All Articles

Converting between Oxide Weight %, Mole % and Unity Formula

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

Formulas have a calculated formula weight (a matter of simple addition of atomic weights). 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 (aluminum 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 a 'standard', so one can be compared to another.

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
 ---------------------------------

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:

• The Seger unity model does not work well at lower temperatures. Some oxides that are powerful fluxes at high temperatures are refractory in low fire. Dynamic reassignment of oxides to the Seger groups by temperature is not practical at this time.
• Oxides have a much more individual presence than the Seger method tends to recognize. Their contributions to particular properties often are not linear according to concentration. Thus a more complex understanding of concentration vs. effect is needed.
• Oxide interplay producing characteristics attributable to the group is not recognized by the Seger system.
• Boron is both a glass and a flux and the logic for its employment at various temperature ranges differs. It does not 'plug into' a Seger formula very well.

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 make up the fired glass.

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%

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 LEGOblocks 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. Insight-live.com stores a material's analysis in its materials database exactly as you enter it. Of course, you need to enter the LOI as part of the analysis. Since it 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

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 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 molecular 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
---------------------------------------------------

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 principle 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%

Related Information

Ceramic Oxide Periodic Table

Pretty well all common traditional ceramic base glazes are made from less than a dozen elements (plus oxygen). Go to the full picture of this table and click or tap each of the oxides to learn more (on its page at digitalfire.com). When materials melt, they decompose, sourcing these elements in oxide form. The kiln builds the glaze from them, it does not care what material sources what oxide (assuming, of course, that all materials do melt or dissolve completely into the melt to release those oxides). Each of these oxides contributes specific properties to the glass. So, you can look at a formula and make a good prediction of the properties of the fired glaze. And know what specific oxide to increase or decrease to move a property in a given direction (e.g. melting behavior, hardness, durability, thermal expansion, color, gloss, crystallization). And know about how they interact (affecting each other). This is powerful. A lot of ceramic materials are available, hundreds - that is complicated when individual materials source multiple oxides. Viewing a glaze as a simple unity formula of ceramic oxides is just simpler.

Retro glaze chemistry calculation - 1980

This picture has its own page with more detail, click here to see it.

I did this batch-to-formula glaze chemistry calculation to help a potter with a transparent cone 10 glaze for a Plainsman P500 (a 25x4 porcelain). This version of Desktop Insight ran on the TRS-80 Model I and III, they were the first popular consumer microcomputers for business (outselling Apple 5-to-1). Notice the report uses capital letters; the machines did not support lower case! The dot matrix printers of the time lasted forever on an ink ribbon. Fanfold paper fed from a box, I could tear off only as much as was needed for a report. Boot time was less than 5 seconds. Here is what is amazing: In 2021 I found this same recipe in my Insight-live account (the green screenshot)! The results are a little different; I had the chemistry of talc wrong in 1980. Through the years, I wrote code to migrate from one system to another, and eventually it got to Digitalfire.

Links

Projects	Oxides
URLs	https://digitalfire.com/services/database.php?list=labs Laboratories who can can do a chemical analysis on a material
URLs	https://archive.org/details/gri_33125001394697/mode/2up The collected writings of Hermann August Seger - Internet Archive The “Seger Formula” was not introduced in one single paper with that title. Rather, it emerged gradually through Hermann Seger’s technical writings on glaze chemistry and ceramic analysis during the 1870s–1880s, and was later consolidated in his collected works. Modern ceramic texts later called it the “Seger Formula” or “Seger Unity Formula.”
Glossary	Oxide Molecular Formula In ceramics, the chemistry of fired glazes is expressed as an oxide formula. It expresses the relative molar proportions of the oxides contributed by a glaze recipe. There are direct links between the oxide chemistry and the fired physical properties.
Glossary	Glaze Chemistry Glaze chemistry is the study of how the oxide chemistry of glazes relate to the way they fire. It accounts for color, surface, hardness, texture, melting temperature, thermal expansion, etc.
Glossary	Unity Molecular Formula The chemistry of ceramic glazes are normally expressed as formulas. A unity formula has been retotaled to make the numbers of flux oxides total one.

PayPal	No tracking, No ads, No paywall, No transient content! Just organized, concise information constantly updated and improved. Was this helpful? Consider supporting me.

By Tony Hansen Follow me on

Got a Question?

Buy me a coffee and we can talk

 

---

https://digitalfire.com, All Rights Reserved
Privacy Policy