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Calculated Thermal Expansion

Calculation of the thermal expansion of glazes is a very useful comparative glaze-fit tool. But it’s not a laboratory measurement.

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Calculated thermal expansion is one of the most useful numbers in glaze chemistry—but it is important to understand what it is, and what it is not.

Digitalfire Insight-live calculates a coefficient of thermal expansion (CTE) from the oxide analysis of a glaze. Using the traditional weight-percent method, the amount of each oxide is multiplied by an expansion factor assigned to that oxide and the contributions are summed. If the analysis is not already normalized to 100%, it is normalized as part of the calculation. Insight-live also performs a secondary calculation using mole percentages and the corresponding molar expansion factors.

The default oxide expansion factors are found on the Preferences page and can be changed. For example, the West & Gerrow weight-percent factors used by Digitalfire include SiO₂=0.035 and K₂O=0.331. These numbers are scaled for convenience so that a typical glaze calculates to a familiar single-digit number such as 6.3 or 7.0. Laboratory CTEs are commonly expressed as ×10^-6/°C or ×10^-6/K, but the number calculated by Insight-live should be regarded primarily as a comparative value, not as a laboratory measurement. That distinction is important.

Where do the oxide expansion factors come from?

It is tempting to imagine that each oxide has its own inherent thermal expansion and that a glaze calculation simply adds those expansions together. That is not really what is happening.

The coefficients used in these calculations are empirical contribution factors derived from observations of glasses and glazes having different compositions. Hall, for example, developed an additive calculation from measurements of 118 glasses and glazes. Other researchers developed other coefficient sets, sometimes producing substantially different numbers.

The model assumes that the expansion of a glass can be approximated by adding the contributions associated with its constituent oxides. This works surprisingly well within many related families of glasses, but it is still an approximation. Oxides interact to build the glass structure, so their effects are not completely independent or necessarily linear.

Different published coefficient sets therefore give different calculated values. Some include oxides that others omit. Some use weight percentage and others use molar proportions. These factors must be used with the calculation method for which they were intended.

At Digitalfire, we compared measured thermal expansions of hundreds of frits with values calculated using various coefficient sets. We found the West & Gerrow values particularly useful - not necessarily because they predicted the absolute laboratory CTE best, but because they produced useful comparative relationships between compositions. That comparative role is the key to making calculated thermal expansion useful.

Calculated CTE works best within a glaze system

Calculated thermal expansion values are much more reliable for predicting direction of change than absolute expansion. They work best when comparing closely related glazes. Suppose you have a balanced cone 6 transparent glaze that crazes. If you alter the recipe so that K₂O and Na₂O decrease, MgO increases and SiO₂ increases, and the calculated expansion falls from 7.0 to 6.5, there is a good probability that the fired glaze will also have a lower thermal expansion. That is staying “within a system.” The comparison becomes progressively less reliable as you move outside that system - for example, by introducing new oxides, changing significantly from raw materials to frits, changing firing temperature, producing crystallization or phase separation, or altering the degree to which materials actually dissolve into the melt.

Calculated expansion is least useful when applied to an unfamiliar glaze having no fired history at all. A value of 6.5 does not, by itself, tell you whether that glaze will fit a particular clay body. The number becomes useful when you know that this glaze at 7.0 crazes and want to calculate a version at 6.7 or 6.5 and test it.

Oxide effects are not always linear

The simple additive calculation assumes that the contribution of an oxide changes proportionally with its amount. Real glasses are more complicated. Changes in B₂O₃, Li₂O, SiO₂ and other oxides can restructure a glass in ways that make their effects composition-dependent. Published expansion models even assign variable coefficients to some oxides depending on composition. Thus the direction predicted by calculation is usually more trustworthy than the exact magnitude of the change. This is another reason experience within a particular glaze family is so valuable. After several calculate-test-adjust cycles, you begin to know what a change from, say, 7.0 to 6.7 actually means for that glaze and body combination.

A glaze must actually become the glass being calculated

The calculation is fundamentally a glass-composition model. It therefore becomes less representative when the fired glaze is not a homogeneous glass.

Frits begin as homogeneous glasses and generally melt predictably. Raw glaze materials, by contrast, can contain particles of quartz, feldspar, clay minerals, zircon, rutile and other phases having very different decomposition and dissolution behaviours.

If firing produces a well-melted homogeneous glass, much of that mineralogical history disappears and the calculated oxide chemistry becomes highly relevant. But if substantial particles remain undissolved, or if crystals precipitate during cooling, the fired glaze is no longer simply the homogeneous glass assumed by the calculation.

Particle size can therefore matter. Fine silica, for example, generally dissolves into a glaze melt more readily than coarse silica. Two recipes having identical calculated chemistry can consequently fire differently if one leaves significantly more residual quartz than the other.

Zircon is an obvious example. Much of it normally remains as discrete crystalline particles suspended in the glaze. Its effect on the thermal expansion of the fired coating is therefore not equivalent to simply treating its ZrO2 and SiO₂ as if they had dissolved completely into the glass.

Can clay-body expansion be calculated?

Not with this method. More precisely, the thermal expansion of a fired clay body cannot be usefully predicted from its bulk oxide analysis using an additive glaze-expansion calculation. A fired body is not a homogeneous glass. It is a composite of crystalline and glassy phases whose identities and proportions depend on the original minerals, particle sizes and firing history.

Consider SiO₂. Two bodies can have exactly the same bulk SiO₂ percentage while having very different expansion behaviour. One might contain substantial residual quartz grains. In another, much more of the SiO₂ might have entered a feldspathic glass or participated in the formation of other phases.

Quartz is especially important because residual quartz undergoes its α-β inversion near 573°C. Cristobalite, when present, produces another prominent expansion event at much lower temperature. Mullite, feldspathic glass, residual minerals, porosity and microcracking all contribute differently to the overall expansion behaviour.

Thus body expansion is a product not simply of chemistry but of mineralogy plus firing history plus microstructure. Variables such as particle size distribution, mineralogy, quartz content, firing temperature, firing duration, atmosphere and cooling schedule can all change the phase assemblage of the fired body without substantially changing its bulk chemical analysis. That is why calculated glaze chemistry can be so useful while calculated body chemistry cannot predict expansion in the same way.

What does a dilatometer tell us? It measures the dimensional change of an actual fired specimen as temperature changes. That makes it especially valuable for clay bodies.

But even a measured CTE is not a single, immutable property that covers every temperature. The dilatometer actually produces an expansion curve. A reported CTE is normally the average slope of some specified portion of that curve.

That distinction matters greatly for ceramic bodies because quartz and cristobalite transformations can produce pronounced changes in slope. A single number cannot describe all of this behaviour. Measured expansion data are nevertheless extremely useful. If several bodies are measured by the same method over the same temperature range, they can be ranked reliably from lower to higher expansion.

Suppose a glaze crazes on body A. If body B has a somewhat higher thermal expansion over the relevant temperature range, the glaze will normally be placed under greater compression on B and may fit it better. Too much difference in the opposite direction, of course, introduces the possibility of shivering or body failure.

Dilatometry is therefore extremely useful for comparing bodies with bodies and glasses with glasses. What should be avoided is assuming that an uncalibrated calculated glaze value of 6.5 and a laboratory body value of 6.5 are necessarily a matched pair. They were arrived at in completely different ways.

Glaze/body stress also depends on more than CTE alone. Glaze stiffness, thickness, body stiffness, geometry and the temperature at which the glaze becomes rigid enough during cooling to sustain stress all play roles.

How should calculated thermal expansion actually be used? Comparatively. Suppose a glaze crazes and Insight-live calculates its expansion at 7.0. That tells you nothing absolute about whether 7.0 is “good” or “bad.” But you now have a starting point. Adjust the chemistry to lower the calculated expansion. For a badly crazing glaze, you might initially target 6.5. Fire it on the same body using the same schedule and subject it to an appropriate thermal-stress test. If it still crazes, move the calculated value lower. If crazing disappears, test sufficiently to make sure the glaze has not moved too far toward excessive compression and shivering. If the original glaze crazes only after severe thermal stressing, a much smaller calculated change may be enough.

Of course, changing chemistry to control expansion can have side effects. Increasing SiO₂ can alter melt fluidity. Trading K₂O and Na₂O for MgO can change gloss, crystallization and surface character. Changing B₂O₃ can alter melting behaviour. Successful fit adjustment therefore requires maintaining the other properties of the glaze while moving its expansion in the required direction.

But this is exactly where calculated thermal expansion becomes so valuable. Instead of blindly changing recipes and hoping something works, you can make directed changes, fire tests and build experience correlating calculated movement with actual glaze fit. That is what the number is for.

Related Information

Adding silica will fix crazing, right? Not here.

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G2926B (center and right) is a clear cone 6 glaze created by simply adding 10% silica to Perkins Studio clear (a glaze that had a slight tendency delay-craze on common porcelains we use). Amazingly that glaze tolerated the silica addition very well, continuing to fire to an ultra gloss crystal clear. That change eliminated the crazing issues on most of our bodies. The cup on the right is one of them, that body is vitreous, near-zero-porosity, and fits most glazes. Why? Because it has 24% silica in the recipe. The center porcelain is also dense and vitreous, but it only has 17% silica, that is why it is crazing this glaze. Then I added 5% more silica to the glaze, it continued to produce an ultra smooth glossy, and applied it to the 17% body on the left. Why did not fix the crazing? That silica addition to the glaze only reduces the calculated expansion from 6.0 to 5.9, clearly not enough to fix the problem. So, the obvious solution seems to be use the porcelain on the right. Are you wondering why adding silica to a body raises its thermal expansion, and adding it to a glaze lowers it? Mineralogy is the reason.

Comparing glaze melt fluidity balls with their chemistries

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Ten-gram GBMF test balls of these three glazes were fired to cone 6 on porcelain tiles. Notice the difference in the degree of melt? Why? You could just say glaze 2 has more frit and feldspar. There is a better explanation, compare these yellow and blue numbers: Glaze 2 and 3 have much more B₂O₃ (boron, the key flux for cone 6 glazes) and lower SiO₂ (silica, it is refractory). But notice that glaze 2 and 3 have the same chemistry, but 3 is melting more? Why? Because of the mineralogy of Gerstley Borate. It release its boron earlier in the firing, getting the melting started sooner. Notice it also stains the glaze amber, it is not as clean as the frit. Notice the calculated thermal expansions: The greater melting of #2 and #3 comes at a cost, their thermal expansions are considerably higher, so they will be more likely to craze. Which of these is the best for functional ware? #1, G2926B (left). Its high SiO₂ and enough-but-not-too-much B₂O₃ make it more durable. And it runs less during firing. And does not craze.

A down side of high feldspar glazes: Crazing!

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This reduction celadon is crazing. Why? High feldspar. Feldspar supplies the oxides K₂O and Na₂O, they contribute the brilliant gloss and great color but the price is very high thermal expansion. Scores of recipes being traded online are high-feldspar, some more than 50%! There are ways to tolerate the high expansion of KNaO, but the vast majority are crazing on all but high quartz bodies. Crazing is a plague for potters. Ware strength suffers dramatically, pieces leak, the glaze can harbor bacteria and customers return pieces. The simplest fix is to transplant the color and opacity mechanism into a better transparent, one that fits your ware (in this glaze, for example, the mechanism is simply an iron addition). Fixing the recipe may also be practical. A 2:1 mix of silica:kaolin has the same Si:Al ratio as most glossy glazes, this glaze could possibly tolerate 10% of that. That would reduce running, improve fit and increase durability. Failing that, the next step is to substitute some of the high-expansion KNaO, the flux, for the low-expansion MgO, that requires doing some glaze chemistry.

These common Ferro frits used in traditional ceramics

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I added Veegum to a slurry of each of these to form 10-gram GBMF test balls and fired them at cone 08 (1700F). Frits melt really well; they do have an LOI like raw materials. These contain boron (B₂O₃), it is a low-expansion super-melter that raw materials don’t have. Frit 3124 (glossy) and 3195 (silky matte) are balanced-chemistry bases (just add 10-15% kaolin for a cone 04 glaze, or more silica+kaolin to go higher). Consider Frit 3110 a man-made low-Al₂O₃ super feldspar. Its high sodium makes it high thermal expansion. It works really well in bodies and is great to make glazes that craze. The high-MgO Frit 3249 (made for the abrasives industry) has a very low expansion; it is great for fixing crazing glazes. Frit 3134 is similar to 3124 but without Al₂O₃. Use it where the glaze does not need more Al₂O₃ (e.g. already has enough clay). It is no accident that these are used by potters in North America; they complement each other well (equivalents are made around the world by others). The Gerstley Borate is a natural source of boron (with issues frits do not have).

Secret #5 of crystalline glazes:

They craze. But there is a way to fix that

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The mug on the left, made by Holly McKeen, is a typical cone 10 Grolleg kaolin mullite porcelain (highly vitrified, low in residual quartz). Its glaze is crazed. Crystalline glazes are high in Na₂O, making crazing virtually certain. Since most pieces are decorative, crystal glazers just accept this as part of the process. But these are functional mugs, the glaze needs to fit (if only for ware strength).

But what if the thermal expansion of the body could be significantly raised? The body on the right is Crystal Ice, it contains 40% silica (vs 20-25% in a typical porcelain). The percentage of Nepheline has been reduced, lowering vitrification to about 1.5% porosity. As a result, more quartz survives undissolved and less mullite develops, raising the body’s thermal expansion. The result is a body with a much higher thermal expansion, so it can not only relieve the glaze tension but actually put a squeeze on it. There is a downside: These are less resistant to dunting and thermal shock failure during use.

Could the glaze be adjusted instead? Yes. Some of the Na₂O could be substituted for Li₂O, the latter is also a strong melter but has a much lower thermal expansion. Glaze chemistry could be used to source it from Spodumene (to avoid solubility issues with lithium carbonate). However, zinc-silicate crystalline glazes are very sensitive systems, so the more lithia is introduced the more likely the effect on the firing window, crystal size/density and background clarity.

Insight-Live comparing two recipes:

A glossy and matte cone 6 bases

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Insight-live is calculating the unity formula and mole% formula for the two glazes. Notice how different the formula and mole% are for each (the former compares relative numbers of molecules, the latter their weights). The predominant oxides are very different. The calculation is accurate because all materials in the recipe are linked (clickable to view to the right). Notice the Si:Al Ratio: The matte is much lower. Notice the calculated thermal expansion: The matte is much lower because of its high levels of MgO (low expansion) and low levels of KNaO (high expansion). Notice the LOI: The matte is much higher because it contains significant dolomite.

High thermal expansion talc body cannot be COE-calculated

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Talc is employed in low-fire bodies to raise their thermal expansion (to put the squeeze on glazes to prevent crazing). These dilatometer curves make it very clear just how effective that strategy is! The talc body was fired at cone 04 and the stoneware at cone 6. The former is porous and completely non-vitreous and the latter is semi-vitreous. This demonstrates something else interesting: The impracticality of calculating the thermal expansion of clay bodies based on their oxide chemistry. Talc sources MgO and low fire bodies containing it would calculate to a low thermal expansion. But the opposite happens. Why? Because these bodies are composed of mineral particles loosely sintered together. A few melt somewhat, some change their mineral form, many remain unchanged. The body's COE is the additive sum of the proportionate populations of all the particles. Good luck calculating that!

Match calculated COE to dilatometer-measured body COE? No!

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Why? Firing temperature, schedule and atmosphere affect the result. Dilatometers are only useful when manufacturers monitor bodies AND glazes over time and in the same firing conditions. Calculated values for glazes are only relative (not absolute). The best way to fit glazes to your clay bodies is by testing, evaluation, adjustment and retesting. For example, if a glaze crazes, adjust its recipe to bring the expansion down (your account at Insight-live has the tools and guides to do this). Then fire a glazed piece and thermal stress it (300F-to-ice-water IWCT test). If it still crazes, move it further. If you have a base glossy glaze that fits (and made of the same materials), try comparing its calculated expansion as a guide. Can you calculate body expansion from oxide chemistry? Definitely not, because bodies do not melt.

A high-expansion glaze can actually bow a plate

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The calculated thermal expansion of this glaze is 8.8, very high because of its high KNaO and low SiO₂. These plates are unglazed on the underside. The upper one has a well-fitting glaze and its base remains flat. On the lower one, the high-expansion glaze on the inside contracts much more on cooling and, because it is bonded to the body, ends up in tension. The resulting stress is enough to pull the plate out of shape, bowing the base upward. This issue is common with ceramic tile, where an otherwise flat tile bows as the two layers contract differently on cooling.

A glaze this far into tension will also be highly prone to crazing. And its combination of high alkali and low silica raises another red flag: chemical durability. The solution is to reformulate, reduce KNaO in favour of lower-expansion fluxes (among which MgO is most effective), and increase SiO₂ as much as the desired melting behaviour and surface will permit.

Two matte mechanisms: One crazes, the other does not

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These two glazes look the same, they are both cone 6 satin mattes. On the same porcelain. But the matteness "mechanism" of the one on the left, VC71, is a low Si:Al ratio melted by zinc and sodium. The mechanism of the one on the right, G2934, is high MgO melted by enough boron to also have plenty of SiO₂ and Al₂O₃. The "baggage" of the mechanism on the left is high thermal expansion and crazing (drastically reducing strength and providing a space for a germ zoo). If your ware develops this your customers will bring it back for replacement. No change in firing will fix this, the body and glaze are not expansion compatible. Period.

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