Crystallization Kinetics

  • Johannes A. Kalb


The classical theory of steady state crystal nucleation is discussed, as originally developed by Gibbs, Volmer, Weber, Becker, Döring, Turnbull and Fisher. A particular focus is drawn on the implications of heterogeneous nucleation sites, which can increase the homogeneous nucleation rate by many orders of magnitude. Classical theory of crystal growth is covered as well.

In Sect. 7.2, these theories are applied to measurements of nucleation and growth parameters in amorphous and liquid phase change materials by calorimetry and microscopy. The results contribute to a better understanding of the kinetics of the phase transformation in these materials, which helps to develop next-generation phase change media and to scale them to smaller dimensions.


Nucleation Rate Phase Change Material Crystallization Kinetic Homogeneous Nucleation Crystal Nucleation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [7.1]
    Gibbs, J.: The scientific papers of J. Willard Gibbs. Dover Publications, New York (1961)Google Scholar
  2. [7.2]
    Christian, J.: Transformation in metals and alloys, 2nd edn. Pergamon Press, Oxford (1975)Google Scholar
  3. [7.3]
    Kelton, K.: Crystal nucleation in liquids and glasses. Solid State Physics 45, 75-177 (1991)CrossRefGoogle Scholar
  4. [7.4]
    Volmer, M. and Weber, A.: Keimbildung in übersättigten Gebilden. Zeitschrift für Physikalische Chemie 119, 277 (1926)Google Scholar
  5. [7.5]
    Becker, R. and Döring, W.: Kinetische Behandlung der Keimbildung in übersättigten Dämpfen. Annalen der Physik 24, 719 (1935)CrossRefGoogle Scholar
  6. [7.6]
    Turnbull, D. and Fisher, J.: Rate of nucleation in condensed systems. J. Chem. Phys. 17, 71-73 (1949)CrossRefGoogle Scholar
  7. [7.7]
    Landau, L. and Lifshitz, E.: Statistical Physics. Pergamon Press, Oxford (1969)Google Scholar
  8. [7.8]
    Thompson, C. and Spaepen, F.: Homogeneous crystal nucleation in binary metallic melts. Acta Metallurgica 31, 2021-2027 (1983)CrossRefGoogle Scholar
  9. [7.9]
    Herlach, D.: Non-equilibrium solidification of undercooled metallic melts. Materials Science and Engineering R 12, 177-272 (1994)CrossRefGoogle Scholar
  10. [7.10]
    Angell, C., Ngai, K., McKenna, G., McMillan, P. and Martin, S.: Relaxation in glass- forming liquids and amorphous solids. J. Appl. Phys. 88, 3113-3157 (2000)CrossRefGoogle Scholar
  11. [7.11]
    Debenedetti, P. and Stillinger, F.: Supercooled liquids and the glass transition. Nature 410, 259-267 (2001)CrossRefGoogle Scholar
  12. [7.12]
    Götze, W.: Liquids, freezing and the glass transition. Les Houches LI. North-Holland, Amsterdam (1991), p. 287Google Scholar
  13. [7.13]
    Hodgdon, J. and Stillinger, F.: Stokes-Einstein violation in glass-forming liquids. Phys. Rev. E 48, 207-213 (1993)CrossRefGoogle Scholar
  14. [7.14]
    Shao, Y. and Spaepen, F.: Undercooling of bulk liquid silicon in an oxide flux. J. App. Phys. 79, 2981-2985 (1996)CrossRefGoogle Scholar
  15. [7.15]
    Spaepen, F.: The identification of the metallic glass state. In: Mat. Res. Soc. Symp. Proc., vol. 57, p. 161-184 (1986)Google Scholar
  16. [7.16]
    Thompson, C., Greer, A. L. and Spaepen, F.: Crystal nucleation in amorphous (Au100-yCuy)77Si9Ge14 alloys. Acta Metallurgica 31, 1883-1894 (1983)CrossRefGoogle Scholar
  17. [7.17]
    Turnbull, D.: Kinetics of solidification of supercooled liquid mercury droplets. J. Chem. Phys. 20, 411-424 (1952)CrossRefGoogle Scholar
  18. [7.18]
    Turnbull, D.: Under what conditions can a glass be formed? Contemp. Phys.10, 473-488 (1969)CrossRefGoogle Scholar
  19. [7.19]
    Kalb, J.: Crystallization kinetics in antimony and tellurium alloys used for phase change recording. Ph.D. thesis, RWTH Aachen, Germany (2006). URL www. Scholar
  20. [7.20]
    Spaepen, F.: Physics of Defects. Les Houches XXXV. North-Holland, Amsterdam (1981), pp. 133-174Google Scholar
  21. [7.21]
    Spaepen, F. and Turnbull, D.: Metallic glasses. Ann. Rev. Phys. Chem. 35, 241-263 (1984)CrossRefGoogle Scholar
  22. [7.22]
    Elliott, S.: Physics of amorphous materials, 2nd edn. Longman, London (1990)Google Scholar
  23. [7.23]
    Volmer, M.: Über Keimbildung und Keimwirkung als Spezialfälle der heterogenen Katalyse. Zeitschrift für Elektochemie 35, 555 (1929)Google Scholar
  24. [7.24]
    Wu, D.: Nucleation theory. Solid State Physics 50, 37-187 (1997)CrossRefGoogle Scholar
  25. [7.25]
    Holland-Moritz, D.: Short-range order and solid-liquid interfaces in undercooled melts. Int. Journ. Non-Equilibrium Processing 11, 169-199 (1998)Google Scholar
  26. [7.26]
    Crank, J.: The mathematics of diffusion, 2nd edn. Clarendon Press, Oxford (1975)Google Scholar
  27. [7.27]
    Coombs, J., Jongenelis, A., van Es-Spiekman, W. and Jacobs, B.: Laser-induced crystallization phenomena in GeTe-based alloys. II. Composition dependence of nucleation and growth. J. Appl. Phys. 78, 4918-4928 (1995)CrossRefGoogle Scholar
  28. [7.28]
    van Pieterson, L., Lankhorst, M., van Schijndel, M., Kuiper, A. and Roosen, J.: Phase-change recording materials with a growth-dominated crystallization mechanism: A materials overview. J. Appl. Phys. 97, 083520 (2005)CrossRefGoogle Scholar
  29. [7.29]
    van Pieterson, L., van Schijndel, M., Rijpers, J. and Kaiser, M.: Te-free, Sb-based phase-change materials for high-speed rewritable optical recording. Appl. Phys. Lett. 83, 1373-1375 (2003)CrossRefGoogle Scholar
  30. [7.30]
    Weidenhof, V., Friedrich, I., Ziegler, S. and Wuttig, M.: Laser induced crystallization of amorphous Ge2Sb2Te5 films. J. Appl. Phys. 89, 3168-3176 (2001)CrossRefGoogle Scholar
  31. [7.31]
    Yamada, N., Ohno, E., Nishiuchi, K., Akahira, N. and Takao, M.: Rapid phase transitions of GeTe-Sb2Te3 pseudobinary amorphous thin films for an optical disk memory. J. Appl. Phys. Physics 69, 2849-2856 (1991)CrossRefGoogle Scholar
  32. [7.32]
    Friedrich, I., Weidenhof, V., Njoroge, W., Franz, P. and Wuttig, M.: Structural transformations of Ge2Sb2Te5 films studied by electrical resistance measurements. J. Appl. Phys. 87, 4130-4134 (2000)CrossRefGoogle Scholar
  33. [7.33]
    Jeong, T., Kim, M., Seo, H., Kim, S. and Kim, S.: Crystallization behavior of sputter- deposited amorphous Ge2Sb2Te5 thin films. J. Appl. Phys. 86, 774-778 (1999)CrossRefGoogle Scholar
  34. [7.34]
    Kooi, B. and De Hosson, J.: On the crystallization of thin films composed of Sb3.6Te with Ge for rewritable data storage. J. Appl. Phys. 95, 4714-4721 (2004)CrossRefGoogle Scholar
  35. [7.35]
    Libera, M. and Chen, M.: Time-resolved reflection and transmission studies of amorphous Ge-Te thin-film crystallization. J. Appl. Phys. 73, 2272-2282 (1993)CrossRefGoogle Scholar
  36. [7.36]
    Lu, Q. and Libera, M.: Microstructural measurements of amorphous GeTe crystallization by hot-stage optical microscopy. J. Appl. Phys. 77, 517-521 (1995)CrossRefGoogle Scholar
  37. [7.37]
    Njoroge, W., Dieker, H. and Wuttig, M.: Influence of dielectric capping layers on the crystallization kinetics of Ag5In6Sb59Te30 films. J. Appl. Phys. 96, 2624-2627 (2004)CrossRefGoogle Scholar
  38. [7.38]
    Njoroge W. and Wuttig, M.: Crystallization kinetics of sputter-deposited amorphous AgInSbTe films. J. Appl. Phys. 90, 3816 (2001)CrossRefGoogle Scholar
  39. [7.39]
    Pedersen, T.L., Kalb, J., Njoroge, W., Wamwangi, D., Wuttig, M. and Spaepen, F.: Mechanical stresses upon crystallization in phase change materials. Appl. Phys. Lett. 79, 3597-3599 (2001)CrossRefGoogle Scholar
  40. [7.40]
    Privitera, S., Bongiorno, C., Rimini, E. and Zonca, R.: Crystal nucleation and growth processes in Ge2Sb2Te5. Appl. Phys. Lett. 84, 4448-4450 (2004)CrossRefGoogle Scholar
  41. [7.41]
    Ruitenberg, G., Petford-Long, A. and Doole, R.: Determination of the isothermal nucleation and growth parameters for the crystallization of thin Ge2Sb2Te5 films. J. Appl. Phys. 92, 3116-3123 (2002)CrossRefGoogle Scholar
  42. [7.42]
    Wamwangi, D., Njoroge, W. and Wuttig, M.: Crystallization kinetics of Ge4Sb1Te5 films. Thin Solid Films 408, 310-315 (2002)CrossRefGoogle Scholar
  43. [7.43]
    Kalb, J., Spaepen, F. and Wuttig, M.: Kinetics of crystal nucleation in undercooled droplets of Sb-and Te-based alloys used for phase change recording. J. Appl. Phys. 98, 054910 (2005)CrossRefGoogle Scholar
  44. [7.44]
    Kissinger, H.: Reaction kinetics in differential thermal analysis. Analyt. Chem. 29, 1702 (1957)CrossRefGoogle Scholar
  45. [7.45]
    Avrami, M.: Kinetics of phase change. I. General theory. J. Chem. Phys. 7, 1103-1112 (1939)CrossRefGoogle Scholar
  46. [7.46]
    Johnson, W. and Mehl, R.: Reaction kinetics in process of nucleation and growth. Trans. Amer. Inst. of Mining, Metallurgical and Petroleum Engineers 135, 416 (1939)Google Scholar
  47. [7.47]
    Kalb, J., Spaepen, F. and Wuttig, M.: Atomic force microscopy measurements of crystal nucleation and growth rates in thin films of amorphous Te alloys. Appl. Phys. Lett. 84, 5240-5242 (2004)CrossRefGoogle Scholar
  48. [7.48]
    Kalb, J., Wen, C., Spaepen, F., Dieker, H. and Wuttig, M.: Crystal morphology and nucleation in thin films of amorphous Te alloys used for phase change recording. J. Appl. Phys. 98, 054902 (2005)CrossRefGoogle Scholar
  49. [7.49]
    Kooi, B., Groot, W. and De Hosson, J.: In situ transmission electron microscopy study of the crystallization of Ge2Sb2Te5. J. Appl. Phys. 95, 924-932 (2004)CrossRefGoogle Scholar
  50. [7.50]
    Weidenhof, V., Friedrich, I., Ziegler, S. and Wuttig, M.: Atomic force microscopy study of laser induced phase transitions in Ge2Sb2Te5. J. Appl. Phys. 86, 5879-5887 (1999)CrossRefGoogle Scholar
  51. [7.51]
    Kalb, J., Wuttig, M. and Spaepen, F.: Calorimetric measurements of structural relaxation and glass transition temperatures in sputtered films of amorphous Te alloys used for phase change recording. J. Mater. Res. 22, 748-754 (2007)CrossRefGoogle Scholar
  52. [7.52]
    Spaepen, F.: Private communicationGoogle Scholar
  53. [7.53]
    Kalb, J.: Stresses, viscous flow and crystallization kinetics in thin films of amorphous chalcogenides used for optical data storage. Diploma thesis, RWTH Aachen, Germany (2002). URL Scholar
  54. [7.54]
    Kalb, J., Spaepen, F., Pedersen, T.L. and Wuttig, M.: Viscosity and elastic constants of thin films of amorphous Te alloys used for optical data storage. J. Appl. Phys. 94, 4908-4912 (2003)CrossRefGoogle Scholar
  55. [7.55]
    Borg, H., van Schijndel, M., Rijpers, J., Lankhorst, H., Zhou, G., Dekker, M., Ubbens, I. and Kuijper, M.: Phase-change media for high-numerical-aperture and blue-wavelength recording. Jpn. J. Appl. Phys. 40, Part 1, 1592-1597 (2001)CrossRefGoogle Scholar
  56. [7.56]
    Shackelford, J.: Introduction to Materials Science for Engineers, 2nd edn. Macmillan, New York (1988)Google Scholar
  57. [7.57]
    Kalb, J., Spaepen, F. and Wuttig, M.: Calorimetric measurements of phase transformations in thin films of amorphous Te alloys used for optical data storage. J. Appl. Phys. 93, 2389-2393 (2003)CrossRefGoogle Scholar
  58. [7.58]
    Peng, C., Cheng, L. and Mansuripur, M.: Experimental and theoretical investigations of laser-induced crystallization and amorphization in phase-change optical recording media. J. Appl. Phys. 82, 4183-4191 (1997)CrossRefGoogle Scholar
  59. [7.59]
    Kaiser, M., van Pieterson, L. and Verheijen, M.: In situ transmission electron microscopy analysis of electron beam induced crystallization of amorphous marks in phase-change materials. J. Appl. Phys. 96, 3193-3198 (2004)CrossRefGoogle Scholar
  60. [7.60]
    Ohshima, N.: Crystallization of germanium-antimony-tellurium amorphous thin film sandwiched between various dielectric protective films. J. Appl. Phys. 79, 8357-8363 (1996)CrossRefGoogle Scholar
  61. [7.61]
    Haring-Bolivar, P., Merget, F., Kim, D.H., Hadam, B. and Kurz, H.: European Symposium on Phase Change and Ovonic Science (EPCOS), Balzers, Liechtenstein, unpublished (2004)Google Scholar
  62. [7.62]
    Lankhorst, M., Ketelaars, B., Wolters, R.: Low-cost and nanoscale non-volatile memory concept for future silicon chips. Nature Materials 4, 347-352 (2005)CrossRefGoogle Scholar
  63. [7.63]
    Hudgens, S. and Johnson, B.: Overview of phase-change chalcogenide nonvolatile memory technology. Materials Research Society Bulletin 29, 829-832 (2004)Google Scholar
  64. [7.64]
    Kelton, K., Greer, A.: Transient nucleation effects in glass formation. Journal of Non-Crystalline Solids 79, 295-309 (1986)CrossRefGoogle Scholar
  65. [7.65]
    Friedrich, I., Weidenhof, V., Lenk, S. and Wuttig, M.: Morphology and structure of laser-modified Ge2Sb2Te5 films studied by transmission electron microscopy. Thin Solid Films 389, 239-244 (2001)CrossRefGoogle Scholar
  66. [7.66]
    Wöltgens, H.W., Detemple, R., Friedrich, I., Njoroge, W., Thomas, I., Weidenhof, V., Ziegler, S. and Wuttig, M.: Exploring the limits of fast phase change materials. In: Materials Research Society Symposia Proceedings, vol. 674, p. V1.3 (2001)Google Scholar
  67. [7.67]
    Ziegler, S.: Rekristallisationskinetik von Phasenwechselmedien. Ph.D. thesis, RWTH Aachen, Germany (2005)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Intel Corporation Technology and Manufacturing Group Robert Noyce BuildingSanta ClaraUSA

Personalised recommendations