding to the enthalpy and bν to the excess entropy of mixing. As was already said, there are no published data neither for the enthalpy of mixing of the liquid nor for the liquidus line; in this situation it is not possible to determine independently the two coefficients aν and bν of the model parameters of the liquid phase. Thus, the Tanaka–Gokcen–Morita relationship between the excess entropy and the enthalpy of mixing of liquid binary alloys [47] was used. The Tanaka–Gokcen–Morita relationship for an alloy A–B can be written: S EX ∝ HMIX (1/Tm,A + 1/Tm,B ), where Tm,A and Tm,B are the melting temperatures of the pure components; in terms of Eq. (5), this amounts to write aν = K0 bν . A value of K0 = 13000 K was used for calculations in the Ta–V system. In addition, an enthalpy of mixing of the liquid of −1000 J/mol of atoms at 3373 K was fixed as input for the equiatomic alloy, using liquid Ta and V at the same temperature as reference states. In this way, we make sure that the enthalpy of mixing will have the correct sign according to the features of the phase diagram, which does not display any liquid miscibility gap. For the bcc solid solution, only one independent coefficient (aν ) was considered. 3.2. Laves phases in the Ta–V binary system As pointed out in Section 2.1, the experimental evidence indicates that the Laves phase has an homogeneity range and it was modeled in that way in the present work. In view of the conflicting situation concerning experimental data on Laves phase stability, we decided in a first approach to model the Ta–V system including only the C15 Laves phase and then, in a final version, to introduce both the C14 and C15 Laves phases. We will expand on this point in Section 5. 3.2.1. Laves phase C15 The Laves phase C15 (prototype MgCu2 , Pearson symbol cF24) contains two distinct crystallographic Wyckoff positions, namely, 8(a) (coordination number: 16) and 16(d) (coordination number: 12). A two-sublattice model is thus a reasonable choice for the thermodynamic description of this phase. Since the experimental homogeneity range of the Laves C15 phase extends on both sides of the stoichiometric composition, the adopted unit formula for its description was (Ta, V)(Ta, V)2 . This approach should be considered as a preliminary one, as we have no experimental information on the nature of the defects (substitution or vacancies) that account for the off-stoichiometric width at both sides of the ideal composition.

The accepted criterion to define the reference state for the thermodynamic functions is to assign the fcc reference state to species occupying a site with coordination 12 and the bcc reference state to species occupying a site with coordination >12. In the current status of the TCFe2000 database that is true for the systems Fe–Nb and Fe–W. However, to keep the coherence with the existing description of the Laves phase in the Cr–Ta [39] and Cr–Ni–Ta [48] systems—which could play a role in Ta-containing steels—we have defined the reference state for the thermodynamic functions as bcc V and bcc Ta, irrespectively to the coordination number. In addition, the Wagner–Schottky model for sublattices [49] was used to describe the Laves C15 phase. In this way, the complete thermodynamic description of this phase gives ref

0 λ 0 λ Gλ = yTa yV GTa:V + yTa yTa GTa:Ta 0 λ 0 λ + yV yV GV:V + yV yTa GV:Ta

0

0 bcc GλTa:V = 0 Gbcc Ta + 2 GV + a + bT

id

(7)

Gλ = RT [(yTa ln yTa + yV ln yV ) ln yV + yTa ln yTa )] + 2(yV

E

(6)

(8)

0 λ 0 λ Gλ = yTa yV (yTa LTa,V:Ta + yV LTa,V:V ) 0 λ 0 λ + yTa yV (yV LV:Ta,V + yTa LTa:Ta,V ) 0 λ + yTa yV yTa yV LTa,V:Ta,V

0

GλV:Ta = −0 GλTa:V + 0 GλV:V + 0 GλTa:Ta

(9) (10)

where yi and yi refer to the site fractions of component i in the first and second sublattices, respectively, and a and b in Eq. (7) are coefficients to be optimized. The four terms 0 Gλ represent the Gibbs energy of the stable or metastable stoichiometric compounds TaTa2 , TaV2 , VTa2 and VV2 . The excess parameters 0 Lλ in Eq. (9), which account for the interaction of species in each sublattice, were considered independent of the occupation in the other sublattice, that is 0 λ LTa,V:Ta

= 0 LλTa,V:V = 0 LλTa,V:∗

(11)

0 λ LV:Ta,V

= 0 LλTa:Ta,V = 0 Lλ∗:Ta,V

(12)

and they were optimized with no dependence on temperature. Finally, Eq. (10) accounts for the Wagner–Schottky constraint. The molar Gibbs energies of formation of the hypothetical phase formed with pure elements were fixed at the value 5000 J/mol of atoms in order to be consistent with the thermodynamic description of systems given in [39–43]. 3.2.2. Laves phase C14 The Laves phase C14 (prototype MgZn2 , Pearson symbol hp12) contains three sublattices from the crystallographic point of view. To simplify the thermodynamic description of this phase, only two sublattices were considered: the first

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one for the site with coordination number 16 (Wyckoff symbol: 4(f)) and the second one by combining all sites with coordination number 12 (Wyckoff symbols: 2(a) and 6(h)) into one sublattice, obtaining in this way a stoichiometry 1–2. Regarding the reference states for thermodynamic functions and the Gibbs energy of formation of the end member compounds, we adopted the same criterion as for the Laves C15 phase; we also imposed a Wagner–Schottky constraint in the description of the Laves C14 phase. Indications for additional thermodynamic constraints related to the C14–C15 phase transition have been given in [40,42], in which it was assumed an entropy of transformation of 1 J/(K mol of atoms) for the C14 ↔ C15 and C14 ↔ C36 phase transitions, respectively. At the same time, in [43] a value of 3300 was used for the ratio of the enthalpy to the entropy of formation of the ideal stoichiometric C36 phase. In view of the lack of experimental thermochemical data, we have assumed an entropy of 1 J/(K mol of atoms) for the C14 ↔ C15 transformation as well. In addition, a value of −1000 J/mol of atoms for the enthalpy of formation of the C15 Laves phase, estimated independently by Kaufman [38] and Niessen et al. [50] was introduced as input along with constitution data.

4. Optimization The first approach to optimization was done by means of the Parrot module of the Thermocalc program package using the experimental data of Carlson et al. [9] for the solidus line and Nefedov et al. for the solidus line and the solid phases, the last ones taken from their second paper [13]. In Nefedov et al.’s case, the data set was considered the more reliable one as additional control experiments were performed starting from materials with a higher purity. It must be emphasized that Nefedov et al.’s second phase diagram was drawn without taking into account the polymorphism of the Laves phase, even if the existence of such a polymorphism is proposed in the work. On the other hand, we did not consider Eremenko et al.’s data [11] because they assigned a range of homogeneity of 13 at.% to TaV2 , which seems to be somewhat broad for a binary phase having severe packing constraints. As experimental determinations of the liquidus line are lacking, the equilibria used to calculate the liquid–bcc two-phase region were taken from Nefedov et al. and Carlson et al.’s estimation of that line; hence, the calculated liquidus should be judged cautiously. The selection of the adjustable coefficients for the different parameters, explained in Section 3 above, allowed to work with a minimum number of optimizing variables. The set of optimized parameters of all the stable phases in the Ta–V system is listed in Appendix A and the corresponding phase diagram is shown in Fig. 1. The calculated values for the singular points are shown in Table 3. In order to check for the presence of the expected stable phases

Fig. 1. Calculated first approach to the Ta–V phase diagram: (a) complete diagram; (b) azeotropic melting minimum.

(and only of them) in each case, phase equilibria calculations were performed in the entire range of temperature (298 < T < 6000 K) and composition (0 < x < 100) in which the parameters describing the Gibbs energy of phases are defined. Such a procedure is not redundant as poor modeling could lead to the incorrect stabilization of phases in the wrong regions of the phase diagram. Optimization of the final version was done assuming that the C14 Laves phase is a true equilibrium phase, using the experimental data of Savitskii and Efimov [14] for the solid phases and those of Carlson et al. [9] and Nefedov et al. [13] for the solidus line. The Ta-rich boundary of the (bcc+Laves C15) two-phase field at 1073 K was also taken from Nefedov et al.’s data as Savitskii and Efimov’s value turned out to be much greater than any other reported value. The values of the different parameters obtained in the previous calculation were introduced as initial values for each phase.

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Table 3 Experimental and calculated values for singular points in the Ta–V system Equilibrium phases

Reaction

T (K) Experimental

Liquid ↔ bcc

A

Calculated

Composition (at.% Ta)

Reference

Experimental

Experimental

2182.3

Calculated 2.65

2153 2098 2093 Not given

11 15 ∼10.8 12

[17] [13] [9] [16]

Calculated (this work) Calculated

T (K)

Composition (at.% Ta)

[17]

2114a

12.5a

2099b

12.9b

bcc ↔ C14

C

1693 1693

∼33 ∼33

[11] [14]

1702b

32.7b

bcc ↔ C15

C

1593 1583

∼33 ∼33

[9] [13]

1565a

34a

1574

33.3

[38]

C14 + bcc ↔ C15

P

1553

36 (C14) 55 (bcc) 37 (C15)

[14]

1548

36 (C14) 50.4 (bcc) 37.4 (C15)

C14 ↔ C15 + bcc

E

1398

29 (C14) 31 (C15) 9 (bcc)

[14]

1400

31 (C14) 31.3 (C15) 6.4 (bcc)

A: azeotropic melting minimum; C: congruent transformation; P: peritectoid; E: eutectoid. a First approach. b Final version.

In the case of the Laves C14 phase the values obtained for the Laves C15 phase were used as initial values. The result presented here is the best compromise we could obtain between an accurate fitting of the solidus line and other phase field boundaries and critical points in the framework of the selected description; for the sake of soundness, the decision was made not to increase the number of adjustable coefficients. The stability of the expected phases was checked in the entire range of temperature and composition as well as in the first approach. The optimized parameters, calculated values for the singular points and the calculated phase diagram are shown in Appendix A, Table 3 and Fig. 2, respectively. The calculated enthalpy of mixing of the liquid phase is shown in Fig. 3.

5. Discussion A good agreement was obtained between the calculated phase diagram and the experimental data of Savistskii and Efimov [14], as shown in Fig. 2. The obtained values for the enthalpy of mixing of the equiatomic liquid and the enthalpy of formation of the Laves phase (V, Ta)0.3333 (V, Ta)0.6667 in the first approach of the optimization were −1415 and −1075 J/mol of atoms, respectively, which compare well with the value of −1000 J/mol of atoms introduced as input. In the final version the obtained value for the liquid (−926.9 J/mol of atoms) is still in agreement, but the obtained value for the Laves C15 phase (−5706.52 J/mol of atoms) is higher than the input.

As for the intermediate Laves phase, the lack of experimental thermochemical information and the uncertain observed behavior regarding stability have introduced a problem to model the Ta–V binary system. In the present assessment, we assumed that the high-temperature C14 TaV2 phase is a true equilibrium phase and that the final version of the phase diagram (Fig. 2) is the valid one. We summarize below the reasons which led us to adopt such a statement. It has been argued so far that contamination plays a central role to explain the contradictory observations regarding the stability of Laves phases at different temperatures. Without discarding this argument, it is also possible to think of kinetics as a factor that will affect the observed phase equilibria as far as a very sluggish transformation could be involved in the case of the Laves C14 → C15 phase transition. This seems to be reasonable in light of many investigations produced in the last years concerning binary systems formed with transition metals which contain both the C14 and C15 Laves phases and undergo a C14 → C15 transition. Laves phase transformations are thought to occur by shear, and shear transformation kinetics are believed to be dictated by temperature dependence of dislocation mobility [51]. In such conditions, a nearly stoichiometric alloy annealed at high temperature within the C14 single-phase field could metastably retain its crystalline structure upon cooling. Nucleation of the C15 structure in crossing the (C14 + C15) two-phase field would be difficult as some composition adjustment via diffusion would be demanded before the shear transformation would occur and these two requirements (compositional adjustment and shear) could not be achieved on cooling. Eventually, the C14 metastable

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Fig. 2. Calculated Ta–V phase diagram including both the C14 and C15 Laves phases: (a) complete diagram; (b) C14–C15 phase transition (the dotted line accounts for the stoichiometric composition); (c) azeotropic melting minimum.

phase can be transformed to the C15 stable one by annealing at a suitable temperature, but even in this case the transformation could be expected to be sluggish, as effectively as the transformation bcc → C15 (see Table 2). The addition of a selected third substitutional alloying element contributes also to modify the relative stability of the C14 and C15 structures, as shown in [35] for Mo and Nb, [36] for W and [37] for Zr. Thus, the observation of the C14 structure at low (<∼1273 K) temperatures could be a consequence of kinetics and/or alloying effects. In the same way, the experimental observation of the C15 Laves phase in alloys annealed at temperatures as high as 1473–1523 K (see Table 2) could not necessarily indicate that this is the only stable phase at such temperatures. Indeed, from the phase diagram of Fig. 2 it is seen that alloys located in the Ta-rich side of the single-phase field could retain the C15 structure up to such a high temperature. In this sense, it is interesting to note that, despite the erroneous crystal structure determination, the measured lattice parameters

Fig. 3. Calculated enthalpy of mixing in the liquid for the Ta–V system at 3373 K.

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of the alloys annealed at 1473 K in the single-phase field in [9] increased for increasing Ta content. Such an increment should be also expected for the C15 structure, and in fact, the different values for the a lattice parameter reported for this structure and shown in Table 2 range within the interval 7.14–7.16 Å. This variation could be associated with composition differences within the single-phase field TaV2 , as has been already shown in detail for Nb–Cr, Nb–Co and Nb–Fe alloys [52]. The higher lattice parameters would correspond to alloys located in the Ta-rich side of the single-phase field, which is, according to the diagram of Fig. 2, the one that extends to the higher temperatures. Now, the C15 structures observed at 1473–1523 K have a lattice parameter close to 7.16 Å, which suggests a composition shift to the Ta-rich side. In this way, we could conciliate contradicting observations on the stable structure at 1473 K. Some experimental measurements, however, remain in disagreement with our calculated phase diagram, in particular, the presence of the C15 phase found in [9] for two alloys substoichiometric in Ta treated for 100 h at 1473 K. We have also verified that both structures C14 and C15 can be easily separable by powder X-ray diffraction analysis on the basis of the most intense peak in each pattern. Simulations of the diffraction patterns were carried out with the software Fullprof [53] using Cu K␣ radiation and the lattice parameters a = 5.058 Å, c = 8.25 Å and a = 7.16 Å, respectively. The (1 0 3) reflection at 2θ = 38.63◦ for the C14 phase and the (3 1 1) reflection at 2θ = 41.93◦ for the C15 phase are sufficient to separate them without ambiguity, if no preferential orientation is present to affect the intensity of the peaks.

Appendix A New optimized thermodynamic parameters for the Ta–V binary system. The energies are given in J/mol. A.1. First approach to the Ta–V phase diagram A.1.1. Phase liquid Description: (Ta, V) 0 liq LTa,V

A.1.2. Phase bcc-A2 Description: (Ta, V)(Va)3 0

0 bcc Gbcc Ta:Va − HTa (298.15 K) = GHSERTa

0

0 bcc Gbcc V:Va − HV (298.15 K) = GHSERV

0 bcc LTa,V:Va

= 4773.14

1 bcc LTa,V:Va

= −13469.8

A.1.3. Phase Laves C15 Description: (Ta, V)(Ta, V)2 0

0 bcc GLaves Ta:Ta − 3 HTa (298.15 K) = +15000 + 3GHSERTa

0

0 bcc GLaves V:V − 3 HV (298.15 K) = +15000 + 3GHSERV

0

0 bcc 0 bcc GLaves V:Ta − HV (298.15 K) − 2 HTa (298.15 K)

= 30000 + 3228.25 + 7.93T + GHSERV + 2GHSERTa 0

Acknowledgements Authors are indebted to Professor Bogdan Kotur, from the Ivan Franko National University of Lviv, Ukraine, for his kind help in bibliographic research.

0 bcc 0 bcc GLaves Ta:V − HTa (298.15 K) − 2 HV (298.15 K)

= −3228.25 − 7.93T + GHSERTa + 2GHSERV

6. Conclusions A complete set of parameters which describe the thermodynamic behavior of the various phases existing in the Ta–V system was obtained in the framework of the Calphad–Thermocalc approach. This set of parameters accounts for the version of the phase diagram that takes into account the polymorphism of the intermediate Laves phase. The calculated phase diagram shows a reasonable agreement between the calculated values and the measured values for the different phase boundaries and singular points. More experimental evidence would be needed to establish definitely the behavior of the Laves phase TaV2 . On the basis of the calculated phase diagram, the thermodynamic optimization of the C–Ta–V ternary system is currently in progress.

= −5661.4 + 0.435T

0 Laves L∗:Ta,V

= 17754.65

0 Laves LTa,V:∗

= 10843.4

where ‘∗’ stands either for Ta or V. A.2. Final version of the Ta–V phase diagram A.2.1. Phase liquid Description: (Ta, V) 0 liq LTa,V

= −3707.72 + 0.285T

A.2.2. Phase bcc-A2 Description: (Ta, V)(Va)3 0

0 bcc Gbcc Ta:Va − HTa (298.15 K) = GHSERTa

0

0 bcc Gbcc V:Va − HV (298.15 K) = GHSERV

0 bcc LTa,V:Va

= 5476.65

1 bcc LTa,V:Va

= −16527.68

C.A. Danon, C. Servant / Journal of Alloys and Compounds 366 (2004) 191–200

A.2.3. Phase Laves C15 (low temperature) Description: (Ta, V)(Ta, V)2 0

C15 bcc GLaves − 30 HTa (298.15 K) = +15000 + 3GHSERTa Ta:Ta

0

C15 GLaves − 30 HVbcc (298.15 K) = +15000 + 3GHSERV V:V

0

C15 bcc GLaves − 0 HVbcc (298.15 K) − 20 HTa (298.15 K) V:Ta

= 30000 + 17547.3 − 1.99T + GHSERV + 2GHSERTa 0

C15 bcc GLaves − 0 HTa (298.15 K) − 20 HVbcc (298.15 K) Ta:V

= −17547.3 + 1.99T + GHSERTa + 2GHSERV 0 Laves C15 L∗:Ta,V

= 10330.84

0 Laves C15 LTa,V:∗

= 8751.51

A.2.4. Phase Laves C14 (high temperature) Description: (Ta, V)(Ta, V)2 0

C14 bcc GLaves − 30 HTa (298.15 K) = +15000 + 3GHSERTa Ta:Ta

0

C14 GLaves − 30 HVbcc (298.15 K) = +15000 + 3GHSERV V:V

0

C14 bcc GLaves − 0 HVbcc (298.15 K) − 20 HTa (298.15 K) V:Ta

= 30000+13897.16+1.006T +GHSERV+2GHSERTa 0

C14 bcc GLaves − 0 HTa (298.15 K) − 20 HVbcc (298.15 K) Ta:V

= −13897.16 − 1.006T + GHSERTa + 2GHSERV 0 Laves C14 L∗:Ta,V

= 18461.85

0 Laves C14 LTa,V:∗

= 9971.59

where ‘∗’ stands either for Ta or V.

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