Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter November 17, 2014

Thermodynamic description of the Ta–W–Zr system

  • Cuiping Guo , Changrong Li , Shunli Shang and Zhenmin Du


The Ta–W, W–Zr and Ta–W–Zr systems are critically reviewed and modeled using the CALPHAD technique. The enthalpy of formation of the stoichiometric compound W2Zr in the W–Zr system is predicted from first-principles calculations. The solution phases (liquid, bcc and hcp) are modeled by the substitutional solution model. The compound W2Zr is treated with the formula (Ta,W)2Zr in the Ta–W–Zr system because of a significant solid solubility of Ta in W2Zr. All experimental data, including the Gibbs energy of formation, enthalpy of formation, activity of Ta and W of bcc phase at 1 200 K, Ta–W and W–Zr phase diagrams, and three isothermal sections of the Ta–W–Zr system at 1 073, 1 098, and 1 873 K, are reproduced in the present work. A set of self-consistent thermodynamic parameters of the Ta–W–Zr system is obtained.

* Professor Zhenmin Du, Department of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, P.R. China. Tel./Fax: +86-10-6233 3772, E-mail:


[1] Z.Lin, E.J.Lavernia, F.A.Mohamed: Acta Mater.47 (1999) 11811194. 10.1016/S1359-6454(98)00361-9Search in Google Scholar

[2] R.W.Buckman: Int. J. Refract. Met. Hard Mater.18 (2000) 253257. 10.1016/S0263-4368(00)00024-XSearch in Google Scholar

[3] K.J.Leonard, J.T.Busby, S.J.Zinkle: J. Nuclear Mater.366 (2007) 353368. 10.1016/j.jnucmat.2007.03.025Search in Google Scholar

[4] K.J.Leonard, J.T.Busby, S.J.Zinkle: J. Nuclear Mater.366 (2007) 336352. 10.1016/j.jnucmat.2007.03.025Search in Google Scholar

[5] X.Yu, L.Tan, K.Yang: Mater. Rev.26 (2012) 7982.Search in Google Scholar

[6] E.Rudy: Compendium of Phase Diagrams Data, Air Force Materials Lab., Wright-Patterson Air Force Base, OH, Rep. No. AFML-TR-65-2, Part V (1969).Search in Google Scholar

[7] R.Krishnan, S.P.Garg, N.Krishnamurthy: J. Alloy Phase Diag.3 (1987) 1.Search in Google Scholar

[8] T.B.Massalski, ed., Handbook of Alloy Phase Diagrams, ASM, Materials Park, Ohio (1990).Search in Google Scholar

[9] S.C.Singhal, W.L.Worrell: Met. Trans.4 (1973) 895898. 10.1007/BF02645586Search in Google Scholar

[10] L.Kaufman, P.E.A.Turchi, W.Huang, Z.-K.Liu: CALPHAD25 (2001) 419433. 10.1016/S0364-5916(01)00039-6Search in Google Scholar

[11] P.E.A.Turchi, A.Gonis, V.Drchal, J.Kudmocský: Phys. Rev. B64 (2001) 085112. 10.1103/PhysRevB.64.075113Search in Google Scholar

[12] P.E.A.Turchi, V.Drchal, J.Kudmocský, C.Colinet, L.Kaufman, Z.-K.Liu: Phys. Rev. B71 (2005) 094206. 10.1103/PhysRevB.71.094206Search in Google Scholar

[13] K.Masuda-Jindo, V.V.Hung, N.T.Hoa, P.E.A.Turchi: J. Alloys Compd.452 (2008) 127132. 10.1016/j.jallcom.2006.12.163Search in Google Scholar

[14] X.B.Li, Y.Q.Xie, F.X.Yu: Chin. J. Rare Met.29 (2005) 302306. 10.1007/s12598-010-0053-zSearch in Google Scholar

[15] A.F.Guillermet: J. Alloys Compd.226 (1995) 174184. 10.1016/0925-8388(95)01582-5Search in Google Scholar

[16] R.F.Domagala, D.J.McPherson, M.Hansen: J. Met.5 (1953) 7379.Search in Google Scholar

[17] G.A.Geach, G.F.Slattery, R.F.Domagala, D.J.McPherson, M.Hansen: Trans. AIME197 (1953) 747748.Search in Google Scholar

[18] Y.A.Chang: J. Less-Common Met.17 (1969) 325328. 10.1016/0022-5088(69)90151-9Search in Google Scholar

[19] R.J.Ackermann, E.G.Rauh: High Temp. Sci.4 (1972) 272282.Search in Google Scholar

[20] S.P.Garg, R.J.Ackermann: Scr. Metall.13 (1979) 611613. 10.1016/0036-9748(79)90119-4Search in Google Scholar

[21] S.V. NagenderNaidu, P. RamaRao, in: Binary Alloy Phase Diagrams, 2nd Ed., Vol. 3, T.B.Massalski (editor-in-chief), Materials information Soc., Materials Park, Ohio (1990).Search in Google Scholar

[22] S.V. NagenderNaidu, P. RamaRao, in: Phase Diagrams of Binary Tungsten Alloys, S.V. NagenderNaidu, P. RamaRao (Eds.), Monograph Series on Alloy Phase Diagrams, The Indian Institute of Metals, Calcutta (1991).Search in Google Scholar

[23] M.Y.Chu, J.G.Guo, S.L.Shang, J.Sun, J.Y.Shen: Chin. J. Rare Met.27 (2003) 701705.Search in Google Scholar

[24] L.F.Pease, J.H.Brophy: J. Less-Common Met.6 (1964) 118131. 10.1016/0022-5088(64)90116-XSearch in Google Scholar

[25] A.T.Dinsdale: SGTE Pure elements (unary) database, version 4.5 (2006).Search in Google Scholar

[26] G.Kresse, J.Furthmüller: Comp. Mater. Sci.6 (1996) 1550. 10.1016/0927-0256(96)00008-0Search in Google Scholar

[27] G.Kresse, J.Furthmüller: Phys. Rev. B54 (1996) 1116911186. 10.1103/PhysRevB.54.11169Search in Google Scholar PubMed

[28] G.Kresse, D.Joubert: Phys. Rev. B59 (1999) 17581775. 10.1103/PhysRevA.59.1758Search in Google Scholar

[29] J.P.Perdew, K.Burke, M.Ernzerhof: Phys. Rev. Lett.77 (1996) 38653868. 10.1103/PhysRevLett.77.3865Search in Google Scholar PubMed

[30] M.Methfessel, A.T.Paxton: Phys. Rev. B40 (1989) 36163621. 10.1103/PhysRevB.40.3616Search in Google Scholar PubMed

[31] P.E.Blöchl, O.Jepsen, O.K.Andersen: Phys. Rev. B49 (1994) 1622316234. 10.1103/PhysRevB.49.16223Search in Google Scholar

[32] S.L.Shang, Y.Wang, D.Kim, Z.-K.Liu: Comp. Mater. Sci.47 (2010) 10401048. 10.1016/j.commatsci.2009.12.006Search in Google Scholar

[33] B.Sundman, B.Jansson, J.O.Andersson: CALPHAD9 (1985) 153190. 10.1016/0364-5916(85)90021-5Search in Google Scholar

[34] J.O.Andersson, T.Helander, L.Höglund, P.F.Shi, B.Sundman: CALPHAD26 (2002) 273312. 10.1016/S0364-5916(02)00037-8Search in Google Scholar

[35] Q.Guo, O.J.Kleppa: J. Alloys Compd.321 (2001) 169182. 10.1016/S0925-8388(01)00956-2Search in Google Scholar

[36] H.L.Lukas, S.G.Fries: J. Phase Equilib.13 (1992) 532542. 10.1007/BF02665766Search in Google Scholar

[37] A.L.Giorgi: Physica B & C135 (1985) 420422. 10.1016/0378-4363(85)90521-2Search in Google Scholar

[38] J.S.Shah, M.E.Straumanis: J. Appl. Phys.42 (1971) 32883289. 10.1063/1.1660727Search in Google Scholar

[39] S.Basavaiah, S.R.Pollack: J. Appl. Phys.39 (1968) 55485556. 10.1063/1.1656012Search in Google Scholar

[40] P.E.Friebertshauser, J.W.McCamont: J. Vac. Sci. Technol.6 (1969) 184187. 10.1116/1.1492655Search in Google Scholar

[41] W.Buckel, G.Dummer, W.Gey: Phys. kondens. Materie1 (1962) 6777. 10.1007/BF02422325Search in Google Scholar

[42] Ö.Rapp, J.Invarsson, T.Claeson: Phys. Lett. A50 (1974) 159160. 10.1016/0375-9601(74)90770-1Search in Google Scholar

[43] Ö.Rapp: J. Less-Common Met.21 (1970) 2744. 10.1016/0022-5088(70)90162-1Search in Google Scholar

[44] B.T.Matthias, V.B.Compton, E.Corenzwit: J. Phys. Chem. Solids19 (1961) 130133. 10.1016/0022-3697(61)90066-XSearch in Google Scholar

[45] B.T.Matthias, T.H.Geballe, V.B.Compton: Rev. Mod. Phys.35 (1963) 122. 10.1103/RevModPhys.35.1Search in Google Scholar

[46] F.Schrey, R.D.Mathis, R.T.Payne, L.E.Murr: Thin Solid Films5 (1970) 2940. 10.1016/0040-6090(70)90048-9Search in Google Scholar

[47] Y.Makino, S.Miyake: J. Alloys Compd.313 (2000) 235241. 10.1016/S0925-8388(00)01182-8Search in Google Scholar

[48] M.Sigalas, D.A.Papaconstantopoulos, N.C.Bacalis: Phys. Rev. B: Condens. Matter45 (1992) 57775783. 10.1103/PhysRevB.45.5777Search in Google Scholar

[49] S.J.Liu, S.Q.Shi, H.Huang, C.H.Woo: J. Alloys Compd.330/332 (2002) 6469. 10.1016/S0925-8388(01)01451-7Search in Google Scholar

[50] Springer Materials Database, in Google Scholar

Received: 2014-01-11
Accepted: 2014-05-28
Published Online: 2014-11-17
Published in Print: 2014-11-10

© 2014, Carl Hanser Verlag, München

Downloaded on 4.3.2024 from
Scroll to top button