Glazes - for the Self-reliant Potter (GTZ, 1993, 179 p.) 16. Glaze formula calculations (introduction...) 16.1. Glaze formula chemistry 16.2. Seger formula 16.3. Frit calculation

Glazes - for the Self-reliant Potter (GTZ, 1993, 179 p.)

16. Glaze formula calculations

Glazes are expressed in several different forms:

Recipe: a list of actual materials and weights, used directly to make the glaze.

Molecular formula: shows the relative proportion of molecules of flux, alumina and silica in the glaze. Must be converted to recipe to make the glaze.

Chemical analysis: shows the percentage of oxides in the glaze. Also known as ultimate composition.

Seger formula: a special molecular formula, which makes it easier to compare glazes. It is also known as the "empirical formula".

16.1. Glaze formula chemistry

Why glaze formulas?

As you already know, glaze materials are complicated and if you only work with clay, limestone, talc, quartz etc. there is no way to theoretically understand how they combine in the glaze. For this reason, in order to make glazing scientific and systematic, it is necessary to use chemistry. This makes it possible to write materials as chemical symbols and to make calculations that help to invent new glazes and to alter existing recipes.

16.1.1. USING CHEMICAL SYMBOLS

Chemical symbols are a language for describing atoms, molecules and the way they are combined to make up the various materials used in chemistry and in glazes.

As already described at the beginning of the book, there are more than 100 elements, which are the basic building blocks of glaze materials. Each one has a chemical symbol:

Calcium = Ca
Copper = Cu
Iron = Fe
etc.

16.1.2. CHEMICAL REACTIONS

Elements are usually not found by themselves in nature. The basic nature of elements is to combine with each other: this process is called a chemical reaction and takes place in nature through the effects of heat, pressure etc. When elements combine, they are called compounds and they can be described by chemical formulas, which show the number of atoms and how they are attached to each other.

For example, china clay is written as Al₂O₃ · 2SiO₂ · 2H₂O. Each element is followed by a number written below the line: this is the number of atoms in the compound.

Al₂ means 2 atoms of alumina and O₃ means 3 atoms of oxygen. This is the compound aluminum oxide.

If no number follows the element symbol, it is understood to be only 1 atom.

The raised period (·) shows that the compounds are joined together chemically to form a complex compound. The large numbers before each compound mean the number of molecules that combine. If there is no number in front, it is understood to mean 1 molecule.

Al₂O₃ means 1 molecule of aluminum oxide.

2SiO₂ means 2 molecules of silicon oxide.

So AL₂O₃ · 2SiO₂ · 2H₂O is a complex compound consisting of 1 molecule of aluminum oxide, 2 molecules of silicon oxide and 2 molecules of water.

These compounds cannot be broken down physically but can combine with other compounds when heated sufficiently in the kiln.

16.1.3. MOLECULAR WEIGHTS

Each kind of molecule has a specific weight. We all know that 1 kg of lead is much smaller than 1 kg of aluminum. This is because the molecules are heavier and are packed together more closely.

Because it is impossible to weigh individual molecules, they have all been assigned molecular weights, which are relative to hydrogen, which has been given the molecular weight of 1. The molecular weights of all the other elements are based on how much heavier they are compared to hydrogen.

So the molecular weight of oxygen = 16, meaning it is 16 times heavier than hydrogen.

16.1.4. FORMULA WEIGHT OF MINERALS

The molecular weights of all the elements in a compound can be added together to get the total molecular weight. This is called the formula weight. In our example of kaolin clay, we can look in the table of elements and oxides in the appendix to find out the individual molecular weights. Molecular weight is abbreviated to "MW". In order to simplify calculations we round up the MW figures. This is accurate enough since we seldom know the exact composition of our raw materials anyway.

Al2O3 · 2SiO2 · 2H2O

ELEMENT	MW	NUMBER OF ATOMS		OXIDE WEIGHT	COMPOUND WEIGHT
Al	27	2	2 x 27 = 54
O	16	3	3 x 16 = 48	102	1 x 102 = 102
Si	28	1	1 x 28 = 28
O	16	2	2 x 16 = 32	60	2 x 60 = 120
H	1	2	2 x 1 = 2
O	16	1	1 x 16 = 16	18	2 x 18 = 36
So the total MW of Al2O3 · 2SiO2 · 2H2O					= 258

This is known as formula weight.

16.1.5. PERCENTAGE TO FORMULA

Glaze formulas are often given as percentages of the various oxides. In order to find out the chemical formula, the rule is to:

Divide each oxide by its molecular weight!

In the appendix you will find the molecular weight of glaze oxide and materials.

Example:

Calculation of molecular formula of kaolin with the following chemical composition:

OXIDE	SYMBOL	PERCENT	MW	CALCULATION
Silica	SiO2	46.51%	60	46.51/60 = 0.775
Alumina	Al2O3	39.53%	102	39.53/102 = 0.387
Water	H2O	13.96%	18	13.96/18 = 0.775

The molecular formula is 0.387Al2O3 · 0.775SiO₂ · 0.775H₂O

Because this is difficult to use, we divide all the numbers by the smallest one.

0.387/0.387 = 1Al₂O₃
0.775/0.387 = 2SiO₂
0 775/0.387 = 2H₂O

The formula comes out neatly as the familiar Al₂O₃ · 2SiO₂ · 2H₂O, or kaolin!

For using a material in glaze calculation we need to calculate its formula weight. This is done as shown above for kaolin.

16.2. Seger formula

About 100 years ago a German ceramist, Hermann Seger, developed Seger cones for measuring temperatures in kilns. He also proposed writing the composition of glazes according to the number of different oxides in the glaze instead of listing the raw materials used in the glaze.

For example: Aluminum oxide can be added to the glaze either in the form of clay (Al₂O₃ · 2SiO₂ · 2H₂O) or feldspar (K₂O· Al₂O₃ · 6SiO₂).

The oxides used in glazes are divided into three groups according to the way the oxides work in the glaze.

Fluxes

This group of oxides functions as melter, and fluxes are also called basic oxides or bases. They are written RO or R₂O, where R represents any atom and O represents oxygen. So all the fluxes are a combination of one or two element atoms and one oxygen atom.

Stabilizers

These work as stiffeners in the melted glaze to prevent it from running too much. They are considered neutral oxides and are writen as R₂O₃ or two atoms of some element combined with three oxygen atoms.

Glass formers

These form the noncrystalline structure of the glaze. They are called acidic oxides and are written as RO₂ or one element atom combined with two oxygen atoms.

Seger formulas allow all glaze formulas to be expressed in a table, keeping the groups separate in order to make comparison of different formulas easy (see below).

In the table form, the sum of the fluxes must always equal 1, which makes different formulas easy to compare.

Examples
The organization of the Seger formula is always according to the table shown below.

FLUXES	STABILIZER	GLASS FORMERS
RO, R2O	R2O3	RO2
Alkalis:	Al2O3	SiO2
K2O	B2O3	TiO2
Na2O	B2O3
Li2O
Alkaline earths:
CaO
MgO
BaO
Other:
PbO
ZnO

Note: B₂O₃ is sometimes listed under stabilizers and sometimes under glass formers, since it has both characteristics.

TABLE OF LIMIT FORMULAS*

NOTE: "KNaO" is a symbol for either sodium or potassium oxide.

c012 - 08 Lead Glazes
PbO	0.7 - 1.0	Al2O3	0.05 - 0.2	SiO2	1.0 - 1.5
KNaO	0 - 0.3
ZnO	0 - 0.1
CaO	0 - 0.2
c08 - 01 Lead Glazes
PbO	0.7 - 1.0	Al2O3	0.1 - 0.25	SiO2	1.5 - 2.0
KNaO	0 - 0.3
ZnO	0 - 0.2
CaO	0 - 0.3
c08 - 04 Alkaline Glazes
PbO	0 - 0.5	Al2O3	0.5 - 0.25	SiO2	1.5 - 2.5
KNaO	0.4 - 0.8
ZnO	0 - 0.2
CaO	0 - 0.3
c08 - 04 Lead-Boron
PbO	0.2 - 0.6	Al2O3	0.15 - 0.2	SiO2	1.5 - 2.5
KNaO	0.1 - 0.25			B2O3	0.15 - 0.6
ZnO	0.1 - 0.25
CaO	0.3 - 0.6
BaO	0 - 0.15
c2 - 5 Lead Glazes
PbO	0.4 - 0.6	Al2O3	0.2 - 0.28	SiO2	2.0 - 3.0
KNaO	0.1 - 0.25
ZnO	0 - 0.25
CaO	0.1 - 0.4
c2 - 5 Boron
KNaO	0.1 - 0.25	Al2O3	0.2 - 0.28	SiO2	2.0 - 3.0
ZnO	0.1 - 0.25			B2O3	0.3 - 0.6
CaO	0.2 - 0.5
BaO	0.1 - 0.25
c2 - 5 Lead Borosilicate
PbO	0.2 - 0.3	Al2O3	0.25 - 0.35	SiO2	2.5 - 3.5
KNaO	0.2 - 0.3			B2O3	0.2 - 0.6
ZnO	0 - 0.1
CaO	0.35 - 0.5
c8 - 12 Stoneware and Porcelain
KNaO	0.2 - 0.4	Al2O3	0.3 - 0.5	SiO2	3.0 - 5.0
ZnO	0 - 0.3			B2O3	0.1 - 0.3
CaO	0.4 - 0.7
BaO	0 - 0.3
MgO	0 - 0.3

* D. Rhodes: Clay and Glazes for the Potter.

For example, a simple unfritted lead glaze would look like this:

FLUXES	STABILIZER	GLASS FORMERS
RO, R2O	R2O3	RO2
PbO 1.0	Al2O3 0.1	SiO2 1.5

Remember that the flux column always totals 1.0.

A more complicated formula is the unfritted boron glaze:

CaO	.414	Al2O3	.322	SiO2	2.291
MgO	.414			B2O3	.931
K20	.172
	1.000

There are some basic rules for the ratio of oxides in the 3 different groups, according to glaze temperature. These are called limit formulas (see page 139). They should only be considered guidelines, as many glazes exceed the limits m practice.

- Addition of 0.1 part SiO₂ to a glaze will increase the melting point by about 20°C.
- Addition of 0.05 part B₂O₃ will lower the melting point by 20°C.

The formulas of pyrometric Seger cones are listed in the appendix. These can also be used as a guide for glazes by choosing a cone formula 4 to 5 cones below the glaze firing temperature. If you need a glaze for cone 9, 1280°C, you can use the cone 5 formula for the glaze.

16.2.1. BENEFITS OF USING SEGER FORMULA

The main usefulness of the Seger formula is that it presents glazes in a way that is easy to compare. It is used for:

Originating new glazes

Glazes with desired characteristics of color, mattress etc. can first be written as Seger formulas, selecting oxides that are known to produce the effects.

Comparing glaze recipes

It is difficult to look at two recipes and see how they are different. If they are converted into Seger formulas, the differences can easily be seen.

Substituting materials

If a material is no longer available, other materials can be substituted by working out the quantities in the Seger formula.

Modifying glazes

Glazes that change character, have problems etc. can be analyzed as Seger formulas, and directions for testing decided.

The Seger formula should be considered a guide only, as most theoretical glazes do not react as expected and still require empirical testing to develop them fully. If you want to use Seger formulas for your glazes it is nice to have exact chemical analysis of your raw materials, but this is seldom the case. Instead you will have to pick one of the materials listed in the appendix. They may be close enough for practical work.

16.2.2. GLAZE RECIPE FROM FORMULA

To get the glaze recipe from the formula, there is a standard series of calculations.

Simple lead glaze example

PbO 1.0

Al2O3 0.1

SiO2 1.5

First decide which raw materials to use. For lead oxide, PbO, the choices are red lead, white lead or litharge. Al2O3 is almost always obtained from china clay, and SiO2 usually from quartz powder.

The calculation is helped a table like this:

Material and formula	Mol. Parts	PbO 1.0	Al2O3 0.1	SiO2 1.5
Litharge, PbO	1.0	1.0
Kaolin, Al2O3 · 2SiO2 · 2H2O	0.1		0.1	0.2
Quartz, SiO2	1.3			1.3
TOTAL		1.0	0.1	1.5

1.0 molecular part (MP) of litharge provides all PbO needed. We enter kaolin and its formula in the table and write 0.1 for MP. When we take 0.1 part kaolin, we get 0.1 Al₂O₃ and we enter this on the right. In the kaolin formula we have 2 SiO₂ so when we take 0.1 kaolin we get 0.2 SiO₂. We list this under SiO2. We need 1.5 SiO₂ so 1.3 remains and we get this from quartz.

Next the required molecular parts, MP, of each material are multipled by their molecular weights, MW, to get the batch weight of each material:

Material	MP	MW	Calculation	Batch weight
Litharge	1.0	223	223 x 1	223
Kaolin	0.1	258	258 x 0.1	25.8
Quartz	1.3	60	60 x 1.3	78.0

To change the recipe into percentages, all the figures are divided by the total:

Litharge	223/326.8 = .68 = 68%
Kaolin	25.8/326.8 = .08 = 8%
Quartz	78.0/326.8 = .24 = 24%

Boron glaze example

A more complicated formula is the unfritted boron glaze.

CaO	.414	Al2O3	.322	SiO2	2.291
MgO	.414			B2O3	.931
K2O	.172

Again, the first step is to select materials. Because materials that supply more than one oxide usually work better in glazes, they are preferred if available. We need both CaO and MgO, which are supplied by dolomite, CaCO3 · MgCO3. Potash feldspar supplies K2O along with Al2Ok3 and SiO2. Quartz provides SiO2. For boron, boric acid is selected.

CALCULATION PROCEDURE

1. Enter formula at top of calculation table.
2. Select materials, enter formula and MW.
3. Multiply each material's MW with its MW and enter result in part's weight.
4. Enter MP of each oxide of the material under the formula to check oxide balance.
5. Convert parts' weight into a percentage recipe.

As before we change the recipe to percentage:

Dolomite	76/384 x 100 = 19.8	20%
Potash
feldspar	96/384 x 100 = 25	25%
Kaolin	39/384 x 100 = 10.2	10%
Quartz	58/384 x 100 = 15.1	15%
Boric acid	115/384 x 100 = 29.9	30%

When calculating from formula to recipe, there is no need to carry out results beyond round figures, particularly when we do not know the exact chemical analysis of our materials.

Figure 16.2.2.A Copy this example of a calculation table.

16.2.3. FORMULA FROM GLAZE RECIPE

Calculating from a recipe to the Seger formula is the same process in reverse. We will use the same raw boric acid glaze as an example. Again we use the calculation table and the following steps:

1. Enter recipe materials and their formulas in the left column and MW and recipe figures in MP's weight column.

2. Write oxides of the materials at top of table.

3. Divide each recipe figure with its MW and enter result under MP.

4. Multiply MP with each oxide in material formula and enter result under respective oxide in the right columns.

5. Add together all oxides and list them according to RO-R2O3-RO2.

6. Add oxides in RO and divide all RO figures with the total.

Note that from dolomite only CaO and MgO are entered in the formula. CO2 is released during heating and does not take part in the glaze melt. H2O of kaolin and boric acid likewise evaporates.

The oxides are set up in the standard Seger formula:

K2O	.045	Al2O3	.084	SiO2	.598
CaO	.109			B2O3	.244
MgO	.109
	.263

The formula is brought to unity by dividing all the figures by the total, .263, in the left column.

K2O	.171	Al2O3	.319	SiO2	2.27
CaO	.414			B2O3	.928
MgO	.414

NOTE: The figures are not exactly the same as the original formula above, due to rounding off the figures. This is accurate enough for practical work.

If you have a chemical analysis of materials you want to use in a glaze, you first have to calculate the formula of the material as described on page 137. Then you enter this formula and its formula weight in the table under MW.

16.3. Frit calculation

Frit calculation is done in the same way as calculating a glaze, but the calculation is slightly more complicated. As with glazes it is important to follow the recipes accurately.

This also means that you have to make sure that the raw materials are not wet when you weigh them. Also remember that materials like calcined soda and borax will absorb moisture from the air if they are not kept in a sealed container.

16.3.1. MOISTURE COMPENSATION

If you have to weigh materials with a high moisture content you can compensate for this. Weigh 100 g of the material, dry it and then weigh it again. Moisture content is:

(wet weight -dry weight x 100)/dry weight = x%

This x % is added to the amount you are weighing to compensate for its moisture content. Example:

100 g kaolin weighs 92 g after drying.

(100 -92)/92 x 100 = 8.7 %

kaolin in recipe	3500 g
compensation 8.7 % x 3500	304.5 g
total amount needed	3804.5 g

16.3.2. FORMULA RULES FOR FRIT

The practice of fritting was described in section 7. The main reason for fritting is to make glaze materials insoluble, which is possible if the frit materials are mixed in the right proportion. In formula terms they should fall within these limits:

- Ratio flux: SiO₂ should be between l: 1.5 and 1:3.

- The sum of K₂O and Na₂O should not exceed 0.5 molecular parts on the flux side, the rest being other fluxes like PbO, CaO, ZnO, BaO.

- B₂O₃ to SiO₂ not less than 1:2, but with other materials like PbO, CaO, MgO, K₂O in the frit the proportion can go down to 1:1.5.

- A little Al₂O₃ at least 0.05 mol. parts, reduces solubility but it should not exceed 0.2 mol. parts because it reduces the fluidity of the frit melt.

We have a glaze formula of an opaque boron glaze for 1100°C:

K2O	.23	Al2O3	.30	SiO=	2.60
ZnO	.27			B2O3	.80
CaO	.50

Initially we calculate the recipe as it was done for the unfritted glaze. We get the K2O from potash feldspar. Borax cannot be used for boric oxide because no Na2O is needed in the formula and so boric acid is required. We get the CaO from whiting and the rest of the materials will be kaolin, quartz and zinc oxide.

We now decide what material to include in the frit batch and what to include in the ball milling only. This is done according to the above rules. We need to include all the soluble boric acid. Along with that we can also include whiting and zinc oxide and some potash feldspar but not all because its Al2O3 will reduce the frit's fluidity.

A frit formula could be:

K2O	.1	Al2O3	.1	SiO2	1.60
ZnO	.27			B2O3	.80
CaO	.50

One problem still remains. When the frit melts, a large amount of H2O and CO2 is lost. Thus loss does not influence the recipe if we weigh the raw frit materials, melt the frit and use all the melted frit in the glaze, adding the other material according to the original amount of raw frit. But it is much more practical to produce a large batch of frit at a time and later weigh the melted frit to produce smaller batches of glaze. We need to find out how much weight is lost.

16.3.4. FRIT LOSS CALCULATION

Practical loss

The loss can be found simply by weighing the amount of melted frit that is produced from a batch of frit. Example:

Raw frit batch weighs in total 500 kg.
After firing the (dry) frit weighs 280 kg.

Loss in % = (500 -280)/500 x 100 = 44 %

Theoretical loss

The loss can also be calculated based on the formula of the frit. On heating, whiting changes to calcium oxide:

CaCO₃ + heat ® CaO + CO₂

Only CaO enters the melted frit and we can calculate how much this weighs:

The MW of calcium carbonate is 100 and that of calcium oxide is 56 so loss is 44 parts. In percentage this is 44 % The number used to find the amount of oxide entering fusion is called the conversion factor, CF. In the material table in the appendix one column lists the conversion factor for all materials. At the bottom of the left column there is a list for the most common frit materials.

Material	CF	% loss
Barium carbonate	0.777	22.3
Borax (crystal)	0.526	47.4
Boric acid	0.563	43.7
Dolomite	0.523	47.7
Kaolin	0.861	13.9
Laed carbonate (white)	0.863	13.7
Lead oxide (red)	0.977	2.3
Magnesium carbonate	0.478	52.2
Pearl ash	0.682	31.8
Soda ash	0.585	41.5
Soda crystals	0.217	78.3
Whiting	0.561	43.9

Frit glaze example

We can now calculate the loss of our frit from before.

Frit Recipe:	Raw	CF	Melted
Potash feldspar	55.6		55.6
Whiting	50.0	x 0.561	28.1
Quartz	60.0		60.0
Zinc oxide	21.9		21.9
Boric acid	98.4	x 0.563	55.4
Total	285.9		221.0

Theoretically we get only 77.3 % melted frit from our raw frit batch. We found that 286.3 parts raw frit equal 221.2 parts melted frit so finally we can establish our glaze recipe based on melted frit:

Final glaze recipe:

Frit	221.0	69.9%
Potash feldspar	72.3	22.9%
Kaolin	18.1	5.7%
Quartz	4.8	1.5%

16.3.5. GLAZE RECIPE WITH STANDARD FRIT

Very often a ceramics producer gets the frit from a commercial supplier or wants to use only a few standard frits. Above we calculated a new frit based on the glaze formula. We will now calculate a glaze recipe from formula using a standard frit instead.

Example of a standard frit formula:

K2O	.26	Al2O3	.05	SiO2	2.5
ZnO	.13			B2O3	1.0
CaO	.61

We will try to use the frit for the following glaze:

K2O	.30	Al2O3	.40	SiO2	3.5
ZnO	.20			B2O3	0.8
CaO	.50

The calculation is done as with the unfritted glaze. First oxides are entered at the top of the table and we start to select materials to satisfy them. Before starting, we need to know the formula weight of the frit. In the appendix we get the MW of all the oxides and these we total.

K2O	.26 x 94	=	24.4
Na2O	.13 x 62	=	8.1
CaO	.61 x 56	=	34.2
Al2O3	.05 x 102	=	5.1
SiO2	2.5 x 60	=	150.0
B2O3	1.0 x 70	=	70.0
Frit MW			291.8
This we round off to			292

The frit is entered in the calculation table like other materials with many oxides. The MP is selected according to the need of B2O3 It takes 0.8 MP of frit to get the needed 0.8 B2O3 and all the oxides listed in the frit formula are multiplied by this number and the results entered on the right of the table.

Glaze Recipe	Parts	%
Frit	233.6	61.7
Potash feldspar	51.2	13.5
Soda feldspar	50.3	13.3
Kaolin	42.7	11.2
Whiting	1	0.3

16.3.6. HINTS FOR USING UNKNOWN LOCAL MATERIALS

We have already discussed above calculating local materials by guessing their closest theoretical formula. This will usually give a good starting point for making line blends, which then can be used to get a working glaze or frit.

What do you do when you have a recipe or formula but do not know the analysis of your local materials and cannot get pure ones? Usually you can create a glaze using the formula or recipe as a starting point, but it is unlikely to match the description in the book.

The most common local materials are usually:

Clays

Common clays can be used in most glazes instead of kaolin, since they all contain Al2O3 and SiO₂. But they will have lower melting points and probably change the glaze color, since they will introduce K₂O, Na₂O, Fe₂O₃, CaO, MgO and perhaps other fluxes. Probably the easiest way to work with them is simply to substitute directly for the kaolin, fire a sample and then use it as the basis for line blends to get a working glaze.

Feldspars

There are a tremendous number of different feldspars, all of which vary in the relative amounts of K₂O, Na₂O, CaO, MgO, Al₂O₃ and SiO₂ they supply. This means that directly substituting feldspars will affect the melting point of the glaze, and possibly its color response. Try them out as direct substitutions, and then the result can be altered using line blends. If the new glaze seems underfired (dry surface), the fluxes can be increased. If it seems overfired (too fluid), the clay content can be increased.

CaO sources

Calcium is introduced into glazes from a large variety of raw materials: calcium carbonate, whiting, limestone, marble, seashells, coral, agricultural lime, etc. Usually, substituting will not make much difference, but again the result can be developed using line blends of the new material.

Glass cullet

Glass cullet means waste glass, which can be used as the basis for cheap glazes. The best glass to use is window glass, which can usually be obtained free of charge or cheap from glass suppliers. Window glass consists of soda-lime-silica and can be used as a frit in glazes. It melts at about 1100°C. With the addition of some flux and clay, it can be made into a low temperature glaze. However, because of its high CE, it will usually craze.

Unknown materials

If you find new materials that are completely unknown, the easiest way to find out what they do is to first fire a small sample of the material alone, to see if it melts or not and what color it becomes. If it melts, it is a strong flux. If it does not melt, it may still be a flux. Check the test carefully to see if it has reacted with the clay body. If it develops a strong color, it will probably affect the glaze colour.

The material should also be tested by adding it to a known glaze recipe as a line blend.