Phase diagram calculations of Al Cr Nb Ti quaternary system

Transcription

1 Phase diagram calculations of Al Cr Nb Ti quaternary system Y. Q. Liu*, W. T. Xu, D. Xie and Z. M. Li The phase diagrams and thermodynamics of the complex systems are of great importance for the materials development and processing optimisation. The Calphad method is a powerful tool to predict the phase diagrams and thermodynamic properties of multicomponent systems from the corresponding database. In this work, a reliable thermodynamic database of the Al Cr Nb Ti quaternary system, which is the basis for high performance gamma titanium aluminide alloys, was constructed based on the thermodynamic descriptions of its subsystems. The database contains 27 phases. The thermodynamic models used for each phases were brielfy introduced. The thermodynamic descriptions of the six sub-binary and four sub-ternary sytems were discussed. The effects of the alloying element on the stabilities of phase were predicted. Keywords: Al Cr Nb Ti system, Calphad, Phase diagram, Thermodynamics, Gamma titanium aluminide Introduction Gamma titanium aluminide alloys have the characteristics of high melting point, low density, high specific strength and stiffness, good structural stability, good resistance against oxidation, corrosion and titanium fire. This characteristics make the alloy potentially applicable for power plant turbines, gas turbine engines and automotive industry. 1,2 Alloying and suitable processing technology play important roles in the development of alloys. For gamma titanium aluminide, properties are dependent on microstructure, which is highly sensitive to composition. Accurate information of the phase diagrams and thermodynamics of the multicomponent systems are of great value in designing alloys and choosing suitable heat treatments. The Calphad (CALculation of PHAse Diagrams) approach, developed in 1970s, provides an effective way to predict the phase diagrams and thermodynamic properties of the multicomponents using database built from the combination of the thermodynamic description of lower order sub-systems. 3 In order to improve the properties and/or the processability, different alloying elements have been added to gamma titanium aluminide. 1,2,4,5 For examples, addition of niobium has been reported to improve the high temperature strength, creep resistance and oxidation resistance, while addition of chromium is helpful to improve the ductility and creep life at high stresses. To understand the interactions of niobium and chromium on the phase transformations and reactions of gamma titanium aluminide, knowledge of the phase equilibrium and thermodynamic properties of the School of Materials Science and Technology, China University of Geosciences, Beijing , China *Corresponding author, liuyuqin@cugb.edu.cn Al Cr Nb Ti system is necessary. In this study, a thermodynamic database for the Al Cr Nb Ti quaternary system, in a format compatible with the Pandat software, 6 was established under the framework of the Calphad approach. Thermodynamic models The core of Calphad is the use of all available experimental and theoretical data to assess the parameters of the Gibbs energy models selected for each phase presented. For the Al Cr Nb Ti system, the models used for the pure elements, solution phase and intermediate compounds were briefly described as follows. Pure elements The Gibbs energy function for the pure elements, including lattice stability data, is given by the following expression according to the Scientific Group Thermodata Europe (SGTE) G Q i (T){HSER i,298 : 15 ~azbtzct ln TzdT 2 ze=tz (1) where Hi,298 SER : 15 is the molar enthalpy of a pure element i at 298?15 K in its stable state (standard element reference SER), and T is the absolute temperature. In this work, these functions were taken from the most recent compilation by Dinsdale. 7 Solution phases The Gibbs energies of solution phase, liquid, bcc, fcc and hcp, were modelled by substitutional solution model G Q ~ X x 0 i G Q i zrt X x i ln x i z E G Q zgmag Q (2) i i where x i is the molar fraction of component i (i5al, Cr, Nb and Ti) and 0 G Q i is the molar Gibbs energy of the pure component i with a Q structure and taken from ß W. S. Maney & Son Ltd Received 15 September 2013; accepted 12 December 2013 DOI / Z Materials Research Innovations 2014 VOL 18 SUPPL 2 S2-573

2 Ref. 4, R is the gas constant. Gmag Q is the magnetic contribution to the Gibbs energy which is given by the Hillert Jarl Inden model. 8 Gmag Q is zero for the liquid phase. The excess Gibbs energy is defined by E G Q ~ Xn{1 X n i~1 j~iz1 X n{2 Xn{1 x i x j X m X n v~0 i~1 j~iz1 k~jz1 v L Q vz i,j x i {x j x i x j x k L Q i,j,k (3) where v L Q i,j and L Q i,j,k are the binary and ternary interaction parameters respectively. Intermediate compounds Sublattice model was used to describe the Gibbs energy of the intermediate compounds in the system. The Gibbs energy is written as G h ~G h,ref zdg h,id mix ze G h (4) The first term in the right side of equation (4) is the Gibbs energy reference surface defined by the end members generated when only the pure components exist on the sublattice. G h,ref is expressed by G h,ref ~ X 0 G h end Pys i (5) where 0 Gend h is the Gibbs energy of the end-member in the structure of the phase h, y s i is the site fraction of species i in the sublattice s. For example, G h,ref for a phase described by the two sublattice model with the formula (A,B) a (C,D) c can be written as G h,ref ~ X X y i y :0 j Gi:j h (6) i~a,b j~c,d where y i (resp. y j ) is the site fraction of species i (resp. j) in the first (resp. second) sublattice. 0 Gi:j h is the Gibbs energy of the end member i a j c in the crystallographic structure of the phase h. The second term in the right side of equation (4), DG h,id mix, is the contribution of ideal entropy of mixing. In the sublattice model, the ideal entropy of mixing is made up of the configurational contributions by components mixing on each of the sublattices. DG h,id is expressed by X DG h,id mix ~RT X n s y s i ln ys i (7) s i where n s is the stoichiometric coefficient for sublattice s. The third term in the right side of equation (4), E G h,is the contribution of excess Gibbs energy. For a two sublattice model with the formula of (A,B) a (C,D) c, E G h is expressed by E G h ~ X y 0 i y00 C y00 D L i:c,d z i~a,b X j~c,d mix y 0 A y0 B y00 j L A,B:jzy 0 A y0 B y00 C y00 D L A,B:C,D (8) In which L i:c,d, L A,B:j and L A,B:C,D are the interaction parameters. The Gibbs energy of the ordered B2 phase was obtained by adding the contribution of ordering to the Gibbs energy of the disordered bcc phase. Details can be found in Ref. 9. Results and discussion The Al Cr Nb Ti system contains six sub-binary systems Al Cr, Al Nb, Al Ti, Cr Nb, Cr Ti, Nb Ti, and four sub-ternary systems Al Nb Ti, Al Cr Ti, Cr Nb Ti and Al Cr Nb. The thermodynamic database Table 1 Crystal structure and models employed of phases in Al Cr Nb Ti quaternary system Phase Pearson symbol Space group Strukturbericht designation Models in the present description Liquid (Al,Cr,Nb,Ti) 1 bcc ci2 Im-3m A2 (Al,Cr,Nb,Ti) 1 (Va) 3 B2 ci2 Pm-3m B2 (Al,Cr,Nb,Ti) 0?5 (Al,Cr,Nb,Ti) 0?5 (Va) 3 fcc cf4 Fm-3m A1 (Al,Cr,Nb,Ti) 1 (Va) 1 hcp hp2 P63/mmc A3 (Al,Cr,Nb,Ti) 1 (Va) 0?5 (Nb,Ti)Al 3 (H) ti8 I4/mmm D022 (Al%,Cr,Nb,Ti) 3 (Al,Cr,Nb%,Ti%) 1 TiAl 3 (L) ti32 I4/mmm (Al%,Nb,Ti) 3 (Al,Nb,Ti%) 1 TiAl 2 ti24 I41/amd (Al%,Cr,Nb,Ti) 2 (Al,Nb,Ti%) 1 Ti 2 Al 5 tp28 P4/mmm (Al%,Cr,Nb,Ti) 5 (Al,Nb,Ti%) 2 Ti 3 Al 5 tp32 P4/mbm (Al) 5 (Nb,Ti%) 3 TiAl tp4 P4/mmm L10 (Al%,Cr,Nb,Ti) 1 (Al,Cr,Nb,Ti%) 1 Ti 3 A1 hp8 P63/mmc D019 (Al%,Cr,Nb,Ti) 3 (A1,Cr,Nb,Ti%) 1 Al 7 Cr mc104 C2/m (Al) 7 (Al,Cr) 1 Al 11 Cr 2 mp48 P2 (Al) 11 (Al,Cr) 2 Al 4 Cr mp180 P2/m (Al) 4 (Al,Cr) 1 Al 8 Cr 5 (L) Hr26 R3m D8 10 (Al,Cr) 8 (Al,Cr) 5 Al 8 Cr 5 (H) ci52 I-33m D8 2 (Al,Cr) 8 (Al,Cr) 5 AlCr 2 ti6 I4/mmm C11 b (Al,Cr) 1 (Al,Cr) 2 Nb 3 Al cp8 Pm-3n A15 (Al,Nb%,Ti) 3 (Al%,Cr,Nb,Ti) 1 Nb 2 Al tp30 P42/mm D8b (Al,Cr,Nb,Ti) 8 (Al,Cr,Nb,Ti) 5 (Nb,Ti) 2 C14 hp12 P6 3 /mmc C14 (Al,Cr%,Nb,Ti) 2 (Al,Cr,Nb%,Ti%) 1 C15 cf24 Fd-3m C15 (Al,Cr%,Nb,Ti) 2 (Al,Cr,Nb%,Ti%) 1 C36 hp24 P6 3 /mmc C36 (Al,Cr%,Nb,Ti) 2 (Al,Cr,Nb,Ti%) 1 Al 3 NbTi 4 (s) hp6 P63/mmc B82 (Al) 3 (Nb) 1 (Ti) 4 Ti 2 AlNb(O1) oc16 Cmcm (Al,Nb,Ti) 0?75 (Al,Nb,Ti) 0?25 Ti 2 AlNb(O2) oc16 Cmcm (Al,Nb,Ti) 0?5 (Al,Nb,Ti) 0?25 (Al,Nb,Ti) 0?25 Ti 25 Cr 8 Al 67 (t) cp 4 Pm-3m (Al) 67 (Cr) 8 (Ti) 25 S2-574 Materials Research Innovations 2014 VOL 18 SUPPL 2

3 1 Calculated constituent binary phase diagrams of Al Cr Nb Ti system: a Al Ti system; b Cr Ti system for this quaternary system was constructed based on its sub-binary and sub-ternary systems. Table 1 presented the crystal structure data and models employed of the phases in the Al Cr Nb Ti system in the present description. Sub-binary systems A thermodynamic description of the Al Ti system is crucial for the development of a reliable thermodynamic description of the Al Cr Nb Ti system. The Al Ti system has been studied numerously, both in experimental investigations and by thermodynamic calculation. Schuster and Palm 10 critically reviewed this system in 2006 and reevaluated each invariant reaction. Witusiewicz et al. remodeled the Al Ti system using information from the assessment of Schuster and Palm and their own experimental results, 11 and their thermodynamic parameters were directly used in the present work. Figure 1a is the calculated Al Ti phase diagram. This system contains 11 phases. The maximum solubility of Al in the b-ti is 44?6 at-% at the peritectic temperature of 1491uC in the invariant reaction of Liquidzbcc (b)«hcp (a). The maximum solubility of Al in the a-ti is 51?5 at-% at the peritectic temperature 1456uC in the invariant reaction of Liquidzhcp (a)«alti. A lot of research has been carried out to investigate the Cr Ti system. The stable phases in this system include liquid, bcc, hcp and three polytypes of Laves phase C14, C15 and C36. Thermodynamic calculations of this system have been studied by several groups, in which the solution phases were modeled as substitutional solution. The major differences are the lattice stabilities of pure chromium, the number of sublattices used to describe the Laves phase, and the homogeneity range of the Laves phases. The thermodynamic descriptions of Pavlů et al., 15 obtained via first principle calculation combined with Calphad based optimisation, was used in this work. Figure 1b is the calculated Cr Ti phase diagram. The thermodynamic description of the Nb Ti, Al Cr, Al Nb and Cr Nb systems were taken from the work of Hari Kumar et al., 17 Liang et al., 18 Witusiewicz et al. 19 and Pavlů et al. 20 Sub-ternary systems Understanding the phase diagram of the Al Nb Ti system is critical for the titanium aluminides. As critically reviewed by Gama, 21 Raghavan 22 and Tretyachenko, 23 numerous studies concerning the phase relationships in this system were reported. Thermodynamic assessments were carried out by Kattner and Boettinger, 24 Servant et al., 25 Servant and Ansara, 26 Witusiewicz et al., 19 Cupid et al., 27 and Liu et al. 28 Reviews of these assessments were carried out by Raghavan. 22,29,30 In this work, the thermodynamic description of Witusiewicz et al. 19 was used. This system contains substitutional solutions phases, binary phases extended to the ternary composition range and three ternary compounds, Ti 2 AlNb (O1), Ti 2 AlNb(O2) and Ti 4 NbAl 3. Figure 2a shows the calculated 1000uC isothermal sections of the Al Nb Ti system. As reviewed by Ghosh, 31 a fairly large number of experimental studies were carried out to establish the Cr Nb Ti phase equilibrium. In this work, the thermodynamic description was taken from our recent work which was obtained by key experiments to verify the phase relations at 1200uC, first principle calculations to get the formation energies of end members of the Laves phases and thermodynamic assessment to obtain the ternary interaction parameters. 32 Figure 2b shows the calculated 1000uC isothermal sections of the Cr Nb Ti system. The Al Cr Ti system has been investigated considerably both in experiments and thermodynamic calculations. Shao and Tsakiropoulos, 33 Kaufman, 34 Chen et al., 35 Cupid et al. 36 developed thermodynamic descriptions for this system. Neither details of the thermodynamic modelling and final thermodynamic parameters were given in Shao and Tsakiropoulos, 33 and Kaufman. 34 Chen et al. 35 adopted the thermodynamic descriptions of the binary systems from Chen et al. for Al Cr, 37 Witusiewicz et al. for Al Ti, 11 and Ghosh for Cr Ti. 38 Cupid et al. used the constituent descriptions for the Al Cr and Al Ti from COST 507 and Cr Ti from their own assessment. 36,39,40 Owing to the inconsistency in the thermodynamic descriptions of the used sub-binary systems, the Al Cr Ti system was remodelled based on the parameters of Chen et al. 35 Figure 2c shows the calculated 1000uC isothermal sections of the Al Cr Ti system. Experimental determined phase equilibrium information of the Al Cr Nb system was reviewed carefully by Ivanchenko. 41 Based on the three new measured isothermal sections at 1150, 1300 and 1450uC as well as the available earlier literature data, He et al. assessed Materials Research Innovations 2014 VOL 18 SUPPL 2 S2-575

4 2 Calculated 1000uC isothermal sections of constituent ternary phase diagrams of Al Cr Nb Ti system: a Al Nb Ti system; b Cr Nb Ti system; c Al Cr Ti system; d Al Cr Nb system this system. 42 The thermodynamic parameters for the three sub-binary systems were taken from Liang et al. 18 for Al Cr, Witusiewicz et al. 19 for Al Nb and Costa Neto et al. 43 for Cr Nb. The thermodynamic parameter for the Cr Nb system is inconsistent with what we chose. This system was reassessed to solve the inconsistency. Figure 2d shows the calculated 1000uC isothermal sections of the Al Cr Nb system. 3 Calculated vertical sections of Al Cr Nb Ti system: a Ti 48Al 2Nb xcr; b Ti 46Al 2Nb xcr S2-576 Materials Research Innovations 2014 VOL 18 SUPPL 2

5 Extrapolation to Al Cr Nb Ti quaternary system Combining the sub-binary and sub-ternary systems, the phase equilibrium in the Al Cr Nb Ti system can be modelled by extrapolation. Figure 3 gives the calculated vertical section of Ti 48Al 2Nb xcr and Ti 46Al 2Nb xcr. It can be seen that the difference of Al content greatly influences the phases presented in the alloys. Decreasing the Al content from 48 to 46 at- % will greatly increase the TiAlzTi 3 Al two phase field. When the Al content is 46 at-% and Nb content is 2 at-%, the additions of Cr will narrow the temperature ranges of the TiAlzTi 3 Al two phase field. When the Cr addition is larger than around 3 at-%, the TiAlz Ti 3 Al two phase field disappear. Increase in the Cr content will promote the formation of Laves phase. Conclusion In this paper, a thermodynamic database for the Al Cr Nb Ti quaternary system, which is the basis for high performance gamma titanium aluminides, was constructed based on the thermodynamic descriptions of its six sub-binary and four sub-ternary systems. The database contained four elements and 27 phases. The thermodynamic models for each phase was briefly described. The thermodynamic descriptions of the six sub-binary and four sub-ternary sytems were discussed. The effects of the alloying element on the stabilities of TiAlzTi 3 Al two phase field were predicted. Acknowledgements This project was supported by National Natural Science Foundation of China (no ) and Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China. The authors would like to thank CompuTherm LLC for providing the Pandat software. References 1. I. J. Polmear: Light alloys, 4th edn, 299; 2006, Oxford, Butterworth-Heinemann. 2. F. Appel and R. 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