1. LaMaV Fundamentals of Crystal Nucleation and Growth in Glasses Edgar D. Zanotto www.certev.ufscar.br 1

2. LaMaV Outline Introduction Importance of crystal nucleation, growth and overall crystallization Brief overview of glass transition Fundamentals Crystal nucleation in undercooled inorganic GF liquids Crystal growth in.... 2

3. LaMaV Crystal nucleation and growth curves I max U max 3 Linear x Log scale?

4. LaMaV Crystal Growth in Glass Forming Liquids Marcio Luis Ferreira Nascimento Edgar Dutra Zanotto Federal University of São Carlos, Brazil Vitreous Materials Laboratory lamav.weebly.com

5. LaMaV Introduction Introduction Growth models? Growth models? Normal Growth Normal Growth Screw Dislocation Growth Screw Dislocation Growth Surface Nucleation Growth Surface Nucleation Growth Some Examples Some Examples Experimental Results Experimental Results Acknowledgments Acknowledgments Bibliography Bibliography Outline

6. LaMaV undercooling = i ) The undercooling = measure of the driving force for crystal growth; ii ) The site factor = the fraction of sites on the crystal/ glass interface that can incorporate molecules; iii ) The effective diffusivity through the crystal / liquid interface = a measure of the resistance to molecular motion and structural rearrangement. Crystal growth rates depend basically on three factors: Introduction

7. LaMaV Crystal growth on a cordierite glass surface - video https://www.youtube.com/ watch?v=a4EiW7Pxntk Simulation of nucleation and growth- video: https://www.youtube.com/watch?v=Flk rBSh4514

8. LaMaV Devitrite and cristobalite in SLS glass

9. LaMaV THEORY

10. LaMaV How Crystals Grow? Painting by Paolo Massacci

11. LaMaV Example of Crystal Growth  -phase growth on NS2 at 780 o C / 1 min intervals Na 2 O  2SiO 2

12. LaMaV Growth in situ: Diopside 2min 00s 950 o C

13. LaMaV 2min 30s Growth in situ: Diopside

14. LaMaV 950 o C 3min 00s Growth in situ: Diopside

15. LaMaV 950 o C 3min 30s Growth in situ: Diopside

16. LaMaV 950 o C 4min 00s Growth in situ: Diopside

17. LaMaV i)NORMAL or CONTINUOUSGROWTH Three Classical Mechanisms SiO 2 & GeO 2

18. LaMaV ii ) SCREW DISLOCATION GROWTH MODEL E.g. Na 2 O  2SiO 2, Na 2 O  4B 2 O 3 & Diopside G. H. Gilmer, J. Crystal Growth 42 (1977) George Gilmer

19. LaMaV PbO  SiO 2 & Anorthite iii ) SURFACE NUCLEATION or 2D

20. LaMaV NORMAL OR CONTINUOUS GROWTH Explain the origen of the word “continuous”

21. LaMaV Normal Growth crystalliquid crystal-liquid interface S. Glasstone, K. J. Laidler, H. Eyring, The Theory of Rate Processes (1941)

22. LaMaV i) Normal (N) ii) Screw Dislocations (SD) iii) Surface Nucleation (2D) Summary: Growth Mechanisms

23. LaMaV i) Normal (N) ii) Screw Dislocations (SD) iii) Surface Nucleation (2D) Summary: Growth Mechanisms Large crystal case:

24. LaMaV Jackson’s Criterium Molar melting entropy  S m =  H m /T m < 2R : normal growth  rough surface Molar melting entropy  S m > 4R : SD or 2D  smooth surface Kenneth Jackson  H m is the melting enthalpy and T m the melting temperature

25. LaMaV Growth rates: Diopside ~ 1.5 A SD 1.1Tg

26. LaMaV bond Si  O bond 1.62Å bond O  O bond 2.64Å SiO 2 glass Silica Type I Normal growth 1.1T g  ~ 1 A Nascimento & Zanotto, PRB (2006)

27. LaMaV Summary normalscrew2D Three classical types: normal, screw & 2D TurnbullHoffmann  G (T)= Exp., Turnbull or Hoffmann = Stokes-Einstein / Eyring  G D = Stokes-Einstein / Eyring melting enthalpy  H m = melting enthalpy viscosity  = viscosity Validity of crystal growth models using the SEE equation in a wide temperature range T>1.1T g

28. LaMaV The decoupling of D u and D 

29. LaMaV New crystal growth rate data at deeper undercoolings and model fitting Td ~ 1.1T g ~ 3Å New data at low T Daniel Cassar 29

30. LaMaV New crystal growth rates and fitting for PS ~1Å T d ~ 1.25T g Bruno Batoqui & M. Nascimento 30

31. LaMaV Li 2 O  2SiO 2 2D TgTgTgTg 1.1T g LS 2

32. LaMaV Applications of Crystal Growth Glass formation / avoid crystallization Development of glass-ceramics Industrial crystallization (from sugar to  – quartz) Advanced materials (alloys, glasses, pharmaceuticals...) Geophysics (rain, fog, snow, magma...)

33. LaMaV Bibliography The Vitreous State Ivan Gutzow & Jürn Schmelzer – Springer (1995) Glasses and the Vitreous State Jerry Zarzycki - Cambridge (1991) Fundamentals of Inorganic Glasses Arun Varshneya – Academic Press (1994) Amorphous Inorganic Materials & Glasses Adalbert Feltz – VCH (1993) Physics of Amorphous Materials Stephen Elliott – Longman Scientific & Technical (1990)