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Modeling of phase transitions in three-phase polymorphic systems: Part I. Basic equations and example simulation

Published online by Cambridge University Press:  12 July 2011

Andrzej Ziabicki*
Affiliation:
Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland
Beata Misztal-Faraj
Affiliation:
Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland
*
a)Address all correspondence to this author. e-mail: aziab@ippt.gov.pl
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Abstract

Development of phase composition in one-component, three-phase systems containing a liquid phase (melt) and two polymorphic solids has been discussed. Two types of polymorphic systems have been analyzed: enantiotropic systems composed of three thermodynamically stable phases and monotropic systems with two stable and one metastable phase. Detailed relations between transition rates, molecular characteristics, and external conditions have been derived. Simulation of isothermal crystallization of a model system has been performed and discussed.

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Articles
Copyright
Copyright © Materials Research Society 2011

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References

REFERENCES

1.Ziabicki, A.: Nucleation-controlled multiphase transitions. J. Chem. Phys. 123, 174103 (2005).CrossRefGoogle ScholarPubMed
2.Mitscherlich, E.: Ann. Chim. Phys. 19, 350 (1822); cited after Caira M.R., Crystalline polymorphism of organic compounds, in Topics in Current Chemistry, Vol. 168, (Springer Verlag, 1998), pp. 164–204.Google Scholar
3.Kolmogoroff, A.N.: A statistical theory for crystallization of metals (in Russian). Izv. Akad. Nauk SSSR Ser. Math. 1, 355 (1937).Google Scholar
4.Johnson, W.A. and Mehl, R.F.: Reaction kinetics in processes of nucleation and growth. Trans. A. I. M. E 135, 416 (1939).Google Scholar
5.Avrami, M.: Kinetics of phase change. I–III. J. Chem. Phys. 7, 1103 (1939); 8, 212 (1940); 9, 177(1941).CrossRefGoogle Scholar
6.Evans, U.R.: The laws of expanding circles and spheres in relation to the lateral growth of surface films and the grain-size of metals. Trans. Faraday Soc. 41, 365 (1945).CrossRefGoogle Scholar
7.Turnbull, D. and Fisher, J.C.: Rate of nucleation in condensed systems. J. Chem. Phys. 17, 71 (1949).CrossRefGoogle Scholar
8.Lauritzen, J.L. and Hoffman, J.D.: Crystallization of bulk polymers with chain folding: Theory of growth of lamellar spherulites. J. Res. Nat. Bur. Stand. 65A, 297 (1961).Google Scholar
9.Frank, F.C. and Tosi, M.: On the theory of polymer crystallization. Proc. R. Soc. Lond. 263, 323 (1961).Google Scholar
10.Umemoto, S. and Okui, N.: Master curve of crystal growth rate and its corresponding state in polymeric materials. Polymer 43, 1423 (2002).CrossRefGoogle Scholar
11.Di Lorenzo, M.L., Cimmino, S., and Silvestre, C.: Non-isothermal crystallization of isotactic polypropylene blended with poly(alpha-pinene). Macromolecules 33, 3828 (2000).CrossRefGoogle Scholar
12.Roskosz, M., Toplis, M.J., and Richet, P.: Experimental determination of crystal growth rates in highly supercooled alumino-silicate liquids: Implications for rate-controlling processes. Am. Mineral 90, 1146 (2005).CrossRefGoogle Scholar
13.Roytburd, A.L.: Kurdjumov and his school in martensite of the 20th century. Mat. Sci. Eng., A 273275, 1 (1999).Google Scholar
14.Sajkiewicz, P., Gradys, A., Ziabicki, A., and Misztal-Faraj, B.: On the metastability of β phase in isotactic polypropylene: Experiments and numerical simulation. e-Polymers 124, 1 (2010).Google Scholar
15.Turnbull, D.: Formation of crystal nuclei in liquid metals. J. Appl. Phys. 21, 1022 (1950).CrossRefGoogle Scholar
16.Menczel, J. and Varga, J.: Influence of nucleating agents on crystallization of polypropylene. J. Therm. Anal. 28, 161 (1983).CrossRefGoogle Scholar
17.Frenkel, J.: Kinetic Theory of Liquids (Oxford University Press, London, 1946).Google Scholar
18.Zeldovich, Ya.B.: Theory of formation of a new phase: Cavitation. Acta Physico-Chimica USSR 18, 1 (1943).Google Scholar
19.Kashchiev, D.: Nucleation: Basic Theory with Applications (Butterworth-Heinemann, Oxford, 2000.Google Scholar
20.Glasstone, S., Laidler, K.J., and Eyring, H.: The Theory of Rate Processes (McGraw-Hill, New York, 1941).Google Scholar