Overview of existing glass property models

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Glass models can be classified into empirical (based on observation with the senses), deductive (based on reasoning), and semi-empirical (based on observation and reasoning) types. The empirical models are primarily created to accurately reflect observations, while deductive models are mainly developed to enhance scientific understanding. Semi-empirical models stand in between. The focus on this website is on empirical models for glass engineers and applied researchers. A few examples for deductive and semi-empirical models are also listed.
Empirical models may be further subdivided into local and general ones. Local models are based on limited data, either from one specific glass composition region and/or data from one specific investigator. Some researchers developed stepwise several local models to obtain overall enhanced validity limits for a conglomerate of local models. Among the local models the additivity models should be mentioned that are entirely built on the classical additivity principle. This principle implies that the relation between the glass composition and a specific property is linear to all component concentrations. Some researchers incorporated structural parameters, derived from empirical glass chemistry experience, into their models to enhace the model validity limits, thereby establishing structural models.
If data from several investigators are considered over a wide glass composition region in a unified approach general models are developed. Some structural models can be termed as general (as long as the approach is not stepwise that would make them to a conglomerate of local models). Statistical models are (mostly general) models that do not take into account glass chemistry experience like structural models and which are predominantly based on statistical analysis.

For references see below

Classical additivity glass models
Additivity models are often pioneering work about previously unknown glass composition regions, notably the models by Winkelmann and Schott (1894), who established scientific glass research at the end of the 19th century in Jena, Germany. Later studies include works by English (1924-26) and Gehlhoff et al. (1926). Well known is the viscosity model for commercial soda-lime-silica glasses by Lakatos et al. (1972); other models such as by Öksoy et al. (1994) and Lyon (1974) are based on it. Models by Hrma et al. (1994) and Vienna (1996) were specifically developed for glasses used in nuclear waste vitrification. Hrma (2006) also published viscosity models for several commercial glass types. Further additivity models were developed by Boow and Turner (1942), Winter (1959), Bottinga et al. (1972) (viscosity), Shcherbakova et al. (2001) (light transmission), Fluegel et al. (2003) (viscosity), and Kucuk et al. (1999) (surface tension). Bottinga's viscosity models are noteworthy because they are based on a total of 2440 data, applying the additivity principle stepwise to glasses with different silica concentrations.

Structural and semi-empirical glass models
The advantage of structural and semi-empirical models is the prediction of glass properties even beyond the limits of the available experimental data, based on empirical glass chemistry experience (structural models) or basic principles (semi-empirical models). This enables wide model application, but at the same time inaccurate predictions are possible because glass chemistry experience is not perfect and principles might be insufficiently understood. Many structural models are a conglomerate of several local models to account for a change of the glass chemistry. Huggins and Sun (1943) created an additivity model based on atomic fractions. The oxides PbO, CaO, and BaO were considered by special equations. Furthermore, B2O3 was regarded as either tree- or fourfold coordinated to account for the boric oxide anomaly. The work of Appen (1970) is based on additivity models that contain 1500 experimental data in total. Stepwise correction functions were introduced for many major components to account for coordination changes, for example in his thermal expansion model. Gan Fuxi (1974) extended the models by Appen to wider glass composition regions and further properties. Demkina (1976) published addidivity models for optical glasses including various correction functions according to the glass composition. Among the most recent structural models are those by Priven (2004). Priven derived chemical equilibrium factors from the properties of binary and ternary glasses, and stepwise applied various property equations, depending on the glass composition. The obtained factors and equations are extended and compared to glasses with complex compositions.
In semi-empirical models it is tried to combine fundamental equations with experimental observation, such as in the model by Ghiorso and Kress (2004), applicable for the calculation of the density of and sound speed in glass melts.

Statistical glass models
The statistical models are based on statistical analysis, in particular on linear or non-linear regression, mostly considering non-linear composition-property functions. Since no previous (possibly incorrect) glass chemistry experience is taken into account the statistical models are often very accurate. Systematic differences between investigators can be detected and corrected. Predictions beyond the limits of the model input data are not possible, however, in contrast to structural models.
One of the first statistical models was developed by Lyon (1974), based on 77 literature data. Selected datasets were considered as correct, and the remaining datasets were evaluated according to those standards. Interactions and non-linear terms were stated based on experience, bringing Lyon's work close the structural models. The model by Mazurin and Prokhorenko (2005) is applicable for predicting the electrical resistivity of commercial soda-lime-silica glasses and for sodium borosilicate melts. Mazurin and Prokhorenko list about 600 experimental data from various sources in the literature, but not all values were considered for the model development. Further statistical models were published by Fanderlik (1971) and Dvorak (1973) within rather narrow validity limits. Also the above mentioned additivity model by Lakatos et al. (1972) is of the statistical type.
On this website the most recent and accurate general statistical glass models are given in more detail, in particular for the viscosity, the liquidus temperature, the density at room temperature, the density and thermal expansion of melts, the thermal expansion below the glass transition, the electrical conductivity of melts, the thermal conductivity, the water solubility in melts, and the surface tension of melts.

Deductive glass models
Strictly speaking, all glass property models are empirical by nature because all are based on observations of one kind or another. Besides the thinking process itself, nothing is perceived ab-initio (from the beginning) as shown by R. Steiner (1894). However, models derived from basic scientific principles are commonly not termed as empirical because the empirical character is hidden behind fundamental laws and theories. Nevertheless, deductive glass property models should be better termed more specifically after the method applied, e.g., molecular dynamics simulation (based on atomic volume, bond strength, atomic size, etc.) or thermodynamic modeling (based on chemical equilibrium constants, energy of formation, etc.). Those models are good to enhance the scientific understanding of glass, to establish property relations, and to form the basis of new discoveries. This does not mean that empirical or semi-empirical do not lead to any discoveries, as demonstrated by Markova et al. (2006). Accurate predictions for complex commercial glasses are hardly possible using deductive models.
Makishima and Mackenzie (1976) pioneered the thermodynamic approach to glass. They based their models on the packing density of mass particles and bond strengths, derived from thermochemical data of crystals. Their work has theoretical importance. However, because of the introduction of uncertain factors, e.g. the ionic radii and coordination numbers, Makishima and Mackenzie's models are rather inaccurate. Advanced thermodynamic models were published by Pelton et al. (1999), Nemilov (1995), Shakhmatkin and Vedishcheva et al. (2001), Conradt (2001), Spear and Besmann et al. (2003), and others. An example of "ab-initio" molecular dynamics simulation is given by Kresse (2002).


Appen (1970)
A. A. Appen: "Chemistry of Glass", 1970, Khimiya, Leningrad (In Russian).

Boow and Turner (1942)
J. Boow, W. E. S. Turner; J. Soc. Glass Technol., vol. 26, 1942, p 215.

Bottinga et al. (1972)
Y. Bottinga, D. F. Weill: "The viscosity of magmatic silicate liquids: a model for calculation", Am. J. Sci., vol. 272, May 1972, p 438-475.

Conradt (2001)
R. Conradt: "Thermodynamic Approach to viscosity in the glass transition"; Glastech. Ber. Glass Sci. Technol., vol. 67, no. 11, 1994, p 304-311.
R. Conradt: "Modeling of the thermochemical properties of multicomponent oxide melts"; Zeitschrift für Metallkunde / Materials Research and Advanced Techniques, vol. 92, no. 10, October 2001, p 1158-1162.

Demkina (1976)
L. I. Demkina: "Investigation of the Dependence of the Glass Properties on their Composition" (in Russian), Moscow, 1958.
L. I. Demkina: "Physicochemical Principle of the Manufacture of Optical Glass" (in Russian), Izd. Chimia, Leningrad, 1976.

Dvorak (1973)
J. Dvorak; IP 1973 (Microhardness) (in Czech), vol. 16, no. 2/1973.

English (1924-26)
S. English: "The effect of composition on the viscosity of glass"; J. Soc. Glass Technol., 1924, no. 8, p 205-48; 1925, no. 9, p 83-98; 1926, no. 10, p 5266.

Fanderlik (1971)
I. Fanderlik, M. Skrivan; Communications, IX Congres Intern. du verre, Versailles 1971, vol. I, I-2, p 237.

Fluegel et al. (2003)
A. Fluegel, A. K. Varshneya, T. P. Seward, D. A. Earl: "Viscosity of commercial glasses in the softening range"; in: Proceedings 7th International Conference, Advances in the Fusion and Processing of Glass III (Ceramic Transactions, Volume 141; Eds.: J. R. Varner, T. P. Seward, H. Schaeffer), Rochester, New York, USA, July 27-31, 2003, p 379-386.

Gan Fuxi (1974)
Gan Fuxi; Scientia Sinica, vol. 12, 1963, p 1365; vol. 17, 1974, p 533-551.

Gehlhoff et al. (1926)
G. Gehlhoff, M. Thomas; Z. techn. Physik 6 (1925), p 544; Z. techn. Physik 7 (1926), p 105 and p 260; "Lehrbuch der technischen Physik", J. A. Barth-Verlag, Leipzig, 1924, p 376.

Ghiorso and Kress (2004)
M. S. Ghiorso, V. C. Kress: "An Equation of State for Silicate Melts. II. Calibration of Volumetric Properties at 105 Pa" Am. J. Sci., vol. 304, Oct/Nov 2004, p 679-751.

Hrma et al. (1994)
P. R. Hrma, G. F. Piepel et al.: "Property / Composition Relationships for Hanford High-Level Waste Glasses Melting at 1150°C"; PNL Report 10359 to the US Department of Energy, vol. 1 and vol. 2, December 1994.
P. Hrma, R. J. Robertus: "Waste glass design based on property composition functions"; Ceram. Eng. Sci. Proc., vol. 14, no. 11/12, 1993, 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, p 505-513.

Huggins and Sun (1943)
M. L. Huggins, K.-H. Sun; J. Amer. Ceram. Soc., vol. 36, 1943, p 6-11.

Kresse (2002)
G. Kresse: "Ab initio molecular dynamics: recent progresses and limitations"; J. non-Cryst. Solids, 2002, vol. 312-314, p 52-59.

Kucuk et al. (1999)
A. Kucuk, A. G. Clare, L. Jones: "An estimation of the surface tension of silicate glass melts at 1400°C using statistical analysis"; Glass Technol., vol. 40, no. 5, Oct 1999, p 149-153.

Lakatos et al. (1972)
T. Lakatos, L.-G. Johansson and B. Simmingsköld, "Viscosity temperature relations in the glass system SiO2-Al2O3-Na2O-K2O-CaO-MgO in the composition range of technical glasses"; Glass Technology, vol. 13, no. 3, June 1972, p 88-95.

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

Makishima and Mackenzie (1976)
A. Makishima, J. D. Mackenzie: "Direct calculation of Young's moidulus of glass"; J. Non-Cryst. Solids, vol. 12, 1973, p 35; "Calculation of bulk modulus, shear modulus and Poisson's ratio of glass", vol. 17, 1975, p 147; "Calculation of thermal expansion coefficient of glasses", vol. 22, 1976, p 305.

Markova et al. (2006)
T. S. Markova, O. V. Yanush, I. G. Polyakova, B. Z. Pevzner: "Glass property calculations and prediction of new compounds on the basis of raman spectroscopy of borate glasses" Phys. Chem. Glasses - Europ. J. Glass Sci. Technol. B, vol. 47, no. 4, August 2006, p 476-483.

Mazurin and Prokhorenko (2005)
O. V. Mazurin, O. A. Prokhorenko: "Electrical conductivity of glass melts"; Chapter 9 in: "Properties of Glass-Forming Melts" ed. by D. L. Pye, A. Montenaro, I. Joseph; CRC Press, Boca Raton, Florida, May 2005, ISBN: 1574446622.

Nemilov (1995)
S. V. Nemilov: "Thermodynamic and kinetic aspects of the vitreous state", CRC Press, Boca Raton - Ann - Arbor - London - Tokyo, 1995.

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

Pelton et al. (1999)
A. D. Pelton, P. Wu: "Thermodynamic modeling in glass-forming melts"; J. Non-Cryst. Solids, 1999, vol. 253, no. 1-3, p. 178-191.
A. D. Pelton, M. Blander: "Thermodynamic analysis of ordered liquid solutions by a modified quasichemical approach - application to silicate slags"; Metallurgical Transactions B (Process Metallurgy), vol. 17B, no. 4, Dec 1986, p 805-815.
P. Chartrand, A. D. Pelton: "Modeling the charge compensation effect in silica-rich Na2O-K2O-Al2O3-SiO2 melts"; Calphad: Computer Coupling of Phase Diagrams and Thermochemistry, vol. 23, no. 2, June 1999, p 219-230.

Priven (2004)
A. I. Priven: "General Method for Calculating the Properties of Oxide Glasses and Glass-Forming Melts from their Composition and Temperature"; Glass Technology, vol. 45, Dec 2004, no. 6, p 244-254.
A. I. Priven, Doctoral Thesis, St. Petersburg, 2002.

Shakhmatkin and Vedishcheva et al. (2001)
N. M. Vedishcheva, B. A. Shakhmatkin, M. M. Shultz: "A simulation of the thermodynamic properties of oxide melts and glasses"; Ceramic Transactions, vol. 29, Eds.: A. K. Varshneya, D. F. Bickford, P. P. Bihuniak; The American Ceramic Society, 1993, p 283-288.
N. M. Vedishcheva, B. A. Shakhmatkin: "Thermodynamic studies of oxide glass-forming liquids by the electromotive force method"; J. Non-Cryst. Solids, vol. 171, no. 1, July 1994, p 1-30.
B. A. Shakhmatkin, N. M. Vedishcheva, M. M. Shultz, A. C. Wright: "The thermodynamic properties of oxide glasses and glass-forming liquids and their chemical structure"; J. Non-Cryst. Solids, vol. 177, no. pt 1, 1994, p 249-256.
N. M. Vedishcheva, B. A. Shakhmatkin, M. M. Shultz, A. C. Wright: "The thermodynamic modelling of glass properties: a practical proposition?"; J. Non-Cryst. Solids, vol. 196, March 1996, p 239-243.
B. A. Shakhmatkin, N. M. Vedishcheva, A. C. Wright: "Can thermodynamics relate the properties of melts and glasses to their structure?"; J. Non-Cryst. Solids, vol. 293-295, no. 1, November 2001, p 220-226.
B. A. Shakhmatkin, N. M. Vedishcheva, A.C. Wright: "Thermodynamic modeling of the structure of glasses and melts: single-component, binary and ternary systems"; J. Non-Cryst. Solids, vol. 293-295, November 2001, p 312-317.

Shcherbakova et al. (2001)
N. N. Shcherbakova, V. I. Kondrashov, I. A. Kupriyanova, V. A. Gorokhovskii: "Regression equations for determining light transmission in tinted float glass"; Glass and Ceramics (English translation of Steklo i Keramika), vol. 58, no. 5-6, May/June 2001, p 164-165.

Spear and Besmann et al. (2003)
K. E. Spear, T. M. Besmann, E. C. Beahm: "Thermochemical modeling of nuclear Waste Glass"; Proceedings of the symposium on High Temperature Corrosion and Materials Chemistry, The Electrochemical Society, 10 South Main St., Pennington, NJ (Fall 1998).
T. M. Besmann, K. E. Spear, E. C. Beahm: "Thermochemical models for nuclear waste glass subsystems - MgO-CaO and MgO-Al2O3"; Materials Research Society Symposium - Proceedings, vol. 556, 1999, p 383-389.
K. E. Spear, T. M. Besmann, E. C. Beahm: "Thermochemical modeling of glass: Application to high-level nuclear waste glass"; MRS Bulletin, vol. 24, no. 4, April 1999, p 37-44.
T. M. Besmann, K. E. Spear: "Thermochemical modeling of oxide glasses"; J. Am. Ceram. Soc., vol. 85, no. 12, Dec 2002, p 2887-2894.
T. M. Besmann, K. E. Spear, J. D. Vienna: "Extension of the modified associate species thermochemical model for high-level nuclear waste: Inclusion of chromia"; Materials Research Society Symposium - Proceedings, vol. 757, 2003, p 195-200.
M. D. Allendorf, K. E. Spear: "Thermodynamic analysis of silica refractory corrosion in glass-melting furnaces"; J. Electrochem. Soc., vol. 148, no. 2, Feb 2001, p B59-B67.

R. Steiner (1894)
R. Steiner: "Die Philosophie der Freiheit (The Philosophy of Freedom)" Verlag von Emil Felber, Berlin, 1894.

Vienna et al. (1996)
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°C (Draft)"; PNNL Report 10987 to the US Department of Energy, February 1996.

Winkelmann and Schott (1894)
A. Winkelmann, O. Schott: "Über die Elastizität und über die Druckfestigkeit verschiedener neuer Gläser in ihrer Abhängigkeit von der chemischen Zusammensetzung"; Ann. Physik Chemie, vol. 51, 1894, p 697; and "Über thermische Widerstandscoefficienten verschiedener Gläser in ihrer Abhängigkeit von der chemischen Zusammensetzung", vol. 51, 1894, p 730; and "Über die specifischen Wärmen verschieden zusammengesetzter Gläser", vol. 49, 1893, p 401.

Winter (1959)
A. Winter; Verres refract., vol. 13, 1959, p 293.