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Target Formula, Limit Formula

The term 'limit formula' historically has typically referred to efforts to establish absolute ranges for mixtures of oxides that melt well at an intended temperature and are not in sufficient excess to cause defects. These formulas typically show ranges for each oxide commonly used in a specific glaze type.

Many prefer the term "target formula". This is because the term 'limit formula' suggests that glazes outside the ranges will not work and that ones inside are somehow safe. However this is not the case. Melting well simply carries with it a much higher likelihood a glaze is reasonably functional and balanced (does not have excessive amounts of any individual oxide that might lead to instability or reactivity). These limits are also dependent on the amount of B2O3 present (if more can be tolerated than more Al2O3 and SiO2 can also be tolerated).

Specific ceramic industries have created proprietary limits for the glazes that they make (e.g. super low expansion, high abrasion resistance, resistance to bacteria growth, high elasticity, specific colors, fast fire). These limits are often closely guarded secrets and would be well outside normal the ranges shown here. A common public domain target example is crystalline glazes, they require almost no alumina, much higher than normal sodium and zinc. They also require special treatment during firing.

There is a difference between sourcing an oxide from a frit or raw material. Frits readily release their oxides to the glaze melt giving more time for them to participate intimately in the formation of a homogeneous glaze structure (this is especially important where materials have high melting temperatures). Thus, oxides like BaO, that might potentially leach in a glaze where they are sourced from raw materials might not do so from a frit, especially when levels are relatively low.

However we are mainly concerned with creating glazes for use on functional ware. Using the term "target formula" instead of "limit formula" suggests we are more interested in comparing a new glaze with one we already understand (have used and tested extensively). It recognizes that judging the suitability of glazes is more of a relative than absolute science. This is good.

Here is an example of a typical limit formula for cone 6 glazes.

CaO - 0-0.55
MgO - 0-0.325
KNaO - 0-0.375
ZnO - 0-0.3
BaO - 0-0.4
B2O3 - 0-0.35
Al2O3 - 0.285-0.64
SiO2 - 2.4-4.7

These values refer to comparative numbers of molecules. They are meant to be compared with a glaze who formula has been unified (fluxes, or melters, add up to one). At cone 6 the fluxes are CaO to BaO. They balance against the Al2O3 (stabilizer) and SiO2 (glass former). The B2O3 is a low temperature glass that also functions as a flux.

This suggests that CaO (usually from calcium carbonate or wollastonite) can be anywhere from zero to 0.55. But in actual practice you will almost never see a glaze with zero CaO, there is almost always a significant amount (0.3 or more). In matte glazes the CaO is very often higher than this limit.

-MgO (from talc and dolomite) is less common in than CaO or KNaO in glazes, it tends to matte them when the amount gets to 0.3 and higher. In fact, silky matte glazes, which are very common, will often have 0.35 or more.

-KNaO (combined total K2O and Na2O from feldspars and frits) is a key melter. Like CaO, almost all glazes have it. Glazes fire to a brilliant gloss when this is higher. But KNaO has high thermal expansion so the limiting factor is crazing susceptibility on your body (which will likely place it below limit expressed here).

-ZnO is an auxiliary melter, it is not common in slow-fire glazes (e.g. for pottery), especially when sourced from zinc oxide. Because other melters (especially boron) have so many less side effects (e.g. glaze defects, maleffects on color), that it will almost never reach this 0.3 limit. However in fast-fire industrial applications (1 to 2 hour firings) it can be tolerated when sourced from frits and will reach this limit.

-BaO is treated with caution because of toxicity; any glaze that has 0.4 BaO would be off-the-scale for potential to leach! That aside, the only time BaO would be at this high limit should be for special purpose, non-functional, crystal matte or blue matte glazes. However, even though the glaze is not being used for functional ware, the potter making the ware is exposed to high levels of raw barium. For functional glazes low BaO levels can often be tolerated (e.g. 0.05-0.1) if the glaze chemistry is balanced (enough SiO2 and Al2O3) and melting well (but not crystallizing). Industry often employs frits to source BaO, there are obviously are much safer to use.

-SrO, although not show, could be considered like BaO (it is not toxic and is a common auxiliary flux).

-Li2O is also not shown. Use only a small amount (e.g. 0.05), it is a powerful flux. It also has toxicity issues.

-B2O3 is needed in almost all middle temperature glazes, they just will not melt enough without it. The upper limit here is conservative but a well melting glaze can still be achieved with levels below this (e.g. 0.2). But if you need a glaze that has a high gloss with colorant and opacifiers, or variegated reactive visual effects, then significantly more than 0.35 would likely be needed (double this amount is not unusual!). However this limit is likely a reflection of the needs of industry, they have reason to minimize boron because of its side effects (boron blue and devitrification, micro bubbles, durability issues, difficulty with fast fire).

-Al3O3 is needed in all glazes (except crystalline). It holds the melt from running down off vertical surfaces, stabilizing it. It also imparts hardness and durability. Generally you want as much as possible (but if there is too much gloss will be lost) and more than that it won't melt (it would be very unusual to see the 0.64 upper limit). Around 0.4 would be much more typical.

-SiO2 makes up the bulk of all glazes, it is the glass former. The more the glaze will take (and still melt well) the better. All of its effects are beneficial. This upper limit is conservative, if more boron (or auxiliary fluxes like Li2O, ZnO) are present more SiO2 can be tolerated.

-Colorants (e.g. oxides of Fe, Co, Mn, Cu, Cr). Be sensible. If 1% cobalt gives a bright blue, do not put in 5%. If 5% stain is enough do not put in 10%. Iron is not dangerous. Copper can make a glaze leachable, test it. MnO makes fumes during firing. Cadmium and lead obviously require know-how to use safely.

-Titanium and Rutile: These are commonly added to variegate glazes (crystallize and produce phase changes). They are effective up to about 5%, above that the surface will be usually become rough and matte (a mesh of crystals). There are crow-bar ways to prevent this like incorporating significant zinc or lithium. But such glazes are notoriously finicky and difficult. Beware.

Physical Limits: Is the glaze well melted? Can you scratch it with metal? Will it survive a leaching test? Is it heavily crystallized? (do a closeup with your camera and zoom it). Is the melt glass it full of air bubbles? Is it crazing? These are obvious things but there is much not sense in fussing over chemistry if there are obvious problems like these!

Most people with lots of experience mixing and testing glazes and watching their chemistry would likely rationalize these limits in a similar way as done here. Once you have this outline fixed in mind you will never need to look at another limit chart, it becomes second nature!

There is a link to a lengthy article on limits below.

A Limitation of the Seger Unity Formula

A Limitation of the Seger Unity Formula

Mineral sources of oxides impose their own melting patterns and when one is substituted for another to supply an oxide a different system with its own relative chemistry is entered. An extreme example of this would be to source Al2O3 to a glaze using calcined alumina instead of kaolin. Although the formula may be exactly the same, the fired result would be completely different because very little of the alumina would dissolve into the glaze melt. At the opposite extreme, a different frit could be used to supply a set of oxides (while maintaining the overall chemistry of the glaze) and the fired result would be much more chemically predictable. Why? Because the readily and release their oxides the the melt.

Does adding boron alone always increase glaze melt?

Does adding boron alone always increase glaze melt?

Boron (B2O3) is like silica, but it is also a flux. Frits and Gerstley Borate supply it to glazes. In this test, I increased the amount of boron from 0.33 to 0.40 (using the chemistry tools in my insight-live.com account). I was sure that this would make the glaze melt more and have less of a tendency to craze. But as these GBMF tests for melt flow (10 gram GBMF test balls melted on porcelain tiles) show, that did not happen. Why? I am guessing that to get the effect B2O3 has to be substituted, molecule for molecule for SiO2 (not just added to the glaze).

A limit or target glaze formula. What does this mean?

A limit or target glaze formula. What does this mean?

Recipes show us the materials in a glaze but formulas list oxide molecules and their comparative quantities. Oxides construct the fired glass. The kiln de-constructs ceramic materials to get the oxides, discards the carbon, sulfur, etc. and builds the glass from the rest. You can view glazes as recipes-of-materials or as formulas-of-oxides. Why use formulas? Because there is a direct relationship between the properties a fired glaze has (e.g. melting range, gloss, thermal expansion, hardness, durability, color response, etc) and the oxides it contains (links between firing and recipe are much less direct). There are 8-10 oxides to know about (vs. hundreds of materials). From the formula viewpoint materials are sources-of-oxides. While there are other factors besides pure chemistry that determine how a glaze fires, none is as important. Insight-live automatically shows you the formulas of your recipes and enables comparing them side-by-side. Click the "Target Formula" link (on this post at digitalfire.com) to see what each oxide does.

Out Bound Links

  • (Articles) Limit Formulas and Target Formulas

    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.

  • (Recipes) G3806C - Cone 6 Clear Fluid-Melt Clear Base Glaze

    A base fluid-melt glaze recipe developed by Tony Hansen. With colorant additions it forms reactive melts that variegate and run. It is more resistant to crazing than others.

    2015-09-30 - This is a test to publish Insight-live data here. Many more recipes coming soon.

  • (Recipes) G2926B - Cone 6 Whiteware/Porcelain Transparent Base Glaze

    A base transparent glaze recipe created by Tony Hansen for Plainsman Clays, it fires high gloss and ultra clear with low melt mobility.

    2014-02-06 - A cone 6 transparent general purpose base recipe developed at Plainsman Clays by Tony Hansen (see link to go there below, it contains technical and mi...

  • (Recipes) G2934 - Matte Glaze Base for Cone 6

    A base MgO matte glaze recipe fires to a hard utilitarian surface and has very good working properties. Blend in the glossy if it is too matte.

    2014-03-26 - A cone 6 boron-fluxed MgO matte developed at Plainsman Clays by Tony Hansen (a link below will take you to its page there). This page contains technic...

  • (Glossary) Oxide

    An oxide is a combination of oxygen and another element. There are only about ten common oxides that we need to learn about (most glazes have half that number). CaO (a flux), SiO2 (a glass former) and Al2O3 (an intermediate) are examples of oxides. CaO (calcium oxide or calcia), for example, is cont...

  • (Glossary) Colorant

    Although colorants are added to bodies, most people think of them as materials that transform a colorless transparent or opaque glaze into a colored glaze. Colorants can be raw metal oxides (e.g. iron oxide, chrome oxide), metal oxide containing materials (e.g. rutile) or man-made powders which are ...

In Bound Links

  • (Videos) Lesson 1B - Turning a Feldspar Into a Glaze

    Shows you how to consult a target formula and compare it with the chemistry of a feldspar to determine why a feldspar does not make a good glaze by itself and what materials need to be combined with a...

  • (Glossary) Flux

    On the theoretical glaze chemistry level, a flux is an oxide that lowers the melting or softening temperature of a mix of materials. Fluxes are interactors (they often melt poorly on their own but react strongly with high melting materials where Al2O3/SiO2 predominate). There are less than ten commo...

  • (Glossary) Glaze Chemistry

    Glaze chemistry is learning what each oxide does in a fired glaze and the relative advantages and disadvantages of each material supplying it. The chemistry of a glaze is expressed in a manner similar to its recipe, except that the items are oxides and the amounts can be by weight (an analysis) or n...

  • (Articles) Where Do I Start?

    Break your addiction to online recipes that don't work. Get control. Learn why glazes fire as they do. Why each material is used. Some chemistry. How to create perfect dipping and drying properties. Be empowered. Adjust recipes with issues rather than sta

  • (Articles) Creating Your Own Budget Glaze

    How to take a stockroom full of unused materials and turn them into a good glaze rather than try umpteen online recipes that require buying yet more materials you do not need and do not work.

  • (Glossary) Glaze Durability

    Ceramic glazes vary widely in their resistance to wear (cutlery marking, scratching) and leaching by acids and bases. The principle factors that determine durability are the glaze chemistry and firing temperature. In industry technicians are accustomed to evaluating glazes by looking at their oxide ...

  • (Oxides) BaO - Barium Oxide, Baria
  • (Oxides) ZnO - Zinc Oxide
  • (Oxides) Li2O - Lithium Oxide, Lithia
  • (Oxides) Al2O3 - Aluminum Oxide, Alumina
  • (Oxides) SiO2 - Silicon Dioxide, Silica
  • (Oxides) B2O3 - Boric Oxide
  • (Oxides) CaO - Calcium Oxide, Calcia
  • (Oxides) CoO - Cobalt Oxide
  • (Oxides) Cr2O3 - Chrome Oxide
  • (Oxides) MnO - Manganous Oxide
  • (Oxides) MnO2 - Manganese Dioxide
  • (Glossary) Leaching

    Glazes are not as inert and stable as many people think. All are slightly soluble and will thus leach to some extent, even if minute, into liquids they come into contact with. However some glazes are dramatically more soluble than others. It is common for leaching glazes to suffer from more than one...

  • (Glossary) Limit Recipe

    Because of the proliferation of glaze recipes online, potters and technicians need to develop critical thinking skills to be able identify obvious issues with new recipes presented to them. And testing skills to learn the less obvious ones. And material knowledge to recognize the mechanism of the fi...

By Tony Hansen

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