On the anchoring of solids
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R. ASTHANA 011
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Fig. 2--Stereographic projection of (111)MrC//(112)v (hkl: MrC precipitate, hk_._.~l:austenite matrix).
REFERENCES 1. P.J. James: J. Iron Steel Inst., 1969, vol. 207, p. 54. 2. G.S. Krivonogov, M.F. Alekseyenko, and G.G. Solovkeva: Phys. Met. Metallog., 1975, vol. 39 (4), p. 86. 3. L.I. Lysak, M.F. Alekseyenko, A.G. Drachinskaya, N.A. Storchak, and G.S. Krivonogov: Metallogizika, 1975, vol. 59 (4), p. 29. 4. N.A. Storchak and A.G. Drachinskaya: Phys. Met. Metallogr., 1977, vol. 44 (2), p. 123. 5. G.L. Kayak: Met. Sci. Heat Treat., 1969, vol. 2, p. 95. 6. M.F. Alekseyenko, G.S. Krivonogov, L.G. Kozyreva, I.M. Kachanova, and L.V. Arapova: Met. Sci. Heat Treat., 1972, vol. 14, p. 187. 7. W.K. Choo and D.G. Kim: Metall. Trans. A, 1987, vol. 18A, pp. 759-66. 8. K.H. Han, J.C. Yoon, and W.K. Choo: Scripta Metall., 1986, vol. 20, p. 33. 9. A. Inoue, Y. Kojima, T. Minemura, and T. Masumoto: Metall. Trans. A, 1981, vol. 12A, pp. 1245-53. 10. K.H. Han and W.K. Choo: Metall. Trans. A, 1983, vol. 14A, pp. 973-75. 11. R.E. Cairns, Jr. and J.L. Ham: U.S. Patent No. 3111405, Nov. 1963. 12. W.H. Richardson: U.S. Patent No. 3193384, July 1965. 13. G.T. Haddic, L.D. Thompson, E.R. Parker, and V.F. Zackay: Met. Prog., 1978, p. 37. 14. T.F. Liu, S.W. Peng, Y.L. Lin, and C.C. Wu: Metall. Trans. A, 1990, vol. 21A, pp. 567-74. 15. S.W. Peng and C.P. Chou: Scripta Metall., 1992, vol. 26, p. 243. 16. S.W. Peng and C.P. Chou: Scripta Metall., 1992, vol. 26, p. 1851. 17. S.W. Peng and C.P. Chou: Scripta Metall., 1992, vol. 27, p. 1173. 18. P.J. Maziasz: Scripta Metall., 1979, vol. 13, p. 621. 19. K.H. Kou and C.L. Jia: Acta Metall., 1985, vol. 33, p. 991. 20. A.M. Abdel-Latif, J.M. Corbett, and D.M.R. Taplin: Met. Sci., vol. 16, p. 90.
METALLURGICAL TRANSACTIONS A
The classical capillary problem of anchoring of solid particles at fluid interfaces has significance in several materials processing operations, such as flotation of ores and incorporation of reinforcement in melt during composite synthesis by stir-casting techniques, tl-61 The problem, in essence, deals with the equilibrium position under the influence of gravity of a solid at an interface between two fluids of different surface tensions and densities. The mechanical equilibrium of solids of various geometries, such as spheres, t2,Tj cylinders, tSl and ellipsoids t5'61 approaching a planar interface between fluids of different densities and surface tensions has been analyzed using both a force balance tl-41 and a thermodynamic approach tS-Iq which determines the mechanically stable states of solids at fluid interfaces by minimizing the total free energy of the system. These analyses, however, apply to planar, infinite fluid interfaces which deform locally in the vicinity of the solid when the latter attains equilibrium at the interface. For particles attached to gas bubbles within an infinite melt, the equilibrium states of solids must be deduced at an initially curved interface of finite exten
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