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International Journal of Material Forming

, Volume 4, Issue 4, pp 421–428 | Cite as

Simulation of melt crystallization kinetics

  • Malkhaz BerezhianiEmail author
Original Research
  • 155 Downloads

Abstract

Mathematical model of non-isothermal crystallization process, taking into account changes in the system composition is presented as a differential equation system. Application of the proposed model enables calculation of both general process kinetics and parameters, characterizing the forming structure (graininess) and texture of three-space systems and films. In general the presented mathematical model can be applied for the simulation of phase transition processes, such as crystallisation of melts, glasses and other vitreous solids, polymers, epitaxial growth of films, decomposition of solid solution etc.

Keywords

Mathematical model Simulation Crystallization Kinetics Structure 

Nomenclature

B

kinetic factor in Eqs. 1 and 2

Cf,F,V

shape factors of crystals

c

heat capacity of the system

FULU, NU

summary surface; length and number of crystals respectively in conditions of unlimited growth

F L, N

actual summary surface; length and number of crystals respectively

K

constant of crystal growth rate in Eq. 6

k

slope value in linearized Eq. 2

Km

heat exchange coefficient

M

crystallization degree

Mm

content of a crystallizable component in the system

n = 1,2,3

system space dimension

Nm

maximum number of crystallization centers

J

crystallization nucleation intensity

V

crystal linear growth rate

r

crystal characteristic linear size (radius)

T Ts

system and external medium temperatures

q

heat of phase transformation

Xi

concentration of the i-th component

Greek symbols

αi

inter-phase partition factor of the i-th component

δ

Dirac’s Delta Function

τ

time

References

  1. 1.
    Kolmogorov AN (1937) For statistical theory of melt crystallization. Proceedings of Acad. of Sciences USSR, Math. Series (3):353–359Google Scholar
  2. 2.
    Avrami M (1939) Kinetics of phase change. I. General theory. J Chem Phys 7(12):1103CrossRefGoogle Scholar
  3. 3.
    Avrami M (1940) Kinetics of phase change. II. Transformation-time relations for random distribution of nuclei. J Chem Phys 8(2):212CrossRefGoogle Scholar
  4. 4.
    Belenky VZ (1980) Geometric-probabilistic models of crystallization. Nauka, Moscow, p 84Google Scholar
  5. 5.
    Khodakovskaya RYa, Pavlushkin NM (1983) Kinetics of catalyze glass crystallization. Trudy MkhTI im. Mendeleeva (128):18–27Google Scholar
  6. 6.
    Berezhiani MG (1984) Mathematical modelling of melt crystallization, thesisis of “science for praxis” Conference Reports, “Mecniereba” Tbilisi, pp 138–139. http://www.mediafire.com/?9x19b252b49nx12
  7. 7.
    Berezhiani MG (1985) Mathematical modelling of crystallization kinetics of multicomponent systems. Thesisis of Conference of yung Chemists Dedicated to 40-th anniversary of victory in II Global War, Academy of Sciences of Georgia, “Mecniereba”, Tbilisi, p 13. http://www.mediafire.com/?4c8eyadrc1yjyjj
  8. 8.
    Berezhiani M, Tavartkiladze I (1992) Mathematical modelling of kinetics of melt crystallization processes. Proceedings of the Academy of Sciences of Georgia, Chemical Series 18(2):138–142Google Scholar
  9. 9.
    Schneider W, Köppl A, Berger J (1988) Non—isothermal crystallization crystallization of polymers, system of rate equations. Int Polym Proc 2(3–4):151–154Google Scholar
  10. 10.
    Tobin MC (1974) Theory of phase transition kinetics with growth site imprigement. J Polym Sci Polym Phys Ed 12:399CrossRefGoogle Scholar
  11. 11.
    Ilyn MI (1988) Differential equations for kinetics of first-order phase transition. TOKhT Journal 22(5):606–612Google Scholar
  12. 12.
    Haudin J-M, Chenot J-L (2004) Numerical and physical modeling of polymer crystallization, Part I: Theoretical and numerical analysis. Int Polym Proc 19(3):267–274Google Scholar
  13. 13.
    Piorkowska E, Galeski A, Haudin J-M (2006) Critical assessment of overall crystallization kinetics theories and predictions. Prog Polym Sci 31(6):549–575CrossRefGoogle Scholar

Copyright information

© Springer-Verlag France 2010

Authors and Affiliations

  1. 1.National High Technology Centre of GeorgiaTbilisiGeorgia

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