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Mat E 423
Physical Properties of Glass 2: Thermal Expansion CoefficientUnderstand 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
MatE 423 Thermal Expansion of Glass 2
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
Tshock= E(1+)/
MatE 423 Thermal Expansion of Glass 3
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
Thermal tempering increases strength and reduces large dangerous shards to fine small particles
MatE 423 Thermal Expansion of Glass 4
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
– -spodumene, Li2O.Al2O3.4SiO2
Complex systems with more than one material must have matched or compensated thermal expansions
MatE 423 Thermal Expansion of Glass 7
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 9
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 11
Thermal Expansion of Glass
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
LVP
V
PL
T
V
V
T
L
L
31
1
0
0
MatE 423 Thermal Expansion of Glass 12
Determination of Linear Thermal Expansion
Determine L for 100 – 200,
200 – 300, 100 – 500oC
ranges
P
L
PL
TT
TLTL
L
T
L
L
12
12
0
0
)()(1~
1
MatE 423 Thermal Expansion of Glass 13
Temperature Dependence of Thermal Expansion
Glass undergoes glass transition and transform to supercooled liquid at Tg
Liquid has a larger 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
Td = Tg
Ts
glass
liquid
MatE 423 Thermal Expansion of Glass 14
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)
Td = Tg
Ts
glass
liquid
MatE 423 Thermal Expansion of Glass 15
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
Temperature
Mol
ar V
olum
e
liquid
slow
Fast cooling
supercooledliquid
glassystate
MatE 423 Thermal Expansion of Glass 17
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
Tg
Tg
100%SiO2
MatE 423 Thermal Expansion of Glass 18
Thermal Expansion of Alkali Silicates
Thermal Expansion coefficient increases with alkali modifier
Expansion coefficient is larger for the the larger alkali's
K > Na > Li
Taken as an average value from 150 to 300oC
MatE 423 Thermal Expansion of Glass 19
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 21
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 22
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
For soda lime glasses
= [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 for 20Na2O + 10CaO +70SiO2 glass