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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-quenching
process. 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
Quartz
Tridymite
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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)。
b
I
dS =
dQR
dQ
, ΔS = Sf - Si = ∫ R
T
T
P
a
II
與路徑無關，僅與最初與最後狀態有關
V
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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不同類型玻璃的玻璃轉換溫度
Tg (°C)
Material
Tg (°C)
Chalcogenide ,GeSbTe
150
Material
Polypropylene(PP聚丙烯)
245
Poly(vinyl acetate )
(PVAc聚醋酸乙烯酯)
30
ZBLAN fluoride glass,
ZrF4-BaF2-LaF3-AlF3NaF
70
235
Polyethylene terephthalate
(PET聚對苯二甲酸乙二酯)
80
Tellurium dioxide
280
Poly(vinyl chloride)
(PVC聚氯乙烯)
Polystyrene(PS聚苯乙烯)
95
Soda-lime glass
520600
Fused quartz
~1200
Chalcogenide,
AsGeSeTe
−20
Poly(carbonate)(PC聚碳酸酯) 145
PC
PP
PVAc
PET
PVC
PS
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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
strain point
Tg h=1013P
1P = 1g/(cm．s) 常溫下，水的黏度約 1cP，
空氣的黏度約 0.02cP
strain point h=1014.6P
the thermal expansion curve begins to
deviate from linearity
annealing point h=1013.4P
glass becomes strain-free in 15min
when anneals at this
softening point h=107.6P
glass will elongate under its own weight
work point h=104P
glass can be formed or sealed
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玻璃之特定黏度值
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
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Measurement of viscosity
At low viscosity (up to 108P), the rotating cylinder method is used.
1 1
F
η = ( 2 - 2)
r1 r0 4πhω
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 w.
At high viscosity (high than 108P), rod elongation method is used.
η=
Lmgf
3πr 2 v
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 glasses
1. 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
η = η0 exp( E / RT )
E is activation energy, R is gas constant (8.31 J/(K-mol)).
GeO2 E=75kcal/mol(540~1500 ℃), P2O5 E=41.5kcal/mol(545~655 ℃)
The empirical equation
η = η0 exp( B /( T - T0 ))
h0 and B are temperature-independent .
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Metal oxide (mol%)
Effects of metal oxide on the
viscosity of binary liquid silicates
Energy of activation for viscous
flow (Eh) in binary liquid silicates.
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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)
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.
Super cooled liquid
glass
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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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Refractive index versus time at constant T
n = 1.51493 + 0.00103e-(t/7.77) + 0.00111 - e-(t/64.4)
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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