Comparison of Glass Viscosity Models

For comparison, the glass melting point predictions in ^oC at a viscosity of 10 Pa*s (100 Poise) for the compositions given in Table I according to several models are listed in Table II. All glasses in Table I are standards, where the viscosity (but not the composition except for DGG I) was verified by several laboratories, excluding the soda-lime-silica container glass "CO." CO is listed because of its simple composition, covered by most viscosity models. The experimental results are also shown in Table II for comparison.

Table II: Glass melting point predictions according to several models and experimental results; the values in parentheses were calculated by slightly exceeding the model application limits as often practiced.
Model	Melting point prediction in °C, viscosity = 10 Pa·s
Model	CO	710A	717A	711	710	DGG I	WGS
Experiment	1467	1464	1555	1327	1434	1439	1048
Mazurin [8, 9]	1440	/	/	/	/	1428	/
Bottinga [10]	1494	1525	/	/	1475	1443	/
Lakatos 1972 [11]	1478	(1509)	/	/	(1441)	(1458)	/
Lakatos 1976 [8, 12]	1473	(1471)	/	/	(1444)	(1456)	/
Lyon [13]	1479	(1461)	/	/	(1423)	1454	/
Sasek [12]	1507	(1590)	/	/	(1493)	1498	/
Ledererova [12, 14]	1529	(1571)	/	/	(1498)	1508	/
Cuartas [12, 14]	(1460)	(1545)	/	/	(1491)	1455	/
Braginskii [12, 14]	(1321)	/	/	/	/	(1436)	/
Herbert [15]	/	/	/	1321	/	/	/
Öksoy [16]	1438	(290)^a	/	/	(1406)	(1198)^a	/
Öksoy^b [16]	1476	(1494)	/	/	(1437)	(1456)	/
Priven, [8, 17]	1437	1431	1460	1321	1474	1443	(1282)
Hrma, 1994 [18]	/	/	/	/	/	/	(1075)^c
Hrma^d, 2006 [19]	1475	/	/	/	/	1437	/
Hrma^e, 2006 [19]	1467	(1433)	(1524)	/	1401	1444	/
Fluegel 2004 [20]	1478	1465	1558	1323	1434	1452	/
Fluegel 2005 [21]	1480	(1534)	/	/	(1472)	(1440)	/
Fluegel 2006 [22]	1468	1457	1526	1310	1434	1446	1050
^a Unusual predictions caused by the unrealistic coefficients for Fe₂O₃, TiO₂, and SO₃ ^b Neglecting Fe₂O₃, TiO₂, and SO₃ ^c Counting K₂O as Na₂O because model not valid for glasses containing K₂O ^d Local model for soda-lime container glasses ^eGlobal model for various commercial glasses

[1] P. Hrma, C. A. See, O. P. Lam, K. B. C. Minister: "High-Temperature Viscosity of Commercial Glasses", part of Chapter 7 in: "High temperature glass melt property database for process modeling"; Eds.: T. P. Seward III and T. Vascott; The American Ceramic Society, Westerville, Ohio (2005), ISBN: 1-57498-225-7.

[2] "Standard Reference Material 710A, Soda-Lime-Silica Glass"; National Institute of Standards & Technology (NIST), Gaithersburg, MD, 20899, USA; March 20, 1991.

[3] "Standard Reference Material 717A, Borosilicate Glass"; National Institute of Standards & Technology (NIST), Gaithersburg, MD, 20899, USA; September 18, 1996.

[4] "Standard Sample No. 711, Certificate of Viscosity Values, Lead-Silica Glass"; National Bureau of Standards, U.S. Department of Commerce, Washington, D.C., 20235, USA; July 1, 1964.

[5] A. Napolitano, E. G. Hawkins: "Viscosity of a Standard Soda-Lime-Silica Glass"; J. of Research of the National Bureau of Standards - A. Physics and Chemistry (1964), vol. 68A, no. 5, p 439-448.

[6] G. Meerlender: "Viskositäts-Temperaturverhalten des Standardglases I der DGG" (DGG - Deutsche Glastechnische Gesellschaft, German Society of Glass Technology); Glastechn. Ber. (1974), vol. 47, no. 1, p 1-3.

The Waste Glass Standard was established in Round-Robin tests with several participating laboratories.

[9] O. V. Mazurin, N. I. Tretiakova, T. P. Shvaiko-Shvaikovskaya: "Metod rascheta viazkosti silikatnykh stekol"; Deposited in VINITI (1969), no. DEP1091-69.

[10] Y. Bottinga, D. F. Weill: "The Viscosity of Magmatic Silicate Liquids: A Model for Calculation"; Am. J. Sci. (1972), vol. 272, p 438-475.

[12] H. Scholze: "Glass - Nature, Structure and Properties"; Springer-Verlag (1991), ISBN 0-387-97396-6.

[13] K. C. Lyon: "Prediction of the Viscosities of Soda-Lime Silica Glasses"; J. Res. Nat. Bur. Standards A, Physics and Chemistry (1974), vol. 78A, no. 4, p 497-504.

[14] D. Martlew: "Viscosity of Molten Glasses"; Chapter 5 in: "Properties of Glass-Forming Melts", edited by L. D. Pye, A. Montenaro, I. Joseph, CRC Press, Boca Raton, Florida (2005), ISBN 1-574444-662-2.

[15] J. Herbert, M. Prod'homme, M. Derobert: "Viscosity-Temperature Relations in the SiO₂-Na₂O-K₂O-Al₂O₃-B₂O₃-PbO System in the Composition Range of Lead Crystal Glass"; Verres et Refractaires (1976), vol. 30, no. 2, p 219-221.

[16] D. Öksoy, D. L. Pye, E. N. Boulos: "Statistical analysis of viscosity-composition data in glassmaking"; Glastech. Ber. Glass Sci. Technol. (1994), vol. 67, no. 7, p 189-195.

[17] A. I. Priven: "General Method for Calculating the Properties of Oxide Glasses and Glass-Forming Melts from their Composition and Temperature"; Glass Technology (2004), vol. 45, no. 6, p 244-254.

[18] P. R. Hrma, G. F. Piepel et al.: "Property/Composition Relationships for Hanford High-Level Waste Glasses Melting at 1150^oC"; PNL Report 10359 to the US Department of Energy (1994), vol. 1 and 2.

J. D. Vienna, P. R. Hrma et al.: "Effect of Composition and Temperature on the Properties of High Level Waste (HLW) Glass Melting above 1200^oC (Draft)"; PNNL Report 10987 to the US Department of Energy (1996).

P. Hrma, R. J. Robertus: "Waste glass design based on property composition functions"; Ceram. Eng. Sci. Proc. (1993), vol. 14, no. 11/12, p 187-203.

P. Hrma, G. F. Piepel, P. E. Redgate, D. E. Smith, M. J. Schweiger, J. D. Vienna, D. S. Kim: "Prediction of processing properties for nuclear waste glasses"; Ceramic Transactions, vol. 61, "Environmental Issues and Waste Management Technologies in the Ceramic and Nuclear Industries" (1995), p 505-513.

[19] P. Hrma: "High-Temperature Viscosity of Commercial Glasses"; Ceramics - Silikáty (2006), vol. 50, no. 2, p 57-66.

[20] A. Fluegel, A. K. Varshneya, D. A. Earl, T. P. Seward, D. Oksoy: "Improved compositio-property relations in silicate glasses, part I: Viscosity"; Ceramic Transactions, vol. 170, "Melt Chemistry, Relaxation, and Solidification Kinetics of Glasses" - Proceedings of the 106^th Annual Meeting of the American Ceramic Society (2005), p 129-143.

Table I: Compositions in mol% of glasses for melting point predictions in Table II
Soda-lime-silica (CO) container glass [1]	SiO₂ 74.41, Al₂O₃ 0.75, Na₂O 12.90, K₂O 0.19, MgO 0.30, CaO 11.27, SO₃ 0.16, Fe₂O₃ 0.01, TiO₂ 0.01
NIST 710A [2]	SiO₂ 71.43, Al₂O₃ 1.31, Na₂O 8.25, K₂O 6.27, CaO 9.62, ZnO 2.81, TiO₂ 0.32
NIST 717A [3]	SiO₂ 72.25, B₂O₃ 16.97, Al₂O₃ 2.19, Li₂O 2.14, Na₂O 1.03, K₂O 5.42
711 [4]	SiO₂ 71.28, Al₂O₃ 0.51, PbO 18.90, Na₂O 3.76, K₂O 5.55
710 [5]	SiO₂ 72.74, Al₂O₃ 0.11, Na₂O 8.70, K₂O 5.07, CaO 12.82, SO₃ 0.15, Fe₂O₃ 0.01, Sb₂O₃ 0.40
DGG I [6]	SiO₂ 70.94, Al₂O₃ 0.72, Na₂O 14.34, K₂O 0.21, MgO 6.16, CaO 7.13, SO₃ 0.32, Fe₂O₃ 0.07, TiO₂ 0.10
Waste Glass Standard (WGS) [7]	SiO₂ 53.76, B₂O₃ 8.24, Al₂O₃ 3.04, Li₂O 7.33, Na₂O 12.54, K₂O 1.93, MgO 1.41, CaO 1.77, Fe₂O₃ 6.00, TiO₂ 1.00, MnO₂ 1.84, Cr₂O₃ 0.04, ZrO₂ 0.06, BaO 0.04, NiO 1.00