| INSIGHT Calculation Types |
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A formula expresses an oxide mix according to the relative numbers of molecule types. A formula is suited to analyzing and predicting properties of a fired glaze or glass. This is because it gives us an idea about the molecular structure that is responsible for fired behavior. Since the kiln fires build these oxide molecules one-by-one into a structure, it follows that one will never really “understand” a glaze without seeing its oxide formula. A formula is flexible. We can arbitrarily retotal it without affecting the relative numbers of oxide molecules. In fact, this retotaling of a formula is standard procedure to produce a “Seger unity formula”. With a formula, you need not worry whether there is 1 gram, 1 ton, or one billion molecules, only relative numbers matter. This is why it is allowable to express a formula showing molecule parts (e.g. 0.4 MgO). In reality this would not occur, but on paper a formula helps us compare relative numbers of oxide molecules in a ratio.
| Fluxes RO |
Intermediates R2O3 |
Glass Formers RO2 |
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| K2O CaO MgO ZnO |
0.5 1.3 0.2 0.1 |
Al2O3 | 0.9 | SiO2 | 9.0 |
Notice in the above that oxides are grouped into three columns: the bases, acids, and amphoterics or simply as the RO, R2O3 , and RO2 oxides (where "R" is the element combining with oxygen). Actually, the ratio of R to O is significant. The right column has the greatest oxygen component, the left has the least. Simplistically, we can view these three groups as the silica:alumina:fluxes system. This latter convention is not really correct because there are more glass builders than SiO2 , other intermediates besides Al2O3 , and the RO’s do more than just flux. But because this method evokes immediate recognition, let’s use it anyway. Ancient potters referred to these three as the blood, flesh, and bones of a glaze (not a bad way to think of it).
Any formula has a formula weight, that is, the total calculated weight for that mix of molecules. Atomic weights are published in any ceramic text; so deriving the weight of one molecule of an oxide is a matter of simple addition.
The three column format of expressing a formula was first used by Hermann Seger and today it is still called the "Seger Formula". The unity is normally set to the fluxes. Here is how we would recalculate the above raw formula to a flux unity formula:
Raw Unity
Oxides Formula Formula
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K2O 0.6 / 2.20 = 0.27
CaO 1.3 / 2.20 = 0.59
MgO 0.2 / 2.20 = 0.09
ZnO 0.1 / 2.20 = 0.05
----- ----
Flux Total 2.2 1.0
Al2O3 0.9 / 2.20 = 0.41
SiO2 9.0 / 2.20 = 4.09
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The Mole Percent (Mole%) calculation type has become popular because it provides room to rationalize oxide identity, interplay, concentration, and firing temperature.
Mole% is simply a calculation of the percentage of oxide molecules by number (as opposed to an analysis which compares their weights). Following is an example of how to convert a raw formula to a Mole% formula.
Raw Percent
Oxides Formula Analysis
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K2O 0.6 / 12.1 x 100 = 5.0%
CaO 1.3 / 12.1 x 100 = 10.7
MgO 0.2 / 12.1 x 100 = 1.7
ZnO 0.1 / 12.1 x 100 = 0.8
Al2O3 0.9 / 12.1 x 100 = 7.4
SiO2 9.0 / 12.1 x 100 = 74.3
----- -----
Total 12.1 100.0
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Mole% ignores LOI as do formulas, it just looks at the oxides that makeup the fired glass. The INSIGHT Advisor dialog contains a few examples of target formulas from Richard Eppler and references are based on Mole%. These will give you a feel for how the system is used.
An "analysis" compares oxides by the weights of their molecules, not the numbers of molecules. It is important to note that an analysis comparison between two glazes can look quite different from a Mole% comparison since oxide molecule weights differ greatly.
The analysis format is best suited to showing how much of each individual oxide is in a mix. For example, feldspars are used as a source of flux, although they also provide SiO2 and Al2O3 , so a buyer wants to know how much flux each brand has. A percentage analysis figure shows this, whereas a formula figure does not. An individual item can be extracted from an analysis (e.g. 10% K2O) and it is meaningful. However, an individual item in a unity formula is only significant in the context of other amounts in that formula.
While an analysis can be expressed in only one way, it does provide flexibility in allowing the inclusion of organics, water, and additives which are burned away during firing. For example, if a material loses 10% by weight on firing, we can just say LOI (Loss on Ignition) is 10%. However, it would be difficult to express this 10% loss in a formula. Remember the formula is ideal to express the mix of oxides in a fired ceramic and thus there is no LOI. It is no surprise then that the analysis has become a standard used to express the make-up of raw glaze and clay materials on manufacturers data sheets.
Here is how we would convert the unity formula above into an analysis:
Oxides Formula Weights Percent ------------------------------------------------ K2O 0.27 x 94.2 = 25.43 / 353.78 = 7.19% CaO 0.59 x 56.1 = 33.10 / 353.78 = 9.36% MgO 0.09 x 40.3 = 3.63 / 353.78 = 1.03% ZnO 0.05 x 81.4 = 4.07 / 353.78 = 1.15% Al2O3 0.41 x 101.8 = 41.74 / 353.78 = 11.80% SiO2 4.09 x 60.1 = 245.81 / 353.78 = 69.48% ------------------------------------------------ Formula Weight 353.78
The primary purpose of recipe calculations is to derive the formula for the glass that comes out of the kiln, from the mix of recipe materials that go into the kiln. A fired glass has no organics or carbonates; so it always has zero LOI. This means that LOI is never shown for a glaze formula and you will never need to worry about it for any batch-to-formula or analysis calculations.
However, many raw materials that go into the kiln do lose weight during firing; so they are not sourcing as many oxide molecules as a calculation might suggest. If a raw material loses weight on firing, it must be accounted for in calculations. You can think of LOI as being like the shells which we throw away from a bag of nuts. We compensate for anything lost during firing by increasing the formula weight. For example, 100 grams of kaolin going into a kiln produce only 88 grams of oxides for glass making. By increasing the formula weight of the kaolin by the correct amount, a full calculated oxide yield will result. The INSIGHT software stores a material’s formula in its MDT (materials database) exactly as you enter it. It requires a formula weight for each material; so when needed it can calculate the material’s LOI as the difference between the recorded weight and the actual sum of the weights of the oxides in the formula.
Since INSIGHT knows the LOI for each material in a recipe, it can calculate the LOI of the raw recipe as a whole. This can be very useful. For example, if you are blending materials to create a composite material that will be used in recipes, you need to know its LOI when you add it to INSIGHT's materials database.
If you have an analysis lacking an LOI figure or suspect the accuracy of the analysis delivered by a lab, then you can weigh, fire, and weigh again to derive the LOI and compensate the analysis. Following is mathematical method of applying a 5% measured LOI to an existing analysis. This is called "LOI Compensating an Analysis".
100 - 95 = 5 / 100 = 0.95
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K2O 7.3% x 0.95 = 6.9%
CaO 9.4% x 0.95 = 8.9%
MgO 1.0% x 0.95 = 1.0%
ZnO 1.0% x 0.95 = 1.0%
Al2O3 11.8% x 0.95 = 11.2%
SiO2 69.5% x 0.95 = 66.0%
LOI 5.0%
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100.0% 100.0%
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