1. Physical Properties of Glass 2: Thermal Expansion Coefficient
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

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
DTshock= E(1+n)/a
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
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

5. Typical Thermal Expansion Coefficients of Materials
SLS
MatE 423
Thermal Expansion of Glass

6. Thermal Expansion Values of Materials
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

8. Thermal Expansion of Crystals
g-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

10. Typical Pushrod Dilatometer
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
MatE 423
Thermal Expansion of Glass

12. Determination of Linear Thermal Expansion
Determine aL for 100 – 200,
200 – 300,
100 – 500oC ranges
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 Ts
Td = Tg
aliquid
aglass
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) Ts
Td = Tg
aliquid
aglass
MatE 423
Thermal Expansion of Glass

15. Temperature Dependence of Thermal Expansion
glassy
state
supercooled
liquid
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
liquid
Fast cooling
Molar Volume
slow
Temperature
MatE 423
Thermal Expansion of Glass

16. Thermal Expansion Coefficients for Various Glasses
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
aK > aNa > aLi
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

20. Ultra-low expansion (ULE) glass
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
a = [ Na2O K2O CaO –23.93 MgO – 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
MatE 423
Thermal Expansion of Glass

23. 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