The solubility of titanium diboride in aluminum
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9. V.A. Likhachev, M.M. Myshlyaev, O.N. Senkov, and S.P. Belyayev: Phys. Met. Metallogr., 1981, vol. 52, pp. 156-64. 10. M.E. Kassner and M.E. McMahon: Metall. Trans. A, 1987, vol. 18A, pp. 835-46. 11. M.E. Kassner, M.M. Myshlyaev, and H.J. McQueen: Mater. Sci. Eng., 1989, vol. 108, pp. 45-61. 12. S.J. Hales and T.R. McNelley: Acta Metall., 1988, vol. 36, pp. 1229-39. 13. H. Luthy, A.K. Miller, and O.D. Sherby: Acta Metall., 1980, vol. 28, pp. 169-78. 14. M.E. Kassner and J.J. Oldani: Proc. IXth Inter-American Conf. on Materials Technology, Editorial Universitaria, Santiago, Chile, 1987, pp. 219-23. 15. R.W.K. Honeycombe: J. Inst. Met., 1951, vol. 80, pp. 49-56.
The Solubility of Titanium Diboride in Aluminum ERNEST W. DEWING The interpretation of experimental data on the solubility of TiB2 (or Ti-AIB2?) in liquid aluminum continues to generate discussion, most recently from Abdel-Hamid and Durand I~l and Sigworth. I21 The purpose of this communication is to point out a fact which has hitherto escaped observation and to explore some of its implications. The starting point for this work was to make a thermodynamic check for the possible existence of equilibrium mixed-crystals of TiB2 and A1Bz. (The reader can consult the above references for discussion of that subject.) If the solid phase is TixAt~_xB2, formed by xTi + (1 - x)A1 + 2B = TixAll xB2
[1]
then the equilibrium constant is K = (aTi)~" (aB) 2 = [Ti] x" [B] 2" ('YTi)~" ('yB) 2
This work was supported under the auspices of the United States Department of Energy by the Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48. The TEM work by M. Wall and the helpful comments by Professors H.J. McQueen and M.M. Myshlyaev are appreciated.
[21
at any given temperature. [ ] represents concentration, conveniently in weight percent since all solutions are very dilute, y is the activity coefficient, and the activity of aluminum is essentially unity throughout. By taking logarithms and dividing through by x, this equation can be reduced to log [Ti] = - ( 2 / x ) log [B] - log Yxi
REFERENCES - ( 2 / x ) log TB + ( I / x ) log K 1. H.J. McQueen, J.K. Solberg, N. Ryum, and E. Nes: Phil. Mag., in press. 2. J.K. Solberg, H.J. McQueen, N. Ryum, and E. Nes: Phil. Mag., in press. 3. H.J. McQueen, O. Knustad, N. Ryum, and J.K. Solberg: Scripta Metall., 1985, vol. 19, pp. 73-78. 4. Ch. Perdrix, M.Y. Perrin, and F. Montheillet: M~m. Sci. Rev. M~t. (in French), 1981, vol. 78, pp. 309-20; Trans., Lawrence Livermore National Laboratory Report UCIR-1623, Livermore, CA, 1986. 5. S.L. Kuzmin, V.A. Likachev, M.M. Myshlyaev, Yu.A. Nikonov, and O.N. Senkov: Scripta Metall., 1978, vol. 12, pp. 735-36. 6. S.L. Kuzmin, V.A. Likhachev, M.M. Myshlyaev, Yu.A. Nikonov, and O.N. Senkov: Phys. Met. Metallogr., 1980, vol. 48, pp. 160-63. 7. V.A. Likhachev, M.M. Myshlyaev, O.N. Senkov, and S.L. Kuzmin: Phys. Met. Metallogr., 1980, vol. 47, pp. 129-34. 8. S.P. Belyayev, V.A. Likhachev, M.M. Myshlyaev, and O.N. Senkov: Phys. Met. Metallogr., 1981, vol. 52, pp. 143-52. METALLURGIC
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