Mat E 423
Physical Properties of Glass 2: Thermal Expansion Coefficient
Understand how the thermal expansion coefficient depends upon temperature,
cooling rate, interatomic bonding, and composition
Understand and be able to use relative order of magnitude values for the
thermal expansion coefficient for various oxide glasses
Be able to estimate thermal expansion coefficient for oxide glasses using
simple additive factors models
Thermal Expansion of Glass





Thermal expansion determines
if a glass will be shock
resistant, able to withstand high
thermal stresses
Thermal expansion also
determines if a glass will have
low thermal shock resistance
Small thermal expansion
coefficient leads to high thermal
shock resistance
Large thermal expansion leads
to low thermal shock resistance
DTshock= E(1+n)/a
MatE 423
Thermal Expansion of Glass
2
Thermal Expansion of Glass



Thermal Expansion
also determines
whether a glass can be
thermally “tempered”
to increase its strength
High thermal
expansion leads to high
tempering ability
Low thermal
expansion leads to low
tempering ability
MatE 423
 Thermal
tempering increases
strength and reduces large
dangerous shards to fine small
particles
Thermal Expansion of Glass
3
Thermal Expansion of Materials

Most materials expand as they are heated
– Some more than others

Refractory metals and ceramics
– Expand less

Polymers
– Expand more

Some materials expand very little
– SiO2 glass
– b-spodumene, Li2O.Al2O3.4SiO2

Complex systems with more than one material must
have matched or compensated thermal expansions
MatE 423
Thermal Expansion of Glass
4
Typical Thermal Expansion Coefficients of Materials
SLS
MatE 423
Thermal Expansion of Glass
5
Thermal Expansion Values of Materials
MatE 423
Thermal Expansion of Glass
6
Thermal expansion of Crystals



Polycrystalline materials
under go phase
transformations
Thermal expansion changes
at each phase transition
c-SiO2 has numerous phase
changes and numerous
volume changes that must be
accounted for during heat up
of systems using SiO2
MatE 423
Thermal Expansion of Glass
7
Thermal Expansion of Crystals
g-SiO2
MatE 423
Thermal Expansion of Glass
8
Measurement of the thermal expansion



Expansion dilatometer
Thermal mechanical analyzer
Measures the length of the sample
– Typically a glass rod
– 0.5 cm x 1 cm





As a function of temperature
Linear Variable Differential Transducer (LVDT) accurately
converts distance changes of microns into millivolts.
T/C measures sample temperature
Furnace provides sample heating and/or cooling
Typically slow heating rate 3oC/min
MatE 423
Thermal Expansion of Glass
9
Typical Pushrod Dilatometer
MatE 423
Thermal Expansion of Glass
10
Thermal Expansion of Glass
aL 
1  L 


L0  T  P
aV 
1  V 

 aV  3a L
V0  T  P




For isotropic materials,
homogeneous in three
directions,…
Volume expansion coefficient is 3
times larger than linear expansion
Glasses are isotropic
Fine grained polycrystals are
isotropic
MatE 423
Thermal Expansion of Glass
11
Determination of Linear Thermal Expansion
aL 
1  L 


L0  T  P
1  DL(T2 )  DL(T1 ) 

a L ~ 
L0 
T2  T1
P



Determine aL for
100 – 200,
200 – 300,
100 – 500oC
ranges
MatE 423
Thermal Expansion of Glass
12
Temperature Dependence of Thermal Expansion





Glass undergoes glass
transition and transform to
supercooled liquid at Tg
Liquid has a larger a
At softening point, liquid
begins to be compressed by
force of applied
dilatometer, “dilatometric
hook”
Tg measured by
dilatometry is called Td and
is often < than Tg measured
by DTA
DTA scans at 10 –
20oC/min, dilatometry is
done at 3-5oC/min
MatE 423
Thermal Expansion of Glass
Ts
Td = Tg
aliquid
aglass
13
Temperature Dependence of Thermal Expansion




Properties of glass depend
upon cooling rate
Heating rate of dilatometry
is slow and as such well
annealed samples, or those
cooled at the same slow rate
must be used
Fast quenched glasses will
undergo “sub-Tg”
relaxations, i.e., they try to
relax to slower cooling rate
curve
Eventually, glass undergoes
transition at Td(Tg)
MatE 423
Thermal Expansion of Glass
Ts
Td = Tg
aliquid
aglass
14
Temperature Dependence of Thermal Expansion





As fast cooled glass is reheated
and approaches Tg
The structure begins to “loosen”
Structural relaxation time begins to
shorten
Time is available for the glass to
try to relax “down” to the slow
cooled curve
As glass glass shrinks, it exhibits a
negative thermal expansion
The greater the mismatch between
qc and qh, the greater the sub-Tg
relaxation event
MatE 423
glassy
state
Molar Volume

supercooled
liquid
Fast cooling
liquid
slow
Thermal Expansion of Glass
Temperature
15
Thermal Expansion Coefficients for Various Glasses
MatE 423
Thermal Expansion of Glass
16
Thermal Expansion of Alkali Silicate Glasses







As alkali is added, thermal expansion
increases
Tg decreases with added modifier
Lowest modifier shows anomalous
‘plateau” above Tg
Liquid does not fully relax as it should
Low soda silicate glasses exhibit phase
separation
Liquid phase separates into high silica
and high alkali glasses, two glasses
with different Tgs
High silica liquid does not undergo Tg
until higher temperatures
MatE 423
Thermal Expansion of Glass
Tg
Tg
100%
SiO2
17
Thermal Expansion of Alkali Silicates




Thermal Expansion
coefficient increases with
alkali modifier
Expansion coefficient is
larger for the the larger
alkali's
aK > aNa > aLi
Taken as an average value
from 150 to 300oC
MatE 423
Thermal Expansion of Glass
18
Thermal Expansion of Alkali Borate Glasses







Addition of alkali modifier
decreases thermal expansion
coefficient in alkali borate glasses
Modifier in low alkali borate
glasses, cross links glass structure
Creation of tetrahedral borons
Adding bonds to boron, increasing
connectivity of network
Strengthening the network
Rigidity of the glassy network
increases
Thermal expansion decreases with
modifier
MatE 423
Thermal Expansion of Glass
19
Ultra-low expansion (ULE) glass
MatE 423
Thermal Expansion of Glass
20
Correlation of Thermal Expansion with structure






Materials expand by their average
bond length increasing
Glasses are disordered, so
expansion is isotropic
Expansion is governed by the
interatomic potential well that
binds the atoms and ions together
Tightly bound atoms reside in deep
energy wells that are only slightly
affected by temperature
More weakly bound atoms reside
in shallow energy wells that are
more affected by temperature
NBOs increase thermal expansion,
Bos decrease thermal expansion
MatE 423
Thermal Expansion of Glass
21
Calculation of Thermal Expansion Coefficients




Thermal expansion like many
properties are continuous with
glass composition
Each oxide may have a predictable
affect on the thermal expansion
coefficient
Assuming a linear relationship
between composition and thermal
expansion coefficient
Thermal expansion can be
calculated within limited
composition ranges for many
different glasses
MatE 423
For soda lime glasses
a = [51.3 +210.864 Na2O + 275.584
K2O + 13.887 CaO –23.93 MgO –
88.638 Al2O3] x 10-7/oC
 Note most factors are +’ive
 Factor for Al2O3 is –’ve and
reflects decreasing NBOs
 Factor for K2O is larger than factor
for Na2O
 Which is much larger than factor
for CaO
 Calculate a for 20Na2O + 10CaO
+70SiO2 glass

Thermal Expansion of Glass
22
Calculating Thermal Expansion Coefficients





More general oxide
glasses
Additive factors for
three different models
Some model hold
factors constant
Some models vary
factors with
composition
Compare thermal
expansion of SLS
glass for all four
models
MatE 423
Thermal Expansion of Glass
23