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A glass is defined in ASTM (American Society for Testing and Materials) as ”an inorganic product of fusion which has been cooled to a rigid condition without crystallization”. According to this definition, a glass is a noncrystalline material obtained by a melt-quenchingprocess. Nowadays, noncrystalline materials that can not be distinguished from melt-quenched glasses of the same composition are obtainable by using various techniques such as chemical vapor deposition, sol-gel process, etc. Therefore, most glass scientists regard the term `glass' as covering all noncrystalline solids that show a glass transition regardless of their preparation method.

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SiO2 晶體結構

Tridymite

Quartz 

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玻璃與晶體的結構比較

晶體結構稱為長程有序。玻璃結構成為短程有序，長程無序。

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玻璃與晶體徑向原子分布的比較

Schematic diagram of radial atomic distribution function of gas, liquid, amorphous and crystal

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X 光粉末繞射圖譜可以用來判別玻璃與晶體

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Schematic representation of the temperature dependence of system volume for a liquid that can both crystallize and form a glass.

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Kauzmann temperature ： 玻璃與晶體間熵的差值為零。 一階相變： 有吸熱或放熱反應， 比熱有不連續的變化，例如水變冰、水變水蒸氣。 二階相變： 沒有吸熱或放熱反應， 比熱連續的變化，例如超導的變化、磁性物質的變化，玻璃轉換可視為二階的變化 ( 但不是完全的二階相變化 ) 。

Measurement of Tg by DSC Determination of Tg by dilatometry

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熵 (Entropy)熱力學第零定律引入狀態函數溫度；熱力學第一定律引入狀態函數內能；

熱力學第二定律將引入狀態函數熵 (S)。

I

II

b

a

V

P

T

dQ∫=S-S=ΔS ,

T

dQ=dS R

ifR

與路徑無關，僅與最初與最後狀態有關

物質常見的三態為氣態、液態以及固態，但是物質在某些狀態下，有時可能有多種不同的相。冰、水共存的系統有兩個相，兩物態相之間為液－固界面。 不同相之間的轉變稱為相變 (phase transition) ，一些物理性質會有不連續變化，例如： (1) 氣－液相變：密度發生不連續變化 (2) 超導體的超導態－正常態相變：導電度發生不連續變化。 (3) 液態氦氦Ⅰ ( 正常態 ) －氦Ⅱ ( 超流態 ) 相變：黏滯係數發生不連續變化。 (5) 鐵磁體－順磁體相變：磁化率(magnetic susceptibility) 發生不連續變化 。 　　一階相變之熵不連續，有潛熱 L=T(Sf-Si) 。二階相變的過程不會出現潛熱。

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Material Tg (°C)

Chalcogenide ,GeSbTe 150

Chalcogenide, AsGeSeTe

245

ZBLAN fluoride glass,ZrF4-BaF2-LaF3-AlF3-NaF

235

Tellurium dioxide 280

Soda-lime glass520-600

Fused quartz ~1200

Material Tg (°C)

Polypropylene(PP 聚丙烯 ) −20

Poly(vinyl acetate )(PVAc 聚醋酸乙烯酯 )

30

Polyethylene terephthalate (PET 聚對苯二甲酸乙二酯 )

70

Poly(vinyl chloride) (PVC 聚氯乙烯 )

80

Polystyrene(PS 聚苯乙烯 ) 95

Poly(carbonate)(PC 聚碳酸酯 )

145

不同類型玻璃的玻璃轉換溫度

PP PVAc PET PVC PS

PC

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DSC curve of Li2O-SiO2 glass heated at a rate of 10 /min.℃

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Viscosity of some silicate glasses

work point =104Pglass can be formed or sealed

softening point =107.6Pglass will elongate under its own weight

annealing point =1013.4Pglass becomes strain-free in 15min when anneals at this

strain point =1014.6Pthe thermal expansion curve begins to deviate from linearity

strain point

Tg=1013P

1P = 1g/(cm ． s) 常溫下，水的黏度約 1cP ，空氣的黏度約 0.02cP

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黏度 (Poise) 溫度點 現 象102 熔解點 溶解除氣泡104 作業點 成形作業105 流動點 玻璃液流動107.65 軟化點 受自身重量變形 1010 軟化點 膨脹儀軟化點1011.3 變形點 在壓力下變形1013.4 退火點 十幾分鐘退火1014.5 應變點 幾小時退火103~108 失透區 玻璃產生結晶

104~108 作業區 加工作業範圍1013 ~1014.3 退火區 精密徐冶範圍

玻璃之特定黏度值

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Measurement of viscosity

At low viscosity (up to 108P), the rotating cylinder method is used.

ωhπ4

F)

r

1 -

r

1(=η 2

021

r0, r1 are radii of inner and outer cylinders, h is the height of the liquid, F is the force applied for keeping a constant angular velocity

At high viscosity (high than 108P), rod elongation method is used.

vrπ3

Lmgf=η 2

L is the length of the glass rod, r is the its radius, m is the mass hanging on it,v is the velocity of elongation, f is a calibration factor of the instrument.

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1. SiO2

2. GeO2

3. 0.045mol%Na2O in GeO2

4. 20mol%Na2O in SiO2

5.24.5mol% K2O in SiO2

Four types of glasses1. Strong network liquid show linear behavior: SiO2, GeO2, BeF2.2. Partially broken three-dimensional network: alkali silicate, soda-lime silicate, As2S3.3. Liquids have a more severely distorted structure: CaAl2SiO8, alkali phosphate, ZnCl2. 4. Completely ionic and molecular glasses: 0.4KNO3-0.6Ca(NO3)2.

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The viscosity fits an Arrhenius-type equation over some temperature range

)RT/Eexp(η=η 0

E is activation energy, R is gas constant (8.31 J/(K-mol)).

GeO2 E=75kcal/mol(540~1500 ), P℃ 2O5 E=41.5kcal/mol(545~655 )℃

The empirical equation

))T-T/(Bexp(η=η 00

and B are temperature-independent .

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Effects of metal oxide on the viscosity of binary liquid silicates

Energy of activation for viscous flow (E) in binary liquid silicates.

Metal oxide (mol%)

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玻璃形成子 (glass-former):SiO2 、 B2O3 、 GeO2 、 P2O5 可單獨形成玻璃。玻璃修飾子 (glass modifier):Na2O 、 CaO 、 La2O3… 無法單獨形成玻璃者。中間子 (conditional glass-former):Al2O3 、 V2O5 無法單獨形成玻璃， 但與形成子混合，可以變成形成子

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氧化物如 SiO2 、 P2O5 和 B2O3 本身可快速冷卻形成玻璃的網狀結構稱玻璃形成子。這些氧化物滿足所提玻璃生成條件。這些條件是：

Zachariasen criteria(a) 氧離子和陽離子數相接不超過 2 ，(b) 以陽離子為中心於四周的氧離子的配位數為 4 或更小，(c) 於陽離子為中心的多面體間為共點結合，非共邊或共面結合，(d) 每個氧至少有 3 個鍵角跟其他四面體連結。滿足 Zachariasen criteria: B2O3, SiO2, P2O5, GeO2, P2O3, As2O5, As2O3, Sb2O3, Nb2O5, GeO2, Ta2O5, As2O5, Stanworth criteria(a) 陽離子的價位數必須大於 3 ，(b) 形成玻璃的容易程度隨著陽離子的半徑減小而增加，(c) 陽離子的 Pauling’s electronegativity介於 1.5~2.1 之間滿足 Stanworth criteria : Si, Ge, As, P, B, Sb, V, W, Mo, Te

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Relaxation of glasses

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Fictive temperature (假想溫度 )

Super cooled liquid

glass

glass at temperature T2 has the same structure as a super cooled liquid at temperature Tf. Tf is an artificial temperature used to describe the glassy state.

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The effect of cooling on the Tf

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Change of refractive index, density and viscosity versus equilibrium time

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(t/64.4)-(t/7.77)- e-00111.0+e00103.0+51493.1=n

Refractive index versus time at constant T

Two relaxation time, one fast 7.77mins, one slow 64.4mins.The fast relaxation processes corresponds to the more mobile structure with higher fictive temperature.The slow relaxation processes corresponds to the denser and therefore less mobile structure with lower fictive temperature.

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In the literature, there are three main ways that the Fictive Temperature is defined.

Structure: The fictive temperature is where the structure freezes. The fictive temperature

distribution serves as a map from equilibrium to nonequilibrium phase space distributions.

Property values: May have practical value. Different properties would have different fictive

temperatures. No connection to microscopic physics.

Relaxation processes: Here a new fictive temperature is defined as each relaxation mode freezes.

Does not try to map equilibrium to nonequilibrium states.

Glass transition temperature actually is a glass transition region. The region broadens with

increasing of cooling rate.

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