## Pottery: Glaze Thermal Expansion

#### Calculating expansion

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 method assumes linearity. The expansions of glazes are not linear with temperature - see Mastering Cone 6 Glazes, pp72-81 for some actual expansion curves. Appen, Hall and Gilard&Dubral tested for linearity due to some oxide concentrations in a glaze and found rates that varied markedly with concentration for several oxides. It must be assumed that some of the well known oxide compounds behave differently than the sum of their parts until proven otherwise. I know of no author who has investigated the latter; it seems to have been assumed that such compounds can't occur in a fully melted (glassy) glaze. In the case of iron silicates, we know they do occur.
• The measurements were made by adding small amounts of the oxide under test to a reference glaze, then measuring the difference in expansion compared to the reference glaze alone. Authors used different reference glazes, different firing temperatures and different temperature ranges, and the distances involved are very small. The temperature range of interest to pottery is from the temperature at which the glaze effectively solidifies during cooling (500°C or higher for most pottery glazes) to freezer temperature (-15°C). Most authors measured over a temperature range far smaller than this (English&Turner 25-90°C, Winkelmann&Schott 20-100°C, Mayer&Havas 20-150°C, Appen 20-400°C, Hall 25-500°C, Ron Roy 50-600°C). Still, it's a graphic warning of the complexity of the problem when one author gets a positive value and another a negative, as M&H and Appen did for ZrO2 and SnO2.
• Some elements exist in more than one oxide form and it's not always clear which form is in a glaze. X-ray analysis of iron glazes indicate that even red glazes contain large amounts of black FeO, so the difference in expansion of FeO and Fe2O3 presents an additional uncertainty.

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.

#### Strength & rigidity

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:

 oxide factor BaO SiO2 Al2O3 ZnO PbO Na2O K2O B2O3 CaO MgO 3 7 12 20 20 20 40 61 70 80 (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:

 oxide factor K2O Na2O SiO2 BaO Al2O3 ZnO PbO CaO B2O3 MgO 4.3 5.3 6 7.5 10 10 14.5 15 16 19 (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:

 oxide factor(SiO2=1) BaO SiO2 Al2O3 PbO ZnO Na2O B2O3 MgO CaO K2O 0.3 1.0 1.0 1.2 1.7 3.2 3.3 3.6 4.0 8.0

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.

#### Comparison of expansion data

Primary sources (those who are believed to have measured the values quoted), linear expansion x10-6/K:

molarby weight
oxideSankeyAppenawAppen(aw=60)English & Turner Gilard & DubralHallMayer & HavasWinkelmann & Schott
range(C)20-40020-40025-90?25-50020-15020-100
Li2O2727 29.88 54 6.7
Na2O39.539.5 61.983841. 651 3833
K2O46.546.5 94.20 3039.0423028
BeO 4.5 4.5 25.01 10.8 15.7
MgO 3.4 6  40.31 8.9 4.5 0 2 0.3
CaO1313 56.081416.311#1517
MnO10.510.5 70.948.9 7.3
FeO 5.5 5.5 71.85 4.6  6.6
NiO 5 5 74.69 4.013.3
CoO 5 5 74.93 4.014.6
CuO 3 3 79.55 2.3 7.3
ZnO 5 5 81.39 3.7 7.0 7.7 10 6
SrO1616103.629.3
CdOtoxic11.5128.415.4
BaO2020153.337.814.0 9.11210
PbOtoxicsee below223.203.510.611.5  7.51410
SiO2 3.8see below 60.09  3.8* 0.5 0.44.0* 2.7
TiO2see below see below 79.87 1.1*13.6
ZrO2-6-6123.22 -2.9 2.3 7
SnO2-4.5-4.5150.71 -1.8 6.6
CeO2 4.0 172.1214
B2O3 see below see below 69.62-5 to 0 -6.5-4 2 0.3
Al2O3 4.2-3101.96-1.8 1.4 2  517
Mn2O32121 157.888.0
Cr2O3  4.2151.9917
Fe2O3see below 11159.69 4.113.3
Sb2O3 7.5  7.5285.421.6
P2O5 1414141.945.9 6.7
Sb2O5323.5 2  8.3 6.7
* 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:

• PbO: 13 + (50 * (A - 0.03)) where A is the sum of the molar fractions of Li2O, Na2O and K2O
• SiO2: 3.8 for 0-0.67 molar, 3.8 - (10 * (S - 0.67)) for 0.67-1.00 molar where S is the molar fraction of SiO2
• TiO2: 3 - (15 * (S - 0.5))
• B2O3: (1.25 * (4 - X)) - 5; to obtain the factor X, add the molar fractions of the five oxides Li2O, Na2O, K2O, CaO and BaO then subtract the molar fraction of Al2O3; divide the result by the molar fraction of B2O3. If the result is greater than 4, X = 4.

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 values

Appen 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.
oxideM&HAppenAWratio(AW=60)
CuO2.23.079.551.05
CoO4.45.074.930.93
NiO4.05.074.691.02
Cr2O35.1--- 151.99
The mean ratio between the authors' numbers referred to an atomic weight of 60 is 1.00±0.04 (as it should be). So, the linear molar 'Appen' value for Cr2O3 may be estimated from the cubic by weight of M&H as 5.1/3*1.00*151.99/60 = 4.2x10-6/K. The same method was used to derive the value for CeO2.

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.

#### References

• Appen: quoted by Vargin, Technology of Enamels (English translation of a Russian text)
• English & Turner: quoted by Hewitt&Bailey from J.Am.Ceram.Soc. 10(8),551 (1927), Relationship Between Chemical Composition and the Thermal Expansion of Glasses; ibid. 12,760 (1929) correction
• Gilard & Dubral: quoted by Dodd, Dictionary of Ceramics from Verres Silicates Ind. 5,122,141 (1934)
• Hall: J.Am.Ceram.Soc. 13(3):182-190 (1930), The Influence of Chemical Composition on on the Physical Properties of Glazes
• Mayer & Havas: quoted by Singer&German, Ceramic Glazes, and by Vargin from Sprechsall 42:497; 44:188-207, Coefficient of Expansion of Enamels and their Chemical Composition
• Winkelmann & Schott: Ann.Physik Chemie 51:730-746(1894), Ueber thermische Widerstandcoefficienten verschiedener Gläser in ihrer Abhängigkeit von der chemischen Zusammensetzung
• Hewitt&Bailey quotes Appen's value for Fe2O3 in Vargin as the full oxide; Vargin actually says for ½ the oxide.
• Vargin refers to P2O5 as P2O3.
• Hewitt&Bailey refer to AsO5 which doesn't exist; Vargin uses As2O3 for the same entry.

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:

molar fractional composition
#COE SiO2 Al2O3 K2O Na2O CaO MgO ZnO B2O3 SrO
H&R15.40.6748.0652.0072.0349.1055.0466 -.0631-
H&R25.78.6568.0772.0171.0366.1156.0359 -.0585-
H&R36.36.6476.0927.0294.0357.1213.0248 -.0462-
H&R46.89.6411.0855.0377.0382.1417.0103 -.0441-
H&R57.56.6267.0937.0291.0555.1412.0006 -.0247.0249
H687.9.5472.0501.0012.1410---.2606-
H886.4.7335.1070.0255.0032.1308----
H917.8.6230.0967-.0406.2386.0011---
H924.7.5810.1051-.0380-.2759---
H934.9.5168.1218.0008.0459-.3147---
H988.5622.0773.0502.0742-.1531-.0830-
H1055.8.6591.0586.0396.0256---.2171-
H1106.8.6197.1450.0211.0115.0970-.0794.0 263-
H1127.6.6082.0735.0021.1004-.0521.0711.0 928-
H1137.2.5992.0687.0007.0965-.1041.0410.0 897-
H1227.9.5810.1221.0153.0163.2653----
H1235.9.5471.1440.0167.0229.0074.2619--< td>-
H1245.4.5595.1445.0144.0189.0083.2543--< td>-
H1257.1.7093.1002.0273.0295.1337----
H1276.6.5690.1327.0140.0164.1987.0691--< td>-

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

1. Mix a sample of the glaze.
2. Cut a firebrick to a suitable size with a hacksaw, then make a roughly rectangular hole about 3 cm wide, 9 cm long and 5 cm deep. A carbide masonry drill makes it easy, but a coarse metal file will work.
3. Line the hole with clay. Make the layer as thin as possible while still having no pinholes that would leak. The aim is to have a liquid-tight layer that is more fragile than the glaze sample so it can be removed after firing without breaking the sample.
4. Mix alumina hydrate with 2% Bentonite and moisten with vinegar just enough to allow mixing. Pure alumina will not be dissolved by the glaze, thus modifying its composition and therefore its expansion rate. After firing, the alumina will be crumbly enough to be separated from the sample. The Bentonite and vinegar allows the mixture to stick together just enough to hold its place in the mould. The clay keeps the moisture in the alumina mixture from wicking into the brick, so it dries properly.
5. Line the mould with the alumina mixture, about 5 mm thick. It can be patted into place with a piece of wood. The end result should be a space for glaze that is at least three times as deep as wide, since most glazes shrink to about 50% of their dry volume when melted, and some of the glaze will soak into the alumina.
6. Fill the mould with glaze. Keep topping it up until everything appears dry, then press a finger firmly in the middle - there will be room for more. An oven at 80°C speeds this process up. When really full, dry overnight in the oven.
7. Glaze fire, holding at maximum temperature for half an hour to ensure that the glaze is melted all the way through.
8. You may be able to dig the sample out unbroken without damaging the firebrick, but I usually fail. With a hacksaw, remove excess firebrick, the carefully break away the remaining clay and alumina to reveal the sample.
9. Trim the sample to the precise size required for the dilatometer with a diamond saw.
10. Mount it in the dilatometer sample holder.
11. Program the dilatometer controller for the desired temperature range.
12. Using the temperature range over which the expansion is reasonably linear, calculate the average expansion.
Measuring glaze expansion

cut a hole in firebrick with a carbide tool

line it with clay

line the hole with alumina

fill with glaze and fire

remove brick