Lecture 9, Part 3: Nucleation, growth and transparent glass-ceramics - Crystal growth in glass forming liquids

Transcription

1 Lehigh University Lehigh Preserve US-Japan Winter School Semester Length Glass Courses and Glass Schools Winter Lecture 9, Part 3: Nucleation, growth and transparent glass-ceramics - Crystal growth in glass forming liquids Edgar Dutra Zanotto Federal University of Sao Carlos, Brazil Follow this and additional works at: Part of the Materials Science and Engineering Commons Recommended Citation Zanotto, Edgar Dutra, "Lecture 9, Part 3: Nucleation, growth and transparent glass-ceramics - Crystal growth in glass forming liquids" (2008). US-Japan Winter School This Video is brought to you for free and open access by the Semester Length Glass Courses and Glass Schools at Lehigh Preserve. It has been accepted for inclusion in US-Japan Winter School by an authorized administrator of Lehigh Preserve. For more information, please contact preserve@lehigh.edu.

2 Crystal Growth in Glass Forming Liquids Marcio Luis Ferreira Nascimento Edgar Dutra Zanotto Federal University of São Carlos, Brazil Vitreous Materials Laboratory Presented at the IMI-NFG US-Japan Winter School, Jan 14, 2008 and Reproduced by the International Materials Institute for Glass for use by the glass research community; Available at:

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

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

5 Relevance Crystallization kinetics allows or not the existence of vitreous state The development of glass-ceramics depend on the controlled crystallization of certain glasses

6 THEORY

7 How Crystals Grow? Painting by Paolo Massacci

8 Example of Crystal Growth 10-6 Meling & Uhlmann 10-7 u (m/s) T (K) Na 2 O 2SiO 2 α-phase phase growth on NS2 at 780 o C / 1 min intervals

9 How Crystals Grow? Three Classical Mechanisms i) NORMAL SiO 2 & GeO 2

10 George Gilmer How Crystals Grow? ii) SCREW DISLOCATION MODEL Na 2 O 2SiO 2, Na 2 O 4B 2 O 3 & Diopside G. H. Gilmer, J. Crystal Growth 42 (1977)

11 How Crystals Grow? iii) SURFACE NUCLEATION or 2D PbO SiO 2 & Anorthite

12 NORMAL GROWTH

13 S. Glasstone, K. J. Laidler, H. Eyring, The Theory of Rate Processes (1941) Normal Growth Potential ΔG l ΔG c ΔG liquid crystal-liquid liquid interface Kinetics v cl v lc λ crystal ΔG D Distance crystal v cl = v v lc 0 λ = v 0 exp u = λ ΔG exp RT ΔG D liquid + ΔG RT ( ) v lc v cl D u 0 exp 1 exp RT ΔG ΔG ( T ) = λv D RT

14 Normal Growth H. A. Wilson, Philos. Mag. 50 (1900) Ya. Frenkel, Phys. Z. Sowjetunion 1 (1932) ( ) ΔG ΔG T = fλv D u 0 exp 1 exp RT RT Fraction of prefered growth sites f f constant 1 Harold A. Wilson Yakov Frenkel Main supposition: crystal growth front has a high concentration of growth sites f ~1

15 SCREW DISLOCATION GROWTH

16 W. K. Burton, N. Cabrera, F. C. Frank, Trans. Roy. Soc. London A243 (1951) Screw Dislocation The screw dislocation mechanism was proposed by Burton, Cabrera & Frank. Frederick Frank Nicolás Cabrera

17 Surface is smooth but imperfect at atomic level Screw Dislocation u( T ) = fλv 1 exp ΔG RT dislocation line f Tm T 2 πt m v kbt = λ 3 η SE k T ΔG ( T ) = f ( T ) λ 1 B u exp 3 λ η RT Transport Thermodynamic

18 SECONDARY SURFACE NUCLEATION 2D-GROWTH

19 Surface is smooth but also imperfect at atomic level, but free of intersecting screw dislocations Surface Growth: 2D where: b B u = C exp η TΔG k T ΔH B m b = σ = α 3 λ N V 3 2 A m (small crystal case) B = πλv k m B σ 2 (large crystal case) B = πλv 3k m B σ 2 C λn S A 0 C = 3 5 πn S λ Γ / ( 4 / 3) [ ( ) ] exp ΔG / RT 3 /

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

21 Summary: Growth Mechanisms i) Normal (N) D ΔG ( T ) = 1 u u exp λ RT ii) Screw Dislocations (SD) u u exp λ D ΔG ( T ) = f 1 RT iii) Surface Nucleation (2D) if D u D η u D λ ( T ) = C u exp D u 2 kbt v = λ 3 η B TΔG

22 EXAMPLES OF CRYSTAL GROWTH CURVES Properties required to test models or calculate growth rates i) Diffusivity (or viscosity) vs. T; ii) Crystal-glass free energy vs. T

23 M. L. F. Nascimento, Thesis, Federal University of São Carlos (2004) Gibbs Free Energy Comparison of measured and calculated Gibbs free energies ΔG for LS 2 and diopside in wide range of temperatures. Both approximations are valid near T m. For normal and screw dislocation growth ΔG does not have a strong influence on U compared to the transport term. ΔG (J/mol) ΔG (J/mol) 2,5x10 4 2,0x10 4 1,5x10 4 1,0x10 4 5,0x10 3 0, x10 4 6x10 4 5x10 4 4x10 4 3x10 4 2x10 4 1x10 4 Li 2 O 2SiO 2 CaO MgO 2SiO 2 T (K) T (K) Turnbull Hoffman Burgner & Weinberg Turnbull Hoffman Borisova

24 M. L. F. Nascimento, E. B. Ferreira, E. D. Zanotto, J. Chem. Phys. 121 (2004) Viscosity: Diopside 16 log η (Pa.s) Licko & Danek 15 Kozu & Kani 16 McCaffery et al. 17 Neuville & Richet 18 Sipp et al. 19 Taniguchi 20 Klyuev 21 this work Eduardo Ferreira 2 0 log η = /( T 751) Temperature T (K) CaO Mg MgO 2SiO 2

25 Arrhenius or Vogel-Fulcher- Tammann-Hesse (VFTH) equations describe viscosity data between T g and T m for many systems; but is the Stokes-Einstein/Eyring equation adequate to describe the rearrangements on the crystal growth front? Svante Arrhenius Gordon Fulcher Gustav Tammann

26 Growth in situ: Diopside 950 o C 2min 00s

27 Growth in situ: Diopside 950 o C 2min 30s

28 Growth in situ: Diopside 950 o C 3min 00s

29 Growth in situ: Diopside 950 o C 3min 30s

30 Growth in situ: Diopside 950 o C 4min 00s

31 Growth in situ: Diopside 950 o C 4min 30s

32 Growth in situ: Diopside 950 o C 5min 00s

33 Growth rates: Diopside D ΔG ( T ) = f 1 u u exp λ SD λ ~ 1.5 A RT T ( o C) Growth rate U (m/s) Tg Briggs & Carruthers Fokin & Yuritsyn Kirkpatrick et al. Nascimento et al. Reinsch & Müller Zanotto screw CaO MgO 2SiO Temperature T (K)

34 S. Reinsch, M. L. F. Nascimento, R. Muller, E. D. Zanotto, sub. JACS Cordierite 10-4 Reinsch & Müller's data The mechanism 10-5 depends on the T m of μ cordierite, a metastable phase... If T m = 1350 o C SD If T m = 1467 o C 2D Growth rate u (m/s) R 2 = 0.89 a 0 = (0.161 ± 0.004)Å A = B = K T 0 = K H m = 180 kj/mol T m = 1623 (1350 o C) 2MgO 2Al 2Al 2 O 3 5SiO T (K)

35 Nascimento & Zanotto, PRB (2006) Silica Type I Growth rate u (m/s) 2,0x10-9 SiO 2 Type I - Wagstff's data 1,0x10-9 0,0-1,0x T g k BT u( T ) = 1 exp λη ΔG RT Si O bond 1.62Å O O bond 2.64Å SiO 2 glass λ ~ 1 A Normal growth Temperature T (K)

36 Li 2 O 2SiO 2 B = πλv 3k m B σ 2 LS 2D D B 2 u( T ) = C u exp 2 λ TΔG u (m/s) T g 1.1T g u(t) ajustado com λ = 1,3 Å T (K) Barker et al. Burgner & Weinberg James Matusita & Tashiro Ota et al. Schmidt & Frischat Zanotto & Leite Fokin Soares Jr. Gonzalez-Oliver et al. Deubener et al. Ogura et al. Parcell Ito et al. Leontjeva

37 Summary Three classical types: normal, screw & 2D ΔG = Turnbull or Hoffmann ΔG D = via Stokes-Einstein / Eyring ΔH m = melting enthalpy η = viscosity Validity of crystal growth models & Stokes-Einstein / Eyring equation in a wide temperature range