Web Course Physical Properties of Glass 1. Properties of Glass Melts 2. Thermal Properties of Glasses

Transcription

1 Web Course Physical Properties of Glass 1. Properties of Glass Melts 2. Thermal Properties of Glasses Missouri University of Science & Technology Department of Materials Science & Engineering Melt properties-1

2 Melt and Glass Properties Viscosity- chapter 9 Surface Tension- chapter 9 Thermal Expansion- chapter 10 Heat Capacity- chapter 11 Thermal Conductivity- chapter 12 Melt properties-2

3 Supplementary References on Viscosity Structure, Dynamics and Properties of Silicate Melts, Reviews in Mineralogy, Vol. 32 (1995), ed. JF Stebbins, PF McMillan and DB Dingwell (Mineralogical Society of America)- several outstanding reviews of viscosity, relaxation, etc. CA Angell, Science, 267, (1995), concepts of melt fragility, configurational entropy, etc. JH Simmons and C Simmons, Cer Bull 68[11] 1949 (1989)- Non-Newtonian behavior HE Hagy in Introduction to Glass Science, ed. LD Pye, et al Plenum Press (1972)- nice review of viscosity measurements Melt properties-3

4 Why should we care about melt viscosity? 1. Glass Forming Tendency a. Nucleation, crystallization, phase separation kinetics I HO V 2. Melt Fining Stoke's Law : 3. Manufacturing Process Control N 3 k T K σ exp 3 3π a0 η T ΔGv 0 = V 2 V = d 2 g( ρb ρl ) 12η 4. Annealing Schedules/Permanent Stress 5. What else?? Melt properties-4

5 Viscosity Definitions d A F,V σ Viscosity η = Fd = 0 AV Units: ε (dynes cm)/(cm 2 (cm/s)) = dyne s/cm 2 = Poise or N s/m 2 = Pa s 1 Pa s = 10 P 1 P = 1 dpa s Shear stress (σ) σ 0 Strain (ε) Newtonian Liquids: Time σ = ε 0 η Time Melt properties-5

6 Practical Consequences Melt properties-6

7 Elastic Solid Newtonian Liquid Viscoelastic transition glass forming melting η(t) for SLS melt Melt properties-7

8 Melt properties-8

9 Important Manufacturing Viscosities Name Melting pt (T m ) Melting range Working pt (T w ) Working range Liquidus temp (T l ) Flow point Softening point (T Lit ) Crystallization temp (T x ) Deformation temp (T d ) Glass transition (T g ) Annealing pt (T ap ) Strain pt (T sp ) η (Pa s) ~ ~ Remarks Melting, fining Forming No crystallization for T>T l Littleton, flow under own weight No crystallization for T<T x Dilatometric: expansion compensated by viscous flow Internal stresses relieved <15 min Internal stresses relieved <15 hrs Melt properties-9

10 Defined Viscosities log Pa s log P Working Pt Littleton Softening Pt Annealing Pt Annealing Range Strain Pt Working range η(t) for SLS melt Melt properties-10

11 Viscosity Classifications Working Range: Temperatures (ΔT) between working point and softening point Long glasses: large ΔT (shallow η(t) curves) Short glasses: small ΔT (steep η(t) curves) Hard glasses: Working range at greater temperatures than for S-L-S glass Borosilicates, aluminosilicates, oxynitrides, silica, etc. Sometimes defined as CTE<6x10-6 / C Soft glasses: Working range at lower temperatures than for S-L-S glass Soda-lime silicate, Pb-silicates Sometimes defined as CTE>6x10-6 / C Melt properties-11

12 From Seward and Varshneya (2001) Soft glasses Short glass Hard glasses Long glass Corning Codes: 8363: High PbO radiation shield 0010: Pb-silicate tube 7070: Borosilicate 0080: SLS lamp glass 7740: Pyrex 1720: Alkaline-earth boroaluminosilicate Melt properties-12

13 Measurement of Viscosity Range Method Viscosity Values Melting Falling Sphere/Bubble Rise η<10 4 Pa-s Margules Rotating Cylinder η<10 6 Pa-s Parallel Plate 10 5 Pa-s<η< 10 9 Pa-s Softening Penetration Viscometer 10 5 Pa-s<η< 10 9 Pa-s and Fiber Elongation 10 5 Pa-s<η< Pa-s Annealing Beam Bending 10 7 Pa-s<η< Pa-s Disappearance of Stress Pa-s<η< Pa-s Melt properties-13

14 Rotating Spindle: Pa s (ASTM C965-96) η = 2 2 4π L r R Τ ω r R L Τ = torque ω = rotational velocity Melt properties-14

15 Littleton Softening Point: Pa s (fiber elongation- ASTM C338-93) η = L F 3A ( dl / dt) Applied Stress= F/A Elongation rate=dl/dt Balance of gravitational force (density) and surface tension 2/25/03 Melt properties-15

16 Annealing/Strain Points: 10 12, Pa s (fiber elongation: ASTM-C336-69) dl/dt = 2.5x10-6 l/d 2 at Pa s (anneal pt) Strain pt elongation rate is x annealing pt elongation rate (1.5 log units) 2/25/03 Melt properties-16

17 Beam Bending: Pa-s η = 3 g L 2.4I V c M + A L ρ 1.6 V=deflection rate 2/25/03 Melt properties-17

18 Melt properties-18

19 The temperature dependence of viscosity Melt properties-19

20 layer A σ yx velocity gradient v Ax y B C hole v Bx v Cx x Consider the activated motion of a hole under the action of a shearing stress Melt properties-20

21 Potential energy σ yx Va σ yx 2 ΔG V 0 a σ yx 2 ΔG 0 Jump frequency (υ 0 ), no shear: Same l-r as r-l Depends on barrier energy and probability of finding suitable hole as neighbor (P h ) υ 0 = / k T ] P [ kbt / h]exp[ ΔG0 B h Applied shear biases potential energy function V a is atom volume Forward jump frequency (υ + ) exceeds reverse (υ - ) σ yxv υ+ = [ kbt / h]exp[ ( ΔG0 2 υ = υ exp[ σ V / 2k T ] yx σ yxv υ = [ kbt / h]exp[ ( ΔG0 + 2 υ = υ exp[ σ V / 2k T ] yx a a B B a a ) / k ) / k B B T ] P h T ] P h Melt properties-21

22 σ yx The net forward velocity is Potential energy ΔG 0 σ σ yx yx Va 2 Va 2 ( vbx vax ) = ( υ+ υ ) δx v / y = ( υ υ ) δx / δy ( υ υ ) v / y η = σ yx / [ υ σ V / k T ] = [ h / V ][ exp( ΔG / k T ]( P ) = 2υ sinh( σ V yx a yx shear strain rate is e& B xy a / 2k B + = v / y, a T ) υ σ V 0 yx a 0 / k B B T h Consider the energy required to create a hole (ΔE h ), then P h can be described by P h = exp [ ΔE / k T ] h B substituting P h into the viscosity equation, η = [ h / V ][ exp( ΔG + ΔE )/ k T ] a 0 h B Simplifying as an Arrhenius equation: η = η exp 0 ( ΔH / RT ) η Melt properties-22

23 Most glass-forming liquids are non-arrhenius 2000 C 1500 C 1000 C 500 C SiO 2 NTS 2 NS 3 NS 2 An Ab Di logη = Ab=albite An=anorthite Di=diopside A + T B T 0 From P. Richet and Y. Bottinga, in Reviews in Mineralogy, Vol. 32, (1995), p Melt properties-23

24 Melt Fragility Log (viscosity in poise) Strong Fragile From C. A. Angell, Science, 267, (1995), T g /T Melt properties-24

25 Why the non-arrhenius temperature-dependence? 1. Energy for hole formation (ΔE h ) is low at high temperatures ΔH η is greater at lower temperatures 2. Free-volume increases with temperature 3. Configurational entropy increases with temperature (Adam-Gibbs description) Melt properties-25

26 What accounts for viscous flow in a silicate melt? What has to happen for flow to occur? Melt properties-26

27 What happens at the molecular-level level that affects viscosity? Q 2 At the short timescales, melt structures are similar to glass structures. Raman spectroscopy- probing structure on timescales s Si-O stretching/bending modes remain dominate from room temperature into the melt Some evidence for some melt speciation reactions: 2Q 3 Q 2 + Q 4 Melt properties-27

28 NMR provides structural information about glasses Q 1 Q 2 Q 4 Q 3 Q 2 Q 1 Q 0 Q 3 Q 4 n i xli 2 O (1-x)SiO 2 Melt properties-28

29 Chemical exchange in melts: silicate species and viscous flow Experimental Simulated Spectra 697 C 2 khz NMR exchange frequencies (khz range) are comparable to the timescales for viscous flow in silicate melts The lifetimes for Si-O bonds in a melt can be determined and compared with timescales associated with viscous flow At high temperatures, the Q 3 -Q 4 exchange (Si-O bond rupture) is fast compared to the experimental time frame. 774 C 800 C 847 C 997 C 10 khz 25 khz 50 khz 500 khz Melt properties-29

30 NMR exchange and viscosity timescales coincide 1. Maxwell relationship: η = τ shear G 2. Assume that τ shear τ ex 3. Calculate diffusivity (D) from τ ex : D =d 2 /6τ, d is jump distance 4. Calculate viscosity from η = k B T/(dD) Melt properties-30

31 Stebbins model for viscous flow Si-O bond-rupture through Q 3 -Q 4 site exchange Conversion of one bridging oxygen to a nonbridging oxygen Diffusion of modifying cation from one silicate unit to another initial Creation of an SiO 5 transitional site? transitional? transitional Potential energy initial final final Melt properties-31

32 NMR evidence for transitional sites frozen into quenched glass structures Q 3 /Q 4 peak SiO 5 Na 2 Si 4 O 9 Fast quench Slow quench Cs 2 Si 4 O 9 Melt properties-32

33 Effects of composition on viscosity Viscosity is determined by Molecular attractive forces, especially associated with glass-forming oxides Si-O vs. Ge-O Number of non-bridging oxygens in structure Alkali oxide additions reduce viscosity Water (-OH) and fluorine reduce viscosity Coordination number of the cation B[3] vs B[4] Melt properties-33

34 Melt properties-34

35 Reminder: Effect of Modifier Additions on Silicate Glass Networks O O Si O Si O +R 2 O O O O O O Si O -- O Si O O R + R + O O B0 +R 2 O 2NBO 2Q 4 + R 2 O 2Q 3 Melt properties-35

36 Increasing the modifier content reduces viscosity Water is a particularly effective flux Na-K-Zn-Al-silicate (Wu, JNCS, , 1980) Melt properties-36

37 The effect of water on T g (η Pa s) of silicate glasses Deubener, et al., JNCS 330, 268 (2003). Melt properties-37

38 The effects of modifier content on melt viscosity H. Rawson, Properties and Applications of Glass, Elsevier, Melt properties-38

39 Isokom temperatures for mixed alkali melts Log η (Poise) Nemilov (1969) Melt properties-39

40 Reminder: Effect of Alumina Additions on Silicate Glass Networks O O Si O -- O Si O O R + R + O O O O Si O Al O Si O O 1/2Al 2 O 3 for 1/2R 2 O O O R + O O Melt properties-40

41 Viscosity of alkali aluminosilicate melts is greatest when Al/Na 1- fully cross-linked networks. Toplis et al., Geochim. Cosmochim. Acta. 61[13] 2605 (1995) Melt properties-41

42 Reminder: Effect of Alkali Addition on Borate Glass Networks O O B O [O]/[B]=1.5 +1/2R 2 O O O R + B O O +1/2R 2 O [O]/[B]=2.0 R +- O R +- O B O - R + +1/2R 2 O R +- O R +- O B O [O]/[B]=3.0 [O]/[B]=2.5 Melt properties-42

43 Alkali borate melt viscosity 2BØ 3 + Na 2 O 2(BØ 4- Na + ) 2(BØ 4- Na + ) + Na 2 O 2(BØO 2 2-2Na + ) Note the loss of the borate anomaly effect at high temperatures (low viscosity) Melt properties-43

44 38.6Li 2 O 61.4B 2 O 3 glass and melt Raman spectra indicate that the BØ 2 O - triangles replace BØ 4 - tetrahedra in the melt Cormier et al., JACerS, (2006) Melt properties-44

45 Raman spectra indicate that the BØ 2 O - triangles replace BØ 4- tetrahedra in the melt BØ 4- Li + BØ 2 O - Li + Note that B-O bonds are broken, and that such configurational changes will contribute to changes in heat capacity. Cormier et al., JACerS, (2006) Melt properties-45

46 Effects of composition on viscosity Component Alkali oxide Alkaline earths PbO Al 2 O 3 B 2 O 3 OH - /F - Effect on Viscosity High Low Temp Temp Glass Softer Shorter Softer Harder Shorter Softer Modifications to soda-lime silicate melt viscosity, after Beerkens, Melt properties-46

47 Viscosity dependence on temperature and composition Vogel-Fulcher-Tamman (VFT) Equation logη = A + T B T Lakatos Method*: empirical additivity factors A = B T 0 = = t *T. Lakatos, et al., Glass Technology, (1972) i b i a i p i p i p i 0 For S-L-S melts, T ( C) and η (Pa s), p i (mole fraction oxide per mole SiO 2 ) Melt properties-47

48 Lakatos additivity parameters (after Beerkens, 1997) a i b i t i Na 2 O K 2 O MgO CaO B 2 O 3 Al 2 O 3 PbO Valid for the log(viscosity) range 1-12 Pa s Melt properties-48

49 Not all liquids exhibit Newtonian viscosity behavior Bingham Plastic Shear Stress (σ) Pseudoplastic (decreasing η) Newtonian (constant η) Dilatant (increasing η) Shear Rate Melt properties-49

50 Non-Newtonian Newtonian Viscosity Shear thinningdecreasing effective viscosity with increasing deformation rates fiber drawing press-and-blow Greater problem at higher temperatures Yue & Brückner Glastech. Ber (1996) Melt properties-50

51 Non-Newtonian Newtonian Viscosity Simmons and Simmons, Cer Bull 68[11] 1949 (1989) [ 1+ ( e& ) η ] η η = 1/ / σ / 0 xy 0 η 0 is Newtonian viscosity σ is the cohesive shear strength Melt properties-51

52 Cohesive strength increases with viscosity Viscosity becomes nonlinear at high shearing rates Shear stress builds up if stress relaxation rate is sufficiently low If shear stress>σ, then liquid fracture can occur Simmons and Simmons, Cer Bull 68[11] 1949 (1989) Melt properties-52

53 Consequences of Non-Newtonian Viscosity High-speed glass processing Fiber attenuation Container processing Source for glass inhomogeneities Induced phase separation or crystallization in high shear regions Melt properties-53

54 Fibers heated below T x Stress in bent regions reduces effective viscosity Examine differences in crystallization behavior Melt properties-54

55 Melt properties-55

56 Another example Melts prepared in micro-gravity have greater glass-forming tendencies than melts on earth at comparable quench rates Hypothesis*: gravity-driven fluid-flow increases overall strain rate within melt Reduced local viscosity through shear thinning Increased local crystallization rates *CS Ray et al, Trans. Indian Inst. Met. 60[2] 143 (2007) Melt properties-56

57 Calculated for LS 2 melts at 1400 C and a 5 C temperature gradient Wall shear stress (Pa) Maximum strain rate (s -1 ) Normalized acceleration due to gravity Trans. Indian Inst. Met. 60[2] 143 (2007) Melt properties-57

58 Normalized acceleration due to gravity Shear-thinning behavior is reduced when gravitational effects are reduced. Melt properties-58

59 From J. H. Simmons, in Experimental Techniques of Glass Science, (1993), p Phase separation affects viscosity Melt properties-59

60 Crystallization affects viscosity Example: crystallizable sealing glass From H. E. Hagy, in Introduction to Glass Science, (1972), p Melt properties-60

61 Viscosity Summary Viscosity is the most important melt property Critical for processing, from melting through annealing Compositional dependence can be understood in terms of melt/glass structure Stronger networks = greater viscosity Fraction of NBO s on silicate tetrahedra Aluminosilicate networks Borate anomaly - tetrahedral sites Viscosity is sensitive to changes in melt structure Temperature dependence is non-arrhenian VFT equation is a useful empirical description Fragile/strong classification can be related to configurational changes Shear-thinning has processing consequences Melt properties-61

62 Glass formation is crystallization avoidance c T η AT 2 m ( at 0. 77T ) m exp ( 0.212B) 1 exp 0.3ΔH RT m 3/ 4 Kinetic Nucleation barrier barrier Reduce critical cooling rate to improve glass formation Lower T m Increase η at T m If T g (η=10 13 P) is near T m, then η(t m ) will be high Free energy driving force T m ( C) η(t m ) BeF >10 6 P B 2 O 3 GeO 2 SiO 2 LiCl Glass formation expected when T g /T m >2/3 Fe Zn P 10 7 P 10 7 P 0.02 P Good glass formers Poor glass formers Melt properties-62

63 Eutectic compositions are good glass-formers From Dingwell in Rev. Mineral. 32 (1995) G=U -1 W. Vogel, Chemistry of Glass, 1985 ΔT g ~30 C T g ( C) Mole% Na 2 O ΔT liq ~800 C T g /T liq is a maximum (~0.7) at the eutectic Melt properties-63