Part 7 Glass What is glass • • • • A supercooled liquid A solid material with no long-range order A liquid that lost is ability to flow A solid assembly of vertex-sharing tetrahedra lacking long range order Glass is typically formed through solidification from the melt -Discontinuous change in volume at the melting point (Tm) if the liquid crystallizes -Expansion coefficients for glass and crystal are similar Suppress crystal formation Tg glass transition temperature intersection between curve for the glassy state and the supercooled liquid The critical radius The critical radius r = rc Þ maximum in DGexec dDGexec 2g sl Vm = 0 Þ rc = T dr DH f (1- ) Tm And the energy barrier 16pg sl3 Vm2 DGexec = 2 Þ Þ T 3DH 2f Þ1- Þ Þ Tm Þ The rate of homogeneous nucleation (nuclei per cubic meter per second) I v µ vN eq n DGc kT NvkT Iv µ e 3 3pl h Assumptions Homogeneous nucleation Steady state rate No compositional changes No volume changes (no strain energy) frequency of successful jumps across the nucleus liquid interface Nneq metastable equilibrium concentration (per volume of nuclei) l jump distance The time-temperature-transformation diagram or how fast do I need to cool to form glass Number of new particles, Nt, formed in a time interval dt in a volume V should be Nt = I vVdt Assuming constant, isotropic growth rate, u, the radius of the spherical particle after time t will be t > t Þ r = u(t - t ) t <t Þ r -0 And the volume of the particle after a time will be 4 3 3 Vt = p u (t - t ) 3 The growth in volume due to nuclei appearing at dt 4𝜋 3 3 𝑑𝑉𝜏 = 𝑢 𝑡 − 𝜏 𝑉𝐼𝑣 𝑑𝜏 3 And integrating the volume that appears in an interval time 𝜏=𝑡 𝜋 𝑉𝑡 = 𝑑𝑉𝜏 = 𝑉𝐼𝑣 𝑢3 𝑡 4 3 𝜏=0 𝑉𝑡 𝜋 3 4 = 𝐼𝑣 𝑢 𝑡 𝑉 3 A more exact equation (Johnson-Mehl-Avrami) p 34 - In u t 3 Vt =1- e V What did I forget to take into account in the previous slide? Using the previous equation we can calculate the fraction crystallized at a function of time for a given temperature Repeat for other temperatures and join points with same volume fraction transformed The time –temperature-transformation (TTT) diagram We can use the diagram to define a critical cooling rate (CCR) from a given liquid temperature, TL, to limit the transformation a set volume TL - Tn CCR= tn Havermans et al. Can you make a glass with any compound? Criteria for Glass Formation • High nucleation barrier: Small entropy of fusion (DSf) and/or higher gsl • Low nucleation and growth rates High viscosity near the melting point (hm). • Absence of nucleating heterogeneities that can act as nucleating agents • Useful parameter (the smaller the better) Þ1 Þ DSf Þ Þ Þhm Þ Zachariasen rules Zachariasen (1932) proposed a set of rules for the case when an oxide forms a glass. The rules are based on 2 key observations: -Glasses and crystalline ceramics have similar Young Modulus-bonding should be similar -Glasses do not have long range order Zachariasen rules For the formation of an oxide glass Each oxygen ion should be linked to not more than two cations The coordination number of oxygen ions about the central cation must be small, 4 or less Oxygen polyhedra share corners, not edges or faces At least three corners of each polyhedron should be shared Silica Glass Structure. • Arrangements of silicate tetrahedra with short range order (all Si4+ are surrounded identically by 4 O2-) but no long range order. The building block of silicates The (SiO4)4- is the building block Si-O bond is strong Large covalent component (40% ionic) Fused Silica Some glass compositions What is the role of each component? Multicomponent glasses Multicomponent glasses • The components of glasses can play one of these three roles • Network formers • Network modifiers • Intermediates Multicomponent glasses – network formers • Glass forming-oxygen polyhedra are triangles and tetrahedra, and the cations forming such coordination polyhedra are the network formers • e.g. Si-in silicate glasses • There are other network formers such as B or Al Network modifiers • Alkali or alkali earths occupy random positions distributed through the structure, located to provide local charge neutrality • They provide addional oxygen ions (non-bridging) modifying/breaking the network • They also modify the glass properties • Addition of modifiers tend to reduce the glass transition temperature Tg, addition of network formers increases it Network modifiers Intermediates • Cations of higher valence and lower coordination number than the alkalis and alkaline earths that may contribute in part to the network structure • Ti, Zn, Pb, Al, Be….. Bridging and non-bridging oxygen O O Si O O O Si O O O + M2O O M+ O- Si O O Si OM+ O O Oxygen atom bonded to two Si atoms is a bridging oxygen (BO) Oxygen atom bonded to one Si atom is a non-bridging oxygen (NBO) NBOs formed mostly by adding alkali or alkali-earth metal oxides Balance between bridging and non-bridging oxygens R X Y SiO2 2 0 4 P2O5 2.5 1 3 Na2O.SiO2 3 2 2 Only one network former surrounding by Z (3 or 4) oxygens X non bridging and Y bridging per polyhedron R number of oxygen atoms per forming ion Z=X+Y X+0.5Y=R X=2R-4 Y=8-2R Phosphate glasses P-tetrahedron Qi where i is the number of bridging oxygens per tetrahedron (same terminology for silica glasses) R. K. Brow Journal of Non-Crystalline Solids Volumes 263–264, 1 March 2000, Pages 1-28 The glass transformation temperature Tg Glass is typically formed through solidification from the melt -Discontinuous change in volume at the melting point (Tm) if the liquid crystallizes -Expansion coefficients for glass and crystal are similar Suppress crystal formation Tg glass transition temperature intersection between curve for the glassy state and the supercooled liquid Specific volume The glass transformation temperature depends on the cooling rate Fast cooling It is not a thermodynamic ”property” rather a kinetic one Slow cooling Tg1 Tg2 Tm Temperature How to measure Tg? Heat capacity There is a “jump” in heat capacity Crystal Glass Tg2 Tm Temperature Differential Thermal Analysis traces for a glass that does not crystallize (a) and one that crystallizes at Tg<T<Tm (b) Fundamentals of Ceramics M.W. Barsoum Taylor & Francis Thermal expansion One possibility is to measure the jump in thermal expansion at Tg Liquid Glass Crystal Tg1 Tm Temperature Dilatometry Displacement sensor Glass https://glassproperties.com/tg/ Effect of composition on Tg • Network modifiers tend to decrease Tg α(×10− 6×°C−1) Ts(°C) Tg(°C) Winkel English mann and and Hall10 Turner Schott 12 11 Guard and Dubrul l8 Bioglas 15.1 s© 557 511 15.6 15.9 15.8 11.9 6P44-a 15.6 503 449 15.1 16.4 15.7 12.3 6P44-b 13 560 516 13.3 13.9 13.5 13.5 6P44-c 11.3 599 527 11.5 11.5 11.3 14.6 6P50 12.2 560 522 12.4 12.7 12.5 12.4 6P53-a 12.9 565 530 12.6 12.9 12.8 11.4 6P53-b 11.5 608 531 10.8 10.5 10.6 12.6 6P55 11 602 548 11.2 11.1 11.1 12.0 6P57 10.8 609 557 10.7 10.3 10.5 11.5 6P61 10.2 624 564 10.1 9.5 9.8 10.5 6P64 9.1 622 565 9.7 9.0 9.4 9.8 6P68 8.8 644 565 9.0 8.0 8.6 9.1 Properties of bioactive glasses Increasing SiO2 content Lopez-Esteban et al. Journal of the European Ceramic Society Volume 23, Issue 15, 2003, Pages 2921-2930 Glass viscosity t= shear stress=F/A dv dr Newtonian liquid dv t h L coefficient of viscosity dr dv 𝑑𝑣 g 𝛾 = − t → gh L𝜏 dr 𝑑𝑟 . = 𝛾𝜂𝐿 General behaviour n = shear thinning constant However not all the liquids are newtonian. In general: K = consistency index n 1 n 𝑛h⟹ t 𝜏 K=g𝐾𝛾 K g a 𝜂𝑎 = 𝐾𝛾 𝑛−1 ha = apparent viscosity . . h<106dPas h<109dPas The glass viscosity Strain point, h=1015.5 Pa.s Internal strains reduced to acceptable levels in 4 h Annealing point h=1014 Pa.s internal strains reduced to acceptable levels in 15 min Softening point h=108.6 Pa.s at this temperature a glass article elongates at roughly 3%/s. Maximum temperature at which glass may be handled without causing significant dimensional changes. Working point h=105 Pa.s glass can be worked. Glass is easily deformed at this viscosity. Temperature dependence of the viscosity of different glass systems: examples Theoretical Treatment of Viscosity • Glasses are newtonian liquids • Theoretical expression describing temperature dependence of viscosity of silica glass is Frenkel-Andrade equation: h = A eUh/RT where Uh is the activation energy of temperature dependence of viscosity, R is gas constant, T is the temperature, A is a constant. • Hence is a linear dependence of logarithm of glass viscosity ln(h) with inverse temperature (1/T). This is valid only in limited ranges of temperature since by changing the temperature Uh changes as well. Theoretical Treatment of Viscosity. • This dependence illustrated for a pure silica glass in Table. (1cal = 4.18 J) Activation energy of viscosity for silica glass. T, oC Uh , kcal/mol 1300-1450 1720-2000 1925-2060 1935-2320 170 8 151 10 134 9 89 21 • Activation energy fall with increasing temp. attributed to network break-up reducing the energy barriers for flow. Page 47 VFT Equation. • Frenkel-Andrade equation can be rewritten as Over a wide range of temperatures another relationship is used, namely the Vogel-FulcherTamann phenomenological equation: where A, B and To are constants. For example, a SiO2-Al2O3-MgO-Na2O-K2O-F glass has A = -2.105, B = 6780 and To = 177.9oC • • • In the Frenkel-Andrade equation this corresponds to Uh = 314 kJ/mol. The silica glass above has A = -2.487, B = 15,004, To = 253 oC. Although VFT Equation is empirical, it provides an excellent fit for typical commercial glasses. Constants A, B and To have been related to composition as a result of extensive compositionproperty surveys. Use of these composition factors provides a more accurate determination of viscosity than experimental measurement. Commercial software is available for such calculations. Viscosity and Composition. • Glass viscosity is also a strong function of composition. • Glasses can be made more fluid at lower temperature through control of their composition. • Lower temp. processing avoids evaporation of some species. • Alkalis and B2O3 – break up glass network and make the glass less viscous. – Are fluxes for silicates (bringing down their melting temperatures) and help liquid to spread and penetrate a ceramic microstructure but potentially reducing their durability in aqueous environments. Glass Shape Forming. • Carried out within working range — between the working and softening temperatures. • These temps. depend on glass composition. • E.g. softening points for soda–lime-silica (SLS) and 96% silica glasses are ~700 and 1550oC, respectively so forming operations may be carried out at significantly lower temperatures for SLS glass. • Formability of a glass is influenced to a large degree by its composition Page 50 Working Range Glass Shape Forming • Blowing automated for production of bottles/jars etc. • Drawing can be followed by floating glass sheet on bath of molten tin at elevated temperature, which improves significantly its flatness and surface finish. Glass Forming Processes Fibre Blowing Drawing Pressing Forming Page 51 Float Glass Manufacture. • Sheet glass floated on bath of molten tin held at high temperature for enough time to produce a smooth firepolished surface. • The basis of this process is that a ribbon of molten glass floating on a pool of molten tin will come to an equilibrium thickness, with both surfaces perfectly flat over most of its width, under the influence of interfacial tensions and gravitational forces. Page 52 Page 53 Float Glass Manufacture. Solid Powder Batch (Na2CO3-CaCO3-SiO2) Liquid Formation (melting/homogenising) Temperature/viscosity control/casting onto liquid Sn Spreading of liquid glass on liquid metal - equilibrium shape and thickness Cooling to viscous glass - lift off solid Anneal Cut to size Continuous Service. • Glass tanks must operate continuously, 24/7 for years. • Refractories failure rare but disastrous. • Refractories designed via in situ mechanism to last > a decade. • Cost of reline is several £M + loss of production downtime. Page 57 Silica frost defect Zirconia stone Aluminosilicate defects Refining and Homogenising in Conditioning Chamber. • Molten glass from melting chamber passes through a throat (aka bridge) in a divider wall into the conditioning chamber, where temperatures for SLS glass are held at ~1300°C. • Here fine bubbles are removed and glass is homogenized by diffusive mixing. • Bubbles are removed in the process of fining (refining). • Refining agents such as (As2O3, Sb2O3, NaCl, Na2SO4) are added to the batch and help to accelerate bubble removal. They either aid solution of the gases in the bubbles or make the bubbles grow and hence rise faster. • As2O3 has largely been replaced by sodium sulphate (Na2SO4 aka saltcake) due to concerns over heavy metal pollution. Page 62 Bubble Removal by Rising. • Simplest model for refining is that of bubble rise to the surface where they burst. Stokes law predicts the terminal velocity (vs) for a solid sphere moving under gravity in a viscous liquid and can be adapted to give the expected rate of rise of a bubble (vb): vb = (3/2) vs = (1/12) (mg/h) d2 where m is melt density, g is gravitational acceleration, h is melt viscosity and d is bubble diameter. • Bubble growth so they rise quickly though the d2 term is thus desirable. • Taking a small 0.2mm dia. bubble in a melt of viscosity 100 dPa s (corresponding to about 15000C) and density 2.2g cm-3 gives a rate of rise of 7.210-4 cm/s. Thus for a glass furnace 120 cm deep, such a bubble would require 46 h to rise to the surface and would take much longer at lower temperatures (higher viscosities). Page 63 Small Bubbles (Seed). • Experimental measurements show that large bubbles behave as expected but small bubbles (termed seed) disappear much more quickly. • Analysis of seed compositions shows significant chemical changes with time: initially bubbles are rich in CO2, then O2 dominates and the small bubbles that are last to dissolve contain predominantly N2. Page 64 Homogenising. • To achieve homogeneity it is necessary to melt completely and mix all raw materials. • Porosity results from small gas bubbles; these must be absorbed into the melt or otherwise eliminated, which requires proper adjustment of the viscosity of the molten material and use of refining agents. • Glass melts need homogenising because the liquids produced initially differ widely in composition; differences can be exaggerated by density separation. • Homogenising requires shear and diffusive mixing. Because of the high melt viscosity and correspondingly slow diffusion rates, diffusion in glass melts is only effective over 0.1mm or less even at the high temperatures present in a glass melting furnace. Page 65 Glass Thickness Control. • Both molten metal and atmosphere above it have very low viscosities compared with the glass, which therefore will spread out to come to equilibrium under a balance between hydrostatic and surface tension. • Two factors control sheet thickness: • 1) Hydrostatic pressure in the glass (Pg) which increases linearly from x = 0 to d • 2) Pressure in the molten metal (Pm) which acts in the opposite direction but only from x = h to d. The balance of the interfacial tensions (σ) gives a net force over unit length of this section of: Page 66 Equilibrium Glass Thickness. • So long as this is positive the ribbon will spread out only until F() is balanced by the forces due to the hydrostatic pressure [F(p)], ρ is density: • If the thickness of the sheet is d and its depth of immersion in the molten metal bath (d - h), applying Archimedes principle requires that: • Equating F(p) with F() gives the equilibrium thickness d to be: • Thickness of glass in float process thus is a function of a balance of interfacial tensions and densities. For commercial glasses equilibrium thickness of glass sheet produced in float process is ~7 mm. Industrial Thickness Control. • In practice when thinner glass is required, control of glass thickness is via temperature and mechanical pulling devices. • Edge rollers stretch the sheet or graphite dams stop it spreading to control thickness. • Sheets as thin as 2 – 2.5 mm can be made. Page 68 Viscosity Control for Melting and Shaping. • Silicate glasses usually melted ~1400 – 1600oC. • Various regions of tank at different temps. with different glass viscosities performing different functions. • Shape forming operations need the melt to be held at higher viscosity, usually requires temperatures of 1050 – 1200oC. Page 69 Glass Defects • • Inhomogeneties in glass product include: – Residual unmelted batch, particularly sand grains, – Devitrification products, – Refractory lining corrosion products, – Foreign matter such as metal bottle caps from recycled frit, – Vaporization of the various glass constituents, particularly boric oxide and alkali. Glass homogenisation is the ratelimiting step in the entire glassmelting process. Page 70 Summary • What is glass • How fast do you need to cool a liquid to make a glass (the TTT diagram) • The structure of glass – Network formers/modifiers/intermediates – Bridging vs non-bridging oxygens • Tg and how to measure • Viscosity – Significance – Importance for processing • The float glass process – – – – Steps Thickness Defects Refractories