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Understanding Glaze Calculation: An Aid to Potters

Section: Glazes, Subsection: Chemistry


Bob Kavanagh explains ceramic glaze calculation as a potter for other potters. He deals with theory and show practical examples.

Article Text


This article is written by a potter with potters in mind. Many of us have a fairly straightforward aversion to the numerical and chemical aspects of glaze calculation and many potters have a problem with crazing. What I do in this article, is to open a couple of doors into understanding the underlying issues involved in glaze calculation, so that potters can become more familiar with this method of addressing a glaze problem. I do this in the context of discussing crazing and using computer programs which help with glaze calculation.[1]

This article is written for the potter who is looking for explanations about glaze and clay chemistry in fairly ordinary language, although of course some language will be technical because we are going to talk about molecules and chemical formulas and several related matters. Relax, the last time I studied chemistry in school was 36 years ago, and even I can understand some of this stuff; and now that we have some of these new computer programs available to help (e.g., Insight, Hyperglaze), it has even become interesting. The beauty of these glaze programs is that they handle a great deal of the actual calculations for us, and they contain an incredible amount of information in them so that we do not have to check our chemistry books every fifteen minutes to know what we're doing.

Glaze calculation in a slightly chemical form is not as customary for us as direct practice and experience in the studio. On top of that, many of the well known leaders in glaze development (those who write books and articles on glazes for potters) present their material in a format which we know and recognize. They offer recipes or instructions which give rise to recipes, which we can just go and try in the studio. This recipe format does not encompass glaze calculation at the molecular level.

Crazing is a glaze fit problem.[2] What is glaze fit? Why should we consider it? How do molecules of a glaze relate to glaze fit? Glaze fit describes the match, a physical relationship, between a fired glaze and clay. Good glaze fit is a fundamentally important consideration for all utilitarian ware. Good glaze fit occurs when the glaze on a pot is slightly compressed and when it holds the clay in a state of slight compression. When we say a glaze fits a body we usually mean that the two most obvious problems - crazing and shivering - are absent. Good glazes add a safe finish to functional ware and increases the strength of the clay. To achieve good glaze fit, we must establish an appropriate balance of ingredients in our recipes to harmonize our glaze-to-clay bond.

This article will help throw light on one approach to establishing this balance by using glaze calculation with the unity formula. This article consists of four major parts: the first addresses expansion, contraction and the general nature of glazes; the second talks about glazes, recipes, and the chemical makeup of the ingredients in our glazes; the third outlines ideas on molecules and the unity formula and how these relate to expansion and contraction; the fourth, approaches the matter of glaze fit, expansion and contraction, glaze calculation and how all of these relate to the glaze in the bucket in the studio.

Theoretical glaze calculation does not replace "doing" in the studio. One of the wonderful things about making pots is that only making and firing them, tells us what actually works. These computer programs are another tool which is available to us.

Part I

1. Expansion and Contraction

In general, ceramic materials expand when heated and contract when cooled and in theory the amount they expand when heated, is the amount they contract when cooled. Glaze-to-clay fit becomes an issue when the clay and the glaze differ significantly in the amounts they expand and contract. If the glaze contracts in cooling much more than the clay, then the glaze will stretch; at its limit, it will develop cracks as it relieves the tension: this is crazing. This is just like jeans which are too small; you bend over, they split. On the other hand, if the clay shrinks a lot more than the glaze, the glaze bunches up and it may "pop" off the pot as the glaze relieves the extreme compression: shivering.

We know that not all things expand and contract the same amount.[3] We know for example, that we warm up the metal lid on a glass jar so that we can get it loose; we do that because the metal expands more than the glass and the lid is therefore more easily removed. Ceramic scientists have done considerable research in this area to try and outline how much specific materials expand and contract; and there is an astounding amount of research done on expansion and contraction in physics, building engineering, the space industry, etc. As a result of this scientific research, there are numbers which indicate how much things expand and contract, when heated and cooled. This number is called the coefficient of thermal expansion (although of course potters are most interested in what happens when glazes contract). The coefficient is a number which tells us how much something expands for a given unit of temperature change (e.g., for every degree increased, the unit length/size of the thing increases by X amount). These numbers are extremely small by any standard of daily life and what I am saying is a simplification.[4] We can make use of these numbers to see how much a glaze expands and contracts according to what's in it.

2. Glaze as Glass

For our purposes, we can think of glazes as akin to glass and clays as akin to composite materials (concrete is a good example of a composite material). Glass is created by melting inorganic earth materials and cooling the melt fairly quickly to form a non-crystalline, congealed, substance; it may also be called a "super-cooled liquid". A composite material is an aggregate of particles held together in a medium. In general, all ceramic products are stronger when slightly compressed than when slightly stretched. This means that they break much more easily if stretched or bent than they do if squeezed or crushed. The normal strength of a clay can actually increase under conditions of slight compression, a feature which makes glazes even more valuable for functional ware.

Like glass, clear glazes are non-crystalline solutions with extremely high viscosity when they are cooled; this means that they do not flow. They do not have a predictable chemical structure. When we shut down our kilns at top cone, the glaze is in a fluid state (we know what happens for example when we fire too high or wait too long at the high end of our firings; the glaze runs all over the place - it is fluid). If we cool our kilns relatively quickly, the fluid glaze freezes in place as a clear glass. If the cooling at the highest temperatures takes a slightly longer time, crystals will likely form in the glaze and an internal structure will develop.

The point here is that as the clay and glaze cool, they contract just as they expanded when heated. If you put them into your freezer after they come out of the kiln, they keep on contracting. If there are tensions between the clay and glaze, these tensions become increasingly important as the clay and glaze become rigid, because only a rigid glaze can craze. The tension in the glaze increases until a moment when the internal strength or tolerance of the glaze can no longer accommodate the stresses being developed by the ongoing contraction of the glaze, and the glaze will crack. Glazes at high temperature never craze; they are fluid.

3. Overview of a Glaze by Internal Function

We can picture glazes as functionally composed of glass-forming agents, melting agents and stabilizing agents.

The main source of the glass forming agent is silica. Silica is silicon dioxide - Si02. Silicon (Si) is very widespread, as is oxygen (O); they naturally combine. Quartz is a very pure crystalline rock which supplies us with silica. There are other sources of silica which vary in degrees of purity and chemical composition, but for now let's just stick with quartz since most of us have some familiarity with quartz crystal rocks.

When silica is in a crystal form like quartz, it has a definite structure and order, and certain properties go along with this crystal state. When silica is melted, it has different properties than in the crystal state. We are all familiar with this sort of thing; for example, ice, water and steam have very different properties even though they are all H2O. For our purposes now, the most important difference in silica is that crystalline silica has a higher expansion/contraction than melted silica. Melted silica (also called fused silica glass) is extremely strong and stable. It expands and contracts very little and seems in many respects to be the ideal glaze. The trouble is that it doesn't melt until about 1710ºC, or around 3115ºF.[5]

Since potters do not fire at this high a temperature, our glazes have other materials in them - fluxes - which aid in the melting of silica at lower temperatures (say, cone 6-cone 10). The main fluxes are materials like feldspar, talc, whiting, dolomite, zinc oxide, etc. Unlike melted silica, however, when these agents are heated and cooled, they expand and contract a fair amount, significantly more than fused silica. It is this expansion and contraction which is the problem in fitting the glaze to the clay.

As a result, we find ourselves in a peculiar situation: we need fluxes to make the glaze melt but they make the glaze expand and contract a fair amount. What we seek, therefore, are fluxes which melt silica at our conventional temperatures but which do not create a glaze fit problem for the clay body we are using. We need the "appropriate balance" between the expansion/contraction of the fluxes, the silica and the clay body we are using.

Stabilizing agents, of which alumina is the prime example, help stabilize glazes and inhibit excessive flow. Alumina does not expand or contract very much, and so it helps the glaze fit by countering some of the high expansion/contraction of the fluxes.

Looking at these three internal functions gives us an idea of the internal operations of a glaze. How do we get to a glaze?

Part II

4. Weight: Recipes, Raw Materials and Molecules

As potters, we start with glaze recipes which outline the percentage composition of raw materials; for example, what I call "base 100" for cone 6-8 oxidation:

"base 100"
nepheline syenite 38 (units) 38%
limestone 13 (units) 13%
zinc oxide 10 (units) 13%
magnesium carbonate 3 (units) 3%
EPK 13 (units) 13%
quartz (flint, silica) 23 (units) 23%

The total of any recipe is always 100%, although it may actually weigh any amount at all. These are percentages by weight of the raw materials which I add to my glaze bucket.

Our raw materials are often fairly complex, but they can be analyzed by industrial or ceramic chemists into a chemical formula. For example, we have kaolin in "base 100". When we look at kaolin from a technical point of view (not as a potter throwing a canister set), it is what we call a hydrated alumino-silicate. This tells us that it is a silicate (has SiO2 chemically bound in it); that it has alumina (Al2O3) in it; and that there is water in it (H2O). To express this as chemical formula we say Al2O3.2SiO2.2 H2O. This tells us not only that this is a hydrated alumino-silicate, but also what the numerical relation of the molecules is in one molecule of clay, namely: that for every molecule of alumina in the kaolin, there are two molecules of silica and two molecules of water.

A molecule is a configuration of atoms held together by internal chemical forces and our ingredients can be seen as a composite of these molecules, which themselves are held together by internal chemical forces. In this case, if water, alumina and silica were not chemically bound together in this way, we would not have clay, but something else. This is a chemical picture and does not tell us anything about the structure of clay platelets, particle size, the relation of physical properties with which we are familiar (such as plasticity), firing characteristics, etc. It tells us about the chemical structure and make-up of kaolin, the internal relation of molecules in naturally occurring clay. Eventually this information will help us understand the chemical makeup of the fired glaze.

Our raw materials can also be presented in the form of a typical analysis. This analysis shows the percentage by weight of each oxide in the raw materials after they have been fired. We could get an analytical chemist to do this for us, but it's too expensive to do the analysis for all our materials ourselves, so we use ones sent by the mines to our suppliers. By understanding the typical analysis of our raw materials we know which raw material provide which oxides in what relative amounts in our fired glazes. Thus, by looking at a typical analysis for all our raw materials, we can begin to see the relationship between the recipe and the oxide composition of the finished glaze.

As you may recall from high school chemistry classes, and from common sense too I guess, molecules weigh something and can be weighed - just not by you and me in our studios. When they are weighed, they are not compared to our normal systems of weight such as ounces or grams. The weights of atoms (called, appropriately enough, "atomic weights") are compared to the hydrogen atom and their weights are assigned according to how many times heavier than hydrogen they are (hydrogen is called "1"). You can go to the local high school or college science teacher, or library, and see a copy of what's called a "periodic table", which amongst the many other things it will tell you, will tell you the atomic weights of the various elements we use in making glazes.

Let's return to the formula for kaolin: Al2O3.2SiO2.2 H2O. We know by checking our periodic table, that: aluminum has atomic weight of 27 (rounded off from 26.981539); silicon has an atomic weight of 28 (rounded off from 28.0855); hydrogen has a weight of 1 and oxygen has a weight of 16 (rounded off from 15.9994). We can simply add them together to determine the weight of molecules since molecules are simply atoms held together. So an alumina molecule - 2 atoms of aluminum and 3 of oxygen - (Al2O3) has an atomic weight of 102 (actually 101.963); a silica molecule is one atom of silicon and two of oxygen (SiO2) with an atomic weight of 60. A water molecule (H2O) weighs 18: 2 times the weight of hydrogen, 1, and the weight of oxygen, 16. We can see, therefore, that one molecule of clay has an atomic weight of 180. As you can imagine, the water, and many other things, like carbon, etc., burn off as the kiln heats up and so the fired molecule weights less than the unfired one.[6]

Now, it so happens that scientists have done a great deal of research using atomic weights and they have devised many useful tools to help in analyses related to them. For our purposes, the most helpful tool is called the "molecular equivalent weight". The molecular equivalent weight of a material is a weight which is numerically the same as the atomic weight of a molecule of that material, but expressed in conventional weights. For example, the molecular equivalent weight of silica (molecular weight, 60), is 60. This could be 60 grams, 60 ounces, 60 kilograms, etc. The molecular equivalent weight of silica is 60 units of weight.

5. Fired Glazes and Oxides

What goes into the glaze which I apply to my pot is not identical with what comes out of the kiln as the fired glaze on the pot. Some material gets burned out in the firing and what is left, melts. We all know things get burned off from the various odours and fumes which we smell when we do the firing and all of the stains and discolouration on the metal jacket on electric kilns and on bricks of all of our kilns. What is burned off is designated as loss on ignition - L.O.I. What goes into the glaze is kaolin, quartz, feldspar (nepheline syenite), limestone, magnesium carbonate, etc. What comes out of the kiln is a glass composed of "oxides" (e.g., silicon dioxide, calcium oxide, magnesium oxide, aluminum oxide, etc.).

The kaolin and nepheline syenite, for example, can be analyzed and presented in a typical analysis, which shows us the percentages of oxides (and the loss on ignition) which result from calcining (firing) the raw materials. EPK (outlined in the table below) breaks down in the following way: silica; alumina; iron oxide; potash; soda; calcium oxide; magnesium oxide; titanium dioxide; phosphorus pentoxide; loss on ignition.

SiO2 Al2O3 Fe2O3 K2O Na2O CaO MgO TiO2 P2O5 L.O.I.
46.08% 37.46% 0.69% 0.40% 0.04% 0.13% 0.12% 0.03% 0.12% 14.66%

Nepheline syenite (outlined in the table below) breaks down into the following: silica; alumina; iron oxide; potash: soda; calcium oxide; magnesium oxide; loss on ignition.

Nepheline Syenite
SiO2 Al2O3 Fe2O3 K2O Na2O CaO MgO TiO2 P2O5 L.O.I.
60.70% 23.30% 0.07% 4.60% 9.80% 0.70% 0.10%     0.70%

If we use this type of analysis and look at "base 100" as a whole, we see that there are various sources for different oxides: nepheline syenite gives us silica, alumina and potash/soda, calcium oxide, magnesium oxide and traces of iron oxide; limestone gives us calcium oxide (everything else burns off); zinc oxide gives us zinc oxide and magnesium carbonate gives us magnesium oxide (everything else burns off); EPK gives us silica and alumina, trace minerals and a fairly important LOI; quartz gives silica. We have three sources of silica, two of alumina and one for potash/soda, etc. In the fired glaze we no longer have kaolin, feldspar, etc. In the fired glaze "base 100", we have glass composed of randomly arranged oxides.

When we do a similar analysis of the fired glaze "base 100" as a whole, and look at a percentage breakdown of all oxides by weight from all sources (outlined in the table below), Insight gives us the following result: silica; alumina; iron oxide; potash; soda; calcium oxide; magnesium oxide; titanium dioxide; phosphorus pentoxide and zinc oxide (leaving out loss on ignition).

Base 100 Glaze
SiO2 Al2O3 Fe2O3 K2O Na2O CaO MgO TiO2 P2O5 ZnO
57.44% 15.31% 0.07 2.0% 4.13% 8.34% 1.64% 0.05% 0.03% 10.99%

The programs Hyperglaze and Insight do this calculation in the blink of the eye.[7] The first several times I went through this without the computer programs to help me, it took a significant amount of time, a dramatic amount of referencing to chemistry books and a fairly disorienting headache.

If you had a way of measuring the weight of your fired glaze on a pot, you would be able to know the actual weight of each oxide in that glass because we know the percentages of the oxides in the fired glaze. In any case, we know the relative weights because we know their percentages of the whole, even if we do not know their exact weight in grams or milligrams.

You can now imagine that since we know the relative percentages by weight of oxides in the glaze and the atomic weights of the oxides at the molecular level, we can begin to calculate the relative numbers of molecules of each oxide in the glaze. Thankfully, we never actually calculate the number of molecules in a glaze. We are able, however, to figure out the ratios of flux molecules to alumina and silica molecules. because we know the relative weights. The reason we want to determine a ratio of molecules is that this ratio will help us calculate the expansion and contraction of the glaze which is made up of these very molecules. This of course takes us back to the issue of glaze fit.

Figuring out ratios of oxide molecules seems like fairly esoteric for work in a potter's studio, given that what we really want is a nice glaze which works well. I agree. How do we do this?

Part III

6. Molecules and Ratios of Molecules

Permit me a couple of extreme examples to make my point about ratios of molecules and then I will move on to a more reasonable example. Choose a glaze recipe with only silica and alumina in it, in equal weights: 50% each. Look at a typical analysis of the fired glaze (below). Because silica and alumina are each quite pure, the typical analysis will give us the same result as the recipe. We should remember that if we use flint or quartz to supply us with the silica, there will be a slight variation because flint and quartz are not pure silica, but for this example we will use silica itself.

Two Part Glaze
SiO2 Al2O3
50% 50%

Half the weight of the fired glaze is provided by silica (with an atomic weight of 60) and half by alumina (which has an atomic weight of 102). That is, 50 units of the glaze weight are alumina and 50 units are silica, regardless what the units are as long as they are a standard weight (grams, pounds, etc.). Remember what I said about molecular equivalent weights above (page 6). We know that to get the same weight of alumina and silica, we need to have more silica molecules than alumina molecules because alumina is so much heavier than silica. We know, for example, that 1.7 molecules of silica equal the weight of 1 molecule of alumina (i.e., 1.7 X 60= 102): i.e., the ratio of silica to alumina molecules is 1.7 to 1 in this fired glaze.

So, let's remember that we have a fired glaze in which 50 units of the weight is silica and 50 units is alumina. If we express the ratio of molecules as a function of the 100 units of weight (100%, 100 atomic weight, 100 grams, etc.), we can see that it would take the weight of 0.83 molecules of silica (50 units of weight divided by the molecular equivalent weight - 50/60) to equal the weight to .49 molecules of alumina (50/102). Remember it is the weights of these molecules (and the molecular equivalent weights) which add up to 100 units, not the numbers of molecules themselves.

Next imagine a glaze recipe which has by weight 50% silica, 25% alumina, 25% potash feldspar. Unlike the two part glaze recipe, however, this recipe uses a feldspar which itself ideally has three ingredients in it (potash, silica, alumina). Note the typical analysis of nepheline syenite above to remember how complex our actual raw materials are (page 7). The composition of the feldspar alters how much silica and alumina there are in the fired glaze, over and above the silica and alumina which are added by themselves. The typical analysis therefore looks like this:

Three Part Glaze
SiO2 Al2O3 K2O
66.2% 29.56% 4.2%

So we can see that 66.2% of the weight of the fired glaze comes from silica (atomic weight - 60), 29.56% from alumina (atomic weight 102) and 4.2% from potash (atomic weight 94). We can assume that the weight of the fired glaze is 100 units of weight, whatever the units happen to be, and we can therefore establish the ratio of the molecules to one another. At this point matters do get a little more elaborate.

For example, if the weight of the glaze were 100 "atomic weight" units, it would take 1.10 molecules of silica (66.2/60), 0.29 molecules of alumina (29.56/102) and 0.04 molecules of potash to give that weight. If the weight of the glaze were 100 grams, the ratio of molecules would stay exactly the same, and if it were 100 pounds, the ratio of molecules would stay the same - even though the numbers of molecules would change absolutely dramatically.

When we look at these kinds of numbers and do further analysis, the traditional way we classify the oxides is according to the three internal functions mentioned above: fluxes, stabilizers, glass formers. The three part glaze appears in the following table in terms of ratios of molecules and put into these functional categories.

Three Part Glaze
Flux Stabilizers Glass Former
K2O 0.04 Al2O3 0.29 SiO2 1.10

The ratio of molecules will eventually help us calculate the expansion and contraction of the glaze and that is the key to calculating a solution to the glaze fit problem in the studio. So yes, ratios of molecules do have something to do with getting a glaze to fit our clay when we use glaze calculation as our main tool.

Now you can perform the same operation for the glaze "base 100" as we did for the two part and the three part glazes, but with more variables. This appears in the table below. In order to undertake this analysis we need to refer to typical analysis of "base 100" above for details (page 8). Once again, I extol the virtues of Insight and Hyperglaze for this purpose.

Base 100 glaze
Fluxes Stabilizers Glass former
CaO 0.14 Al2O3 0.14 SiO2 0.87
MgO 0.04
K2O 0.02
Na2O 0.06
ZnO 0.12

There are no fractions of molecules anywhere; these are ratios of molecules in "base 100"; we are only seeing them as ratios according the three categories.

All of this is leading us to address the question of getting a glaze to fit our pots in the best way. To get to that issue we need to take one more side trip into a more refined analysis. The normal way clay chemists and technically oriented potters study the set of random relations in the glaze, is with a "unity formula".

So, take a deep breath and let's go.

7. The Unity or Molecular Formula and Expansion

The tradition of unity formulas, begun by Hermann Seger about 1886, assumes that the fluxes are the focal point for glaze calculation, and says that the glass formers and the stabilizers should be compared to the fluxes.[8] As a result, the formula assumes that all of the fluxes will be viewed as a single function and designated with the number "1", thereby, unity formula. A "unity formula" looks at the fired glaze from the point of view of ratios of numbers of molecules in the glaze (which is one reason it is also called the molecular formula), rather than chemical relations between oxides, or percentage by weight of oxides.

This means that if there are several fluxes, then they will be seen as fractions of this unity. For example, the calcium oxide, potash, soda, zinc oxide and magnesium oxide are fluxes in the overall melting action of the glaze "base 100". If they were all equal by weight in the fired glaze, then each one would provide one fifth of the flux by weight to melt the glaze. Even if there were all equal by weight in the fired glaze, however, we would know that there would not be the same number of molecules of each oxide, because the atomic weights of the molecules are so different. The ones which have a heavier atomic weight (e.g., potash and zinc) would have less molecules than the others because their molecules weigh so much more, and it would take less of them to add up to the same weight as the others.

So where are we now?

The results of these molecular ratio calculations for "base 100" look like this as a unity formula, when I use Insight:[9]

Base 100 Glaze with Flux Unity
Fluxes Intermediates Glass Formers
CaO .36 Al2O3 .36 SiO2 2.32
MgO .10
K2O .05
Na2O .16
ZnO .33
total 1.00
Coefficient of expansion: 7.56 (times 10-6).
Silica to alumina ration: 6.37

What does this tell us? Overall it says that for the equivalent of one molecule of flux (calcium oxide, magnesium oxide, potash, soda, zinc oxide all taken together),

there are 0.36 molecules of alumina and 2.32 molecules of silica.[10]

Now we are able to calculate the overall expansion and contraction of the glaze by cross reference to expansion charts. How do we do this?

Firstly, we need to know how much our oxides expand and contract so that we can alter the overall expansion in our glaze if we have a glaze fit problem (and almost everyone does). If a glaze consisted of only one molecule type then once we knew the coefficient of that molecule, we would know the expansion of the glaze, but we do not have such a glaze. Now it's a handy feature of clear glazes that "the thermal expansion of a multioxide glass can be estimated by assuming that the coefficient of expansion is an additive property."[11] We can calculate the total coefficient of thermal expansion by simply calculating the addition of the constituent parts. "For example, if a glaze consists of 50% oxide A which has an expansion of 5, and 50% oxide B which has a expansion of 10, then the expansion is: (.50 X 5) + (.50 X 10) = 7.5."[12]

Part IV

8. Glaze Fit and Glaze Calculation: Aiming for Successful Glaze Fit

Now let's suppose that you have a glaze which crazes (and who doesn't?). For now we are addressing only what can be managed through changing the glaze and not yet what can be managed through changing the clay. What should you do?

To get a fairly clear picture of what might be the cause of the specific problem, we would be well advised to find out how much silica, alumina, potash, soda, magnesia, etc., there is in our glaze and then check their coefficients of expansion. Once we know how much of each oxide there is and their expansions, we can see which ones most affect the expansion of the glaze and we can plan from there.

Since we do not know exactly how many molecules there are in "base 100" or what the exact weight of the glaze on the pot is, we work from ratios of molecules for this. We act as if there were 1 molecule of flux (and then we are able to factor in each of their coefficients of expansion) and .36 molecules of alumina (and factor in the coefficient of alumina based on .36) and 2.32 molecules of silica (and factor in its coefficient) Once we get this idea and we have some idea about how much a given ingredient increases or decreases the expansion/contraction of the glaze, we can begin to influence this expansion/contraction to resolve our problem.[13]

Insight suggests that the expansion/contraction of "base 100" is approximately 7.56 (times 10-6) and that the ratio of silica molecules to alumina molecules is 6.37 to 1.

It just so happens that glaze "base 100" crazes slightly on my stoneware body (A) and significantly more on stoneware body (B).

Now, the first question is, how do I modify the expansion of this glaze so that it fits my clay (A), on which it now crazes slightly? To modify the glaze so that it does not craze, I must lower the expansion/contraction of the glaze.

To be able to change my glaze in the most helpful way, I want to alter the glaze at the "recipe - raw materials" level and yet have it show up at in the unity formula level, along with the changes in the thermal expansion. If we can see what changes take place at the molecular level and with thermal expansion at the same time that we are altering our raw materials, we would be able to see the whole picture of glaze calculation at the same time. Lo and behold! This is exactly what these new computer glaze calculation programs do best.

The only way to know anything for certain when testing glaze fit, is to test the glaze on your clay. The point of the glaze calculation software is to facilitate the work of arriving at a glaze recipe which is the most likely to succeed. With the computer doing the actual calculations for me, I looked at several options (101-125) for lowering the coefficient of expansion while trying to keep other features of the glaze as much like the original as possible.

If one has a glaze which crazes slightly ("base 100" on stoneware clay A), the first thing one does traditionally is to add a little quartz because the silica provided by it will certainly lower the coefficient and thereby lower the tension in the crazed glaze. Sometimes, doing this is enough the solve the problem.

Using Hyperglaze or Insight, I can add small amounts of quartz to my recipe and see instantaneously the impact of this change on the ratio of molecules in the unity formula and on the coefficient of expansion. It so happens that by adding 4 units of silica to the glaze (thereby adding up to 104 units), the coefficient drops to 7.39, a healthier number and a thermal expansion which does in fact fit clay A. It does not fit clay B however. You will note that the ratio of silica to alumina has changed slightly: from 6.37 to 1, to 6.86 to 1 suggesting to us that the glaze will have a higher gloss. This is important to note because the silica to alumina ratio is fairly good indicator of the finish of the glaze (whether it is gloss, satin, etc.) and this may slightly alter the visual character of the glaze. In order to know whether it is affected or not, you must fire the piece, look and see.

8.1 "base 101"

nepheline syenite 38 (units) 36.54%
whiting 13 12.50%
zinc oxide 10 9.62%
magnesium carbonate 3 2.88%
EPK 13 12.50%
quartz (flint) 27 25.96%
total 104 100.00%

Base 101 Glaze (Unity Formula)

Fluxes Intermediates Glass Formers
CaO .36 Al2O3 .36 SiO2 2.50
MgO .10
K2O .05
Na2O .16
ZnO .33
total 1.00
Coefficient of expansion: 7.39
Silica to alumina ratio: 6.86 to 1

8.2 "base 102"

Another test which keeps the silica/alumina ratio the same (6.86 to 1) and has a coefficient of 7.39, follows as "base 102". The purpose of this example is to indicate that one can have exactly the same silica/alumina ratio as "base 101" by altering the other raw materials in the glaze and not only the silica. This example is very interesting because the quartz in the recipe is actually less than in the original and yet the coefficient has been lowered significantly and the silica/alumina ratio kept constant. This is possible because other materials add silica and low expansion fluxes. By using these computer programs we can see this in a flash because the program does all the calculations instantaneously and they have in them the data on a large number of raw materials.

"base 102"
nepheline Syenite 36.50 35.56%
whiting 13.25 12.91%
zinc Oxide 10.60 10.33%
magnesium Carbonate 2.00 1.95%
EPK 12.80 12.47%
quartz (flint) 24.25 23.62%
talc 3.25 3.17%
total 102.65 (units) 100.00%

As you can see, all the changes are slight, but the accumulated effect of them is a lower expansion/contraction of the glaze. Does the glaze fit without crazing? Only testing it will tell us for certain. In this particular case, it fit A but did not fit B.

Glaze 102 Base (Unity Formula)
Fluxes Intermediates Glass Formers
CaO .35 Al2O3 .33 SiO2 2.30
MgO .13
K2O .05
Na2O .15
ZnO .33
total 1.0
Silica to alumina ratio - 6.86 to 1
Coefficient of expansion - 7.39

8.3 "base 107"

To address the matter of glaze fit and clay B, it is fairly clear that we cannot simply add more silica ("base 101") because there would be a very significant change in the amount of silica and thereby in the finish of the glaze. The other changes ("base 102") were not enough (remember that the coefficient of expansion on 101 and 102 are the same even though the recipes are different). The materials databases which are in these programs proves to be very helpful at this point, because we can play with types of kaolins, types of feldspars and different ingredients to vary the coefficient of expansion, keep the silica/alumina ratio and maintain a constant watch on our other ingredients while we're at it.

A wonderful feature of Hyperglaze for example, is that we can pull up an information sheet on each material while we are actually in the midst of doing a complex calculation and see it at the same time. Once we see whether the material might be helpful or not, we can immediately insert it into our recipe and see the changes at the level of molecules and thermal expansion.

While we are analyzing this glaze, I would like to go back to the original silica to alumina ratio of 6.37 to 1 because this offers the most likely similarity to the original glaze.

"base 107"
nepheline syenite 43.51 38.61%
whiting 10.90 9.67%
zinc Oxide 8.82 7.83%
talc 7.99 7.09%
EPK 17.60 15.62%
Quartz (flint) 23.88 21.19%
total 112.70 (units) 100.00%

What becomes clear in this example is that there is no magnesium carbonate. The magnesium oxide originally provided by it is now provided by the talc, which also adds silica and has virtually no loss on ignition; the nepheline syenite and kaolin are up slightly and the whiting and zinc are down slightly. It's the overall mix which provides the final result and this appears as a unity formula:

Glaze Base 107
Fluxes Intermediates Glass Formers
CaO .30 Al2O3 .44 SiO2 2.79
MgO .17 K2O .06
Na2O .18
ZnO .28
total 1.0

We have a ratio of silica to alumina of 6.37 to 1 and a projected expansion of 7.16.

In testing "base 107" on clay B, I found that it fit B and it fit A. I then subjected the test results to some severe stresses on both clays to ensure that my initial successes had some foundation. Both of these glazes survived all the stress tests.

9. Recipes Revisited in the Studio

Now what does all of this tell us? Fundamentally we have arrived at a secure, safe glaze for a wide array of functional ware. We have arrived at it through a fairly analytic approach basing as much of our calculations as we could, on scientific information, using glaze chemistry calculation programs to help us zero in on the most likely solutions to a known problem.

Now we take the recipe, mix it, glaze the pot and fire.

Is the glaze as beautiful as it is solid and safe? Ah, well, that is of course an important question. Beauty in a glaze transports aesthetic value into daily use, but, it is the subject for another article.


[1]. Insight is a very fast glaze calculation program with a programmable materials database holding an immense wealth of technical information on a wide variety of common ceramics materials (copies are available for both macs and pc's and now in Windows: by Tony Hansen in Medicine Hat, Alberta, Canada. Hyperglaze is a package of functions including glaze calculation, materials database, glaze and clay recipe database storage, a hypercard support system. It runs on macs: by Richard Burkett at San Diego State University, It is fully integrated and easy to use. Note the highly informative articles by Rick Malgrem in Ceramics Monthly, January 1992 and March 1994.

[2]. "When a glaze is subject to tensile stresses in excess of its ultimate tensile strength, it develops fractures, or crazing. The reverse case is that in which the glaze [expansion] is low and develops excessive compression, resulting in. . .shivering." Cullen W. Parmelee (revised by C.G. Harman), Ceramic Glazes (CBI Publishing: Boston, 1973), p. 251. Note also, W.G. Lawrence, Ceramic Science for the Potter (Chilton Book Company: Radnor, Pennsylvania, 1972), chapter 11. Charles Lynch, Practical Handbook of Materials Science (CRC Press: Boca Raton, Florida, 1990). For a couple of quite technical references on this type of issue, look at: Y.S. Touloukian, Themophysical Properties of Matter (IFI/Plenum: New York, 1977), vol. 12-13; also, on expansion note: Touloukian, Ibid., pp. 14a - 16a.

[3]. We also know that expansion is not uniform and that linear expansion is somewhat different than expansion in volume. In addition, we know that materials may show slightly different expansions depending on the precise context of the experiments. It is comforting to know, however, that the numbers are close enough and consistent enough to be able to undertake high level calculations.

[4]. For example, Lawrence says that silica's coefficient is 0.37 times 10-7 (i.e., 0.000000037) and that alumina's is 0.61 times 10-7, Lawrence, Ibid., pp 142-47.

[5]. One handy item in Hyperglaze is something called "Potter's Friend" which does all kinds of small calculations for the potter, such as converting centigrade and fahrenheit degrees. You can also call up definitions at any time; if for example, you want to be reminded what the unity formula is or the definition of, say,"mole", you call up their explanations as you are working.

[6]. W.E. Worral, Clay and Ceramic Raw Materials (New York: Halstead Press, 1975), note Chapter 6: The Effect of Heat on Clays; Prudence M. Rice, Pottery Analysis: A Sourcebook (Chicago: University of Chicago Press, 1987), chapter 12, "Properties of Clays II: Firing Behavior"; Tony Hansen, Magic of Fire and the Digitalfire Reference Database (Digitalfire Corp.: Medicine Hat, Alberta, 1995). In addition, the material databases of Hyperglaze and Insight outline loss on ignition.

[7]. When you calculate these figures using Insight or Hyperglaze, the exact results may vary slightly from program to program. This divergence should remind us that these programs are, after all, only tools to assist us in formulating better glazes. Practice with one of these programs gives rise to better results when we are consistent in our approach and do not just switch back and forth between them without thinking. We should remember as well, that because all of these numbers are established by experimental investigation, there will be slight variations in test procedures and exact materials studied and this will give rise to divergence of results.

[8]. Read David Green, A Handbook of Pottery Glazes (Watson-Guptill Publications: New York, 1979), chapter 1, for a good review of this matter.

[9]. These numbers are not exactly the same when I use Hyperglaze and I take this opportunity to remind potters that these programs are tools which require constant updating and scouting around with various companies to ensure current data. For example, Ron Roy out of Toronto, uses Insight but has established a unique database which he has collected himself from companies with which he has a wide familiarity. The authors of these programs update them on a regular basis. On top of all of this, there is no complete agreement in the scientific community about coefficients of expansion for example. We should not be surprised; the world is not as consistent and clear-headed as we might want it to be. This lack of agreement only means we must ourselves be careful and be consistent in our use of the data and information available to us.

[10]. There are also 0.13 molecules of boric oxide, 0.09 molecules of phosphoric oxide, and trace amounts of iron oxide or titanium oxide, which I did not mark down, for the sake of simplicity.

[11]. Touloukian, Ibid., page 10a with an example on 11a in Table 1. This feature is not true of clay because of the unpredictable development of crystals, each of which is unknown without empirical investigation. As a result, we cannot calculate the expansion and contraction of a clay body. They can be measured with the proper tools however.

[12]. Tony Hansen, Ibid., p. 82.

[13]. For example, Parmelee (ibid.) suggests simple coefficients for ingredients on pages 242 and Lawrence (ibid.) on pages 144-5. Other books address this matter as well (e.g., Rhodes)

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By Bob Kavanagh

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