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Ceramic Chemistry Basics - Formula, Analysis, Mole%, Unity, LOI

Section: Glazes, Subsection: Introduction

Description

Part of changing your viewpoint of glazes, from a collection of materials to a collection of oxides, is learning what a formula and analysis are, how conversion between the two is done and how unity and LOI impact this.

Article

When an electrical contractor arrives at a job site, he asks for the electrical blueprints. While exterior drawings and overall site plans may be of interest, he needs specific detailed schematics. A similar situation exists with glazes. Most of us have traditionally thought of glazes exclusively in terms of their batch recipes and many have developed expertise on this level, having learned many "dos and don'ts". But let us dig deeper and look at "the blueprints". Besides, there must be a better way to handle problems than a blind an endless quest for that perfect textbook recipe.

Let's review this new viewpoint again. The glaze batch recipe you mix is made from powdered ceramic minerals. However, the kiln fires decompose these materials down to their basic building blocks (called oxides). On cooling in the kiln, a new form of matter is created: a glass. It is built from a structure of oxide molecules contributed by the materials (and is returned to these when re-melted). However, the glass can never again be returned to the recipe materials used to mix the raw batch. this suggests that fired properties of the glass should be controlled and evaluated by "understanding" the oxide make-up of the glass, not the material make-up of the batch recipe. Typically, no direct relationship exists between fired glass properties and individual batch materials because most materials source two or more oxide types. This means there are two viewpoints, the oxide and the recipe, and you can choose between them or use both as appropriate. The oxide viewpoint is the primary tool to analyze fired problems, both are needed to evaluate problems with the physical properties of the glaze slurry.

Fired properties (e.g. expansion and melting temperature) can be predicted from an oxide formula. By contrast, they are normally only indirectly related to the batch recipe, and even then within a limited system. Formulas routinely draw from ten or less oxides, each of which has well documented fired property contributions. Recipes by comparison are complex because they draw on hundreds of materials, each of which can source many oxides.

Sometimes it is clear whether a problem should be analyzed at the recipe or formula level, other times it is not. For example, the oxide formula of a fired body has little to do with its plasticity, texture or even its maturity and color. Therefore analyzing an isolated body formula using chemistry software like INSIGHT to predict fired behavior would not be nearly as common as relating physical properties to its recipe.

Adjusting the firing temperature of a glaze is an ideal problem to approach at the formula level. Using INSIGHT software you can now employ the oxide viewpoint to add, subtract or diversify fluxing oxides while maintaining the SiO2:Al2O3 relationship. This retains the overall Seger balance, and stands the best chance of maintaining fired character (no more line blending of fluxes that introduce unwanted oxides and upset glaze balance).

Adjusting expansion to stop crazing is another problem which is best handled at the formula level. The oxides have clearly defined expansion values and it is normally obvious how to change a formula to reduce expansion. This is just about impossible to do on the recipe level without affecting the fired glaze appearance. For example, you could add silica, but that would make the glaze more glossy. You could add talc, substitute potash spar for soda spar, add a boron frit or kaolin, but all of these upset glaze balance and produce undesired fired effects.

There are many times when a mixed viewpoint is necessary. Consider converting a glaze to a slip. Your experience will determine the amount of ball clay, kaolin or other clays to use to achieve the desired drying shrinkage, but the oxide viewpoint will allow you to introduce these materials without changing the chemistry of the glaze. By doing it this way, you won't have to do blind recipe substitutions (e.g. ball clay for kaolin or one flux for another) that run roughshod over the glaze's chemical balance, changing its fine properties.

There comes a point when recipe level adjustments to a body or glaze will significantly influence the oxide formula. Conversely, there comes a point where oxide level adjustments alter the physical properties of a body or glaze recipe. Therefore, you almost always need to consider both viewpoints.

The oxide viewpoint has long been available, but now the computer puts it within reach, removing the tedium of the calculations. Once you 'score a few points' with it, you will find this new viewpoint a practical addition to our traditional recipe view.

Atoms, Molecules and Oxides

For practical purposes, we can consider atoms to be the most basic building blocks of matter. There are more than one hundred kinds (each is an element). Atoms insist on bonding with others to form molecules. The 15 or so types useful in ceramics like to combine with oxygen to form oxides (e.g. SiO2, CaO). It takes a nuclear reaction to tear an atom apart, but molecules can be dissected and rearranged with the kinds of chemical reactions that occur as a result of melting in a kiln. However, the kiln doesn't normally decompose complex molecules (e.g. feldspar K2O · Al2O3 · 6SiO2 ) any further than the basic oxides which make them up (e.g. K2O).

The kiln fires work their magic by juggling oxide molecules around to combine with each other in infinite ways. The time and temperature provided determine the extent to which the break down (decomposition) and subsequent reconstruction occurs. During this decomposition, some components are given off as gases (e.g. CO2, SO4 , CO, etc.).

We can compare the firing process of decomposition and glaze building to a task many kids attempt, using LEGO blocks. They find all the scattered blocks and items made from blocks and disassemble everything into one big pile. From this pile, the child will make one large wall or box structure utilizing every block. Think of the initial disassembly as the kiln's melting action to liberate all available oxides. The reassembly is analogous to the cooling of the kiln and associated freezing of the melt into a structure of oxides we call a glass.

Much scientific effort has been applied to predicting what kiln fires will do with given mixtures of oxide molecules. A basis for understanding this has been the classification of oxides into a three-group model. Each group contributes definite properties. Each group exists in certain proportions for each glaze type and firing temperature. Individual oxides also impart special properties when they predominate in their group or when they exist in critical proportions with other selected oxides.

Another important factor in the development of understanding what oxide mixtures will do in the kiln has been standardization in the way a mix of oxide molecules is expressed. Two primary standards are important.

The Formula

A formula expresses an oxide mix according to the relative numbers of molecule types. A formula is ideal for analyzing and predicting properties of a fired glaze or glass. This is because it gives us an idea about the molecular structure which is responsible for the 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 till 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 "unity formula" (which we will discuss in a minute). 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.


An Example of a Formula

Fluxes Intermediates Glass Formers
RO R2O3 RO2
K2O 0.6 Al2O3 0.9 SiO2 9.0
CaO 1.3
MgO 0.2
ZnO 0.1

Again, 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).

All formulas have a formula weight, that is, the total calculated weight for that mix of molecules. Atomic weights are known (the appendix in many ceramic texts list them); so deriving the weight of one molecule of an oxide is a matter of simple addition.

The following chart shows how oxide weights are derived and how a formula weight is calculated from an existing formula.

Calculating the Formula Weight
-----------------------------------------------------------------
       Atoms  Num    *wt                               Formula to
       in     of      of    Total    Oxide              Calculate
Oxide  Oxide  Each  Atom       Wt       Wt             Weight For
-----------------------------------------------------------------
K2O     K     2  x  39.1  =  78.2  
        O     1  x    16  =    16   = 94.2 x     0.60 =    56.5
CaO    Ca     1  x  40.1  =  40.1
        O     1  x    16  =    16   = 56.1 x     1.30 =    72.9
MgO    Mg     1  x  24.3  =  24.3
        O     1  x    16  =    16   = 40.3 x     0.20 =     8.1
ZnO    Zn     1  x  65.4  =  65.4
        O     1  x    16  =    16   = 81.4 x     0.10 =     8.1
Al2O3  Al     2  x  26.9  =  53.8
        O     3  x    16  =    48   =101.8 x     0.90 =    91.6
SiO2   Si     1  x  28.1  =  28.1 
        O     2  x    16  =    32   = 60.1 x     9.00 =   540.9
-----------------------------------------------------------------
*Data from Appendix of many textbooks       Formula Wt    778.2

These weights are not grams; they are atomic weight units. They compare the weight of a molecule of the oxide with an atom of hydrogen. CaO weighs 56.1 because Ca (calcium) weighs 40.1 and O (oxygen) weighs 16. This means only that CaO is 56.1 times heavier than a single atom of benchmark hydrogen. Al2O3 (alumina oxide) is 102 times heavier; so for each weight unit it will yield fewer molecules than CaO.

The Unity Formula

The three column format of expressing a formula was first used by Hermann Seger and today it is still called the "Seger Formula". Such formulas are normally 'unified', that is, all the numbers are scaled so that the RO column totals one (if RO oxides are lacking the R2O3 column is unified). A formula thus said to be "unified on the fluxes" or "set to RO unity". Unity formulas are 'standard' and can be compared.

The following chart takes the above formula (which had Al2O3 unity) and recalculates to 'flux unity'. The expression "bring the fluxes to unity" means "make the fluxes add up to one".

Adjusting a Formula to Flux Unity

 ---------------------------------
             Raw            Unity 
 Oxides  Formula          Formula
 ---------------------------------
 K2O        0.6 / 2.20 =     0.3
 CaO        1.3 / 2.20 =     0.6
 MgO        0.2 / 2.20 =     0.1
 ZnO        0.1 / 2.20 =     0.0
          -----            -----
 Flux total 2.2              1.0
  
 Al2O3      0.9 / 2.20 =     0.4
 SiO2         9 / 2.20 =     4.1
 ---------------------------------
As you can see, adjusting unity is rather like calculating percentages.

This format is suitable for expressing all glazes and many materials. However, refractory clays expressed as a formula will, by necessity, be shown with unity on the R2O3 column because they may have little or no flux. Other materials may have nothing but fluxing oxides so one or all can be unified.

Mole Percent

The Mole Percent (Mole%) calculation type has become popular because it provides room to rationalize oxide identity, interplay, concentration, and firing temperature. Here are some reasons why:

Mole% is a calculation of the percentage of oxide molecules by number (an analysis compares their weights). Here is the method used to convert a raw formula to a Mole% formula.

         Raw                  Mole
Oxides   Formula              Percent
------------------------------------
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
-----------------------------------

Mole% ignores LOI as do formulas, it just looks at the oxides that makeup the fired glass (you only need to account for LOI when inserting materials into the MDT). 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.

The Percentage Analysis

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.

Consider this example:


25 Porcelain Body
Formula Analysis
CaO 0.04 0.1%
MgO 0.03 0.1%
K2O 0.61 2.9%
Na2O 0.29 0.9%
Fe2O3 0.03 0.3%
TiO2 0.10 0.4%
Al2O3 4.52 23.7%
SiO2 23.27 71.6%
If you are not sure of the difference between an analysis and formula yet, think of a can of mixed nuts. It may contain cashews, brazils, peanuts, almonds and filberts. The label may specify the percentage of each type of nut in the mix. A mixture of 30% peanuts has 30% peanuts by weight because the nut company mixes by weight (they don't count individual nuts). Think of the label on the can of nuts as an analysis. When you open the can you may be surprised to find many more peanuts than expected. This is because peanuts are the smallest and therefore the lightest, so even though they make up only 30% by weight, they may well outnumber all the others combined. If you actually sorted and counted them, the resultant ratio would be like a formula. It would compare the nuts by number and the results would look quite different.

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 formula is only significant in the context of other amounts in that formula.

An analysis provides flexibility in allowing the inclusion of organics, water, and additives which are burned away during firing. For example, if a material loses 10% 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. Strictly speaking a formula cannot have an LOI because it expresses the mix of oxides in a fired ceramic. 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.

You might have noticed that many, in fact most published analyses do not total exactly 100. There are a variety of reasons for this. It is common for the LOI to be wrong because it does not include all of the volatile materials (even moisture in the sample). Also, labs typically measure the amount of a specific group of oxides, others that are not checked for are not included in the total (most raw materials, especially clays, contain trace amounts of dozens of elements). The amounts of some oxide types are more difficult to quantify and their numbers are thus not as accurate. The fact that companies do not attempt to account for every last half percent of material is generally an admission that the science of practical inexpensive chemical analysis is not exact.

Some people are critical of the use of the formula because it can be very misleading in comparing amounts of a specific oxide in different formulations. To illustrate, consider comparing a pure feldspar with a typical cone 6 transparent glaze recipe.

The formula on the lower right makes it appear that there is more than twice as much silica and three times as much alumina in the feldspar. However in the analysis on the left there is only a little more silica and much less than twice as much alumina. This all relates to the difference in weight of various oxide molecules (refer back to the mixed nut analog used above to rationalize this). Another criticism of formulas in favor of the analysis is that having 1% iron in a body or glaze makes more sense than, for example, 0.05 in the formula. There is a lot of merit in this observation, and most technicians rationalize the effects of coloring and opacifying oxides in terms of their percentage in the analysis, often not even considering them in formula comparisons. However these observations are in no way an indication that formulas are useless. Formulas are very useful as long as you are comparing two similar mixtures (e.g. two cone 6 glazes using similar materials).

Loss On Ignition (LOI)

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. This weight loss could be illustrated with the child and his LEGO blocks already considered. While disassembling existing structures to free up all blocks, he may discard a number that do not lend themselves to inclusion in the intended project. You can think of LOI as being like the shells 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 produces 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. 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. There is a lesson in the INSIGHT manual that demonstrates this. 

Following is a method of applying a 5% measured LOI to an existing analysis. This is called "LOI Compensating an Analysis".

LOI Compensating an Analysis

100 - 95 = 5 / 100 = 0.95
-------------------------------
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     0.05             5.0%
-------------------------------
      100.0%           100.0%

Converting Between Formula & Analysis

In a formula the number of and weight of each oxide molecule are known; so it is just a matter of multiplying these amounts and adding the results to get the total weight. Next, the analysis can be derived by dividing each product by the total weight and multiplying by 100 as shown in the following spreadsheet fragment.

Converting a Formula to an Analysis

Oxides Formula Weights
---------------------------------------------------
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

In an analysis the percentage of each oxide type is known; so dividing these by the molecule weights will produce a raw formula. This can then be unity adjusted. The following spreadsheet fragment demonstrates this.

Converting an Analysis to a Formula

                                           Unity
Oxides Analysis Weights                    Formula
---------------------------------------------------
K2O    7.19%  /  94.2   = 0.0763  /  .2827 = 0.27
CaO    9.36%  /  56.1   = 0.1668  /  .2827 = 0.59
MgO    1.03%  /  40.3   = 0.0254  /  .2827 = 0.09
znO    1.15%  /  81.4   = 0.0141  /  .2827 = 0.05
                          ------
                          0.2827

Al2O3 11.80%  / 101.8   = 0.1159  /  .2827 = 0.41
SiO2  69.48%  /  60.1   = 1.1561  /  .2827 = 4.09
---------------------------------------------------

INSIGHT can accept an analysis and convert it to a formula to store in its native formula format.

Theoretical and Actual Formulas

If a totally pure source of kaolin could be found, it would have a formula of Al2O3 · 2SiO2 . No real deposit in the world has this, but most are close. It has, therefore, been the custom to use a theoretical formula when using kaolin in calculations (since the error introduced is small). this principal applies to most standard materials such as feldspar, whiting, dolomite, talc, etc.)."

However, the error involved with some theoretical formulas can border on unacceptable if the type of material used is not as pure as the formula suggests. this is more serious if different mixtures being compared are using different types or brand names of a material like feldspar, or if a calculation is being done in order to substitute a similar but not identical material into a recipe. It becomes necessary to use a more precise formula, which although more complicated will yield a better calculation. The manufacturer's data sheet is the best source of information on a material's formula.

Notice the differences in the following generic and name-brand feldspars.

G-200 FELDSPAR GENERIC POTSPAR CUSTER FELDSPAR
CaO 0.81% 0.08     0.30% [ 0.03]
K2O 10.75% 0.63 16.92% 1.00 10.28% [ 0.68]
MgO 0.05% 0.01
Na2O 3.04% 0.27     2.91% [ 0.29]
Al2O3 18.50% [ 1.00] 18.32% [ 1.00] 17.35% [ 1.05]
SiO2 66.30% 6.08 64.76% 6.00 69.00% 7.11
Fe2O3 0.08% 0.00     0.12% 0.01
LOI 0.16%       0.04%

If you would like to study the mathematics of ceramic calculations, you can download an INSIGHT spreadsheet from the Digitalfire website.


By Tony Hansen

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