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

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

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

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

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

Thermal Expansion Values of Materials Thermal Expansion of Glass

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

Thermal Expansion of Crystals g-SiO2 MatE 423 Thermal Expansion of Glass

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

Typical Pushrod Dilatometer MatE 423 Thermal Expansion of Glass

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

Determination of Linear Thermal Expansion Determine aL for 100 – 200, 200 – 300, 100 – 500oC ranges MatE 423 Thermal Expansion of Glass

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

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

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

Thermal Expansion Coefficients for Various Glasses MatE 423 Thermal Expansion of Glass

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

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

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

Ultra-low expansion (ULE) glass MatE 423 Thermal Expansion of Glass

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

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 MatE 423 Thermal Expansion of Glass

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