Multi-Component Spinodal Decomposition
While most materials (metallic, crystalline or glassy) of practical interest are multi-ccmponent and much experimental work has been performed on multi-component systems particularly so in glasses [1–18], the theoretical and analytical efforts to understand the phase separation process, have only recently been directed to multi-component systems [19–25]. Several unproved notions are, however, still frequently assumed in analyzing multi-ccmponent phase separation kinetics. One example [8,12,26] is the statement that “in a two phase region if the tie-lines* do not rotate within the temperature range of interest, then a multi-conponent system behaves like a binary along the tie-line.” This, as we show later (section 3.3) is not true particularly when interpreting the kinetics. Clearly it is of importance to examine the validity of such notions and develop simple characterization of coupling effects in multi-component phase separation.
KeywordsPhase Separation Spinodal Decomposition Phosphorous Pentoxide Phase Separation Kinetic Generalize Diffusion Equation
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- 1.E.A. Porai-Koshits and N.S. Andreyev, “Low angle x-ray scattering by sodium boro-silicate glasses.” Trans. Soc. of Glass Tech., XLIII, 235 (1959).Google Scholar
- 5.Y. Moriya, D.H. Warrington and R.W. Douglas “A study of meta-stable liquid-liquid immiscibility in some binary and ternary alkali-silicate glasses”. Phys. & Chem. of glasses, 8, 19 (1967).Google Scholar
- 10.P.F. James and P.W. McMillan “Quantitative measurements of phase separation in glasses using transmission electron microscopy, a study of lithia-silica glasses and the influence of phosphorous pentoxide.” Phys. & Chem. of glasses, 11 (3), 64 (1970).Google Scholar
- 11.D.G. Burnett and R.W. Douglas “Liquid-liquid phase separation in soda-lime-silica system.” Phys. & Chen. of glasses, 11 (5), 125 (1970).Google Scholar
- 22.H. Gaye and C.H.P. Lupis, “On the restrictivity of the thermodynamic conditions for spinodal decomposition in a multi-corrponent system,” Trans. AIME, 245, 2543 (1969).Google Scholar
- 24.G. Bernard, R. Hocine and C.H.P. Lupis, “Thermodynamic conditions for spinodal deconposition in a multi-component system”, Trans. AIME, 239, 1600 (1967).Google Scholar
- 26.A. Sarkar, G.R. Srinivasan, V. Volterra and P.B. Macedo, “Electron microscope observation of the kinetics of composition fluctuations in the SiO2-B2O3-Na2O-Al2O3 system” Phys. and Chem. of Glasses, 14, (6), 114, (1973).Google Scholar
- 31.A.R. Cooper and P.K. Gupta “Analysis of diffusion controlled crystal growth in multi-component systems” Adv. in Nucleation and crystallization in glasses; Ed L. L. Hench, S.W. Frieman, Am. Ceram. Soc. (1972).Google Scholar
- 32.B. Widom, “Critical phenomena in the surface tension of fluids in phase transitions and critical phenomena” Ed. C. Domb and M.S. Green. Acad. Press (1972).Google Scholar
- 34.J.L. Meijering, “Segregation in regular ternary solutions” Philips Res. Rep., 5, 333 (1950).Google Scholar
- 36.See for example; S.R. de Groot and P. Mazur, “Non-equilibrium thermodynamics” North-Holland Publ. Co., (1962).Google Scholar