Mat E 423 Physical Properties of Glass 2

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Mat E 423 Physical Properties of Glass 2: Thermal Expansion Coefficient Understand how thermal

Mat E 423 Physical Properties of Glass 2: Thermal Expansion Coefficient Understand how thermal expansion coefficient depends upon temperature, cooling rate, interatomic bonding, and composition Understand be able to use relative order of magnitude values for 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 u u u Thermal expansion determines if a glass will

Thermal Expansion of Glass u u u 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)/ Mat. E 423 Thermal Expansion of Glass 2

Thermal Expansion of Glass u u u Thermal Expansion also determines whether a glass

Thermal Expansion of Glass u u u 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 Mat. E 423 u Thermal tempering increases strength and reduces large dangerous shards to fine small particles Thermal Expansion of Glass 3

Thermal Expansion of Materials u Most materials expand as they are heated – Some

Thermal Expansion of Materials u Most materials expand as they are heated – Some more than others u Refractory metals and ceramics – Expand less u Polymers – Expand more u Some materials expand very little – Si. O 2 glass – b-spodumene, Li 2 O. Al 2 O 3. 4 Si. O 2 u Complex systems with more than one material must have matched or compensated thermal expansions Mat. E 423 Thermal Expansion of Glass 4

Typical Thermal Expansion Coefficients of Materials SLS Mat. E 423 Thermal Expansion of Glass

Typical Thermal Expansion Coefficients of Materials SLS Mat. E 423 Thermal Expansion of Glass 5

Thermal Expansion Values of Materials Mat. E 423 Thermal Expansion of Glass 6

Thermal Expansion Values of Materials Mat. E 423 Thermal Expansion of Glass 6

Thermal expansion of Crystals u u u Polycrystalline materials under go phase transformations Thermal

Thermal expansion of Crystals u u u Polycrystalline materials under go phase transformations Thermal expansion changes at each phase transition c-Si. O 2 has numerous phase changes and numerous volume changes that must be accounted for during heat up of systems using Si. O 2 Mat. E 423 Thermal Expansion of Glass 7

Thermal Expansion of Crystals g-Si. O 2 Mat. E 423 Thermal Expansion of Glass

Thermal Expansion of Crystals g-Si. O 2 Mat. E 423 Thermal Expansion of Glass 8

Measurement of thermal expansion u u u Expansion dilatometer Thermal mechanical analyzer Measures the

Measurement of thermal expansion u u u Expansion dilatometer Thermal mechanical analyzer Measures the length of the sample – Typically a glass rod – 0. 5 cm x 1 cm u u u 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 3 o. C/min Mat. E 423 Thermal Expansion of Glass 9

Typical Pushrod Dilatometer Mat. E 423 Thermal Expansion of Glass 10

Typical Pushrod Dilatometer Mat. E 423 Thermal Expansion of Glass 10

Thermal Expansion of Glass u u For isotropic materials, homogeneous in three directions, …

Thermal Expansion of Glass u u 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 Mat. E 423 Thermal Expansion of Glass 11

Determination of Linear Thermal Expansion u u u Determine L for 100 – 200,

Determination of Linear Thermal Expansion u u u Determine L for 100 – 200, 200 – 300, 100 – 500 o. C ranges Mat. E 423 Thermal Expansion of Glass 12

Temperature Dependence of Thermal Expansion u u u Glass undergoes glass transition and transform

Temperature Dependence of Thermal Expansion u u u 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 scans at 10 – 20 o. C/min, dilatometry is done at 3 -5 o. C/min Mat. E 423 Thermal Expansion of Glass Ts Td = T g liquid glass 13

Temperature Dependence of Thermal Expansion u u Properties of glass depend upon cooling rate

Temperature Dependence of Thermal Expansion u u 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) Mat. E 423 Thermal Expansion of Glass Ts Td = T g liquid glass 14

Temperature Dependence of Thermal Expansion u u u As fast cooled glass is reheated

Temperature Dependence of Thermal Expansion u u u 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 shrinks, it exhibits a negative thermal expansion The greater the mismatch between qc and qh, the greater the sub-Tg relaxation event Mat. E 423 glassy state Molar Volume u supercooled liquid Fast cooling liquid slow Thermal Expansion of Glass Temperature 15

Thermal Expansion Coefficients for Various Glasses Mat. E 423 Thermal Expansion of Glass 16

Thermal Expansion Coefficients for Various Glasses Mat. E 423 Thermal Expansion of Glass 16

Thermal Expansion of Alkali Silicate Glasses u u u u As alkali is added,

Thermal Expansion of Alkali Silicate Glasses u u u u 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 Mat. E 423 Thermal Expansion of Glass Tg Tg 100% Si. O 2 17

Thermal Expansion of Alkali Silicates u u Thermal Expansion coefficient increases with alkali modifier

Thermal Expansion of Alkali Silicates u u Thermal Expansion coefficient increases with alkali modifier Expansion coefficient is larger for the larger alkali's K > Na > Li Taken as an average value from 150 to 300 o. C Mat. E 423 Thermal Expansion of Glass 18

Thermal Expansion of Alkali Borate Glasses u u u u Addition of alkali modifier

Thermal Expansion of Alkali Borate Glasses u u u u 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 Mat. E 423 Thermal Expansion of Glass 19

Ultra-low expansion (ULE) glass Mat. E 423 Thermal Expansion of Glass 20

Ultra-low expansion (ULE) glass Mat. E 423 Thermal Expansion of Glass 20

Correlation of Thermal Expansion with structure u u u Materials expand by their average

Correlation of Thermal Expansion with structure u u u 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 Mat. E 423 Thermal Expansion of Glass 21

Calculation of Thermal Expansion Coefficients u u Thermal expansion like many properties are continuous

Calculation of Thermal Expansion Coefficients u u Thermal expansion like many properties are continuous with glass composition Each oxide may have a predictable affect on 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 Mat. E 423 For soda lime glasses = [51. 3 +210. 864 Na 2 O + 275. 584 K 2 O + 13. 887 Ca. O – 23. 93 Mg. O – 88. 638 Al 2 O 3] x 10 -7/o. C u Note most factors are +’ive u Factor for Al 2 O 3 is –’ve and reflects decreasing NBOs u Factor for K 2 O is larger than factor for Na 2 O u Which is much larger than factor for Ca. O u Calculate for 20 Na 2 O + 10 Ca. O +70 Si. O 2 glass u Thermal Expansion of Glass 22

Calculating Thermal Expansion Coefficients u u u More general oxide glasses Additive factors for

Calculating Thermal Expansion Coefficients u u u 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 Mat. E 423 Thermal Expansion of Glass 23