Converting a Recipe to a Unity Formula

30 May 2004

Introduction

Conversion of a glaze batch recipe to a unity formula representation is one of the fundamental procedures required to gain an understanding of the glaze in chemical terms. While this process is now very much computerized, I undertook the exercise of performing the conversion manually in order to more fully understand the process. This article presents and explains the methods used.

The work here is not new, nor is it original. This work has been done and reported by many authors. However, some explanations are not as clear or full as they might be. Additionally, it is common, it seems, to use somewhat contrived examples. Thus when, one is presented with a more realistic example one encounters difficulties. I hope, in this article, to address these shortcomings.

What Does Converting a Recipe to a Formula Achieve

The process of converting a glaze recipe to its formula accomplishes two basic things. First, it transforms the glaze materials into a chemical oxide representation, which is useful for determining such key things as the silica to alumina ratio. Secondly, it converts the glaze from an unfired representation to a fired one. This is a very significant point, and the source of some confusion in calculations if one is not careful. It is important because glaze calculation is concerned with the oxide composition of the fired glaze, not the unfired glaze. Thus, no matter which method is used to calculate fired glaze composition from initial raw materials, it must appropriately consider the material which is lost during firing. The fired representation is important, as it has a very direct bearing on understanding critical glaze characteristics.

Loss on ignition, or LOI, is the portion of a material that is lost during firing. This can be very significant in some materials. For example, whiting loses 43.9 % of its unfired weight during firing. This is lost as CO2 due to decomposition of CaCO3 (calcium carbonate) to CaO (calcia). In material analyses used in glaze chemistry, LOI is specified as a percentage of the total weight. In some cases, the lost material is identified. In whiting, it is CO2. In other cases it is merely a percentage of weight that is lost. For example, custer feldspar has an LOI of 0.04 % by weight. Materials analyses do vary. Those used in this paper are in the Materials table at the end of this document.

The basic process of conversion is this :

Produce or obtain a recipe in parts-by-weight form, percentages are ideal, though not necessary.
Obtain analyses of all materials in the recipe. If one is using the second method described here, molecular formulae for all materials are required, as are the formula equivalent weights.
Obtain or produce a table of molecular weights of all oxides in the materials.
Determine the contributions of oxides from each material in the recipe. This may be done either in percent weight, or in molar equivalent terms.
Sum all contributions for each oxide. This will give a total either as weight percent or as molar equivalents.
Convert this formula to a unity formula, a process which differs slightly depending upon whether you are using molar equivalents or percent weights.

The Two Approaches

The two approaches are essentially the same and will achieve the same result. One is conducted largely in weight-percent of each oxide, with the penultimate step converting to moles. The other is conducted using unity molecular formulae. The first method is easier I think, and the number of calculations required is smaller.

The first method was explained to me by John Hesselberth, author of GlazeMaster glaze calculation software, as the method he uses in his software. The second method is that used by Rhodes, Fraser and others. It took some time to be sure that the second method was indeed Rhodes et al. The confusion arose due to their use of theoretical formulae for clays, which contain no fluxes.

Example Recipe

The example recipe in this article is a cone 10 clear glaze. There is no real need to concern ourselves here with a coloured glaze or even an opacified one, as colorants and opacifiers are not used in glaze calculation. Likewise suspenders, flocculents and deflocculants are ignored. There is one exception. In reduction firings Fe2O3 is sometimes considered with the fluxes.

Start with a recipe such as the one below, for a cone 10 clear gloss, known as B Clear.

Material	Parts
Silica	32
Whiting	20
Custer feldspar	33
EPK	15
Bentonite	1

This recipe is already in a percentage form, though this is not necessary.

Material Reference Data

In these example calculations, the information provided in the Materials table in the Data Tables section below, will be used. The materials analysis information came from the ceramicmaterials.info site. Other information, such as the flux unity formula and the formula equivalent weight, are developed in this article.

Materials analyses are published in percent by weight terms for each oxide in the material. Unity formulae though are not so standardised. In some cases the components summing to unity are the fluxes and in other cases they are not. Clays, for example, may be reported with alumina unity. In order to use the second method described here, flux unity formulae were developed for all materials. It transpires that this was not necessary, and indeed silica should have given the game away. It has no fluxes and could not be reckoned in flux unity form. Yet, the calculations still worked.

Suffice to say here, that one could use the unity information on ceramicmaterials.info (or other source) as is, whether flux unity, alumina unity or silica unity were used. What is key, is that the formula equivalent weight (FEW) be calculated for the formula that is used. Calculation of the FEW will be covered in the discussion of the second method. As another example, GlazeMaster displays mole % formulae and a formula weight for that. I see no reason why this could not be used in method 2.

For oxide molecular weight information please refer to the Oxides table in the Data Tables section below. Note that this table may be constructed easily from a Periodic Table of the Elements, by summing atomic weights for each oxide formula. An example appears with the table.

Using this information the unity formula will be determined, first by the method of percent weight, and secondly, by the method of molar contributions.

Method 1 - By Percent Weight

Step 1

Construct a table of this form, in which to enter the oxide contributions, for each glaze material. The table shows the recipe materials vertically, with the parts of each material in the second column. Additional columns are to the right for each oxide provided in the materials.

Material	Parts	CaO	K2O	MgO	Na2O	TiO2	Fe2O3	P2O5	SiO2	Al2O3
Silica	32
Whiting	20
Custer feldspar	33
EPK	15
Total	100

Note that the bentonite is excluded. Its oxide contribution is negligible and it is in the recipe only to aid suspension.

With reference to the data in the Materials and Oxides tables, we may now begin calculation of the oxide contributions from each material in the recipe. Starting with silica, multiply the number of parts by the percentage weight of SiO2 in silica.

SiO2 from Silica = 32 x 100 = 3200.

Enter the value in the table.

Material	Parts	SiO2
Silica	32	3200
Whiting	20
Custer feldspar	33
EPK	15
Total	100

Do the same for Whiting.

CaO from Whiting = 20 x 56.1 = 1122.

Material	Parts	CaO	SiO2
Silica	32		3200
Whiting	20	1122
Custer feldspar	33
EPK	15
Total	100

Repeat for each material, for each oxide that the material contains. Do not include the LOI component in the table. It is burned off during firing.

Custer Feldspar contains a number of oxides but the method is the same. Calculate each oxide contribution and enter it in the table. Thus we have :

CaO from Custer Feldspar = 33 x 0.3 = 9.9.

K2O from Custer Feldspar = 33 x 10.28 = 339.24.

And so on ... entered into the table below.

Material	Parts	CaO	K2O	Na2O	Fe2O3	SiO2	Al2O3
Silica	32					3200
Whiting	20	1122
Custer feldspar	33	9.9	339.24	96.03	3.96	2277	572.55
EPK	15
Total	100

Repeat for the EPK and total the oxides vertically.

Material	Parts	CaO	K2O	MgO	Na2O	TiO2	Fe2O3	P2O5	SiO2	Al2O3
Silica	32								3200
Whiting	20	1122
Custer feldspar	33	9.9	339.24		96.03		3.96		2277	572.55
EPK	15	2.7	4.95	1.5	0.9	5.55	11.85	3.6	685.95	560.4
Total	100	1134.6	344.19	1.5	96.93	5.55	15.81	3.6	6162.95	1132.95

Step 5

At this point we have total oxide contributions by oxide in units of weight. Now, convert each weight to molecular equivalents by dividing each oxide's total by its molecular weight.

Thus moles of CaO = 1134.6/56.08 = 20.2318.

Doing likewise for each oxide yields the following. This is a molecular formula, but it is not yet in flux unity form.

Oxide	CaO	K2O	MgO	Na2O	TiO2	Fe2O3	P2O5	SiO2	Al2O3
Molecular equivalents	20.2318	3.6538	0.0372	1.5639	0.0695	0.0990	0.0254	102.6132	11.1139

Step 6

The final step, to convert the formula to flux unity form, is to sum all the flux components, and divide throughout by that sum.

Thus, the sum of flux molecular equivalents (including CaO, K2O, MgO, and Na2O) is 25.4867. Dividing all terms in the table above by this sum, leads to the following formula.

Oxide	CaO	K2O	MgO	Na2O	TiO2	Fe2O3	P2O5	SiO2	Al2O3
Unity equivalents	0.7938	0.1434	0.0015	0.0614	0.0027	0.0039	0.0010	4.0261	0.4361

The formula would then normally be written this way.

RO		R2O		RO2
CaO	0.7938	Al2O3	0.4361	SiO2	4.0261
K2O	0.1434			P2O5	0.0010
MgO	0.0015
Na2O	0.0614
TiO2	0.0027
Fe2O3	0.0039

This formula may now be compared to other glazes in a meaningful way. The silica to alumina ratio is easily determined, for example. In this case 9.2329. The relative proportions of the various fluxes are also clearly evident.

Method 2 - By Molar Contributions

This method is essentially the same as the percentage weight method, but this time we are using unity molecular equivalents. The method is commonly found in texts, such as Rhodes, Fraser and many others.

Step 1 Unity Formula and Formula Equivalent Weight

In this method it is necessary to use a molecular formula for the materials rather than the analysis. While most materials are shown with flux unity formulae in calculation programs, in books, or on the web, some are not. Most notable among the exceptions are clays.

In the example calculations here, I have used a unity formula for clay. This I had to derive myself. Strictly, this is not necessary as one may use flux unity for some materials and alumina unity for others. The result will be the same, so long as the "molecular weight" used for the material, is derived from the formula that is used for it. As noted earlier, the silica formula is in fact in silica unity. It cannot be otherwise, because there are no other oxide components in the raw material.

The formula equivalent weight (FEW) is calculated from the material's molecular formula. Taking whiting as an example, its FEW is calculated by taking the molecular formula (in this case, a flux unity formula), and multiplying each oxide contribution by its molecular weight. These are then summed. The flux unity formula for whiting is :

CaO 1 LOI (CO2) 0.9971

This may look like an odd unity formula but it is correct nonetheless. Fluxes do total 1. It includes the LOI components in the FEW.

FEW of whiting = 1 x 56.08 + 0.9971 x 44.01 = 99.9643.

The problem of LOI is an interesting one. Components of the raw material that burn off during the firing are not in the finished glaze. However, they are reckoned in the batch weights of materials that are weighed out. Thus, the FEW must reflect this lost weight for the calculations to be correct. The same is true in method one. In that case, the analysis of each material contains the LOI components, as well as the oxides that will survive the firing. A problem exists though. This is that in many cases the LOI is merely specified as an LOI percentage, but the material is not known. In this case, one cannot merely multiply the formula contribution of this LOI by its molecular weight, to add into the FEW. There is no molecular formula to use. In this case the simple expedient of multiplying the FEW, excluding this unknown LOI, by 100/(100 - unknown LOI %) will obtain the true FEW. This is presented below using EPK as an example.

The FEW, for a flux unity formula, of EPK without the 13.2 % unknown LOI is 8380.9840.

Thus the true FEW of EPK is 8380.9840 x 100 / (100 - 13.2) = 9838.0546.

You will see all the required unity formulae for the materials in the examples, in the Materials table. It also includes the FEW for each material.

Step 2

Now, again a table is constructed. This time one begins by calculating the number of moles of each material. This is done by dividing the parts of the material by its FEW. An example of whiting :

moles of whiting = 20 / 99.9643 = 0.2001.

The table is shown below with each material's contribution in parts, and in moles.

Material	Parts	Moles
Silica	32	0.5328
Whiting	20	0.2001
Custer feldspar	33	0.0533
EPK	15	0.0015
Total	100

The table is now filled out in exactly the same way as for method one. For each oxide, multiply the number of moles of the source material by that material's molecular contribution of the oxide. Enter this number in the appropriate cell in the table. Once this is done for all materials and oxides, produce a total for each oxide.

As an example, silica is shown below.

SiO2 contributed by silica = 1 x 0.5328 = 0.5328.

The completed table is shown below.

Material	Parts	Moles	CaO	K2O	MgO	Na2O	TiO2	Fe2O3	P2O5	SiO2	Al2O3
Silica	32	0.5328								0.5328
Whiting	20	0.2001	0.2001
Custer feldspar	33	0.0533	0.0018	0.0360		0.0155		0.0002		0.3791	0.0562
EPK	15	0.0015	0.0005	0.0005	0.0004	0.0001	0.0007	0.0007	0.0003	0.1143	0.0550
Total	100		0.2023	0.0365	0.0004	0.0156	0.0007	0.0010	0.0003	1.0262	0.1112

Step 3

All that remains now is to take the formula from the last row of the table above, convert it to flux unity, and display it in the normal form.

The total of the fluxes in the table above is 0.2549. This includes CaO, K2O, MgO and Na2O. Thus we have the formula in unity form below.

Oxide	CaO	K2O	MgO	Na2O	TiO2	Fe2O3	P2O5	SiO2	Al2O3
Molecular equivalents	0.7938	0.1434	0.0015	0.0614	0.0027	0.0039	0.0010	4.0263	0.4361

Rearranged into the standard form we have :

RO		R2O		RO2
CaO	0.7938	Al2O3	0.4361	SiO2	4.0263
K2O	0.1434			P2O5	0.0010
MgO	0.0015
Na2O	0.0614
TiO2	0.0027
Fe2O3	0.0039

This is the same result that was obtained in method one, allowing for rounding errors in the 4th decimal place. It is more complex as unity formulae for all materials are not expressed with flux unity. Calculating flux unity formulae for materials does however shed some light on their similarities and differences, a very interesting thing in itself.

Data Tables

The following materials and analyses are used in the examples.

Materials

Material	Oxide	Analysis (Weight %)	Unity formula	FEW
Custer feldspar	CaO	0.3	0.0331	619.4649
	K2O	10.28	0.6760
	Na2O	2.91	0.2908
	Fe2O3	0.12	0.0047
	SiO2	69	7.1167
	Al2O3	17.37	1.0543
	LOI	0.04
Silica	SiO2	100.0	1.0	60.06
Whiting	CaO	56.1	1.0	99.9643
	LOI - CO2	43.9	0.9971
EPK	CaO	0.18	0.3159	9838.0546
	K2O	0.33	0.3448
	MgO	0.1	0.2441
	Na2O	0.06	0.0953
	TiO2	0.37	0.4557
	Fe2O3	0.79	0.4868
	P2O5	0.24	0.1664
	SiO2	45.73	74.9334
	Al2O3	37.36	36.068
	LOI - H2O	1.4	7.6545
	LOI - SO3	0.21	0.2581
	LOI	13.2

A note on calculation of FEW, and on molecular formulae in general, is appropriate. If one examines method 2 closely, one notices that there is a mixture of flux unity and silica unity formulae in use. It is also the case that, had one used a more common molecular formula for EPK, there would additionally have been an alumina unity formula. This apparent anomally is in fact no problem at all. Surprising as this may seem, the reason is simple. The "molecular weight" for the material is calculated from the formula. This molecular weight (in my view, more correctly, a formula equivalent weight, or FEW) is then used to determine the number of moles of the substance. Demonstrating this is a simple matter of calculating the oxide contributions of, for example EPK, using alumina unity, with its FEW, and comparing them with those found using flux unity. They will be found to be the same. Thus, it does not matter that some materials' formulae are flux unity and some are alumina unity. What is important, as was said earlier, is that the FEW be calculated for the formula that is used.

Oxides

Oxide	Molecular weight
CaO	56.08
K2O	94.2
Na2O	61.98
MgO	40.32
TiO2	79.9
Fe2O3	159.7
P2O5	141.96
SiO2	60.06
Al2O3	101.94

As an example of the computation of the molecular weight Na2O will be used. The molecular weight is equal to twice the atomic weight of Na (sodium) plus the atomic weight of O (oxygen).

molecular wt. Na2O = 2 x 22.99 + 16 = 61.98.

References

Rhodes, D., Clays and Glazes for the Potter, 1973.

Frazer, H., Glazes for the Craft Potter, 1998.

Hesselberth, J., Email exchange on this topic, 2004.

DigitalFire Corporation, ceramicmaterials.info, for the material analyses.

Harrison, Steve, Rock Glazes, Geology and Mineral Processing for Potters.

GlazeMonkey Clay and Glaze Research