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How Do Crystals Nucleate and Grow: Ostwald’s Rule of Stages and Beyond

  • Jürn W. P. SchmelzerEmail author
  • Alexander S. Abyzov
Chapter
Part of the Hot Topics in Thermal Analysis and Calorimetry book series (HTTC, volume 11)

Abstract

W. Ostwald predicted with the “rule of stages” formulated by him that phase formation processes in complex condensed matter systems may proceed step by step via different evolution paths involving a discrete series of metastable states, which can be formed in a macroscopic form at the given thermodynamic conditions, until finally, the most stable phase will be reached. Advancing this idea, it was shown in recent years by us that in condensation and boiling, as well as in segregation and crystallization processes in multi-component liquid and solid solutions, critical clusters may be formed and evolve via a continuous sequence of states with properties which may differ from the properties of any of the macroscopic phases present in the respective phase diagram. The kinetics of nucleation proceeds hereby via a scenario similar to spinodal decomposition, i.e., via a continuous amplification of density and/or composition differences accompanied eventually by sequential discrete changes of the structure of the system. The basic ideas and results of this theoretical approach developed by us are described in the present chapter. Recently published experimental results on crystal nucleation are discussed in detail giving additional confirmation of these conclusions. As a second man topic devoted also to the theoretical description of crystal nucleation, the relevance of the concepts of fragility of the liquid for the understanding of crystal nucleation and growth in glass-forming liquids is explored. Finally, a number of directions of research are discussed which may lead to new insights into the complex phenomena of crystal formation and growth processes.

Keywords

Glass Transition Temperature Crystal Nucleation Effective Activation Energy Critical Cluster Metal Phosphate 
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.

References

  1. 1.
    Gibbs JW (1928) On the equilibrium of heterogeneous substances, Trans. Connecticut Academy of Sciences 3, 108, 343 (1875–79); The collected works, vol 1, Thermodynamics. Longmans, New York—London—TorontoGoogle Scholar
  2. 2.
    van der Waals JD (1894) Verhandel. Konink. Akad. Weten. Amsterdam (sect. 1), 1, 56 (1893); Z Phys Chemie 13:657Google Scholar
  3. 3.
    Rowlinson JS (1979) Translation of J. D. van der Waals’ The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. J Stat Phys 20:197CrossRefGoogle Scholar
  4. 4.
    Schmelzer JWP, Gutzow IS, Schmelzer J Jr (2000) J Chem Phys 112:3820CrossRefGoogle Scholar
  5. 5.
    Schmelzer JWP, Boltachev GSh, Baidakov VG (2006) J Chem Phys 114:194502Google Scholar
  6. 6.
    Chung S-Y, Kim Y-M, Kim J-G, Kim Y-J (2009) Nat Phys 5:68CrossRefGoogle Scholar
  7. 7.
    Billinge SJL (2009) Nat Phys 5:13CrossRefGoogle Scholar
  8. 8.
    Ostwald W (1897) Z Phys Chemie 22:289Google Scholar
  9. 9.
    Hillert M (1956) A theory of nucleation of solid metallic solutions. Sc.D. Thesis, Massachusetts Institute of TechnologyGoogle Scholar
  10. 10.
    Cahn JW, Hilliard JE (1959) J Chem Phys 28, 258 (1958); 31:688Google Scholar
  11. 11.
    Nishioka K, Kusaka I (1992) J Chem Phys 96:5370CrossRefGoogle Scholar
  12. 12.
    Debenedetti PG, Reiss H (1998) J Chem Phys 108:5498CrossRefGoogle Scholar
  13. 13.
    Baidakov VG, Boltachev GSh, Schmelzer JWP (2000) J Colloid Interface Sci 231:312CrossRefGoogle Scholar
  14. 14.
    Stranski IN, Totomanov D (1933) Z Phys Chemie A 163:399Google Scholar
  15. 15.
    Scheil E (1952) Z Metallkunde 43:40Google Scholar
  16. 16.
    Hobstetter JN (1949) Trans. American Inst Min (Metall) Eng 180:121Google Scholar
  17. 17.
    Burke J (1965) The kinetics of phase transformations in metals. Pergamon Press, New YorkGoogle Scholar
  18. 18.
    Gerlach W (1949) Z Metallkunde 40:281Google Scholar
  19. 19.
    Masing G (1950) Lehrbuch der Allgemeinen Metallkunde. Springer, BerlinCrossRefGoogle Scholar
  20. 20.
    Becker R (1938) Ann Phys 32:128CrossRefGoogle Scholar
  21. 21.
    Abyzov AS, Schmelzer JWP (2007) J Chem Phys 127:114504CrossRefGoogle Scholar
  22. 22.
    Fokin VM, Zanotto ED, Yuritsyn NS, Schmelzer JWP (2006) J Non-Cryst Solids 352:2681CrossRefGoogle Scholar
  23. 23.
    Schmelzer JWP, Gokhman AR, Fokin VM (2004) J Colloid Interface Sci 272:109CrossRefGoogle Scholar
  24. 24.
    Schmelzer JWP, Abyzov AS, Möller J (2004) Chem Phys 121:6900Google Scholar
  25. 25.
    Tatchev D, Hoell A, Kranold R, Armyanov S (2005) Phys B 369:8CrossRefGoogle Scholar
  26. 26.
    Tatchev D, Goerigk G, Valova E, Dille J, Kranold R, Armyanov S, Delplancke J-L (2005) J Appl Crystallogr 38:787CrossRefGoogle Scholar
  27. 27.
    Schmelzer JWP, Abyzov AS (2007) J Eng Thermophys 16:119CrossRefGoogle Scholar
  28. 28.
    Schmelzer JWP (2009) Generalized Gibbs thermodynamics and nucleation-growth phenomena. In: Rzoska S, Drozd-Rzoska A, Mazur V (eds) Proceedings of the NATO advanced research workshop “metastable systems under pressure”, Odessa, Ukraine, 4–8 Oct 2008. Springer, pp 389–402Google Scholar
  29. 29.
    Schmelzer JWP, Fokin VM, Abyzov AS, Zanotto ED, Gutzow IS (2010) Int J Appl Glass Sci 1:16CrossRefGoogle Scholar
  30. 30.
    Gutzow IS, Schmelzer JWP (2013) The vitreous state: thermodynamics, structure, rheology, and crystallization, 1st edn. Springer, Berlin-Heidelberg, 1995; Second enlarged edition. Springer, HeidelbergGoogle Scholar
  31. 31.
    Angell CA (1995) Science 267:1924CrossRefGoogle Scholar
  32. 32.
    Martinez L-M, Angell CA (2001) Nature 410:663CrossRefGoogle Scholar
  33. 33.
    Gallo LSA, Mosca TM, Teider BH, Polyakova IG, Rodrigues ACM, Zanotto ED, Fokin VM (2014) J Non-Cryst Solids 408:102CrossRefGoogle Scholar
  34. 34.
    Orava J, Greer AL (2014) J Chem Phys 140:214504CrossRefGoogle Scholar
  35. 35.
    Wilde G (2014) Early stages of crystal formation in glass-forming metallic alloys. In: Schmelzer JWP (ed) Glass: selected properties and crystallization. de Gruyter, Berlin, pp 95–136Google Scholar
  36. 36.
    Oldekop W (1957) Glastechnische Berichte 30:8Google Scholar
  37. 37.
    Laughlin WT, Uhlmann DR (1972) J Phys Chem 76:2317CrossRefGoogle Scholar
  38. 38.
    Nemilov SV (1995) Thermodynamic and kinetic aspects of the vitreous state. CRC Press, Boca RatonGoogle Scholar
  39. 39.
    Ediger MD, Harrowell P, Yu L (2008) J Chem Phys 128:034709CrossRefGoogle Scholar
  40. 40.
    Schmelzer JWP, Abyzov AS, Fokin VM, Schick C, Zanotto ED (2015) J Non-Crystalline Solids 429:24Google Scholar
  41. 41.
    Schmelzer JWP, Abyzov AS, Fokin VM, Schick C, Zanotto ED (2015) J Non-Crystalline Solids 428:68Google Scholar
  42. 42.
    Schmelzer JWP, Abyzov AS, Fokin VM, Schick C, Zanotto ED (2015) J Non-Crystalline Solids 429:45Google Scholar
  43. 43.
    Tammann G (1933) Der Glaszustand. Leopold Voss Verlag, LeipzigGoogle Scholar
  44. 44.
    Tammann G (1904) Z Elektrochemie 10:532CrossRefGoogle Scholar
  45. 45.
    Schmelzer JWP, Gutzow IS (2011) Glasses and the glass transition. Wiley-VCH, Berlin-WeinheimCrossRefGoogle Scholar
  46. 46.
    Boltachev GSh, Schmelzer JWP (2010) J Chem Phys 133:134509CrossRefGoogle Scholar
  47. 47.
    Schmelzer JWP, Boltachev GSh, Abyzov AS (2013) J Chem Phys 139:034702CrossRefGoogle Scholar
  48. 48.
    Abyzov AS, Schmelzer JWP (2014) J Chem Phys 138, 164504 (2013); 140:244706Google Scholar
  49. 49.
    Schmelzer JWP (2012) J Chem Phys 136:074512CrossRefGoogle Scholar
  50. 50.
    Zanotto ED, Schmelzer JWP, Fokin VM, Nucleation, growth, and crystallization in inorganic glasses, submitted to publicationGoogle Scholar
  51. 51.
    Wright AC (2013) Int J Appl Glass Sci 5:31Google Scholar
  52. 52.
    Johari GP, Schmelzer JWP (2014) Crystal nucleation and growth in glass-forming systems: some new results and open problems. In: Schmelzer JWP (ed) Glass: selected properties and crystallization. de Gruyter, Berlin, pp 531–590Google Scholar
  53. 53.
    Cooper AR (1982) J Non-Cryst Solids 49:1CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of RostockRostockGermany
  2. 2.National Scientific CentreKharkov Institute of Physics and TechnologyKharkovUkraine

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