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Thermodynamic evaluation of the C–Ta–Ti system and extrapolation to the C–Ta–Ti–N system
Int. Journal of Refractory Metals and Hard Materials 40 (2013) 36–42
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Int. Journal of Refractory Metals and Hard Materials journal homepage: www.elsevier.com/locate/IJRMHM
Thermodynamic evaluation of the C–Ta–Ti system and extrapolation to the C–Ta–Ti–N system Yingbiao Peng a, Peng Zhou a, Yong Du a,⁎, KeKe Chang b a b
State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, China Materials Chemistry, RWTH Aachen University, D-52056 Aachen, Germany
a r t i c l e
i n f o
Article history: Received 29 November 2012 Accepted 27 March 2013 Keywords: C–Ta–Ti ternary system C–Ta–Ti–N quaternary system Phase diagram Thermodynamic modeling Miscibility gap
a b s t r a c t Based on a critical review of the literature data, the C–Ta–Ti system has been thermodynamically evaluated. The CALPHAD (CALculation of PHAse Diagrams) approach is applied to assess the Gibbs energies of individual phases in this ternary system. A set of self-consistent thermodynamic parameters is obtained. Comprehensive comparisons between the calculations and literature data show that the reliable experimental information is satisfactorily accounted for by the present thermodynamic description. Based on the present work and the previous assessments of the sub-ternary systems, a thermodynamic description of the quaternary C–Ta– Ti–N system is extrapolated and used to predict the miscibility gap in the fcc carbonitride. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction Cemented carbides have received extensive attention since they are considered as strong replacements for high speed steels, which have been widely applied in cutting tools and wear resistant parts. Cubic carbides or carbonitrides based on Ta and Ti are often added in cemented carbides to increase the resistance to plastic deformation or as gradient formers [1–4]. Knowledge of solubility of alloy elements in cubic carbides or carbonitrides is the basis of studying some properties of cemented carbides, such as grain size, hardness and strength. Miscibility gaps may form in carbonitrides, e.g., (Ta, Ti)(C, N)x, and have been claimed to be of technical importance [5–8]. In the past decades, cemented carbides were mainly developed through a large degree of mechanical testing, which are expensive and time-consuming. Recently, computational thermodynamics has shown to be a powerful tool for processing advanced materials in cemented carbides [9–11]. For instance, thermodynamic calculations can give an easy access to what phases form under various process conditions. In our group, a research project to establish a thermodynamic database for technologically important cemented carbides is in progress [12–16]. Thus, a thermodynamic description of the ternary C–Ta–Ti system and a further extrapolation of the quaternary C–Ta–Ti–N system are of technical importance for design and improvement of cemented carbides. To the best of our knowledge, no thermodynamic description of the C–Ta–Ti system is available in the literature. The present work is intended to 1) initially evaluate the thermodynamic stabilities of the phases in the C–Ta–Ti system from relevant experimental information ⁎ 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.2013.03.012
using the CALPHAD method, 2) extrapolate phase relations in the C– Ta–Ti–N quaternary system based on the new modeling of the C–Ta– Ti system. Some calculations, which may be of interest to the hard metal industry, will be performed. 2. Experimental information To facilitate reading, the symbols to denote the phases in the C– Ta–Ti system are summarized in Table 1. The C–Ta–Ti ternary was firstly investigated by McMullin and Norton [17] by employing optical microscopy and X-ray diffraction (XRD) techniques. They constructed an isothermal section at 1820 °C in the whole composition range and suggested that the continuous solid solutions are formed between fcc TiC and TaC as well as between bcc (Ta) and (Ti) [17]. According to their work [17], the hcp (Ta2C) phase was found to show very small homogeneity ranges in the C–Ta binary system as well as in the ternary system. Samples annealed at different temperatures were analyzed by XRD, and an invariant reaction L + hcp = bcc + fcc at 2025 ± 15 °C was proposed. The major contribution to the C–Ta–Ti ternary phase diagram comes from the extensive work by Rudy [18–20]. Using optical microscopy and XRD, Rudy [19,20] determined seven isothermal sections between 1500 and 3200 °C. By means of differential thermal analysis, XRD and optical microscopy, Rudy [18–20] also determined several vertical sections and solidus surface of the whole system. The invariant reaction L + hcp = bcc + fcc found by McMullin and Norton [17] was also confirmed in the work of Rudy and Progulski [18], which was suggested to be about 2000 °C. As the data reported by Rudy [18–20] show some discrepancies from McMullin and Norton [17], a detailed comparison between their data is discussed as follows.
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Table 1 List of the symbols to denote the phases in the C–Ta–Ti system. Phase
Pearson's Designation Symbol Phase description symbol in Ref. [20]
(Ta, Ti)C
cF8
fcc
δ
(Ta, Ti)2C hP3
hcp
γ or γ′
(Ta, Ti)
cI2
bcc
β
Liquid Graphite
hP4
L C
L C
Continuous solid solution formed between fcc TaC and TiC Solid solution based on hcp Ta2C. γ denotes ordered phase and γ′ denotes disordered phase. Continuous solid solution formed between bcc (Ta) and (βTi) liquid graphite
The phase relationships reported by Rudy [20] and McMullin and Norton [17] show no major difference except for the extension of the Ta2C phase into the ternary system. A maximum content of about 31 at.% Ti at 2000 °C in this phase has been found in Rudy's work [20], which is much larger than the result reported by McMullin and Norton [17]. In the present modeling, we accept Rudy's results [20] for two reasons: 1) the isothermal sections determined by Rudy [18–20] cover a wide temperature range, indicating that the large solubility of Ti in Ta2C has been proved for multiple times at various temperatures, 2) based on experiments, Kud et al. [21] found that the existence of oxides will substantially inhibit the solution of Ti in tantalum carbides and retard the equilibrium, which may account for the low solubility of Ti in Ta2C reported by McMullin and Norton [17]. Furthermore, solid state phase transitions in the binary Ta2C phase as well as into the ternary C–Ta–Ti system have been reported by several investigators [19,22,23]. However, due to the insufficient experimental data and the lack of modeling concerning this order–disorder transition in the C–Ta sub-binary system [24], this information is not included in the present modeling. No experimental data on thermodynamic properties or phase equilibrium data of the quaternary C–Ta–Ti–N system have been reported in the literature. Thus, the thermodynamic description of this quaternary system will be extrapolated based on the new thermodynamic description of the ternary C–Ta–Ti system in combination with the previous assessments of the C–Ta–N [25], C–Ti–N [26] systems and the extrapolation of the Ta–Ti–N system. 3. Thermodynamic models In the present modeling, the Gibbs energy functions for the elements C, Ta and Ti are taken from the SGTE compilation by Dinsdale [27]. The present work is based on the most recent evaluations of the binary systems of C–Ta [24], C–Ti [28] and Ta–Ti [29]. The calculated binary phase diagrams are presented in Fig. 1. The C–Ta–Ti system consists of the following five phases: liquid, fcc, bcc, hcp, and graphite. Different thermodynamic models were applied depending on the crystal structure and thermodynamic property of each phase.
Fig. 1. Calculated binary phase diagrams: (a) C–Ta system [24], (b) C–Ti system [28], (c) Ta–Ti system [29].
3.1. Liquid phase The Gibbs energy of the ternary liquid is described by Redlich– Kister polynomial [30]: 0
L
0
L
0
L
L
Gm ¼ xC GC þ xTa GTa þ xTi GTi
ð1Þ
þ RT ðxC lnxC þ xTa lnxTa þ xTi lnxTi Þ L
L
L
þ xC xTa LC;Ta þ xC xTi LC;Ti þ xTa xTi LTa;Ti þ
ex
reference (SER) state [27], i.e. the stable structure of the element at 25 °C and 1 bar, is used as the reference state of Gibbs energy. The paL rameters Li,j (i, j = C, Ta, Ti) are the interaction parameters from binaL ry systems. The excess Gibbs energy exGC,Ta,Ti is expressed as follows:
GC;Ta;TiL
ex
L 0 L 1 L 2 L GC;Ta;Ti ¼ xC ⋅xTa ⋅xTi ⋅ xC ⋅ LC;Ta;Ti þ xTa ⋅ LC;Ta;Ti þ xTi ⋅ LC;Ta;Ti
ð2Þ
C;Ta;Ti
where R is the gas constant, xC, xTa and xTi are the molar fractions of the elements C, Ta and Ti, respectively. The standard element
L L L where 0LC,Ta,Ti , 1LC,Ta,Ti , and 2LC,Ta,Ti are the ternary parameters to be evaluated in the present work.
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Y. Peng et al. / Int. Journal of Refractory Metals and Hard Materials 40 (2013) 36–42
Table 2 Invariant phase equilibrium in the C–Ta–Ti system together with experimental data. Reaction
Temperature
Composition
Reference
L + hcp = fcc + bcc
T = 1998 °C
xhcp ¼ 0:31xhcp ¼ 0:30 C Ti bcc xTi = 0.45 xCbcc = 0.03 fcc xTi = 0.44xCfcc = 0.35 L xTi = 0.65 xCL = 0.07 ¼ 0:31 xhcp Ti
This work
T = 2000 °C T = 2025 ± 15 °C
[19,20] [17]
3.2. fcc, bcc and hcp phases The Gibbs energies of the fcc, bcc, and hcp phases are described using two-sublattice models developed by Hillert and Staffansson [31] as (Ta, Ti)a(C, Va)c. In this model, it is assumed that Ta and Ti atoms occupy one sublattice while C atoms and vacancies occupy the other one, since C atoms are generally known to occupy only interstitial sites in these phases. 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 the hcp phase. For one formula unit (Ta, Ti)a(C, Va)c, the Gibbs energy of a phase is expressed as follows: 0
0
0
0
Gm ¼ yTa yC GTa:C þ yTa yVa GTa:Va þ yTi yC GTi:C þ yTi yVa GTi:Va
Fig. 3. Calculated isothermal section of the C–Ta–Ti system at 1800 °C together with the experimental data [20].
measured and calculated values. Each piece of selected information was given a certain weight based on the uncertainties of the experimental data, and changed by trial and error during the assessment,
ð3Þ
þ aRTðyTa lnyTa þ yTi lnyTi Þ þ cRTðyC lnyC þ yVa lnyVa Þ þ yTa yTi yC LTa;Ti:C þ yTa yTi yVa LTa;Ti:Va þ yTa yC yVa LTa:C;Va þ yTi yC yVa LTi:C;Va þ yTa yTi yC yVa LTa;Ti:C;Va where yTa and yTi are the site fraction of Ta and Ti in the first sublattice, and yC and yVa are the site fraction of C and Va in the second sublattice. The parameter 0Gi : Va (i = Ta or Ti) is the Gibbs energy of pure element i, and the parameter 0Gi : C (i = Ta or Ti) is the Gibbs energy of a hypothetical state where all the interstitial sites are completely filled with C. Graphite shows a negligible solubility for both Ta and Ti. As a result, it is assumed that only C atoms occupy the sublattice of graphite. 4. Evaluation of model parameters The evaluation of the model parameters was carried out by means of a computer operated optimization program PARROT [32], which works by minimizing the square sum of the differences between
Fig. 2. Calculated isothermal section of the C–Ta–Ti system at 1500 °C together with the experimental data [20].
Fig. 4. Isothermal section of the C–Ta–Ti system at 2000 °C: (a) calculated in the present work, (b) experimental one by Rudy [20].
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39
until most of the selected experimental information was reproduced within the expected uncertainty limits. The optimization began with solid phases using isothermal section information. Since many experimental information concerns the solubility of fcc phase especially at high temperatures, firstly the thermodynamic parameters for fcc phase were evaluated. Most of the isothermal sections in the temperature range of 1500 to 3200 °C and the vertical sections with 30–33.3 at.% C established by Rudy [19,20] were very important to evaluate the temperature dependence of the phase stability of the fcc phase. In view of its continuous solution and the large solubility away from C-rich region, two ternary pa0 fcc fcc rameters 0LTa,Ti : C and LTa,Ti : C,Va were employed in the assessment and then fixed during the subsequent optimization steps. Secondly, the hcp phase was included in the optimization. The isothermal phase equilibrium data at 1500 to 3200 °C and vertical sections of Ti68C32-Ta68C32 and Ti98.5C1.5–Ta89.3C10.7 [19,20] were utilized in the 1 hcp 0 hcp hcp evaluation of the ternary parameters 0LTa,Ti : C, LTa,Ti : C, LTa,Ti : C,Va. For 0 bcc bcc phase, only one ternary parameter LTa,Ti : C was utilized. For liquid, L L L three regular interaction parameters ( 0LC,Ta,Ti , 1LC,Ta,Ti , 2LC,Ta,Ti ), in Eq. (2), were required to reproduce the experimental data on the isothermal sections above 1800 °C, the invariant equilibria associated with the liquid phase, two vertical sections of Ti68C32–Ta68C32 and Ti98.5C1.5–Ta89.3C10.7, and liquidus projection. Finally, the parameters obtained at each step were optimized simultaneously, including all the reliable experimental data mentioned previously.
5. Results and discussion
Fig. 5. Isothermal section of the C–Ta–Ti system at 2400 °C: (a) calculated in the present work, (b) experimental one by Rudy [20].
Fig. 6. Isothermal section of the C–Ta–Ti system at 2600 °C: (a) calculated in the present work, (b) experimental one by Rudy [20].
5.1. The C–Ta–Ti system The thermodynamic parameters for the C–Ta–Ti system obtained in the present work have been compiled into a thermodynamic database for cemented carbides. A series of phase diagrams, including isothermal sections, vertical sections, and the liquidus projection are calculated to account for the rationality of this thermodynamic description. An invariant reaction of the C–Ta–Ti system calculated in the present work is presented in Table 2. Figs. 2 and 3 show the calculated isothermal sections of the C–Ta– Ti system at 1500 and 1800 °C, respectively, together with the experimental data reported by Rudy [20]. The calculated values are in good agreement with the measured data. Figs. 4 to 8 present the calculated isothermal sections in comparison with the literature data from Rudy [20] at 2000, 2400, 2600, 3000 and 3200 °C, respectively. The calculated solubility of Ti in hcp at 2000 °C is 31 at.%, which is in excellent agreement with the experimental data reported by Rudy [20]. Agreements between the calculated and measured data of the isothermal sections at 2000 to 3200 °C are satisfactory while the disagreements are mainly caused by the refinement of the binary phase diagrams. Fig. 9 presents the calculated vertical section at 32 at.% C, in comparison with the one at 30–33.3 at. % C determined by Rudy [20]. Most of the experimental data can be well reproduced within estimated errors.
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Y. Peng et al. / Int. Journal of Refractory Metals and Hard Materials 40 (2013) 36–42
Fig. 7. Isothermal section of the C–Ta–Ti system at 3000 °C: (a) calculated in the present work, (b) experimental one by Rudy [20].
The present result shows that an invariant reaction L + hcp = bcc + fcc occurs at 1998 °C and xhcp Ti ¼ 0:31, which is in good agreement with the experimental data as showing in Table 2. Fig. 10 presents the calculated vertical section of Ti98.5C1.5-Ta89.3C10.7, compared with the experimental data from Rudy [20]. Good agreement is obtained between the thermodynamic calculation and experiment. The calculated liquidus projection of the C–Ta–Ti system is given in Fig. 11(a) and compared with the diagram in Fig. 11(b) from Rudy [20]. Fig. 12 presents the reaction scheme for the C–Ta–Ti system. The invariant reaction types and temperatures from the literature information [20] are well reproduced by the present calculation.
Fig. 8. Isothermal section of the C–Ta–Ti system at 3200 °C: (a) calculated in the present work, (b) experimental one by Rudy [20].
systems, because quaternary interactions are not so strong. Although there might be some uncertainties in the descriptions here obtained, the effect of composition, temperature, or pressure changes on the phase relations can be predicted. In the present work, the extrapolated description is used to calculate some diagrams which might be of interest to the cemented carbide industry. The technical importance of the C–Ta–Ti–N system focuses on the fcc carbonitride. Since the technical interest concerns graphite saturation, all the calculations are performed at unit carbon activity. Fig. 13 shows the calculated miscibility gap of fcc carbonitride in the C–Ta–
5.2. The C–Ta–Ti-N system The TaC and TiC carbides as well as TaN and TiN nitrides all have a fcc arrangement of metal atoms with carbon or nitrogen atoms on the interstitial sites. They form a fcc carbonitride in the quaternary system, and the model in the quaternary system, which is extended from the lower-order systems is (Ta, Ti)1(C, N, Va)1. This model is also applied to the hcp and bcc phases, which are modeled with the sublattices (Ta, Ti)1(C, N, Va)0.5 and (Ta, Ti)1(C, N, Va)3, respectively. For the liquid phase, the model is (Ta, Ti, C, N)1. Since no experimental information for the quaternary C–Ta–Ti–N system is available, the thermodynamic description of this quaternary system is predicted by combining the four sub-ternary systems as presented in Section 2. Generally speaking, there is a less severe limitation to predict a quaternary system from the four sub-ternary
Fig. 9. Calculated vertical section at 32 at.% C of the C–Ta–Ti system, compared with the experimental data reported by Rudy [20].
Y. Peng et al. / Int. Journal of Refractory Metals and Hard Materials 40 (2013) 36–42
41
Fig. 12. Reaction scheme for the C–Ta–Ti system. Fig. 10. Calculated Ti98.5C1.5-Ta89.3C10.7 vertical section of the C–Ta–Ti system, compared with the experimental data reported by Rudy [20].
Ti–N system with unit carbon activity at 1450 °C (a possible sintering temperature) and at 1200 °C(a possible nitriding temperature). As shown in the diagram, the size of the miscibility gap of the fcc carbonitride decreases with the increase of annealing temperature. Fig. 14 shows the effect of nitrogen activity (or pressure) on the miscibility gap of the fcc carbonitride with unit carbon activity at 1450 °C, indicating that the size of the miscibility gap increases with increasing N activity.
Fig. 13. Calculated miscibility gap of the fcc carbide in the C–Ta–Ti–N system with unit carbon activity at 1450 °C (a possible sintering temperature) and at 1200 °C (a possible nitriding temperature).
6. Summary • The phase equilibrium data in the C–Ta–Ti system reported in the literature [17–20], where some discrepancies exist, are critically reviewed. The experimental data reported by Rudy [18–20] are considered to be reliable and applied to the thermodynamic modeling of the C–Ta–Ti ternary system. Comprehensive comparisons between the calculated and experimental phase diagrams [18–20]
Fig. 11. Liquidus projection of the C–Ta–Ti system: (a) calculated in the present work, (b) experimental one by Rudy [20].
Fig. 14. The effect of nitrogen activity (or pressure) on the miscibility gap of the fcc phase, calculated with unit carbon activity at 1450 °C.
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show that most of the experimental data are well accounted for by the present description. • The quaternary C–Ta–Ti–N system is extrapolated based on the present work and previous work of the sub-ternary systems [25,26]. The miscibility gap of the fcc carbonitride in the C–Ta–Ti–N system is predicted, indicating that the size of the miscibility gap of the fcc carbonitride decreases with increasing annealing temperature or decreasing N activity. Acknowledgments The financial support from the Creative Research Group of National Natural Science Foundation of China (Grant No. 51021063), Zhuzhou Cemented Carbide Cutting Tools Limited Company of China, and Doctoral Scientific Fund Project of the State Education Committee of China (Grant No. 20120162110051) is acknowledged. The Thermo-Calc Software AB in Sweden is gratefully acknowledged for the provision of Thermo-Calc software. References [1] Fernandes CM, Senos AMR. Cemented carbide phase diagrams: a review. Int J Refract Met Hard Mater 2011;29(4):405–18. [2] Weidow J, Zackrisson J, Jansson B, Andren H-O. Characterisation of WC–Co with cubic carbide additions. Int J Refract Met Hard Mater 2009;27(2):244–8. [3] Glühmann J, Schneeweiß M, Berg H v d, Kassel D, Rödiger K, Dreyer K, et al. Functionally graded WC–Ti(C,N)–(Ta,Nb)C–Co hardmetals: metallurgy and performance. Int J Refract Met Hard Mater 2013;36:38–45. [4] Janisch DS, Lengauer W, Eder A, Dreyer K, Rödiger K, Daub HW, et al. Nitridation sintering of WC–Ti(C, N)–(Ta, Nb)C–Co hardmetals. Int J Refract Met Hard Mater 2013;36:22–30. [5] Chung H-J, Shim J-H, Lee DN. Thermodynamic evaluation and calculation of phase equilibria of the Ti–Mo–C–N quaternary system. J Alloys Compd 1999;282:142–8. [6] Huang W. Thermodynamic properties of the Nb–W–C–N system. Z Metallkd 1997;88(1):63–8. [7] Frisk K. A thermodynamic analysis of the Ta–W–C and the Ta–W–C–N systems. Z Metallkd 1999;90(9):704–11. [8] Jonsson S. Assessment of the Ti–W–C system and calculations in the Ti–W–C–N system. Z Metallkd 1996;87(10):788–95. [9] Ekroth M, Frisk K, Jansson B, Dumitrescu LFS. Development of a thermodynamic database for cemented carbides for design and processing simulations. Metall Mater Trans B 2000;31B(4):615–9. [10] Ekroth M, Frykholm R, Lindholm M, Andren HO, Agren J. Gradient zones in WC– Ti(C, N)–Co-based cemented carbides: experimental study and computer simulations. Acta Mater 2000;48(9):2177–85. [11] Frisk K, Durnitrescu L, Ekroth M, Jansson B, Kruse O, Sundman B. Development of a database for cemented carbides: thermodynamic modeling and experiments. J Phase Equilib 2001;22(6):645–55.
[12] Sha C, Bu M, Xu H, Du Y, Wang S, Wen G. A thermodynamic modeling of the C–Cr– Ta ternary system. J Alloys Compd 2011;509(20):5996–6003. [13] Zhang W, Sha C, Du Y, Wen G, Xie W, Wang S. Computer simulations and verification of gradient zone formation in cemented carbides. Acta Metall Sin 2011;47(10):1307–14. [14] Chen W, Xu T, Zhang W, Zhang H, Du Y, Tan C, et al. Computer simulation of gradient zone formation in cemented carbides and its verification. Chinese J Nonferrous Met 2012;22(5):1440–7. [15] Zhang W, Peng Y, Zhou P, Chen W, Du Y, Xie W, Wen G, Wang S. Experimental Investigation and Simulation of Gradient Zone Formation in WC–Ti(C, N)–TaC– NbC–Co Cemented Carbides. J Phase Equilib Diffus in press; doi: http://dx.doi. org/10.1007/s11669-013-0225-2. [16] Zhou P, Peng Y, Hu B, Liu S, Du Y, Wang S, et al. A thermodynamic description of the Co–Cr–Ti ternary system over the entire composition and temperature ranges. CALPHAD 2013;41:42–9. [17] McMullin JG, Norton JT. The ternary system titanium–tantalum–carbon. J Met 1953;5(AIME Trans. 197):1205–8. [18] Rudy E, Progulski J. Pirani furnace for the precision determination of the melting temperatures of refractory metallic substances. Planseeber Pulvermetall 1967;15(1): 13–45. [19] Section III Rudy E. E.5 titanium–tantalum–carbon system. Ternary Phase Equilibria in Transition Metal-Boron-Carbon-Silicon Systems. , Techn. Rep. AFML-TR-65-2, Contact No. USAF 33(615)-1249 and 33(615)-67-C-1513Sacramento, CA, USA: Mater. Res. Lab., Aerojet-Gen. Corp; 1969. p. 274–97. [20] Rudy E. Part I. Phase diagrams of the systems titanium–niobium–carbon, titanium– tantalum–carbon, and titanium–molybdenum–carbon. Phase equilibrium investigation of binary, ternary, and higher order systems. , Tech. Rep. AFML-TR-69-117, Contact No. USAF 33(615)-67-C-1513Sacramento, CA, USA: Mater. Res. Lab., Aerojet-Gen. Corp; 1970. p. 1–132. [21] Kud IV, Likhoded LS, Eremenko LI, Makarenko GN, Fedorus VB, Prilutskii EV. Theory, production technology, and properties of powders and fibers: features of (Ti, Me)C solid solution formation. Powder Metall Met Ceram 2006;45(1–2):14–9. [22] Storms EK. The refractory carbides. New York: Academic; 1967284. [23] Em VT, Tashmetov MY. Ordering structures and phase transformations in titanium tantalum carbide (Ti1–yTayC0.63) and titanium niobium carbide (Ti1–zNbzC0.6). Fiz Met Metalloved 1992(3):112–6. [24] Frisk K, Guillermet AF. Gibbs energy coupling of the phase diagram and thermochemistry in the tantalum–carbon system. J Alloys Compd 1996;238:167–79. [25] Frisk K. Analysis of the phase diagram and thermochemistry in the Ta–N and the Ta–C–N systems. J Alloys Compd 1998;278(1–2):216–26. [26] Frisk K, Zackrisson J, Jansson B, Markstroem A. Experimental investigation of the equilibrium composition of titanium carbonitride and analysis using thermodynamic modelling. Z Metallkd 2004;95(11):987–92. [27] Dinsdale AT. SGTE data for pure elements. CALPHAD 1991;15(4):317–425. [28] Frisk K. A revised thermodynamic description of the Ti–C system. CALPHAD 2003;27(4):367–73. [29] Saunders N. COST507. In: Ansara I, Dinsdale AT, Rand MH, editors. COST 507 Report. EUR 18499; 1998. p. 293–6. [30] Redlich O, Kiss A. Algebraic representation of thermodynamic properties and the classification of solutions. Ind Eng Chem 1948;40:345–8. [31] Hillert M, Staffansson LI. Regular solution model for stoichiometric phases and ionic melts. Acta Chem Scand 1970;24(10):3618–26. [32] Sundman B, Jansson B, Andersson JO. The Thermo-Calc databank system. CALPHAD 1985;9(2):153–90.
Contents lists available at SciVerse ScienceDirect
Int. Journal of Refractory Metals and Hard Materials journal homepage: www.elsevier.com/locate/IJRMHM
Thermodynamic evaluation of the C–Ta–Ti system and extrapolation to the C–Ta–Ti–N system Yingbiao Peng a, Peng Zhou a, Yong Du a,⁎, KeKe Chang b a b
State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, China Materials Chemistry, RWTH Aachen University, D-52056 Aachen, Germany
a r t i c l e
i n f o
Article history: Received 29 November 2012 Accepted 27 March 2013 Keywords: C–Ta–Ti ternary system C–Ta–Ti–N quaternary system Phase diagram Thermodynamic modeling Miscibility gap
a b s t r a c t Based on a critical review of the literature data, the C–Ta–Ti system has been thermodynamically evaluated. The CALPHAD (CALculation of PHAse Diagrams) approach is applied to assess the Gibbs energies of individual phases in this ternary system. A set of self-consistent thermodynamic parameters is obtained. Comprehensive comparisons between the calculations and literature data show that the reliable experimental information is satisfactorily accounted for by the present thermodynamic description. Based on the present work and the previous assessments of the sub-ternary systems, a thermodynamic description of the quaternary C–Ta– Ti–N system is extrapolated and used to predict the miscibility gap in the fcc carbonitride. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction Cemented carbides have received extensive attention since they are considered as strong replacements for high speed steels, which have been widely applied in cutting tools and wear resistant parts. Cubic carbides or carbonitrides based on Ta and Ti are often added in cemented carbides to increase the resistance to plastic deformation or as gradient formers [1–4]. Knowledge of solubility of alloy elements in cubic carbides or carbonitrides is the basis of studying some properties of cemented carbides, such as grain size, hardness and strength. Miscibility gaps may form in carbonitrides, e.g., (Ta, Ti)(C, N)x, and have been claimed to be of technical importance [5–8]. In the past decades, cemented carbides were mainly developed through a large degree of mechanical testing, which are expensive and time-consuming. Recently, computational thermodynamics has shown to be a powerful tool for processing advanced materials in cemented carbides [9–11]. For instance, thermodynamic calculations can give an easy access to what phases form under various process conditions. In our group, a research project to establish a thermodynamic database for technologically important cemented carbides is in progress [12–16]. Thus, a thermodynamic description of the ternary C–Ta–Ti system and a further extrapolation of the quaternary C–Ta–Ti–N system are of technical importance for design and improvement of cemented carbides. To the best of our knowledge, no thermodynamic description of the C–Ta–Ti system is available in the literature. The present work is intended to 1) initially evaluate the thermodynamic stabilities of the phases in the C–Ta–Ti system from relevant experimental information ⁎ 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.2013.03.012
using the CALPHAD method, 2) extrapolate phase relations in the C– Ta–Ti–N quaternary system based on the new modeling of the C–Ta– Ti system. Some calculations, which may be of interest to the hard metal industry, will be performed. 2. Experimental information To facilitate reading, the symbols to denote the phases in the C– Ta–Ti system are summarized in Table 1. The C–Ta–Ti ternary was firstly investigated by McMullin and Norton [17] by employing optical microscopy and X-ray diffraction (XRD) techniques. They constructed an isothermal section at 1820 °C in the whole composition range and suggested that the continuous solid solutions are formed between fcc TiC and TaC as well as between bcc (Ta) and (Ti) [17]. According to their work [17], the hcp (Ta2C) phase was found to show very small homogeneity ranges in the C–Ta binary system as well as in the ternary system. Samples annealed at different temperatures were analyzed by XRD, and an invariant reaction L + hcp = bcc + fcc at 2025 ± 15 °C was proposed. The major contribution to the C–Ta–Ti ternary phase diagram comes from the extensive work by Rudy [18–20]. Using optical microscopy and XRD, Rudy [19,20] determined seven isothermal sections between 1500 and 3200 °C. By means of differential thermal analysis, XRD and optical microscopy, Rudy [18–20] also determined several vertical sections and solidus surface of the whole system. The invariant reaction L + hcp = bcc + fcc found by McMullin and Norton [17] was also confirmed in the work of Rudy and Progulski [18], which was suggested to be about 2000 °C. As the data reported by Rudy [18–20] show some discrepancies from McMullin and Norton [17], a detailed comparison between their data is discussed as follows.
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Table 1 List of the symbols to denote the phases in the C–Ta–Ti system. Phase
Pearson's Designation Symbol Phase description symbol in Ref. [20]
(Ta, Ti)C
cF8
fcc
δ
(Ta, Ti)2C hP3
hcp
γ or γ′
(Ta, Ti)
cI2
bcc
β
Liquid Graphite
hP4
L C
L C
Continuous solid solution formed between fcc TaC and TiC Solid solution based on hcp Ta2C. γ denotes ordered phase and γ′ denotes disordered phase. Continuous solid solution formed between bcc (Ta) and (βTi) liquid graphite
The phase relationships reported by Rudy [20] and McMullin and Norton [17] show no major difference except for the extension of the Ta2C phase into the ternary system. A maximum content of about 31 at.% Ti at 2000 °C in this phase has been found in Rudy's work [20], which is much larger than the result reported by McMullin and Norton [17]. In the present modeling, we accept Rudy's results [20] for two reasons: 1) the isothermal sections determined by Rudy [18–20] cover a wide temperature range, indicating that the large solubility of Ti in Ta2C has been proved for multiple times at various temperatures, 2) based on experiments, Kud et al. [21] found that the existence of oxides will substantially inhibit the solution of Ti in tantalum carbides and retard the equilibrium, which may account for the low solubility of Ti in Ta2C reported by McMullin and Norton [17]. Furthermore, solid state phase transitions in the binary Ta2C phase as well as into the ternary C–Ta–Ti system have been reported by several investigators [19,22,23]. However, due to the insufficient experimental data and the lack of modeling concerning this order–disorder transition in the C–Ta sub-binary system [24], this information is not included in the present modeling. No experimental data on thermodynamic properties or phase equilibrium data of the quaternary C–Ta–Ti–N system have been reported in the literature. Thus, the thermodynamic description of this quaternary system will be extrapolated based on the new thermodynamic description of the ternary C–Ta–Ti system in combination with the previous assessments of the C–Ta–N [25], C–Ti–N [26] systems and the extrapolation of the Ta–Ti–N system. 3. Thermodynamic models In the present modeling, the Gibbs energy functions for the elements C, Ta and Ti are taken from the SGTE compilation by Dinsdale [27]. The present work is based on the most recent evaluations of the binary systems of C–Ta [24], C–Ti [28] and Ta–Ti [29]. The calculated binary phase diagrams are presented in Fig. 1. The C–Ta–Ti system consists of the following five phases: liquid, fcc, bcc, hcp, and graphite. Different thermodynamic models were applied depending on the crystal structure and thermodynamic property of each phase.
Fig. 1. Calculated binary phase diagrams: (a) C–Ta system [24], (b) C–Ti system [28], (c) Ta–Ti system [29].
3.1. Liquid phase The Gibbs energy of the ternary liquid is described by Redlich– Kister polynomial [30]: 0
L
0
L
0
L
L
Gm ¼ xC GC þ xTa GTa þ xTi GTi
ð1Þ
þ RT ðxC lnxC þ xTa lnxTa þ xTi lnxTi Þ L
L
L
þ xC xTa LC;Ta þ xC xTi LC;Ti þ xTa xTi LTa;Ti þ
ex
reference (SER) state [27], i.e. the stable structure of the element at 25 °C and 1 bar, is used as the reference state of Gibbs energy. The paL rameters Li,j (i, j = C, Ta, Ti) are the interaction parameters from binaL ry systems. The excess Gibbs energy exGC,Ta,Ti is expressed as follows:
GC;Ta;TiL
ex
L 0 L 1 L 2 L GC;Ta;Ti ¼ xC ⋅xTa ⋅xTi ⋅ xC ⋅ LC;Ta;Ti þ xTa ⋅ LC;Ta;Ti þ xTi ⋅ LC;Ta;Ti
ð2Þ
C;Ta;Ti
where R is the gas constant, xC, xTa and xTi are the molar fractions of the elements C, Ta and Ti, respectively. The standard element
L L L where 0LC,Ta,Ti , 1LC,Ta,Ti , and 2LC,Ta,Ti are the ternary parameters to be evaluated in the present work.
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Table 2 Invariant phase equilibrium in the C–Ta–Ti system together with experimental data. Reaction
Temperature
Composition
Reference
L + hcp = fcc + bcc
T = 1998 °C
xhcp ¼ 0:31xhcp ¼ 0:30 C Ti bcc xTi = 0.45 xCbcc = 0.03 fcc xTi = 0.44xCfcc = 0.35 L xTi = 0.65 xCL = 0.07 ¼ 0:31 xhcp Ti
This work
T = 2000 °C T = 2025 ± 15 °C
[19,20] [17]
3.2. fcc, bcc and hcp phases The Gibbs energies of the fcc, bcc, and hcp phases are described using two-sublattice models developed by Hillert and Staffansson [31] as (Ta, Ti)a(C, Va)c. In this model, it is assumed that Ta and Ti atoms occupy one sublattice while C atoms and vacancies occupy the other one, since C atoms are generally known to occupy only interstitial sites in these phases. 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 the hcp phase. For one formula unit (Ta, Ti)a(C, Va)c, the Gibbs energy of a phase is expressed as follows: 0
0
0
0
Gm ¼ yTa yC GTa:C þ yTa yVa GTa:Va þ yTi yC GTi:C þ yTi yVa GTi:Va
Fig. 3. Calculated isothermal section of the C–Ta–Ti system at 1800 °C together with the experimental data [20].
measured and calculated values. Each piece of selected information was given a certain weight based on the uncertainties of the experimental data, and changed by trial and error during the assessment,
ð3Þ
þ aRTðyTa lnyTa þ yTi lnyTi Þ þ cRTðyC lnyC þ yVa lnyVa Þ þ yTa yTi yC LTa;Ti:C þ yTa yTi yVa LTa;Ti:Va þ yTa yC yVa LTa:C;Va þ yTi yC yVa LTi:C;Va þ yTa yTi yC yVa LTa;Ti:C;Va where yTa and yTi are the site fraction of Ta and Ti in the first sublattice, and yC and yVa are the site fraction of C and Va in the second sublattice. The parameter 0Gi : Va (i = Ta or Ti) is the Gibbs energy of pure element i, and the parameter 0Gi : C (i = Ta or Ti) is the Gibbs energy of a hypothetical state where all the interstitial sites are completely filled with C. Graphite shows a negligible solubility for both Ta and Ti. As a result, it is assumed that only C atoms occupy the sublattice of graphite. 4. Evaluation of model parameters The evaluation of the model parameters was carried out by means of a computer operated optimization program PARROT [32], which works by minimizing the square sum of the differences between
Fig. 2. Calculated isothermal section of the C–Ta–Ti system at 1500 °C together with the experimental data [20].
Fig. 4. Isothermal section of the C–Ta–Ti system at 2000 °C: (a) calculated in the present work, (b) experimental one by Rudy [20].
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until most of the selected experimental information was reproduced within the expected uncertainty limits. The optimization began with solid phases using isothermal section information. Since many experimental information concerns the solubility of fcc phase especially at high temperatures, firstly the thermodynamic parameters for fcc phase were evaluated. Most of the isothermal sections in the temperature range of 1500 to 3200 °C and the vertical sections with 30–33.3 at.% C established by Rudy [19,20] were very important to evaluate the temperature dependence of the phase stability of the fcc phase. In view of its continuous solution and the large solubility away from C-rich region, two ternary pa0 fcc fcc rameters 0LTa,Ti : C and LTa,Ti : C,Va were employed in the assessment and then fixed during the subsequent optimization steps. Secondly, the hcp phase was included in the optimization. The isothermal phase equilibrium data at 1500 to 3200 °C and vertical sections of Ti68C32-Ta68C32 and Ti98.5C1.5–Ta89.3C10.7 [19,20] were utilized in the 1 hcp 0 hcp hcp evaluation of the ternary parameters 0LTa,Ti : C, LTa,Ti : C, LTa,Ti : C,Va. For 0 bcc bcc phase, only one ternary parameter LTa,Ti : C was utilized. For liquid, L L L three regular interaction parameters ( 0LC,Ta,Ti , 1LC,Ta,Ti , 2LC,Ta,Ti ), in Eq. (2), were required to reproduce the experimental data on the isothermal sections above 1800 °C, the invariant equilibria associated with the liquid phase, two vertical sections of Ti68C32–Ta68C32 and Ti98.5C1.5–Ta89.3C10.7, and liquidus projection. Finally, the parameters obtained at each step were optimized simultaneously, including all the reliable experimental data mentioned previously.
5. Results and discussion
Fig. 5. Isothermal section of the C–Ta–Ti system at 2400 °C: (a) calculated in the present work, (b) experimental one by Rudy [20].
Fig. 6. Isothermal section of the C–Ta–Ti system at 2600 °C: (a) calculated in the present work, (b) experimental one by Rudy [20].
5.1. The C–Ta–Ti system The thermodynamic parameters for the C–Ta–Ti system obtained in the present work have been compiled into a thermodynamic database for cemented carbides. A series of phase diagrams, including isothermal sections, vertical sections, and the liquidus projection are calculated to account for the rationality of this thermodynamic description. An invariant reaction of the C–Ta–Ti system calculated in the present work is presented in Table 2. Figs. 2 and 3 show the calculated isothermal sections of the C–Ta– Ti system at 1500 and 1800 °C, respectively, together with the experimental data reported by Rudy [20]. The calculated values are in good agreement with the measured data. Figs. 4 to 8 present the calculated isothermal sections in comparison with the literature data from Rudy [20] at 2000, 2400, 2600, 3000 and 3200 °C, respectively. The calculated solubility of Ti in hcp at 2000 °C is 31 at.%, which is in excellent agreement with the experimental data reported by Rudy [20]. Agreements between the calculated and measured data of the isothermal sections at 2000 to 3200 °C are satisfactory while the disagreements are mainly caused by the refinement of the binary phase diagrams. Fig. 9 presents the calculated vertical section at 32 at.% C, in comparison with the one at 30–33.3 at. % C determined by Rudy [20]. Most of the experimental data can be well reproduced within estimated errors.
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Fig. 7. Isothermal section of the C–Ta–Ti system at 3000 °C: (a) calculated in the present work, (b) experimental one by Rudy [20].
The present result shows that an invariant reaction L + hcp = bcc + fcc occurs at 1998 °C and xhcp Ti ¼ 0:31, which is in good agreement with the experimental data as showing in Table 2. Fig. 10 presents the calculated vertical section of Ti98.5C1.5-Ta89.3C10.7, compared with the experimental data from Rudy [20]. Good agreement is obtained between the thermodynamic calculation and experiment. The calculated liquidus projection of the C–Ta–Ti system is given in Fig. 11(a) and compared with the diagram in Fig. 11(b) from Rudy [20]. Fig. 12 presents the reaction scheme for the C–Ta–Ti system. The invariant reaction types and temperatures from the literature information [20] are well reproduced by the present calculation.
Fig. 8. Isothermal section of the C–Ta–Ti system at 3200 °C: (a) calculated in the present work, (b) experimental one by Rudy [20].
systems, because quaternary interactions are not so strong. Although there might be some uncertainties in the descriptions here obtained, the effect of composition, temperature, or pressure changes on the phase relations can be predicted. In the present work, the extrapolated description is used to calculate some diagrams which might be of interest to the cemented carbide industry. The technical importance of the C–Ta–Ti–N system focuses on the fcc carbonitride. Since the technical interest concerns graphite saturation, all the calculations are performed at unit carbon activity. Fig. 13 shows the calculated miscibility gap of fcc carbonitride in the C–Ta–
5.2. The C–Ta–Ti-N system The TaC and TiC carbides as well as TaN and TiN nitrides all have a fcc arrangement of metal atoms with carbon or nitrogen atoms on the interstitial sites. They form a fcc carbonitride in the quaternary system, and the model in the quaternary system, which is extended from the lower-order systems is (Ta, Ti)1(C, N, Va)1. This model is also applied to the hcp and bcc phases, which are modeled with the sublattices (Ta, Ti)1(C, N, Va)0.5 and (Ta, Ti)1(C, N, Va)3, respectively. For the liquid phase, the model is (Ta, Ti, C, N)1. Since no experimental information for the quaternary C–Ta–Ti–N system is available, the thermodynamic description of this quaternary system is predicted by combining the four sub-ternary systems as presented in Section 2. Generally speaking, there is a less severe limitation to predict a quaternary system from the four sub-ternary
Fig. 9. Calculated vertical section at 32 at.% C of the C–Ta–Ti system, compared with the experimental data reported by Rudy [20].
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Fig. 12. Reaction scheme for the C–Ta–Ti system. Fig. 10. Calculated Ti98.5C1.5-Ta89.3C10.7 vertical section of the C–Ta–Ti system, compared with the experimental data reported by Rudy [20].
Ti–N system with unit carbon activity at 1450 °C (a possible sintering temperature) and at 1200 °C(a possible nitriding temperature). As shown in the diagram, the size of the miscibility gap of the fcc carbonitride decreases with the increase of annealing temperature. Fig. 14 shows the effect of nitrogen activity (or pressure) on the miscibility gap of the fcc carbonitride with unit carbon activity at 1450 °C, indicating that the size of the miscibility gap increases with increasing N activity.
Fig. 13. Calculated miscibility gap of the fcc carbide in the C–Ta–Ti–N system with unit carbon activity at 1450 °C (a possible sintering temperature) and at 1200 °C (a possible nitriding temperature).
6. Summary • The phase equilibrium data in the C–Ta–Ti system reported in the literature [17–20], where some discrepancies exist, are critically reviewed. The experimental data reported by Rudy [18–20] are considered to be reliable and applied to the thermodynamic modeling of the C–Ta–Ti ternary system. Comprehensive comparisons between the calculated and experimental phase diagrams [18–20]
Fig. 11. Liquidus projection of the C–Ta–Ti system: (a) calculated in the present work, (b) experimental one by Rudy [20].
Fig. 14. The effect of nitrogen activity (or pressure) on the miscibility gap of the fcc phase, calculated with unit carbon activity at 1450 °C.
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show that most of the experimental data are well accounted for by the present description. • The quaternary C–Ta–Ti–N system is extrapolated based on the present work and previous work of the sub-ternary systems [25,26]. The miscibility gap of the fcc carbonitride in the C–Ta–Ti–N system is predicted, indicating that the size of the miscibility gap of the fcc carbonitride decreases with increasing annealing temperature or decreasing N activity. Acknowledgments The financial support from the Creative Research Group of National Natural Science Foundation of China (Grant No. 51021063), Zhuzhou Cemented Carbide Cutting Tools Limited Company of China, and Doctoral Scientific Fund Project of the State Education Committee of China (Grant No. 20120162110051) is acknowledged. The Thermo-Calc Software AB in Sweden is gratefully acknowledged for the provision of Thermo-Calc software. References [1] Fernandes CM, Senos AMR. Cemented carbide phase diagrams: a review. Int J Refract Met Hard Mater 2011;29(4):405–18. [2] Weidow J, Zackrisson J, Jansson B, Andren H-O. Characterisation of WC–Co with cubic carbide additions. Int J Refract Met Hard Mater 2009;27(2):244–8. [3] Glühmann J, Schneeweiß M, Berg H v d, Kassel D, Rödiger K, Dreyer K, et al. Functionally graded WC–Ti(C,N)–(Ta,Nb)C–Co hardmetals: metallurgy and performance. Int J Refract Met Hard Mater 2013;36:38–45. [4] Janisch DS, Lengauer W, Eder A, Dreyer K, Rödiger K, Daub HW, et al. Nitridation sintering of WC–Ti(C, N)–(Ta, Nb)C–Co hardmetals. Int J Refract Met Hard Mater 2013;36:22–30. [5] Chung H-J, Shim J-H, Lee DN. Thermodynamic evaluation and calculation of phase equilibria of the Ti–Mo–C–N quaternary system. J Alloys Compd 1999;282:142–8. [6] Huang W. Thermodynamic properties of the Nb–W–C–N system. Z Metallkd 1997;88(1):63–8. [7] Frisk K. A thermodynamic analysis of the Ta–W–C and the Ta–W–C–N systems. Z Metallkd 1999;90(9):704–11. [8] Jonsson S. Assessment of the Ti–W–C system and calculations in the Ti–W–C–N system. Z Metallkd 1996;87(10):788–95. [9] Ekroth M, Frisk K, Jansson B, Dumitrescu LFS. Development of a thermodynamic database for cemented carbides for design and processing simulations. Metall Mater Trans B 2000;31B(4):615–9. [10] Ekroth M, Frykholm R, Lindholm M, Andren HO, Agren J. Gradient zones in WC– Ti(C, N)–Co-based cemented carbides: experimental study and computer simulations. Acta Mater 2000;48(9):2177–85. [11] Frisk K, Durnitrescu L, Ekroth M, Jansson B, Kruse O, Sundman B. Development of a database for cemented carbides: thermodynamic modeling and experiments. J Phase Equilib 2001;22(6):645–55.
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