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Limit Formulas and Target Formulas

Section: Glazes, Subsection: Chemistry


Glaze chemistries for each type of glaze have a typical look to them that enables us to spot ones that are non-typical. Limit and target formulas are useful to us if we keep in perspective their proper use.

Article Text

Target Formulas

I shy away from classifying and pigeon-holing glazes into specific categories. In the past I have over-rated the chemistry of glazes (Digitalfire Insight desktop software focused completely on that for many years). While chemistry is a key factor in understanding why glazes fire the way they do, we must not overlook their physical presence. Insight-live, the successor to desktop Insight, is much more about understanding the physics of glazes (e.g. understanding their flow, color, surface, variegation, crystal formation as impacted by temperature, firing schedule, application, preparation techniques and material selection) and the bodies to which they are applied. Insight-live still does the chemistry but is less idealistic and more realistic about its impact, putting it into context with the physics. I thus find that the term "Limit Formulas" suggests we have a better understanding and control of the chemistry than we actually do and that specific glaze types have a narrow chemistry profile (which they most often do not). This is why I prefer the term "Target Formula". In recent years more and more people do not even use unity formulas, they prefer to compare glazes via percentage analysis or molar percent. The more you know about a recipe the more it defies pigeon-holing in these ways, the physics part of Insight is very much about that. It is about understanding a body or glaze in terms of ones you already know about. When you take a physics approach you are much more inclined to test glazes more thoroughly and in more circumstances and you are less inclined to classify them over-specifically.

A target formula is a formula that is likely to produce a certain effect. Note I am talking about formulas, not recipes. They are the 'universal language' of glazes. You must calculate the mix of materials needed to supply a formula. Consider a crystalline glaze. Among other things, a target formula would specify a low alumina content to encourage a fluid melt so crystals can grow. Likewise mattes, copper reds, chrome-tin pinks, and many special surface effects and colors have 'mechanisms' that we can isolate, that is, rationalize in terms of the formula. In some glazes the balance of the entire formula is critical to producing the effect, in others you can identify the presence of one or two oxides that are responsible. In the latter it is usually possible to 'transplant' the mechanism into a proven base glaze. For the former it is often possible to adjust the chemistry of the base and then transplant in the mechanism.

There is a temptation to identify mechanisms by capturing existing recipes of the desired type (i.e. from the Internet) and studying them as a group. However with this approach the conclusion will be tainted by the effects of 'bad' examples in the study group or recipes that produce the same visual effect using a different mechanism. A better approach is to select a trusted recipe and examine its formula in the light of what is written and what is known about the oxides. Comparison with poorer specimens of the same glaze type could then help identify tolerances.

Limit Formulas

When I talk about limit formulas I am talking about guidelines for base functional glazes. We all want glazes that are reliable, stable, predictable, work with many colors, resist leaching, do not blister or crawl or pinhole, are durable, expansion adjustable, have clarity, do not devitrify, etc. At Digitalfire we advocate a base-with-adjustments approach to provide a solid foundation for subsequent colored, opacified, and variegated versions. In theory it is impossible to come up with a guideline that will always yield all of the above properties for a specific type of glaze. This is because the measures necessary to achieve these properties often oppose each other and have to be balanced and rationalized. This area is certainly such a case, there is no substitute for oxide knowledge when it comes to comparing an existing glaze with limit or target formulas.

However as humans we want numbers anyway, right! Admittedly limit formulas have proven to be a valuable watchdog to spot suspicious glazes and explain obvious lacks in stability, hardness, and other issues. The fact that we can isolate a surface-character mechanism for a glaze type and reproduce it with remarkable success is also a testament to the possible usefulness of limit formulas to achieve specific functional properties in base glazes. Limit formulas can be found in many textbooks and were developed by ceramic industry experienced technicians as conservative guidelines for well melted and durable glazes (not necessarily resistant to leaching however). They are not typically simply 'an average recipe' calculated from a large number of working recipes, each oxide range has been rationalized in the light of testing and manufacturing history and what is known about it and its interaction with others. We can only speculate on the thought processes and testing that go into developing a set of limit formulas. The chart author must balance oxide amounts by considering the fact that some enhance hardness, others accelerate melting, resist leaching, matte the surface, reduce the expansion, stabilize the glass, etc. For example, an oxide that encourages glaze hardness does not necessarily promote chemical stability and vice versa (i.e. CaO). Using limits is admittedly a matter of trust and faith. Still, when students mix up a recipe whose formula is middle-of-the-limits they have a high likelihood of first-fire-success.

Limit formulas typically show preferred ranges for each oxide for a specific type of glaze, they tell us what chemistry a class of glazes have in common. The term 'limit formula' tends to invite non-compliance so we sometimes use the term 'suggestion formula'. Still, if you have a glaze that does not fit within the ranges for its type then you should have a clear rationalization and test results to justify it (see the articles on testing glazes for more information).

Controversy About Limit Formulas

People in the 'ceramics without limits' camp point out that limits are restrictive and arbitrary to the average ceramist, they are intended for professionals, they produce base glazes capable of limited color range and surface qualities, and that durable glazes can be made that fall far outside the limits. Are these things true? I've seen none of them proven. Yet they propose analyses of the formulas of existing glazes to identify commonality to better understand a given glaze type, thus in a sense trying to create limit formulas. I submit that the average person does not have the expertise or testing facilities to select good candidates for group analysis, and that the best range of 'functional' colors and surface qualities are possible when you adhere to limits intended to make glazes functional and durable. I also feel that limit formulas are best employed by inexperienced people as a conservative approach until they develop 'license' to exceed the limits. Let me put this another way: Give me any functional glaze that looks great yet is crazed, soft, leachable, blistered, pinholed, unreliable, and difficult to work with an I'll bet I can reproduce it as a one that is hard, leach resistant, non-crazed, reliable, and functional. And I'll bet it's formula will end up being within typical limits for that type!

It is true that limits do not express the complexity of functional glaze science. But until we have a viable alternative disowning the limits is giving student license for complete abandon. And this is happening. I see textbooks full of glazes that do not belong on functional ware. Beginners should take a conservative approach. When you look at a limit chart visualize an industrial glaze technician with years of experience and testing what works and does not work functionally. Should you ignore him?

Comparing and Learning From These Limit Charts

Unfortunately there is some confusion about limit charts. The following table compares two sets of limit charts (for low, medium, and high fire glazes) and illustrates this. One is a set that we have used for years (from UK Ceramic industry tradition), the other is from Green and Cooper. At first the lesson appears to be that G&C numbers more keenly emphasize the need for adequate silica and alumina in glazes, especially at higher temperatures.



UK Traditional Limits


Green & Cooper Limits

Cone 04-02

Cone 3-7

Cone 8-10

Cone 04

Cone 6

Cone 10

CaO 0.1-0.6 0.1-0.7 0.35-0.8 0-0.3 0-0.55 0-0.7
ZnO -0.20 -0.25 -0.3 0-0.18 0-0.3 0-0.36
BaO -0.3 -0.3 -0.3 0-0.28 0-0.4 0-0.475
MgO -0.3 -0.3 -0.4 0-0.3 0-0.325 0-0.34
KNaO -0.5 0.1-0.5 0.1-0.5 0-0.525 0-0.375 0-0.3
Li2O -0.2     n/a n/a n/a
SrO   -0.4 0.7 n/a n/a n/a
B2O3 0.3-1.1 -0.4 -0.3 0-1.0 0-.35 0-.225
Al2O3 0.1-0.4 0.2-0.35 0.3-0.55 0.1-0.45 0.275-0.65 0.45-0.825
SiO2 1.5-3.0 2.5-3.5 3.0-5.0 1.375-3.15 2.4-4.7 3.5-6.4

So are limits worth the troubles involved with interpreting them? Yes. The performance of colorants in recipes provides an analogy that vindicates the concept of limit formulas. If 2% stain gives a light color and 7.5% achieves the darkest, then why put in 15%? It is wasted, it probably contributes to chemical instability. Thus there is an implied limit of 7.5%. Limit formulas are great references for food-surface glazes, within limits does not guarantee durability or leach resistance, but a well melted glaze is obviously a the best start. Furthermore, I find limit formulas a good frame-of-reference for explaining troublesome glazes, analyzing their deviance from the limits often points out a fruitful strategy to fight the problem.


However, limit formulas go beyond practicality and bring the matter of ethics and accountability into focus. If you are not a glaze chemist and don't have testing equipment, then should you use functional and liner glazes that wildly defy these limits without some testing and clear rationalization? I've never made bread but I'm sure there are some limits, I'm guessing that 1 teaspoon of yeast is good but that one cup is not. Likewise if a glaze formula has twice the maximum of an oxide (I see this all the time with manganese, barium, lithium, fluxes, metallics) or half the minimum (i.e. SiO2 or Al2O3) eyebrows should raise! It is true that 'visual' or reactive glazes often defy the norms (i.e. fluid variegated glazes often lack alumina or have high boron) but no one expects them to be food safe, fit the clay perfectly, and fire to a very hard and abrasion resistant surface either. We also expect that such glazes not be trafficked on the functional glaze market where they quickly develop amnesia about who and what they are.

Remember, the alternative to limit charts is no guidance, or perhaps worse, averaging formulas of unproven textbook recipes. Be conservative when it comes to producing ware that people expect to be durable and food safe.

Limit Charts for Unstable Glazes

Many visual effects can only be achieved by venturing outside typical functional formula limits. For example, matte glazes must push the limits to even be matte. They are therefore unconventional in the sense that they seldom fit nicely without functional limits. However glaze chemistry plays a role in understanding unconventional mechanisms also, perhaps even more so. The term "target formula" is thus very appropriate for this.

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By Tony Hansen

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