Mat E 423

1
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(1n)/a

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

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

5
Typical Thermal Expansion Coefficients of
Materials
SLS
6
Thermal Expansion Values of Materials
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

8
Thermal Expansion of Crystals
g-SiO2
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

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

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Determination of Linear Thermal Expansion

• Determine aL for 100 200,
• 200 300,
• 100 500oC ranges

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 lt than Tg measured by DTA
• DTA scans at 10 20oC/min, dilatometry is done
  at 3-5oC/min

Ts
Td Tg
aliquid
aglass
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
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Temperature Dependence of Thermal Expansion
supercooled liquid
glassy state

• 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
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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
• aK gt aNa gt aLi
• 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

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 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

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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