[PPT] - Web Course Web Course Physical Properties of Glass Physical PowerPoint Presentation

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FS08 Richard K. Brow brow@mst.edu Melt properties-1

Web Course Web Course Physical Properties of Glass Physical Properties of Glass

1. Properties of Glass Melts
1. Properties of Glass Melts
2. Thermal Properties of Glasses
2. Thermal Properties of Glasses

Richard K. Brow Missouri University of Science & Technology Department of Materials Science & Engineering

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Melt and Glass Properties

Viscosity- chapter 9
Surface Tension- chapter 9
Thermal Expansion- chapter 10
Heat Capacity- chapter 11
Thermal Conductivity- chapter 12

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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

utstanding reviews of viscosity, relaxation, etc.
CA Angell, Science, 267, (1995), 1924- concepts
f 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

f viscosity measurements

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Why should we care about melt viscosity?

1. Glass Forming Tendency
a. Nucleation, crystallization, phase separation kinetics
2. Melt Fining
3. Manufacturing Process Control
4. Annealing Schedules/Permanent Stress
5. What else??

η ρ ρ 12 ) ( : Law s Stoke'

2 l b

g d V − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ ⋅ ⋅ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ =

2 3 3

exp 3

v V HO V

G T K a T k N I σ η π

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A d F,V

Newtonian Liquids:

=

= ≡ ε σ η Viscosity AV Fd

Shear stress (σ) Time σ0 Time Strain (ε)

η σ ε =

Viscosity Definitions

Units: (dynes·cm)/(cm2·(cm/s)) = dyne·s/cm2 = Poise or N·s/m2 = Pa·s 1 Pa·s = 10 P 1 P = 1 dPa·s

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Practical Consequences

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Elastic Solid Newtonian Liquid Viscoelastic transition glass forming melting

η(T) for SLS melt

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Important Manufacturing Viscosities

Internal stresses relieved <15 hrs 1013.5 Strain pt (Tsp) Internal stresses relieved <15 min 1012 Annealing pt (Tap) 1011-1012 Glass transition (Tg) Dilatometric: expansion compensated by viscous flow 1010-1011 Deformation temp (Td) No crystallization for T<Tx ~107 Crystallization temp (Tx) Littleton, flow under own weight 106.6 Softening point (TLit) 104 Flow point No crystallization for T>Tl ~104 Liquidus temp (Tl) Forming 102-106 Working range 103 Working pt (Tw) Melting, fining 100.5-101.5 Melting range 101 Melting pt (Tm) Remarks η (Pa·s) Name

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1014.5 1013 107.6 104 log P 1013.5 Strain Pt 1012 Annealing Pt 106.6 Littleton Softening Pt 103 Working Pt log Pa·s

Defined Viscosities Working range Annealing Range

η(T) for SLS melt

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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

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Corning Codes: 8363: High PbO radiation shield 0010: Pb-silicate tube 7070: Borosilicate 0080: SLS lamp glass 7740: Pyrex 1720: Alkaline-earth boro- aluminosilicate

From Seward and Varshneya (2001) Soft glasses Hard glasses Short glass Long glass

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Measurement of Viscosity

Range Method Viscosity Values Melting Falling Sphere/Bubble Rise η<104 Pa-s Margules Rotating Cylinder η<106 Pa-s Parallel Plate 105 Pa-s<η< 109 Pa-s Softening Penetration Viscometer 105 Pa-s<η< 109 Pa-s and Fiber Elongation 105 Pa-s<η< 1015.5 Pa-s Annealing Beam Bending 107 Pa-s<η< 1012 Pa-s Disappearance of Stress 1011 Pa-s<η< 1014 Pa-s

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Rotating Spindle: 10-106 Pa·s

(ASTM C965-96)

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Τ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ = ω π η

2 2

1 1 4 1 R r L

r R L

Τ = torque ω = rotational velocity

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2/25/03

Littleton Softening Point: 106.6 Pa·s

(fiber elongation- ASTM C338-93)

( )

dt dL A F L / 3 ⋅ ⋅ = η

Applied Stress= F/A Elongation rate=dL/dt Balance of gravitational force (density) and surface tension

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2/25/03

Annealing/Strain Points: 1012, 1013.5 Pa·s

(fiber elongation: ASTM-C336-69) dL/dt = 2.5x10-6 l/d2 at 1012 Pa·s (anneal pt) Strain pt elongation rate is 0.0316 x annealing pt elongation rate (1.5 log units)

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2/25/03

Beam Bending: 108-1013 Pa-s

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⋅ ⋅ + ⋅ ⋅ = 6 . 1 4 . 2

3

ρ η L A M V I L g

c

V=deflection rate

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The temperature dependence of viscosity The temperature dependence of viscosity

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hole

σyx

x y

vAx vBx vCx

layer A B C Consider the ‘activated’ motion of a hole under the action of a shearing stress velocity gradient

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σyx

ΔG0

2

a yx

V σ 2

a yx

V σ

Potential energy Jump frequency (υ0), no shear:

Same l-r as r-l
Depends on barrier energy and

probability of finding suitable hole as neighbor (Ph) ΔG0

h B B

P T k G h T k ⋅ Δ − = ] / exp[ ] / [ υ

Applied shear biases potential energy function

Va is atom volume
Forward jump frequency (υ+) exceeds

reverse (υ-)

] 2 / exp[ ] / ) 2 ( exp[ ] / [ ] 2 / exp[ ] / ) 2 ( exp[ ] / [ T k V P T k V G h T k T k V P T k V G h T k

B a yx h B a yx B B a yx h B a yx B

σ υ υ σ υ σ υ υ σ υ − = ⋅ + Δ − = = ⋅ − Δ − =

− − + +

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σyx

2

a yx

V σ 2

a yx

V σ

ΔG0 The net ‘forward velocity’ is

( ) ( ) ( ) ( )

[ ] [

][ ]( )

1

/ exp( / / / , / / ) 2 / sinh( 2 / / /

− − + − + − +

Δ = = ∂ ∂ = ≅ = ∂ ∂ − ≈ − = ∂ ∂ − = −

h B a B a yx yx xy B a yx B a yx Ax Bx

P T k G V h T k V y v e is rate strain shear T k V T k V y v y x y v x v v σ υ σ η σ υ σ υ υ υ δ δ υ υ δ υ υ &

Consider the energy required to create a hole (ΔEh), then Ph can be described by

[ ] [ ]

( )

[ ]

( )

RT H T k E G V h T k E P

B h a B h h

/ exp / exp / / exp

η

η η η Δ = Δ + Δ = Δ − =

substituting Ph into the viscosity equation, Simplifying as an Arrhenius equation: Potential energy

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From P. Richet and Y. Bottinga, in Reviews in Mineralogy, Vol. 32, (1995), p. 67-93

2000°C 1000°C 500°C 1500°C

Most glass Most glass-

forming liquids are non

forming liquids are non-

Arrhenius

Arrhenius

SiO2 Ab An Di NTS2 NS3 NS2 Ab=albite An=anorthite Di=diopside

log T T B A − + = η

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From C. A. Angell, Science, 267, (1995), 1924.

Melt Melt Fragility Fragility

Fragile Strong Tg/T

Log (viscosity in poise)

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Why the non-Arrhenius temperature-dependence?

1. Energy for hole formation (ΔEh) is low at high temperatures

ΔHη is greater at lower temperatures

2. Free-volume increases with temperature 3. Configurational entropy increases with temperature (Adam-Gibbs description)

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What accounts for viscous flow in a silicate melt? What has to happen for flow to

ccur?

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What happens at the molecular What happens at the molecular-

level that affects viscosity?

level that affects viscosity?

At the short timescales, ‘melt structures’ are similar to ‘glass structures’….

Raman spectroscopy- probing

structure on timescales 10-12-10-14 s

Si-O stretching/bending modes remain

dominate from room temperature into the melt

Some evidence for some melt

speciation reactions: 2Q3 ↔ Q2 + Q4 Q2

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NMR provides structural information about glasses NMR provides structural information about glasses

Q4 Q3 Q2 Q1

Q4 Q3 Q2 Q1 Q0

xLi2O (1-x)SiO2

ni

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Chemical exchange in melts: silicate species and viscous flow

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

Q3-Q4 exchange (Si-O bond rupture) is fast compared to the experimental time frame. Experimental Simulated Spectra 697°C 774°C 800°C 847°C 997°C 2 kHz 10 kHz 25 kHz 50 kHz 500 kHz

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NMR exchange and viscosity timescales coincide NMR exchange and viscosity timescales coincide

1. Maxwell relationship: η = τshear · G∞
2. Assume that τshear ≈ τex
3. Calculate diffusivity (D) from τex : D =d2/6τ, d is ‘jump distance’
4. Calculate viscosity from η = kBT/(dD)

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Stebbins model for viscous flow Stebbins model for viscous flow

Si-O bond-rupture through Q3-Q4 site exchange

Conversion of one bridging
xygen to a nonbridging oxygen
‘Diffusion’ of modifying cation

from one silicate unit to another

Creation of an SiO5 transitional

site? Potential energy ? initial final initial final transitional transitional

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NMR evidence for NMR evidence for transitional sites transitional sites ‘ ‘frozen into frozen into’ ’ quenched quenched glass structures glass structures

Na2Si4O9 Cs2Si4O9 Fast quench Slow quench

Q3/Q4 peak

SiO5

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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]

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Na-K-Zn-Al-silicate (Wu, JNCS, 41 381, 1980)

Increasing the modifier Increasing the modifier content reduces viscosity content reduces viscosity

Water is a particularly effective

flux

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The effect of water on Tg (η≈1012 Pa·s) of silicate glasses

Deubener, et al., JNCS 330, 268 (2003).

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The effects of modifier The effects of modifier content on melt viscosity content on melt viscosity

H. Rawson, Properties and Applications of Glass, Elsevier, 1980.

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Log η (Poise) 8 10 12 16

Isokom temperatures for mixed alkali melts Isokom temperatures for mixed alkali melts

Nemilov (1969)

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Viscosity of alkali alumino- silicate melts is greatest when Al/Na≈1- fully cross-linked networks….

Toplis et al., Geochim.

Cosmochim. Acta.

61[13] 2605 (1995)

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Alkali borate melt viscosity

2BØ3 + Na2O → 2(BØ4

Na+)

Note the loss of the ‘borate anomaly’ effect at high temperatures (low viscosity)

2(BØ4

·Na+) + Na2O → 2(BØO2

2-·2Na+)

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38.6Li2O·61.4B2O3 glass and melt

Cormier et al., JACerS, 89 13 (2006)

Raman spectra indicate that the BØ2O- triangles replace BØ4

tetrahedra in the melt

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Cormier et al., JACerS, 89 13 (2006)

Raman spectra indicate that the BØ2O- triangles replace BØ4

tetrahedra in the melt

BØ4

Li+ ↔ BØ2O-Li+

Note that B-O bonds are broken, and that such configurational changes will contribute to changes in heat capacity….

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Effects of composition on viscosity

+
+

+

Low

Temp Softer Shorter Softer Harder Shorter Softer

+
Alkali oxide

Alkaline earths PbO Al2O3 B2O3 OH-/F- High Temp Glass Effect on Viscosity Component

Modifications to soda-lime silicate melt viscosity, after Beerkens, 1997.

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Viscosity dependence on temperature and composition

Vogel-Fulcher-Tamman (VFT) Equation
Lakatos Method*: empirical additivity factors

log T T B A − + = η

∑ ∑ ∑

⋅ + = ⋅ + = ⋅ + − =

i i i i i i

p t T p b B p a A 1 . 198 4 . 5736 4550 . 2

For S-L-S melts, T (°C) and η (Pa·s), pi (mole fraction

xide per mole SiO2)

*T. Lakatos, et al., Glass Technology, 13 88 (1972)

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25.07
321.0
384.0

+544.3 +521.4 +294.4

275.5
6039.7
1439.6

+6285.3

3919.3

+7272.1 +2253.4

5880.0

+1.4788

0.8350
5.4936
1.6030
15.880

+1.5183 +1.3058 Na2O K2O MgO CaO B2O3 Al2O3 PbO ti bi ai Lakatos additivity parameters (after Beerkens, 1997) Valid for the log(viscosity) range 1-12 Pa·s

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

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Non Non-

Newtonian Viscosity

Newtonian Viscosity

Yue & Brückner

Glastech. Ber (1996)

Shear thinning- decreasing effective viscosity with increasing deformation rates

fiber drawing
press-and-blow

Greater problem at higher temperatures

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[ ]

∞

+ = σ η η η / ) ( 1 / 1 /

xy

e &

Non Non-

Newtonian Viscosity

Newtonian Viscosity

η0 is Newtonian viscosity σ∞ is the cohesive shear strength

Simmons and Simmons, Cer Bull 68[11] 1949 (1989)

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Cohesive strength increases with viscosity 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)

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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

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Fibers heated below Tx
Stress in ‘bent’ regions

reduces ‘effective’ viscosity

Examine differences in

crystallization behavior

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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)

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Trans. Indian Inst. Met. 60[2] 143 (2007)

Normalized acceleration due to gravity Wall shear stress (Pa) Maximum strain rate (s-1) Calculated for LS2 melts at 1400°C and a 5°C temperature gradient

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Normalized acceleration due to gravity

Shear-thinning behavior is reduced when gravitational effects are reduced.

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From J. H. Simmons, in Experimental Techniques

f Glass Science, (1993), p. 383-432.

Phase separation affects viscosity

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From H. E. Hagy, in Introduction to Glass Science, (1972), p. 343- 371

Crystallization affects viscosity

Example: crystallizable

sealing glass

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Viscosity Summary Viscosity Summary

Viscosity is the most important melt property

– Critical for processing, from melting through annealing

Compositional dependence can be understood in terms
f 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

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Glass formation is Glass formation is ‘ ‘crystallization avoidance crystallization avoidance’ ’

( ) ( )

4 / 3 2

3 . exp 1 212 . exp 77 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ − − ⋅ − ⋅ ≈

m

m m c

RT H B T . at AT T η

Kinetic barrier Nucleation barrier Free energy driving force Reduce critical cooling rate to improve glass formation

Lower Tm
Increase η at Tm

If Tg (η=1013 P) is near Tm, then η(Tm) will be high Glass formation expected when Tg/Tm>2/3

0.07 1535 Fe 0.03 420 Zn 0.02 P 613 LiCl 107 P 1710 SiO2 107 P 1150 GeO2 105 P 460 B2O3 >106 P 540 BeF2 η(Tm) Tm(°C)

Poor glass formers Good glass formers

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Eutectic compositions are good glass Eutectic compositions are good glass-

formers

formers

W. Vogel, Chemistry of Glass, 1985

Tg(°C) Mole% Na

2O

From Dingwell in Rev. Mineral. 32 (1995)

Tg/Tliq is a maximum (~0.7) at the eutectic

G=U-1 ΔTg~30°C ΔTliq~800°C