Strength & rigidity
Comparison of expansion data
Derivation of recommended values
Expansion Data Fitting
Making a glaze expansion sample
As long as a ceramic melts to form a glass, it is possible to approximate its thermal expansion with a linear model: the proportion of each oxide is multiplied by the expansion of that oxide; the sum of these is then a reasonable approximation to the expansion of the glaze. This method is not applicable to fired clay bodies, as they don't completely melt; their expansion has to be measured directly. Hewitt&Bailey provide a list for one manufacturer at Calculating Crazing.
There have been many tables of oxide thermal expansion published over the years; see Hewitt&Bailey for a summary. The oxide constitution of many minerals and frits is at Digitalfire. Ron Roy has published the recipes and average measured expansions over 50-600°C of five glazes in Mastering Cone 6 Glazes, pp72-81. I currently use the oxide expansion data of Appen, Technology of Enamels because it's the most complete data available from a primary source. Whichever set you use with your glaze calculation program, line fit the calculated to actual values, then use the fit-derived correction. When comparing a glaze expansion to those of my clays using the Sankey coefficients below, I use ExpectedExpansion=(CalculatedExpansion*0.81)+0.63 because this is the best fit to Ron Roy's data and his data is what I have for my clays. However, the best fit with these coefficients to Hall's data is no correction; the reasons for this discrepancy have not yet been resolved.
If you don't have line fitting software, here is a method that can be used with a desk calculator.
Calculated glaze expansions must be treated with caution for several reasons:
The procedure for making a glaze expansion sample is described below and shown at right. Hall made 124! You should appreciate how much work lies behind those numbers in expansion tables when you wonder why so many authors measured so few oxides.
The coefficients of the two clay bodies I use were measured on the same apparatus
and over the same range as used for the glaze expansions:
Tucker Smooth White stoneware: 6.64x10-6/K
Tucker 6-50 porcelain: 7.71x10-6/K
It is generally believed that the expansion for a stable glaze must be 1-10% less than that of the clay. Glaze expansions much less than this can result in shivering - the breaking off of sharp pieces of glaze under thermal stress. Glaze expansions higher than that of the clay can cause crazing - fine cracks in the glaze surface that will trap contaminants, thus making the item unsuitable for containing food.
However, analysis of successful glazes from the Clayart archives calls this into question - glazes can have expansions well outside this range and still be successful. The mean COE of these glazes is 6.2x10-6/K as expected, but the range is far wider than 10%. It should be noted, however, that almost none of the testers performed any functional tests, such as a freezer to boiling water cycle.
The tensile strength of a glaze affects the fit of glaze to body. A high tensile strength enables a glaze to withstand a greater mismatch than a low one. Tensile strength varies inversely with thickness, so the thicker the glaze, the more likely it is to fail. Hall provides factors for tensile strength which are useful as a guide to which glaze compositions will be strongest:
|(units are kg/mm2 for rods 0.35-0.5 mm diameter, by weight)|
The elasticity of a glaze also affects the fit of glaze to body. A low rigidity (high elasticity) enables a glaze to withstand a greater mismatch than high rigidity. Hall provides factors for rigidity which are useful as a guide to which glaze compositions will be the least elastic:
|(units are g/mm2 for rods 0.8-3 mm diameter, by weight)|
What is wanted in a glaze is high tensile strength coupled with low rigidity. Dividing Hall's tensile strength factors by his rigidity factors yields a dimensionless factor of merit:
From this data, the most useful oxide to improve the ability of a glaze to withstand expansion mismatch is K2O, with CaO, MgO, B2O3 and Na2O in second rank. They increase the tensile strength the most and increase the rigidity the least of a glaze containing them.
Primary sources (those who are believed to have measured the values quoted), linear expansion x10-6/K:
|oxide||Sankey||Appen||aw||Appen(aw=60)||English & Turner||Gilard & Dubral||Hall||Mayer & Havas||Winkelmann & Schott|
|TiO2||see below||see below||79.87||1.1*||13.6|
|B2O3||see below||see below||69.62||-5 to 0||-6.5||-4||2||0.3|
* 60% SiO2.
# 10% CaO, all other G&D oxides at 0%.
To use the molar values, divide the weight of each oxide used by its atomic weight, then normalise the sum to unity (1.0). To use the by-weight values, normalise the sum of weights of all oxides in the glaze to unity.
Appen molar formulae for the variable expansion oxides:
Hall's graph for the variable expansion of silica is well fitted by the equation 4.9 + (2.5 * S) - (6.8 * S * S) where S is the molar fraction of SiO2.
Three authors looked for coefficients that vary with concentration: Hall, Appen, and Gilard&Dubral. Hall found no dependence for B2O3, while Appen and Gilard&Dubral did. I have not yet located the original papers of Appen or Gilard&Dubral, but the glazes listed below, most of which are Hall's, do not support any concentration-dependent coefficients.
Derivation of recommended valuesAppen did not measure Cr2O3. Since Mayer&Havas did, and both obtained reasonably consistent measurements of CuO, CoO and NiO (I omit ZrO2 and SnO2, where their results were inconsistent) the missing Appen value can be approximated by proportion. The data of Appen is linear molar, that of M&H cubic by weight, so it is necessary to determine the atomic weights of the comparison oxides to convert between molar and by-weight measures. The average molar weight of practical glazes is very close to that of silica, 60, so that's a good reference molar weight to use for intercomparisons.
When Hall's formula for the expansion of SiO2 is compared to Appen's variable formula and to a constant value with the set of glazes listed below, there is insufficient evidence for a variable coefficient, so Appen's value is retained. Once this is chosen, the best fit for Al2O3 is +4.2 (equivalent to 2.5 by weight), in much better agreement with other data than Appen's value of -3. Following this, the best fit for MgO is 3.4 (5 by weight), also more in agreement with other results.
X-ray analyses show that almost all of the iron in a glaze is FeO; Fe2O3 is restricted to crystals on the surface. There is evidence that other sesquioxides that also exist in a monoxide form do the same. I therefore recommend that all oxides that exist in both forms be converted to monoxide equivalent before calculating expansion or unity values.
The important oxides for pottery glazes where there is major disgreement are shown in red. That's where I'll be focussing my studies for now. I plan basically to correct the molar data of Appen whenever there is clear evidence that he was wrong. Initial trials of iron, zirconia and tin are in progress.
Expansion Data Fitting
Hall's data is of superb quality. However, little of it can be used by modern potters. 50% of his test glazes used lead, which no potter can now use. And, of the remainder that are free of barium and arsenic, most had expansion coefficients far in excess of that required to fit modern clays. Hesselberth&Roy found that a glaze expansion of 7.76x10-6/K crazed on all clays they tested. Only eleven of Hall's non-toxic glazes have lower expansion than this. Here are the glazes useful to potters that are available for data fitting:
H&R: Mastering Cone 6 Glazes, pp72-81.
H: Hall: J.Am.Ceram.Soc. 13(3) pp184-189
The data of Hall and H&R have a serious consistent difference. The best fit of the Sankey molar coefficients above to H&R's data is 0.81*a+0.63 ±0.02, while the best fit to Hall's is 1.05*a-.07 ±0.1 This requires further investigation.
Making a glaze expansion sample
cut a hole in firebrick with a carbide tool
line it with clay
line the hole with alumina
fill with glaze and fire
sample ready for trimming
a sample in the trimmer
the sample holder and dilatometer controller
the dilatometer furnaces
the plot of expansion
photos by John Sankey and Ron Roy