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 part 2-1
Melt and Glass Properties • Viscosity • Surface Tension • Thermal Expansion • Heat Capacity • Thermal Conductivity FS08 Richard K. Brow brow@mst.edu Melt properties part 2-2
Surface Tension Surface Tension FS08 Richard K. Brow brow@mst.edu Melt properties part 2-3
Thermodynamic definitions • To create a stable interface between two phases, the free energy of formation of the interface must be positive (to avoid miscibility.) dx Work (W) done to create new area (dA=l · dx): F W = F · dx l Surface tension ( γ ) resists the creation of new area: γ = F/l , and so W = γ ·dA Units for γ : ergs/cm 2 (or dyn/cm), J/m 2 (or N/m) FS08 Richard K. Brow brow@mst.edu Melt properties part 2-4
Young-LaPlace Equation • Surface tension resists bubble expansion, so work is required to expand bubble radius Δ P· Δ V = γ ·dA γ w r Δ P·(4 π r 2 ·dr) = γ ·(8 π r·dr) β Δ P = 2 γ /r Air dr γ g • This pressure differential explains: γ gw wall – Capillary rise – Increased vapor pressure/solubility of Glass melt curved surfaces – Wetting behavior (Young-Dupree equation) γ w = γ g w + γ g ·cos( π−β ) FS08 Richard K. Brow brow@mst.edu Melt properties part 2-5
What is the source for ‘surface energy’? • Consider a hypothetical lattice ‘Surface atoms’ have lower average coordination numbers (CN) than ‘bulk atoms’; this affects lattice energy (V) which depends on bond energy ( ε ) and number of bonds (CN). ⎛ ⎞ ⎛ ⎞ CN CN ⎜ ⎟ = ε = ε ⎜ ⎟ surf , bulk surface bulk V V ⎜ ⎟ min min 2 2 ⎝ ⎠ ⎝ ⎠ ≡ − > 0 . surface bulk Surface Energy V V CN ≈ − : surface 0 . 6 0 . 8 Note CN bulk Surface energy arises from the incomplete coordination (or charge compensation) of surface atoms compared to bulk atoms. FS08 Richard K. Brow brow@mst.edu Melt properties part 2-6
Does fracture create dangling bonds? O O O O O Si O Si O O Si + - O Si O O O O O No ESR evidence: Hochstrasser and Reconstruction is more likely: Antonini (1972) O - O Edge-shared tetrahedra are Si + Si Si Si commonly sound on silica surfaces O O O O O O O O O O FS08 Richard K. Brow brow@mst.edu Melt properties part 2-7
MD Simulation of silica glass fracture surface EA Leed et al., Phys Rev B 72[15] 155427 (2005) FS08 Richard K. Brow brow@mst.edu Melt properties part 2-8
‘Modified’ surfaces extend several monolayers Pair-distribution functions from a silica fracture surface from a molecular dynamics simulation- compared to the ‘bulk’ PDF (bottom) Levine et al., J. Chem. Phys . 86 2997 (1987). FS08 Richard K. Brow brow@mst.edu Melt properties part 2-9
Surface Tension- - melts melts Surface Tension • Smoothing sharp corners (fire polishing) • Contraction of fibers during fiber-drawing • Equilibrium thickness of ‘float glass’ melts • Adhesion and wetting (contact angles) with forming materials • Penetration of glass melts into refractory pores • Nucleation and growth of gas bubbles in the melt • Eddy currents at melt surfaces due to local differences in γ • Compositional gradients near refractory walls create γ - gradients which drive melt currents- undercutting refractories at ‘melt line’ FS08 Richard K. Brow brow@mst.edu Melt properties part 2-10
Eddy currents at melt surfaces due to local differences in γ • Compositional gradients near refractory walls create γ - gradients which drive melt currents- undercutting refractories at ‘melt line’ FS08 Richard K. Brow brow@mst.edu Melt properties part 2-11
Measuring Surface Tension Measuring Surface Tension Droplet method: Measure weight (m·g) of melt drop that detaches from Pt-rod end of Pt-rod or tube: (radius ‘r’) γ = m·g/(2 π ·r) Bubble-pressure method: Measure pressure ( Δ p) required to blow a bubble from a melt (density ρ ) with a Pt-capillary (radius r) inserted to a depth (l): γ = r·( Δ p-g·l· ρ )/2 Ring method Pt-wire ring (radius ‘R’) immersed in a melt, then pulled out with application of constant force (W); ‘a’ is correction factor.. γ =aW/4 π ·R Elongation of glass fiber FS08 Richard K. Brow brow@mst.edu Melt properties part 2-12
From Beerkens, 1997 Surface Tension Surface Tension Slight temperature dependence: γ (mN/m) Glass type γ decreases 4-10 mN/m per 100°C increase for S-L-S (flint/float) 310 most common glasses Brown bottle 296 SO 3 , Cr 2 O 3 , V 2 O 5 all E-glass 315 significantly decrease γ , TV-glass 248 as does water MgO, Al 2 O 3 increase γ water 72 • Low surface tension mercury 550 melts may foam Na 2 SO 4 (liq) has lower surface tension (266 mN/m) than an SLS melt- Na 2 SO 4 (liq) spreads on top of melt (continuous glassmelting tank operation) where it wets and dissolves unmelted sand…. FS08 Richard K. Brow brow@mst.edu Melt properties part 2-13
Compositional Effects on Surface Tension Compositional Effects on Surface Tension Polarizable ions (K + vs. Na + ) reduce γ FS08 Richard K. Brow brow@mst.edu Melt properties part 2-14
Compositional Effects on Surface Tension Compositional Effects on Surface Tension Polarizable ions (Pb 2+ ) reduce γ Note: γ for B 2 O 3 liquids is 80 mN/m at ~900°C (Varshneya, p. 243) FS08 Richard K. Brow brow@mst.edu Melt properties part 2-15
Compositional Effects on Surface Tension Compositional Effects on Surface Tension Polarizable ions reduce γ and γ decreases with temperature FS08 Richard K. Brow brow@mst.edu Melt properties part 2-16
Thermal Expansion Thermal Expansion FS08 Richard K. Brow brow@mst.edu Melt properties part 2-17
Definitions Average volume expansion coefficient when temperature increases from T 1 to T 2 ∂ ⎛ ⎞ = 1 V β ⎜ ⎟ ∂ ⎝ ⎠ V T P The instantaneous volume expansion coefficient is given by − V V β = 2 1 ( ) − m V T T 1 2 1 The corresponding linear expansion coefficients ( α ) are obtained by replacing volume with length, e.g. Δ l α = Units: 10 -7 /ºC, reported over Δ designated temperature l T 0 range FS08 Richard K. Brow brow@mst.edu Melt properties part 2-18
FS08 Richard K. Brow brow@mst.edu Melt properties part 2-19
Dilatometric softening pt, T d : η ~ 10 9 -10 10 Pa·s well annealed rapid cool FS08 Richard K. Brow brow@mst.edu Melt properties part 2-20
Shelby, 1997 FS08 Richard K. Brow brow@mst.edu Melt properties part 2-21
Note too: Networks can expand/contract by bond- bending as well as ‘bond- internuclear separation’ repulsion Coulombic attraction Shelby FS08 Richard K. Brow brow@mst.edu Melt properties part 2-22
B 2 O 3 BeF 2 Note: Tetrahedral framework glasses exhibit ‘anomalous’ CTE behavior at low temperatures- GeO 2 Δ l Tetrahedral rotations and bond l 4.2K angle changes Zn(PO 3 ) 2 SiO 2 Temp. (K) FS08 Richard K. Brow brow@mst.edu Melt properties part 2-23
51.15% SiO 2 67.11% SiO 2 77.30% SiO 2 What accounts for this unusual CTE behavior? 88.17% SiO 2 xNa 2 O·(100-x)SiO 2 glasses FS08 Richard K. Brow brow@mst.edu Melt properties part 2-24
Reducing ‘ ‘network polymerization network polymerization’ ’ usually increases CTE usually increases CTE Reducing xR 2 O·(100-x)SiO 2 glasses FS08 Richard K. Brow brow@mst.edu Melt properties part 2-25
The ‘ ‘borate anomaly is evident in CTE data for borate glasses borate anomaly is evident in CTE data for borate glasses The xR 2 O·(100-x)B 2 O 3 glasses BØ 3 → BØ 4 - Na + BØ 4 - Na + → BØO 2 2- (2Na + ) FS08 Richard K. Brow brow@mst.edu Melt properties part 2-26
xTiO 2 ·(100-x)SiO 2 glasses Ultralow expansion (ULE) FS08 Richard K. Brow brow@mst.edu Melt properties part 2-27
FS08 Richard K. Brow brow@mst.edu Melt properties part 2-28
Shelby 1997 FS08 Richard K. Brow brow@mst.edu Melt properties part 2-29
Li-Zn-borosilicates (Donald, et al. residual J. Mat. Sci., 24 3892 (1989) glass Glass- ceramics α−β cristobalite transition glass FS08 Richard K. Brow brow@mst.edu Melt properties part 2-30
Brief CTE Case Study: Li-aluminosilicate glass-ceramics FS08 Richard K. Brow brow@mst.edu Melt properties part 2-31
FS08 Richard K. Brow brow@mst.edu Melt properties part 2-32
Li 2 O-Al 2 O 3 -nSiO 2 : β -spodumene/ β -quartz solid solutions FS08 Richard K. Brow brow@mst.edu Melt properties part 2-33
Low thermal expansion Low thermal expansion due to open tetrahedral due to open tetrahedral crystalline networks crystalline networks FS08 Richard K. Brow brow@mst.edu Melt properties part 2-34
‘Corning ware’: (1-2 μ m) From Beall, “Glass-Ceramics, in Commercial Glasses (Advances in Ceramics, 18) , 1986 ‘Transparent’ glass-ceramic (~0.1 μ m) FS08 Richard K. Brow brow@mst.edu Melt properties part 2-35
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