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 →
gh 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=g𝐾𝛾

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 7.210-4 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