A thermodynamic description of the C–Ta–Zr system

Int. Journal of Refractory Metals and Hard Materials 41 (2013) 408–415

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A thermodynamic description of the C–Ta–Zr system Peng Zhou a, Yingbiao Peng a, Yong Du a,⁎, Shequan Wang b, Guanghua Wen b, Wen Xie b, Keke Chang c a b c

State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, PR China Zhuzhou Cemented Carbide Cutting Tools Co. Ltd., Zhuzhou, Hunan 412007, PR China Materials Chemistry, RWTH Aachen University, D-52056 Aachen, Germany

a r t i c l e

i n f o

Article history: Received 25 March 2013 Accepted 26 May 2013 Keywords: C–Ta–Zr ternary system Carbides Phase diagram Thermodynamic modeling

a b s t r a c t Based on critical evaluation of the literature data, the C–Ta–Zr ternary system has been reviewed and assessed by means of the CALPHAD technique. There is no ternary compound in this system. The individual solution phases, i.e., liquid, fcc, hcp and bcc, have been modeled. The modeling covers the whole compositional range of this system and the temperature range from 200 to 3600 °C. A self-consistent thermodynamic description for the C–Ta–Zr system has been developed. Comprehensive comparisons between the present calculations and measured phase diagrams in the literature show that the reliable experimental information is satisfactorily accounted for by the present thermodynamic description. The liquidus projection and reaction scheme of the C–Ta–Zr system have been presented. © 2013 Elsevier Ltd. All rights reserved.

1. Introduction

2. Evaluation of literature information

TaC and ZrC are typical carbides that possess high melting temperature, hardness, and resistance to ablation [1–6]. Due to these excellent properties, they have been employed in the fabrication of ultra high temperature C–C composites to produce aeronautical materials. Also, Ta and Zr have been widely used in WC–Co based cemented carbide and TiC based cermets to produce advanced cutting tool materials [7–16]. Thus, the C–Ta–Zr system is of a great interest for commercial applications. A good thermodynamic knowledge of this system is essential to define conditions for the production of carbides and predict heat treatment parameters so as to obtain optimal engineering properties. It is realized that the CALPHAD (CALculation of PHAse Diagram) approach is a useful tool used to establish thermodynamic databases, which are bases for prediction of thermodynamic properties/phase diagrams, DICTRA (Diffusion-Controlled TRAnsformation) modeling [17] and phase-field simulation [18]. The method combining both thermodynamic and kinetic calculation has been applied in the development of Co–W–Ti–Ta–Nb–C–N cemented carbides [19]. Up to now, no thermodynamic description of the C–Ta–Zr system is available in the literature. The present work thus aims to develop a set of selfconsistent thermodynamic parameters for the C–Ta–Zr system, which is a continuing effort of our previous attempts to establish a multicomponent thermodynamic database for cemented carbide [20–28].

To facilitate reading, the symbols to denote the stable phases in the C–Ta–Zr system were summarized in Table 1. Due to lack of experimental information on the transition between αTa2C and βTa2C, the two types of Ta2C were treated as the same hcp phase in the present work, which was also generally accepted in the binary C–Ta system [29]. Among the available experimental information concerning the phase diagrams of the C–Ta–Zr system, the results reported by Rudy [30], Gladyshevsky et al. [31], and Avgustinik and Ordan'yan [32] were the major contributions to the constitution of this ternary system. Using metallography, X-ray diffraction (XRD), and Differential Thermal analysis (DTA), Rudy [30] studied the C–Ta–Zr system within the temperature range from 1500 to 4000 °C. Although the experimental details were not presented in the publication, Rudy [30] gave information about extensive phase equilibria, e.g., vertical sections, isothermal sections, a three-dimensional isometric view of the ternary system, and a reaction diagram. According to Rudy [30], a continuous solid solution formed between TaC and ZrC, and the Zr could be solved in Ta2C with a solubility of up to ~ 20 at.% Zr. Based on metallography and XRD analysis of 37 alloys, Gladyshevsky et al. [31] investigated the C–Ta–Zr isothermal section at 1450 °C. Using metallography, XRD, and chemical analysis of alloys, Avgustinik and Ordan'yan [32] constructed the isothermal section at 2000 °C and the ZrC–Ta vertical section. Both groups [31,32] suggested that the (Ta,Zr)C was a continuous solution, which was in agreement with the result of Rudy [30]. However, the solubility of Zr in Ta2C reported by them [31,32] was less than ~ 5 at.%, which was significantly lower than that in Ref. [30]. Due to lack of experimental evidence, the

⁎ Corresponding author. Tel.: +86 731 88836213; fax: +86 731 88710855. E-mail address: [email protected] (Y. Du). 0263-4368/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijrmhm.2013.05.015

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Table 1 List of the symbols to denote the phases in the C–Ta–Zr system. Phase

Pearson's symbol

Designation

Phase description

(Ta, Zr)C

cF8

fcc

(Ta, Zr)2C (Ta, βZr) Graphite Liquid

hP3 cI2 hP4 –

hcp bcc C L

Continuous solid solution formed between fcc TaC and ZrC Solid solution based on αTa2C or βTa2C Solid solution based on bcc Ta or βZr Solid solution based on graphite C Liquid

stability of (Ta,Zr)2C reported by the researchers [31,32] was not accepted in the present work. Instead, the data reported by Rudy [30] were accepted because the result was based on XRD analysis on a sufficient number of alloys which show the lattice parameter variation of (Ta,Zr)2C with Zr additions. Rudy [30] reported a quasibinary eutectic reaction at the Zr-rich side, i.e., L = (Ta,Zr)C + (Ta,βZr) at 1830 °C. Avgustinik and Ordan'yan [32] suggested that several alloys with low ZrC concentration melted after isothermal treatment at 2477 °C. These data were accepted in the present work. Rudy [30] presented a liquidus projection showing a four phase equilibrium, L + (Ta,Zr)2C = (Ta,βZr) + (Ta,Zr)C, at 2350 °C with a liquid composition of ~ 3 at.% C and ~ 90 at.% Ta. This reaction was accepted in the present work except for the liquid composition. The reasons for not accepting the liquidus composition [30] were as follows. Firstly, the liquid composition contradicted the binary Ta–Zr phase diagram [30] which indicated a solubility of ~67 at.% Ta in liquid at 2350 °C. Secondly, such a high Ta content in the liquid phase resulted in a small primary crystallization field of the (Ta,Zr)2C, which was not consistent with the reported solubility of Zr in Ta2C (~ 20%) [30]. Jangg et al. [33] reported the immiscibility of TaC and ZrC at low temperatures using auxiliary-metal-bath technique. By applying the order-parameter functional method, Gusev [34] theoretically predicted a miscibility gap between TaC and ZrC at low temperatures with the critical point at 939 °C and 35.5 at.% Ta. Unfortunately, no experimental information was available to support this miscibility gap. Since numerous experiments indicate that (Ta,Zr)C was a continuous solid solution above 1000 °C [30,35–39], we assumed that the miscibility gap was stable below 1000 °C. 3. Thermodynamic models In the present modeling, the Gibbs energy functions for the pure elements C, Ta and Zr are taken from the SGTE compilation by Dinsdale [40]. The present work is based on the most recent evaluations of the binary systems of C–Zr [41],C–Ta [29],and Ta–Zr [42], which take into account liquid, fcc, hcp, and bcc phases during their modeling. The calculated phase diagrams are presented in Fig. 1. 3.1. Liquid Phase The Gibbs energy of the ternary liquid is described by the Redlich– Kister–Muggianu polynominal [43,44]: 0

L

0

L

0

L

L

Gm ¼ xC GC þ xTa GTa þ xZr GZr

ð1Þ

þ RT ðxC ln xC þ xTa ln xTa þ xZr ln xZr Þ L

L

L

þ xC xTa LC;Ta þ xC xZr LC;Zr þ xTa xZr LTa;Zr ex

Fig. 1. Calculated binary phase diagrams: (a) C–Zr system [41], (b) C–Ta system [29], and (c) Ta–Zr system [42].

and 1 bar, is used as the reference state of Gibbs energy. The parameters LLi,j(i, j = C, Ta,Zr) are the interaction parameters from binary systems. The excess Gibbs energy exGLC,Ta,Zr is expressed as follows:

L

þ GC;Ta;Zr where R is the gas constant, xc, xTa and xZr are the molar fractions of the elements C, Ta and Zr, respectively. The standard element reference (SER) state [40], i.e., the stable structure of the element at 25 °C

ex

  L 0 L 1 L 2 L GC;Ta;Zr ¼ xC ⋅ xTa ⋅ xZr ⋅ xC ⋅ LC;Ta;Zr þ xTa ⋅ LC;Ta;Zr þ xZr ⋅ LC;Ta;Zr

ð2Þ

where 0LLC,Ta,Zr, 1LLC,Ta,Zr, and 2LLC,Ta,Zr are the ternary parameters to be evaluated in the present work.

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3.2. Solid solution phase

4. Procedure of optimization

The Gibbs energies of the solid solution phases are described using two-sublattice models developed by Hillert and Jarl [45] as (Ta,Zr)a(C, Va)c. In this model, the first sublattice is a substitutional one which is occupied by Ta and Zr atoms, while the second sublattice is an interstitial one which is occupied by C atoms and vacancies. The symbols a and c denote the numbers of sites on each sublattice and have values of a = 1 and c = 1 for the fcc phase; a = 1 and c = 3 for the bcc phase; a = 1 and c = 0.5 for hcp phase. For one formula unit (Ta,Zr)a(C, Va)c, the Gibbs energy of a phase is expressed as follows:

The evaluation of the model parameters was carried out using the computer operated optimization program PARROT [46], which works by minimizing the sum of the square of the differences between measured and calculated values. The thermodynamic parameters for liquid, fcc and hcp were adjusted by using experimental data selected in Section 2. Each piece of selected information was given a certain weight based on the uncertainties of the experimental data. The weights were changed by trial and error during the assessment until most of the selected experimental information was reproduced within the expected uncertainty limits. Firstly, the optimization is conducted on solid phases using the experimental isothermal section at 2000 °C suggested by Avgustinik and Ordan'yan [32] and the solubility information given by Rudy 0 fcc [17]. For fcc phase, two regular parameters, 0Lfcc Ta,Zr:C and LTa,Zr:C,Va, , are used to describe the solubility of and a sub-regular one, 1Lfcc Ta,Zr:C 0 hcp Ta in ZrC. For hcp, two regular parameters, 0Lhcp Ta,Zr:C and LTa,Zr:C,Va, are assessed to reproduce the solubility of Zr in Ta2C reported by Rudy [30]. Secondly, the optimization is extended to a wide temperature range from 1450 to 3600 °C based on the experimental data [30,31]. In this step, the temperature-dependent parameters for solid phases are taken into account. For fcc, two additional sub-sub-regular 2 fcc parameters for fcc (2Lfcc Ta,Zr:C and LTa,Zr:C), are used to properly describe the phase equilibrium data over the whole temperature and composition range. Thirdly, the liquid phase was assessed according to the experimental data of vertical sections and the invariant equilibria [30,32]. 1 liquid For liquid phase, three constant regular parameters (0Lliquid C,Ta,Zr, LC,Ta,Zr, 2 liquid LC,Ta,Zr) are required to describe the measured liquidus, solidus and

Gϕm ¼ y;Ta y;;C 0 GϕTa:C þ y;Ta y;;Va 0 GϕTa:Va þ y;Zr y;;C 0 GϕZr:C þ y;Zr y;;Va 0 GϕZr:Va þ aRTðyTa ln yTa þ yZr ln yZr Þ þ cRTðyC ln yC þ yVa ln yVa Þ

ð3Þ

þ y;Ta y;Zr y;;C LϕTa;Zr:C þ y;Ta y;Zr y;;Va LϕTa;Zr:Va þ y;Ta y;;C y;;Va LϕTa:C;Va ;

;; ;;

ϕ

;

;

;; ;;

ϕ

þ yZr yC yVa LZr:C;Va þ yTa yZr yC yVa LTa;Zr:C;Va where y,Ta and y,Zr are the site fractions of Ta and Zr in the first sublattice, and y,,C and y,,Va are the site fractions of C and Va in the second sublattice. The parameter 0Gi:Va(i = Ta or Zr) is the Gibbs energy of pure element i, and the parameter 0Gi:C(i = Ta or Zr) is the Gibbs energy of a hypothetical state where all the interstitial sites are completely filled with C. LϕTa,Zr:Va is the binary parameter from the Ta–Zr sub-system [42]. LϕTa,Zr:C and LϕTa,Zr:C,Va are the ternary parameters that will be optimized in the present modeling. Graphite shows a negligible solubility for both Ta and Zr [30,31]. As a result, it is assumed that only C atoms constitute the graphite phase.

Table 2 Summary of the thermodynamic parameters in the C–Ta–Zr system.a Liquid: (C, Ta, Zr)1 0 liquid LC,Ta 0 liquid LC,Zr 0 liquid LTa,Zr

1 liquid LC,Ta 1 liquid LC,Zr 1 liquid LTa,Zr

= −173, 413.25 − 7.1858292T = −305, 420.6 + 16.01676T = 13, 832.1

0 liquid LC;Ta;Zr

1 liquid LC;Ta;Zr

¼ −195; 137

= +23, 643.159 = +50, 000

= −7150 2 liquid LC;Ta;Zr

¼ −42; 274

2 liquid LC,Zr

= −39, 269.66 ¼ −37; 323

fcc-(Ta, Zr)C: (Ta,Zr)1(C, Va)1 0

SER SER 2 Gfcc Ta:C −H C −H Ta ¼ −163; 843:55 þ 266:90346T−44:957558T lnðT Þ−0:0036198014 T

0

7 3 SER SER 2 1 Gfcc −8:30054316  108 T 3 Zr:C −H C −H Zr ¼ −224; 784:9 þ 297:0288T−48:14055TlnðT Þ−0:001372273T −1:015994  10 T þ 517; 213T

þ 594; 677:55T −1 −2:3106742  109 T −3 þ 1:1923702  1013 T −5 −3:5155676  1016 T −7

0 fcc LTa:C,Va

= −60, 408.461 + 4.172556T

0 fcc LZr:C,Va

= −41, 870.2 − 35.70271T + 6.042424T ln(T) − 0.001326472T2

1 fcc LZr:C,Va

= −81, 870.2 − 35.70271T + 6.042424T ln(T) − 0.001326472T2

0 fcc LTa;Zr:C

¼ −105; 455:64 þ 19:19T

0 fcc LTa;Zr:C;Va

1 fcc LTa;Zr:C

¼ þ107; 377:09−29:11T

1 fcc LTa;Zr:C;Va

¼ þ217; 458:59−71:21T

2 fcc LTa;Zr:C

¼ −130; 539:59 þ 43:57 T

2 fcc LTa;Zr:C;Va

¼ 0

¼ þ104; 885:63

hcp-(Ta, Zr)2C: (Ta, Zr)1(C, Va)0.5 0 hcp GTa:C

2 − 0.5HSER − HSER C Ta = −107, 522.86 + 142.26601T − 26.879883T ln(T) − 0.0057393884T

SER 0 hcp GZr:C −0:5H SER C −H Zr 0 hcp LTa:C,Va

0 hcp LTa;Zr:C

¼ −115; 822:7 þ 212:2971T−36:10565T lnðT Þ−0:001375489T 2 −1:361587  10−7 T 3 þ 217; 131T −1 −1:9505689  108 T −3

= −6917.5538 ¼ −26; 409:30 5:11T

0 hcp LZr:C,Va

= +3206.881

0 hcp LTa;Zr:C;Va

0 hcp LTa,Zr:Va

= +30, 051.7

¼ −160; 000

bcc-(Ta, βZr): (Ta, Zr)1(C, Va)3 0 bcc GTa:C

0

graphite − 0Gbcc = +601, 379.32 − 61.123315T Ta − 3GC

SER SER Gbcc ¼ −142; 838:2 þ 631:7121T−96:28173T lnðT Þ−0:001856037T 2 −9:2968513  108 T 3 þ 2; 261; 356T 1 −7:933899  109 T 3 Zr:C −H Zr −3H C

0 bcc LTa:C,Va 0 bcc LTa,Zr:Va a

= −749, 073.01 = 29, 499.6 + 2.6723T

0 bcc LZr:C,Va

= −22, 3221.3

1 bcc LTa,Zr:Va

= −4396.2 + 4.4302 ∗ T

2 bcc LTa,Zr:Va

= −6353.3 + 4.9066T

All parameters are given in J/(mole of atoms); Temperature (T) in K. The Gibbs energies for the pure elements are taken from the compilation of Dinsdale [40]. The parameters of C–Zr, C–Ta and Ta–Zr sub-binary systems are taken from [29,41,42]. The underlined parameters are assessed in the present work.

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Fig. 2. Calculated isothermal sections at 1450 °C in comparison with the experimental data reported by Gladyshevsky et al. [31].

Fig. 4. Calculated isothermal sections at 2000 °C in comparison with the experimental data reported by Avgustinik and Ordan'yan [32].

invariant equilibria [30]. Finally, the parameters obtained at each step are optimized simultaneously, including all the reliable experimental data mentioned previously. Over the whole optimization procedure, we found that the bcc parameters from the descriptions of the sub-systems are adequate to reproduce the phase relations of C–Ta–Zr ternary alloys and thus no additional bcc parameters are introduced.

The thermodynamic parameters obtained in the present work are listed in Table 2. The parameters assessed in the present modeling are underlined. Using this set of parameters, all the phase equilibrium information, i.e., isothermal sections, vertical sections, and liquidus projection are calculated to prove the rationality of the present modeling. Figs. 2 and 3 show the calculated isothermal section at 1450 °C and 1700 °C together with the experimental data from Gladyshevsky et al. [31] and Rudy [30], respectively. It can be seen from the figures that the calculated results are in good agreement with the experimental

data within expected experimental errors. Fig. 4 presents the calculated isothermal section at 2000 °C in comparison with the experimental data reported by Avgustinik and Ordan'yan [32]. Figs. 5–7 compare the calculated isothermal sections with the experimental data reported by Rudy [30] at 2750, 3300 and 3600 °C, respectively. Most experimental data are well reproduced by the present modeling within estimated errors. Fig. 8 gives information about the calculated ZrC–Ta quasi-binary vertical section together with the experimental result presented by Avgustinik and Ordan'yan [32]. Fig. 9 compares the calculated Zr75C25– Ta75C25 vertical section with the experimental one given by Rudy [30]. Despite of the α/βTa2C transition which is not considered in the present modeling, the calculated result is consistent with the experimental one. Figs. 10–12 show the calculated vertical sections compared with the experimental data [30] at 33.3 at.% C, 60 at.% C, and that of Zr55C45–Ta52.5C47.5, respectively. It is revealed from the figures that most experimental points are well reproduced within estimated experimental uncertainties. Fig. 13 shows the vertical section at 50 at.% C, which indicates a miscibility gap of the cubic phase at low temperatures. This miscibility gap is predicted with a critical point at 930 °C

Fig. 3. Calculated isothermal sections at 1700 °C in comparison with the experimental data reported by Rudy [30].

Fig. 5. Calculated isothermal sections at 2750 °C in comparison with the experimental data reported by Rudy [30].

5. Result and discussion

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Fig. 6. Calculated isothermal sections at 3300 °C in comparison with the experimental data reported by Rudy [30].

and 33 at.% Ta, which is close to the result of the theoretical calculation given by Gusev [34]. Fig. 14 presents the liquidus projection calculated by present modeling in comparison with that reported by Rudy [30]. Fig. 15 gives the reaction scheme for the entire C–Ta–Zr system. The calculated invariant equilibria are compared with the experimental ones [30] in Table 3. The reaction types and temperatures from the literature

Fig. 7. Calculated isothermal sections at 3600 °C (a) in comparison with the measured one by Rudy [30] (b).

Fig. 8. Calculated ZrC–Ta vertical section of the C–Ta–Zr system, compared with the experimental data reported by Avgustinik and Ordan'yan [32].

information [30] are well reproduced by the present calculation. The difference between the calculated and measured temperatures is within ±14 °C. The four-phase equilibrium, L + (Ta,Zr)2C = (Ta,Zr) C + (Ta,βZr) calculated by the present modeling shows a lower Ta

Fig. 9. Calculated Zr75C25–Ta75C25 vertical section of the C–Ta–Zr system (a), compared with the experimental data reported by Rudy [30]. The αTa2C and βTa2C are treated as the same hcp phase in this work.

P. Zhou et al. / Int. Journal of Refractory Metals and Hard Materials 41 (2013) 408–415

Fig. 10. Calculated vertical section at 33.3 at.% C of the C–Ta–Zr system, compared with the experimental data reported by Rudy [30].

413

Fig. 13. Calculated ZrC–TaC vertical section of the C–Ta–Zr system at low temperatures.

content in liquid (~ 69.18 at.% Ta) than that reported by Rudy [30] (~ 90 at.% Ta). The calculated result is reasonable as it is in agreement with the Ta–Zr subbinary system [42]. The primary crystallization field of the (Ta,Zr)2C calculated by the present modeling is larger than that

Fig. 11. Calculated vertical section at 60 at.% C of the C–Ta–Zr system, compared with the experimental data reported by Rudy [30].

Fig. 12. Calculated Zr55C45–Ta52.5C47.5 vertical section of the C–Ta–Zr system, compared with the experimental data reported by Rudy [30].

Fig. 14. Calculated liquidus projection of the C–Ta–Zr system according to the present work (a), in comparison with the one reported by Rudy [30] (b).

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Fig. 15. The reaction scheme for the C–Ta–Zr system according to the present calculation with temperature in °C. The invariant reactions among solid phases are not indicated in the figures.

Table 3 Comparison between calculated and measured invariant reactions in the C–Ta–Zr system. Reaction

U1:L + (Ta,Zr)2C = (Ta,Zr) C + (Ta,βZr) e5,min:L = (Ta,Zr) C + (Ta,βZr)

T (°C)

2364 2350 1837 1825

Liquid composition

Source

at.% C

at.% Ta

at.% Zr

8.43 ~3 1.24 ~2

69.18 ~90 23.67 ~10

22.39 ~7 75.09 ~88

This work Rudy [30] This work Rudy [30]

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