[R2O] < 3 mol%, otherwise coefficient for PbO
= 11.5 + 0.5·[R2O]|
|
|
Older Glass Thermal Expansion Models |
This table shows older thermal expansion models by various authors. For calculation all weight fractions are multiplied by the displayed coefficients below, and the products are summed to obtain the thermal expansion coefficient in ppm/K. For example, a glass with the composition in wt% 75 SiO2 + 25 Na2O would have a thermal expansion coefficient of 0.75*2.67 + 0.25*33.33 = 10.335 ppm/K (= 103.35 * 10-7 oC-1) according to Winkelmann and Schott.
|
Oxide |
Coefficients based on weight fraction of oxide (Appen based on mol fraction) |
||||
|
Winkelmann and Schott [1] |
Appen [2] |
Lederova et al. [3] |
English and Turner [4] |
Hall [5] |
|
|
SiO2 |
2.67 |
0.5…3.8a |
0b |
0.50 |
1.4 |
|
B2O3 |
0.33 |
-5.0…0.0c |
/ |
-6.53 |
2.0 |
|
P2O5 |
6.67 |
14.0 |
/ |
/ |
/ |
|
Al2O3 |
16.67 |
-3.0 |
1.685 |
1.40 |
5.0 |
|
Li2O |
6.67 |
27 |
/ |
/ |
/ |
|
Na2O |
33.33 |
39.5 (41)d |
32.172 |
41.60 |
38.0 |
|
K2O |
28.33 |
46.5 (49) |
38.068 |
39.00 |
30.0 |
|
BeO |
/ |
4.5 |
/ |
/ |
/ |
|
MgO |
0.33 |
6.0 |
3.059 |
4.50 |
2.0 |
|
CaO |
16.67 |
13 |
11.680 |
16.30 |
15.0 |
|
SrO |
/ |
16 |
/ |
/ |
/ |
|
BaO |
10.00 |
20 |
5.375 |
14.00 |
12.0 |
|
Fe2O3 |
13.33 |
5.5g |
/ |
/ |
/ |
|
ZnO |
6.00 |
5.0 |
/ |
7.00 |
10.0 |
|
PbO |
13.00 |
13…19e |
/ |
10.60 |
7.5 |
|
TiO2 |
13.67 |
-1.5…3.0f |
/ |
/ |
/ |
|
As2O3 |
6.67 |
/ |
/ |
/ |
/ |
|
ZrO2 |
/ |
-6.0 |
/ |
/ |
/ |
|
Sb2O5 |
12.00 |
7.5 |
/ |
/ |
/ |
|
P2O5 |
6.67 |
14.0 |
/ |
/ |
/ |
|
SnO2 |
6.67 |
-4.5 |
/ |
/ |
/ |
|
Cr2O3 |
17.00 |
/ |
/ |
/ |
/ |
|
MnO |
7.33 |
10.5g |
/ |
/ |
/ |
|
NiO |
/ |
5.0 |
/ |
/ |
/ |
|
CoO |
14.67 |
5.0 |
/ |
/ |
/ |
|
CuO |
7.33 |
3.0 |
/ |
/ |
/ |
|
CdO |
/ |
11.5 |
/ |
/ |
/ |
|
Ga2O3 |
/ |
-2.0 |
/ |
/ |
/ |
|
Applicable temperature range in oC |
|||||
|
/ |
20-100 |
20-400 |
20-300 |
25-90 |
25-Tg |
Footnotes:
a Coefficient for SiO2 = 10.5 – 0.1·[SiO2] for [SiO2] ≥ 67 mol%; otherwise 3.8 (expressions in brackets represent mol%)
b SiO2 is excluded from the calculation in the model by Lederova et al. Instead, a constant of 2.976 ppm/K is added.
c For glasses containing B2O3 the proportion F must be formed first, whereby the expressions in brackets represent mol%:
F = {([Na2O]+[K2O]+[BaO])+0.7([CaO]+[SrO]+[CdO]+[PbO])+0.3([Li2O]+[MgO]+[ZnO])–[Al2O3]}/[B2O3]
One then obtains: Coefficient for B2O3 = –1.25F for F ≤ 4; otherwise –5.0.
d Values in parentheses are valid for binary glasses SiO2-R2O. The coefficient for K2O of 46.5 applies only to those glasses that contain more than 1 mol% Na2O; otherwise, it is 42.0.
e Coefficient for PbO = 13.0 for glasses
with [R2O] < 3 mol%, otherwise coefficient for PbO
= 11.5 + 0.5·[R2O]
f Coefficient for TiO2 = 10.5 – 0.15·[SiO2] for 80 ≥ [SiO2] ≥ 50
g The coefficients for Fe2O3 and MnO are valid for the normally occurring oxidation states.
References:
[1] A. Winkelmann, O. Schott: "Über thermische Widerstandscoefficienten verschiedener Gläser in ihrer Abhängigkeit von der chemischen Zusammensetzung (Dependence of the thermal resistance of various glasses from the chemical composition)"; Annalen der Physik, 1894, vol. 287, issue 4, p 730-746 (in German).
H. Scholze, Glass - Nature, Structure and Properties, Springer-Verlag, 1991.
M. B. Volf, “Mathematical Approach to Glass," Glass Science and Technology, vol. 9, Elsevier, 1988.
[2] A. A. Appen, Glass Chemistry, 2nd Edition, Leningrad, 1974.
H. Scholze, Glass - Nature, Structure and Properties, Springer-Verlag, 1991.
[3] V. Ledererova, A. Smrcek, J. Rysavy, Sklar Keram. 36 (1986) 304 (Orig. Czech).
H. Scholze, Glass - Nature, Structure and Properties, Springer-Verlag, 1991.
[4] S. English, W. E. S. Turner; J. Am. Ceram. Soc. 10 (1927) 551.
[5] F. P. Hall, J. Am. Ceram. Soc. 13 (1930) 182.