& INORGANIC GLASSES POLYMER METALLIC. Na 2 O 2CaO 3SiO 2. Polypropilene. Zr 55 Cu 30 Ni 5 Al 10

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1 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: Crystal Nucleation in POLYMER METALLIC & INORGANIC GLASSES Polypropilene Zr 55 Cu 30 Ni 5 Al 10 Na 2 O 2CaO 3SiO 2 Edgar Dutra Zanotto & Marcio L. F. Nascimento Vitreous Materials Laboratory Federal University of São Carlos, Brazil

2 Vitreous Materials Lab., Fed. Univ. São Carlos

3 Objective To discuss the validity and utility of the CNT using relevant findings on crystal nucleation in deeply undercooled liquids reported in the last 50 years

4 Crystal nucleation and growth rate curves 5x10 9 I max 1,0x10-4 Nucleation Rate I (m -3.s -1 ) 4x10 9 3x10 9 2x10 9 1x10 9 Li 2 O.2SiO 2 Nucleation Crystal Growth U max 8,0x10-5 6,0x10-5 4,0x10-5 2,0x10-5 Crystal Growth Rate U (m/s) T (K)

5 Simulation of nucleation and growth T. Pusztai, G. Bortel, L. Gránásy, Europhys. Lett. 71 (2005)... Courtesy of László Gránásy

6 Real nucleation and growth in PDMS 63 C, ΔT=6min. Surface nucleation 63 C, ΔT=4min. Internal nucleation

7 Outline i) The CNT: Theory and tests in the last 50 years a) the diffusion mechanism? b) surface energy = f (T, size)? c) metastable phases? d) what is next? ii) How useful is CNT to the understanding of glass-formation and to the development of GC?

8 Importance and motivation If crystallization is averted on the cooling path any liquid can vitrify to a glass; The development of useful glassceramics with designed micro/nano structures...

9 CNT Theory and tests in the last 50 years

10 CNT Researchers Gallery Josiah W. Gibbs Iwan Stranski Gustav Tammann Yakov Frenkel Ladislau Farkas Max Volmer Rostislav Kaischew Yakov Zeldovich Richard Becker David Turnbull

11 Undercooling viscous liquids followed by isothermal crystallization Treatment of glasses at deep undercoolings direct measurement of I Spec.volume liquid supercooled liquid glass Zero4 glass-ceramic T g 12 T m Temperature

12 Types of nucleation Homogeneous: spontaneous formation from the melt; any volume element of the undercooled liquid is equally prone to nucleation; Heterogeneous: nuclei form preferentially on a 'foreign' surface: solid impurities, crucible walls, bubbles, seeds, etc.

13 CNT: Critical Nucleus Size ΔG ΔG r = 4 3 πr 3 = 4πr ΔG 2 V ΔG V + 4πr 2 σ + 8πrσ ΔG 2σ = 0, so rcritical= = r r ΔG V * ΔG * critical = 3 16πσ ( ΔG ) V 3 2 = ΔG * W*

14 Work of Formation of a Spherical Nucleus, W* ΔG Work for nucleus formation r * critical nucleus size πr ΔG V W * ΔG 4πr 2 σ Droplet radius () r = πr ΔG + 4πr σ V r

15 CNT. Free Energy metastable stable Kinetic Barrier (ΔG D ) Driving Force (ΔG V ) Atomic position

16 CNT: Expression and main assumptions Homogeneous nucleation of the stable phase Driving force = that of a stress free macroscopic crystal; ΔG(T)= ΔG 0 (T) Interfacial energy = independent of nucleus size (R) and temperature, σ = σ 0 If molecular rearrangements controlled by viscous flow & the SE eq. is valid I D/λ 2 * ΔG D W v0 exp nv exp [m -3.s -1 ] kbt kbt Transport kbt D 3 πλη Thermodynamic W * = K Δ 3 σ 0 2 G V σ σ (R,T) ΔG(T) ΔG(R,T)

17 Let us then test CNT s predicting power

18 Peter James. CNT test I st = 1T K 1 exp η W k T B * W * = K Δ 3 σ 0 2 G V Using experimental I (T), η(t) and ΔG v (T) ln (I.η/T) vs. 1/(T.ΔG v2 ) should give a straight line: Intercept = K 1 Slope = σ 0 (unknown) σ 0 ~ α.δh m P. F. James: Advances in Ceramics 4 (1982)

19 Parameters needed to test CNT Viscosity (T) & I(T)... in the same temperature range using a glass of the same batch/ melting operation! Deltha G (T) measured or calculated (see next slide)

20 Thermodynamic John Hoffman driving force 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 T (K) T (K) Turnbull Hoffman Burgner & Weinberg Turnbull Hoffman Borisova Turnbull Hoffman ΔG ΔG = ΔH m ΔT T m ΔH m ΔTT T 2 m The expressions of Turnbull and Hoffmann bound the experimental ΔG = Comparison of measured Gibbs free energies ΔG and approximations of Turnbull and Hoffman for L 2 S and diopside in wide range of temperatures.

21 Tests of CNT David Turnbull Homogeneous nucleation in supercooled liquid metals : Vonnegut, Turnbull and others: droplet technique for liquid metals. The maximum undercoolings and crystal growth rates were measured and then the nucleation rates were estimated.

22 Liquid metals (1950 s) Homogeneous nucleation rates in liquid mercury. only 2 o C! D. Turnbull, J. Chem. Phys. 20 (1952)

23 Kenneth Kelton Liquid metals (1950 s) Straight lines: Pre-exponential 7 o.m. higher than predicted K. Kelton, Sol. State Phys. 45 (1991)

24 Homogeneous nucleation rate in polyethylene. Polymers (1960 s) Increased to 3 o C! Droplet technique: isothermal nucleation rates of unfractionated linear polyethylene The pre-exponential constant was 12 orders of magnitude larger than the theoretical value F. Gornick, J. D. Hoffman, Ind. Eng. Chem. 58 (1966)

25 Glassy metallic alloys ( s) Fe 40 Ni 40 P 14 B 6. The linear portion with σ 0 gives pre-exponential factor 20 o.m. larger than predicted. R. S. Tiwary, J. C. Claus, M. Vonheimendhal, Mat. Sci. Eng. 55 (1982)

26 Homogeneous Nucleation in Stoichiometric Silicate Glasses Na 2 O 2CaO 3SiO 2 Very few silicate glasses spontaneously display internal homogeneous nucleation (+ surface) Li 2 O 2SiO 2

27 Measurement of nucleation n V rates Fixed temperature number of crystals per unity volume n V Li 2 O.2SiO 2 I [1/m 3 s] τ time

28 Deeply Undercooled Oxide Glasses ( s) Log(I st, m -3 s -1 ) B 2 TS 2 N 2 CS 3 NC2 S 3 BS 2 LS 2 +H 2 O NS LS 2 0,50 0,52 0,54 0,56 0,58 0,60 0,62 Fokin, Kalinina & Filipovich; Neilson & Weinberg; Rowlands, Gonzalez-Oliver, Ito, Zanotto & James; Hishinuma&Uhlmann and others have tested CNT using direct measurements of homogeneous nucleation rates in glasses in wide temperature ranges. T/T m

29 Testing CNT for Oxide Glasses G. F. Neilson, M. C. Weinberg, J. Non-Cryst. Solids 34 (1979) P. F. James, E. G. Rowlands, Phys. Chem. Glasses 20 (1979) C. J. R. Gonzalez-Oliver, P. F. James, J. Non-Cryst. Solids (1980) E. D. Zanotto, P. F. James, J. Non-Cryst. Solids 104 (1988) BS 2 NC 2 S 3 ln(i η/t) vs.(1/δg 2 T) for BS 2. ln(i η/t) vs. (1/ΔG 2 T) for NC 2 S 3.

30 Results for LS2 glass S. Manrich, E. D. Zanotto, Cerâmica 41 (1995) om

31 Results Silicate Glasses BS 2 Varying ΔG V Turnb α ΔC p exp Discrepancy in I max (o. m.) σ = αδh m 3 2 N A V m LS 2 NC 2 S N 2 CS B 2 TS ? 26 -? Reduced surface energy, α, was fit to give the best T dependence.

32 Summary With a constant σ 0, CNT describes the temperature dependence, but not the magnitude of I(T). Possible problems: diffusion mechanism (breakdown of the SE?), size and temperature dependent surface energy, metastable phase formation, effect of elastic stresses, etc?