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+)/

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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

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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

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Typical Thermal Expansion Coefficients of Materials

SLS

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Thermal Expansion Values of Materials

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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

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Thermal Expansion of Crystals

g-SiO2

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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

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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

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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

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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

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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

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Thermal Expansion Coefficients for Various Glasses

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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

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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

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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

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Ultra-low expansion (ULE) glass

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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

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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

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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