Fundamentals of Crystal Nucleation and Growth in Glasses

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

Outline n n n 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. . La. Ma. V 2

Crystal nucleation and growth Linear x Log scale? curves Imax Umax La. Ma. V 3

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 La. Ma. V

Outline • Introduction • Growth models? • Normal Growth • Screw Dislocation Growth • Surface Nucleation Growth • Some Examples • Experimental Results • Acknowledgments • Bibliography La. Ma. V

Introduction Crystal growth rates depend basically on three factors: 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. La. Ma. V

Crystal growth on a cordierite glass surface - video https: //www. youtube. com/ watch? v=a 4 Ei. W 7 Pxntk Simulation of nucleation and growthvideo: https: //www. youtube. com/watch? v=Flk r. BSh 4514 La. Ma. V

Devitrite and cristobalite in SLS glass La. Ma. V

THEORY La. Ma. V

How Crystals Grow? Painting by Paolo Massacci La. Ma. V

Example of Crystal Growth Na 2 O 2 Si. O 2 La. Ma. V -phase growth on NS 2 at 780 o. C / 1 min intervals

Growth in situ: Diopside 950 o. C 2 min 00 s La. Ma. V

Growth in situ: Diopside 950 o. C 2 min 30 s La. Ma. V

Growth in situ: Diopside 950 o. C 3 min 00 s La. Ma. V

Growth in situ: Diopside 950 o. C 3 min 30 s La. Ma. V

Growth in situ: Diopside 950 o. C 4 min 00 s La. Ma. V

Three Classical Mechanisms i) NORMAL or CONTINUOUS GROWTH Si. O 2 & Ge. O 2 La. Ma. V

George Gilmer ii) SCREW DISLOCATION GROWTH MODEL E. g. Na 2 O 2 Si. O 2 , Na 2 O 4 B 2 O 3 & Diopside G. H. Gilmer, J. Crystal Growth 42 (1977) La. Ma. V

iii) SURFACE NUCLEATION or 2 D Pb. O Si. O 2 & Anorthite La. Ma. V

NORMAL OR CONTINUOUS GROWTH Explain the origen of the word “continuous” La. Ma. V

S. Glasstone, K. J. Laidler, H. Eyring, Theory of Rate Processes (1941) Normal Growth crystal-liquid interface Kinetics v Potential cl crystal v lc DG DGD l | DG c Distance liquid La. Ma. V crystal liquid

Summary: Growth Mechanisms i) Normal (N) ii) Screw Dislocations (SD) iii) Surface Nucleation (2 D) La. Ma. V

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

Kenneth Jackson’s Criterium n n Molar melting entropy Sm = Hm/Tm < 2 R : normal growth rough surface Molar melting entropy Sm > 4 R : SD or 2 D smooth surface Hm is the melting enthalpy and Tm the melting temperature La. Ma. V

Growth rates: Diopside SD 1. 1 Tg La. Ma. V ~ 1. 5 A

Nascimento & Zanotto, PRB (2006) Silica Type I Si. O 2 glass 1. 1 Tg Si O bond 1. 62Å O O bond 2. 64Å ~ 1 A Normal growth La. Ma. V

Summary Three classical types: normal, normal screw & 2 D DG (T)= Exp. , Turnbull or Hoffmann DGD = Stokes-Einstein / Eyring DHm = melting enthalpy h(T) = viscosity Validity of crystal growth models using the SEE equation in a wide temperature range T>1. 1 Tg La. Ma. V

The decoupling of Du and Dh La. Ma. V

New crystal growth rate data at deeper undercoolings and model fitting New data at low T ~ 3Å Td ~ 1. 1 Tg Daniel Cassar La. Ma. V 29

New crystal growth rates and fitting for PS Td ~ 1. 25 Tg ~1Å Bruno Batoqui & M. Nascimento La. Ma. V 30

Li 2 O 2 Si. O 2 LS 2 2 D 1. 1 Tg Tg La. Ma. V

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

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) La. Ma. V