Measurement Errors of Glass Properties

When searching glass science and technology literature or the SciGlass database for reliable experimental data it is recommended to try eliminating the following errors:

1) Unreliable or insufficiently documented measurement procedures,
2) Accidental measurement and typing errors,
3) Systematic differences of whole data-series compared to the majority of all other series,
4) Decreasing reliability of modern glass literature data for some properties in the course of the last 50 to 80 years, and
5) Trends caused by evaporation losses and contamination during glass melting.

Problem 1) must be considered based on subject-matter knowledge while 2) to 5) are addressed through statistical analysis. Accidental measurement and typing errors lead to incorrect results to be discarded in about 2 to 10% of all glass literature data. Systematic differences of whole data-series result in about 5 to 20% of all glass literature data to have deviations from the majority of other series that can be corrected mathematically. The reliability of glass literature data in the system SiO2-Na2O decreased 3 to 4 times for the refractive index and for the density at 20°C in the most recent 50 to 80 years. Evaporation losses and contamination during glass melting cause, for example, the following trend in constant-viscosity points (isokom) at 100 Poise: A 100-Poise isokom at 1500°C is typically reported about 9°C too high compared to a 100-Poise isokom at 1400°C in the same data-series, based on the majority of all other series. Those error trends can be mitigated by statistical analysis.


1) Unreliable or insufficiently documented measurement procedures
Measurement procedures must be evaluated before experimental data are used, e.g., the glass thermal expansion that was carefully measured by recording several heating and cooling curves, allowing appropriate sample settling and residual stress removal (ASTM E1545), should be preferred over quick measurements obtained from a single heating curve. This reliability evaluation must be performed by an expert familiar with the subject matter. Some guidelines concerning the viscosity, thermal expansion, glass transition temperature Tg, and electrical conductivity measurement are provided on this website.


2) Accidental measurement and typing errors
Accidental errors occur in any human work. In the scientific glass literature as many as 11% of all available data for one property may be inaccurate as shown in Figure 1. The outliers in Figure 1 (density in binary system SiO2-Na2O) may be downloaded for further reference. Accidental errors can be recognized as outliers during comparison with similar data by statistical analysis. The error percentage may vary from property to property. Further examples for accidental errors can be found in the erroneous data references of the room temperature glass density model, the refractive index model, the dispersion model, and on the liquidus temperature modeling site (outlier by Ota et al., 1995). A comprehensive overview "Questionable experimental data on glass properties published in refereed journals" is provided by O. V. Mazurin.

Figure 1: Density in the binary system SiO2-Na2O based on 155 different investigators from SciGlass, 11% outliers (click image to enlarge)

3) Systematic differences of whole data-series compared to the majority of all other series
A closer examination of accidental errors often shows that they are not evenly distributed. Some investigators are using more reliable equipment than others, or they take greater care during experiments. Figure 2 displays a systematic error from the literature. The influence of water on the viscosity in the glass system 3 SiO2 - Na2O is compared based on two publications by Shelby & McVay (1976) and Jewell & Shelby (1988):

Figure 2: Systematic error, influence of water on the viscosity in a 3 SiO2 - Na2O glass according to Shelby & McVay (1976) and Jewell & Shelby (1988) (click image to enlarge)

Given the significantly different series by Shelby & McVay (1976) and Jewell & Shelby (1988) alone, it is not possible to decide which might come closer to the truth. In 1988, Jewell & Shelby knew about the earlier paper by Shelby & McVay from 1976, but they did not offer an explanation for the different results. To the contrary, Jewell & Shelby (1988) state a good agreement in the way that they performed new measurements of the transition temperature, Tg, on the old samples from Shelby & McVay and found agreement with their own newly prepared samples (Jewell & Shelby (1988), p 26]. No references to other authors were researched in either paper regarding the viscosity curve of a Na2O - 3 SiO2 glass. Later on in 1992, Jewell & Shelby again published a temperature at a viscosity of log(η in Pa·s) = 11 for a Na2O - 3 SiO2 glass of 495°C that contradicts the earlier data by the same authors (Jewell & Shelby, 1988) and agrees with Shelby & McVay (1976), without referring to their earlier work. A typographic error in the paper by Jewell & Shelby from 1988 caused by the journal editor appears possible, such as a unit confusion between Poise and Pa·s, but even then, systematic differences remain. The SciGlass database is of tremendous help in such unclear situations because it includes many references that can be used for comparison. According to SciGlass, the temperature at a viscosity of log(η in Pa·s) = 11 of a 3 SiO2 - Na2O glass is 482 ± 7°C, which indicates a systematic error by Jewell & Shelby (1988).
A further systematic error example is displayed in Figure 3. Mazurin & Gankin (2006) list systematic errors for the density of borate glasses, including rather serios errors by Singh et al. (2003).

Figure 3: Refractive index (n_d) curve in the binary system SiO2-Na2O, 6% outliers, systematic error by Matusita et al., 1984 (click image to enlarge)

4) Decreasing reliability of modern glass literature data for some properties
The difference between an experimental value, e.g., in Figures 1 and 3, and the displayed model fit is the residual. If those residuals are sorted according to the year of publication, and if the average of the absolute residuals is formed for each decade, one obtains the unsettling result displayed in Figure 4. Unfortunately, the error of 613 glass literature data for the density at 20°C in the system SiO2-Na2O significantly increased about three times in the last 50 years when advances in technology would suggest the opposite. Astonishing is the high-quality work in the 1930s. Among the 33 outliers in the last two decades, 21 were analyzed further and cross-checked with 14 original papers because of the rather high outlier percentage of 25 to 30% seen in Figure 4. Among those 21 data, 17 could be independently verified as outliers, 2 were incorrectly reported in SciGlass, and 2 cannot be counted because of the special preparation technique (sol-gel). All outlier data since 1990 were published in well respected journals (see outlier list, density in binary system SiO2-Na2O) with an average of 13 glass-density data per publication. However, the focus of 13 out of 14 papers was not on density, but on advanced glass-science issues. This indicates that the outlier percentage is still unacceptably high in the last two decades and that too many scientists focused on advanced research without a sound basis in regard to the density. A similar decreasing reliability trend applies also to the refractive index seen in Figure 3, where the error level increased 4 times over 80 years (see outlier list, refractive index in binary system SiO2-Na2O). In multi-component systems the error for refractive index and dispersion measurements increased about 50% in the recent decades. For advanced research it is advisable not to measure "simple" properties at all, whenever possible, but to take advantage of statistical models such as displayed in Figure 1 or by Fluegel (2007) where outliers are eliminated, providing the most reliable property values. Journal reviewers should question auxiliary experimental results in papers dedicated to otherwise completely different subjects.
According to O. V. Mazurin the frequency of measurements of easily determined properties, e.g., Tg and room-temperature density, increases while the frequency of some important but labor-consuming property measurements decreases in recent times (see Table 1, History and Prospect). One might conclude that financial reasons are behind this fact, which also influence the glass data reliability negatively. The decreasing reliability seems to be related to an economic approach to science, i.e., to obtain the highest output with the lowest input. The meaning of the word "science" itself is often not mentioned as first priority.
The decreasing reliability of modern glass literature data does not apply to all properties. For example, the reliability of chemical durability measurements increased in time, possibly caused by relevant commercial interest.
It is advisable to independently control measurement reliability with an accreditation system, applied to new acticles in high quality journals.

Figure 4: Decreasing reliability of modern glass literature data for density at 20°C in the binary system SiO₂-Na₂O, one outlier from the 19^th century (year 1889) not considered (click image to enlarge)

5) Trends caused by evaporation losses and contamination during glass melting
Not all systematic errors are caused by carelessness during property measurement. For example, it has been observed that viscosity depends on glass-batch materials possessing different evaporation behaviors (Frolow & Frischat, 1993) as seen in Figure 5. Similarly, systematic errors caused by evaporation can be observed not only when different batch materials are used, but also when melting at different temperatures as required by the viscosity curve, or when using various crucible materials, or when applying otherwise different experimental conditions. Therefore, trends of about 9°C residual increase per 100°C viscosity isokom increase occur during statistical analysis within the majority of individual series, depending on experimental conditions that hardly can be avoided. However, such trends can be mitigated by careful chemical analysis of the glasses after measurement (Fluegel, 2007).

Figure 5: Influence of different alumina batch materials on the viscosity of a soda-lime-silica glass with a target Al₂O₃ content of 2.5 wt% after Frolow & Frischat (1993) (click image to enlarge)

ASTM E1545-00, Standard Test Method for Assignment of the Glass Transition Temperature by Thermomechanical Analysis, (2000)

Fluegel (2007)
A. Fluegel: "Glass Viscosity Calculation Based on a Global Statistical Modeling Approach"; Glass Technol.: Europ. J. Glass Sci. Technol. A, vol. 48, 2007, no. 1, p 13-30.

Frolow & Frischat (1993)
P. Frolow, G. H. Frischat: "Influence of Different Al2O3 - Containing Batch Materials on Melting, Fining and Properties of Soda-Lime-Silica Glass"; Glastechn. Ber., vol. 66, 1993, no. 6/7, p 143-150.

Jewell & Shelby (1988)
J. M. Jewell, J. E. Shelby: "Effect of Water Content and Alumina Additions on the Transformation Range Properties of Na2O - 3 SiO2 Glasses"; J. Non-Cryst. Solids, vol. 102, 1988, no. 1-3, p 24-29.

Jewell & Shelby (1992)
J. M. Jewell, J. E. Shelby: "Effects of Water Content on the Properties of Sodium Aluminosilicate Glasses"; J. Am. Ceram. Soc., vol. 75, 1992, no. 4, p 878-883.

Matusita et al. (1984)
K. Matusita, C. Ihara, T. Komatsu, R. Yokota: "Photoelastic Effects in Silicate Glasses"; J. Am. Ceram. Soc., vol. 67, 1984, p 700-704.

Mazurin & Gankin (2006)
O. V. Mazurin, Yu. Gankin: "On effective use of existing experimental data in glass science "; Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B, vol. 47, no. 6, Dec. 2006, p 627-630.

Ota et al. (1995)
R. Ota, T. Wakasugi, W. Kawamura, B. Tuchiya, J. Fukunaga: "Glass formation and crystallization in Li2O-Na2O-K2O-SiO2"; J. Non-Cryst.Solids, vol. 188, 1995, no. 1-2, p 136-146.

Shelby & McVay (1976)
J. E. Shelby, G. L. McVay: "Influence of Water on the Viscosity and Thermal Expansion of Sodium Trisilicate Glasses"; J. Non-Cryst. Solids, vol. 20, 1976, no. 3, p 439-449.

Singh et al. (2003)
H. Singh, K. Singh, G. Sharma, L. Gerward, R. Nathuram, B. S. Lark, H. S. Sahota, A. Khanna: "Barium and calcium borate glasses as shielding materials for x-rays and gamma-rays"; Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B, vol. 44, no. 1, Feb. 2003, p 5-8.