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 FS08 Richard K. Brow brow@mst.edu Melt properties-1
Melt and Glass Properties • Viscosity- chapter 9 • Surface Tension- chapter 9 • Thermal Expansion- chapter 10 • Heat Capacity- chapter 11 • Thermal Conductivity- chapter 12 FS08 Richard K. Brow brow@mst.edu Melt properties-2
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), 1924- 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 FS08 Richard K. Brow brow@mst.edu Melt properties-3
Why should we care about melt viscosity? 1. Glass Forming Tendency a. Nucleation, crystallization, phase separation kinetics ⎛ ⎞ ⎡ ⎤ ⋅ − ⋅ σ 3 k T K ⎜ ⎟ = 0 exp HO ⎢ ⎥ I N ⎜ ⎟ π ⋅ 3 ⋅ η ⋅ Δ 2 V V 3 ⎝ ⎠ ⎣ ⎦ a T G 0 v 2. Melt Fining ρ − ρ 2 ( ) d g = Stoke' s Law : b l V η 12 3. Manufacturing Process Control 4. Annealing Schedules/Permanent Stress 5. What else?? FS08 Richard K. Brow brow@mst.edu Melt properties-4
Viscosity Definitions Newtonian Liquids: Shear stress ( σ ) A F,V σ 0 d Time σ ≡ η = = Fd Viscosity 0 • AV ε Strain ( ε ) Units: (dynes·cm)/(cm 2 ·(cm/s)) • σ = dyne·s/cm 2 = Poise or ε = 0 η N·s/m 2 = Pa·s 1 Pa·s = 10 P Time 1 P = 1 dPa·s FS08 Richard K. Brow brow@mst.edu Melt properties-5
Practical Consequences FS08 Richard K. Brow brow@mst.edu Melt properties-6
Elastic Solid Newtonian Liquid Viscoelastic transition glass forming melting η (T) for SLS melt FS08 Richard K. Brow brow@mst.edu Melt properties-7
FS08 Richard K. Brow brow@mst.edu Melt properties-8
Important Manufacturing Viscosities η (Pa·s) Name Remarks Melting pt (T m ) 10 1 Melting range 10 0.5 -10 1.5 Melting, fining Working pt (T w ) 10 3 Working range 10 2 -10 6 Forming Liquidus temp (T l ) ~10 4 No crystallization for T>T l Flow point 10 4 Softening point (T Lit ) 10 6.6 Littleton, flow under own weight Crystallization temp (T x ) ~10 7 No crystallization for T<T x Deformation temp (T d ) 10 10 -10 11 Dilatometric: expansion compensated by viscous flow Glass transition (T g ) 10 11 -10 12 Annealing pt (T ap ) 10 12 Internal stresses relieved <15 min Strain pt (T sp ) 10 13.5 Internal stresses relieved <15 hrs FS08 Richard K. Brow brow@mst.edu Melt properties-9
Defined Viscosities log Pa·s log P Working Pt 10 3 10 4 Littleton 10 6.6 10 7.6 Softening Pt Annealing Pt 10 12 10 13 Strain Pt 10 13.5 10 14.5 Annealing Range Working range η (T) for SLS melt FS08 Richard K. Brow brow@mst.edu Melt properties-10
Viscosity Classifications • Working Range: Temperatures (Δ T ) between ‘working point’ and ‘softening point’ – Long glasses : large Δ T (shallow η (T) curves) – Short glasses : small Δ T (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 FS08 Richard K. Brow brow@mst.edu Melt properties-11
From Seward and Varshneya (2001) Soft glasses Hard glasses Corning Codes: 8363: High PbO radiation Long glass shield Short 0010: Pb-silicate tube glass 7070: Borosilicate 0080: SLS lamp glass 7740: Pyrex 1720: Alkaline-earth boro- aluminosilicate FS08 Richard K. Brow brow@mst.edu Melt properties-12
Measurement of Viscosity Range Method Viscosity Values η <10 4 Pa-s Melting Falling Sphere/Bubble Rise η <10 6 Pa-s Margules Rotating Cylinder 10 5 Pa-s< η < 10 9 Pa-s Parallel Plate 10 5 Pa-s< η < 10 9 Pa-s Softening Penetration Viscometer 10 5 Pa-s< η < 10 15.5 Pa-s and Fiber Elongation 10 7 Pa-s< η < 10 12 Pa-s Annealing Beam Bending 10 11 Pa-s< η < 10 14 Pa-s Disappearance of Stress FS08 Richard K. Brow brow@mst.edu Melt properties-13
Rotating Spindle: 10-10 6 Pa·s (ASTM C965-96) ⎛ Τ ⎛ ⎞ ⎞ 1 1 1 η = − ⎜ ⎟ ⎜ ⎟ π ⋅ ω 2 2 4 ⎝ ⎠ ⎝ ⎠ L r R Τ = torque ω = rotational velocity L r R FS08 Richard K. Brow brow@mst.edu Melt properties-14
Littleton Softening Point: 10 6.6 Pa·s (fiber elongation- ASTM C338-93) ⋅ L F Applied Stress= F/A η = ( ) 3 ⋅ / Elongation rate=dL/dt A dL dt Balance of gravitational force (density) and surface tension FS08 Richard K. Brow 2/25/03 brow@mst.edu Melt properties-15
Annealing/Strain Points: 10 12 , 10 13.5 Pa·s (fiber elongation: ASTM-C336-69 ) dL/dt = 2.5x10 -6 l/d 2 at 10 12 Pa·s (anneal pt) Strain pt elongation rate is 0.0316 x annealing pt elongation rate (1.5 log units) FS08 Richard K. Brow 2/25/03 brow@mst.edu Melt properties-16
Beam Bending: 10 8- 10 13 Pa-s ⋅ + ⋅ ⋅ ρ 3 ⎛ ⎞ g L M A L η = ⎜ ⎟ ⋅ 2 . 4 ⎝ 1 . 6 ⎠ I V c V=deflection rate FS08 Richard K. Brow 2/25/03 brow@mst.edu Melt properties-17
FS08 Richard K. Brow brow@mst.edu Melt properties-18
The temperature dependence of viscosity The temperature dependence of viscosity FS08 Richard K. Brow brow@mst.edu Melt properties-19
σ yx velocity layer gradient A v Ax B v Bx hole y C v Cx x Consider the ‘activated’ motion of a hole under the action of a shearing stress FS08 Richard K. Brow brow@mst.edu Melt properties-20
σ yx V σ a yx 2 Potential energy Δ G 0 V σ a yx 2 Δ G 0 Applied shear biases potential energy function Jump frequency (υ 0 ), no shear: • V a is atom volume • Same l-r as r-l • Forward jump frequency ( υ + ) exceeds • Depends on barrier energy and reverse ( υ - ) probability of finding suitable hole σ V as neighbor (P h ) υ = − Δ − ⋅ [ / ] exp[ ( yx a ) / ] k T h G k T P + 0 B B h 2 υ = − Δ ⋅ [ / ] exp[ / ] k T h G k T P 0 0 υ = υ σ B B h exp[ / 2 ] V k T + 0 yx a B σ V υ = − Δ + ⋅ yx a [ / ] exp[ ( ) / ] k T h G k T P − 0 B B h 2 υ = υ − σ exp[ / 2 ] V k T − 0 yx a B FS08 Richard K. Brow brow@mst.edu Melt properties-21
σ yx The net ‘forward velocity’ is ( ) ( ) V σ − = υ − υ δ a v v x + − yx 2 Bx Ax ( ) ( ) Potential energy ∂ ∂ = υ − υ δ δ ≈ υ − υ / / V v y x y σ + − + − a yx 2 ∂ ∂ = υ σ ≅ υ σ / 2 sinh( / 2 ) / Δ G 0 v y V k T V k T 0 0 yx a B yx a B = ∂ ∂ / , & shear strain rate is e v y xy [ ] [ ][ ] ( ) − 1 η = σ υ σ = Δ / / / exp( / V k T h V G k T P 0 0 yx yx a B a B h Consider the energy required to create a hole ( Δ E h ), then P h can be described by [ ] = − Δ exp / P E k T h h B substituting P h into the viscosity equation, [ ] [ ] ( ) η = Δ + Δ / exp / h V G E k T 0 a h B Simplifying as an Arrhenius equation: ( ) η = η Δ exp / H RT η 0 FS08 Richard K. Brow brow@mst.edu Melt properties-22
Most glass- -forming liquids are non forming liquids are non- -Arrhenius Arrhenius Most glass 2000°C 1500°C 1000°C 500°C SiO 2 NS 3 NTS 2 NS 2 Ab=albite An=anorthite Di=diopside Ab B An η = + log A − T T 0 Di From P. Richet and Y. Bottinga, in Reviews in Mineralogy , Vol. 32, (1995), p. 67-93 FS08 Richard K. Brow brow@mst.edu Melt properties-23
Melt Melt Fragility Fragility Log (viscosity in poise) Strong Fragile T g /T From C. A. Angell, Science , 267 , (1995), 1924. FS08 Richard K. Brow brow@mst.edu Melt properties-24
Why the non-Arrhenius temperature-dependence? Energy for hole formation ( Δ E h ) is low at high 1. temperatures Δ H η is greater at lower temperatures � 2. Free-volume increases with temperature 3. Configurational entropy increases with temperature (Adam-Gibbs description) FS08 Richard K. Brow brow@mst.edu Melt properties-25
What accounts for viscous flow in a silicate melt? What has to happen for flow to occur? FS08 Richard K. Brow brow@mst.edu Melt properties-26
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