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Tyler Miller

Glaze calc the hard way, or, How I learned to stop worrying and love Hermann Seger

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In my experience, the more technology is involved with something, the further removed you are from the realities of what you're working on.   An example is wood working.  A table saw, router, and screws, removes the carpenter from the nature and feel of the wood.  One upon a time, all carpentry was done with wedges, froes, chisels, planes, etc.  Ripping (sawing with the grain) was unheard of.  You used a froe and riving brake for that.  Items and structures this way are inherently stronger than and superior to those made with sawn timber.  It was the law that parliamentary furniture in the UK had to be made with split timbers until it wasn't feasible to do so anymore.

I feel the same about glaze software.  Even the best of it tends to be buggy, fussy, and prone to a lot of transcription errors.  I don't find it saves me too much time if I'm serious about a glaze, and I also just enjoy math and being hands on about things.  For this reason, I thought I'd share how I like to do my glaze calculations.  I don't tend to adhere to the usual limit formulae, because they make boring glazes, but in a lot of academic literature, glazes are either expressed as analysis (% by weight) or in unity formulas.  That is, they're useful for replicating effects without being tied to a fixed material set.

If you get really good, and have a little geological know how, you can actually take mineralogical analyses of chunks of random rock, and formulate glazes around them (or fit them to existing glaze recipes), figuring out how much feldspar, silica, lime, etc are in the rock.

So this is how I do glaze calcs, with just a periodic table, some chem. knowledge, a pencil, paper, and an antique solar powered calculator.  The info I've presented here comes from Digitalfire's discussion of unity formulae, Linda Arbuckle's discussion of the same, and Michael Cardew's Pioneer Pottery.  All present basically the same stuff, but I find each presentation a little opaque in its own way.

I'm going to keep things simple, and I'll start with a theoretically pure mineral to keep the math convenient and short.  Let's say we have the following analysis for a feldspar:  SiO2: 68.74% ; Al2O3 19.44% ; Na2O 11.82% .  Theoretical soda feldspar.  To be any use in calculation, we need to convert this to a unity formula.  Hermann Seger was the first to express things this way, and it's based on the theoretical K-Spar formula 1 K2O. 1 Al2O3. 6 SiO2.  The idea is that all the ROs and R2Os add up to 1 and the rest are expressed in terms of this as a ratio.  But, this is expressed in terms of numbers of molecules, not molecular weight.  So we need to figure that out.  Period table time.  I'll do soda and just give the rest.  Sodium has an atomic weight of 22.9898 g/mol, oxygen 15.999.  There are two atoms sodium, one of oxygen, so that's 2(22.9898) + 15.9999 = 61.9796.  The molecular weight of "soda" is 61.9796 g/mol--we'll knock that back to 61.98 to keep the math nicer. I should add that a mole is a fixed number of atoms or molecules.  Alumina's molecular weight is 101.96, and Silica's is 60.08.  Knowing this, we can say the percentage is a portion of a 100 gram sample of the feldspar.  So, 68.74/60.08 = 1.1441.  There is 1.1441 mol of Silica in our feldspar.  11.82/61.98 = 0.1907.  There is 0.1907 mol of Soda.  19.44/101.96 = 0.1907.  There is 0.1907 mol of alumina.  To get the unity, you would add up all the fluxes (RO's and R2O's) and divide each individual flux by the sum.  There is only one flux in my example, but if there were two or more (as there almost always is), you would add up all the molar amounts and then divide each by the sum.  Like, if there were 0.2 mol CaO and 0.1 mol Na20, you'd add those to get 0.3 and then divide both to get your unified fluxes (0.66666 Ca0, 0.3333 Na20).  But, since we just have the soda, we just get 1.  Then, we divide the silica and alumina by the 0.1907 (our sum of fluxes).  We get 5.999 Silica, and 1 Alumina.  The formula for theoretical soda spar: 1 Na2O. 1 Al2O3. 6 (ish) SiO2.

Then, we want the formula weight.  We multiply each by its molar mass, and add the products.  61.98 + 101.96 + 5.999 (60.08) = 524.35992.  We'll call it 524.36.  Note that Tony Hansen is a little off this, because, I think, of a transcription error.

Ingredients that are pure flux, like limestone, are just a 1.  The one exception to this unity is kaolin, which is expressed in terms of "ideal" kaolin, 1 Al2O3. 2 SiO2.  The actual formula is something like 1 Al2O3. 1.996 SiO2

But now we have all the info we need to make a glaze.  In this case, a 4-3-2-1 cone 8-10.  What I call "toilet bowl clear."  40% spar, 30% quartz, 20% limestone, 10% kaolin.

Make a chart, with the materials down one side, and the ROs, R2Os, RO2s, and R2O3s all expressed across the top, like below.  Divide each percent by the formula weight, to get the equivalent weight.  And then multiply the equivalent weight by each member of the unity formula.  Plug the product into the relevant box.  For the soda feldspar, this means 1 x 0.07628 for the Na2O box, 1 x 0.07628 for the Al2O3 box, and 5.999 x 0.07628 for the SiO2 box.  When you have all the relevant boxes filled.  You do the same unifying procedure as you did above.  Add all the fluxes together to get a sum, then divide each flux by this sum.  We get 0.27628. And 0.2/0.27628 = 0.7239 (CaO), then 0.07628/0.27628 = 0.2761 (Na2O).  These total 1 for unity.  Then 1.036/0.27628 = 3.75 (ish) for SiO2.  And finally 0.4188 for Al2O3.  So our unity formula is CaO: 0.7239; Na2O: 0.2761; SiO2: 3.75; Al2O3: 0.4188.  Which ain't bad for a cone 10 glaze according to established limits.  Our "toilet bowl clear" glaze should be a success--according to the math, at any rate.

This is a grossly simplified example, but I encourage you to seek out this info on Tony Hansen's site, and anywhere you can so that you can use a pencil and paper to do this on your own, with your own numbers.  Even if you do it only once.  It will help your understanding of glazes immensely.  And you can seriously use anything you have an analysis for to make a glaze.  Get a rock analyzed and go from there.  Math and Science are fun!

 

 

 

glazechart.jpg

Edited by Tyler Miller

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That's how I learned Tyler, "a long time ago in a galaxy far, far away" at UMass in the late 60's.  Used a slide rule to do the math.  Keeping track of decimal points was a real bear.

When I teach glaze calc I always teach people what the software is doing because like you, I believe that an understanding of "what is under the hood" is important to really "get" this stuff.

The repetitive math steps and table lookups is what eventually drove me to write early glaze calc software for a PC about 1979-80. 

Thanks for sharing this stuff.  :)

best,

................................john

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Programming was in some ways easier back then.  At least, the way my mind works it was.

I still prefer by hand because I like to check my work and don't mind repetition.  Plus, I can pull numbers from anywhere and do it on the fly.

I was up in a remote area last week, and I had otherwise unpublished numbers from a gov't official and I was playing with glaze ideas in my tent using local minerals.  Too exciting.

Edited by Tyler Miller
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I stopped writing and selling glaze calc software as the programming technology sped rapidly away from me .  Wanted to be a potter.... not a programmer.  I started on a mainframe in college and with .... punch cards!  Learned machine code, Fortran4 , COBOL, and BASIC.    Continued a bit into early Visual BASIC..... and haven't had time since. 

Yeah, in some ways it was easier before the heavy display graphics business took over for very "mathematic / chemistry" input/output.

I can still do it by hand.... but I 've gotten "lazy".  ;)

best,

..........................john

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It's good to know where the numbers come from but I trust software to make less mistakes than me doing calculations :D

Never had the chance to program with a punch card inserted into the mainframe but it seems so easy to program right now. Most of the time somebody else has done the work for you and shared it for free.

 

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I agree that it's good to know how to do the calculations by hand, but having software take care of the maths frees you up to juggle other variables. When I use the software I'm working on (not that I've done much work lately), I can specify a particular oxide composition, and then play with the ingredients to make sure the glaze has enough clay for suspension, or minimal LOI, or minimal soluble ingredients, etc.

That said, the UMF only tells part of the story. The ingredients you source the oxides from make a difference. I picked up some schorl in Nambia earlier this year, and used it to make a glaze with the same oxide composition as another glaze I'm working in, but which obtains its boron from a frit. It turned out quite differently.  Then again, I was using a generic analysis for schorl, so perhaps the oxide compositions were different too.

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2 hours ago, Pieter Mostert said:

When I use the software I'm working on (not that I've done much work lately), I can specify a particular oxide composition, and then play with the ingredients to make sure the glaze has enough clay for suspension, or minimal LOI, or minimal soluble ingredients, etc.

You can do this too by hand--the steps can be reversed if you have known or desired values and work back to ingredients.  Usually pretty easy.  Just simple algebra.

I agree with you that testing's the only way to be sure.  Heck, even manufacturer's analysis is sometimes wrong--custer spar, e.g.

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The ability of the computer to do the math fast allows you to spend the time analyzing the large amount of DATA you can generate, and then making conclusions or hypotheses from that data....... instead of spending that time doing repetitive math steps.  THAT is the main reason to use it, and the driving reason that I did the program I did "back in the day".

best,

.......................john

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15 minutes ago, JBaymore said:

The ability of the computer to do the math fast allows you to spend the time analyzing the large amount of DATA you can generate, and then making conclusions or hypotheses from that data....... instead of spending that time doing repetitive math steps.  THAT is the main reason to use it, and the driving reason that I did the program I did "back in the day".

best,

.......................john

My sentiments exactly. In the glaze calc class I teach, I have a fully annotated step-by-step spreadsheet table to show all the details of the derivation of the unity for a single simple recipe, which I give to the students and walk through once. They can study it on their own to work the math if they want to, but this shows exactly what is going on with the math already done (but annotated and visible) so one knows how it works. And then we go to the computer which does all the math (and more) so we can start making conclusions and hypotheses about a recipe. Doing the math by hand only proves pedantry.

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16 minutes ago, JBaymore said:

The ability of the computer to do the math fast allows you to spend the time analyzing the large amount of DATA you can generate, and then making conclusions or hypotheses from that data....... instead of spending that time doing repetitive math steps.  THAT is the main reason to use it, and the driving reason that I did the program I did "back in the day".

best,

.......................john

John,

I don't find UMF formulas to be data, per se--or a means of producing it.  They strike me more as a useful form comparative notation.  Test tiles are data, formulae are expressions of that data.

Like, if I'm doing line blends, I'll do the formulae for the significant ones (either epic fails, nearly theres, or dead ons), but the data doesn't come from the formulae.

Like, I know that the high calcia in the glaze example I provided gives it a narrower firing range.  But the formulae don't provide that, the testing does.  Conclusions come from the tests, formulae just express it in a comparative way.

The implications of whether I use wollastonite or flint and whiting doesn't show up in the numbers.  And the math isn't what tells me what makes a stable glaze, someone's experience does.  And playing in the wiggle room doesn't take that much effort.  writing out the above formulae took less time than the accompanying text.  

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Tyler,

The UMF is one piece of data in the exploration.  It is not the only one.  Physical tests of varying types supply others.  Any conclusions come from amazing all of the possible data and then trying to "connect the dots".

Anyone who has looked into this subject knows that material sourcing has a huge impact as well as firing cycles.  UMF is just one component. 

best,

....................john

 

 

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John, I'm not sure I follow what you're saying.  Maybe I should ask, what data beyond being a convenient form of comparative notation does a UMF provide?  Since otherwise we're in complete agreement, that firing schedules and material sourcing matter as well.

Edited by Tyler Miller
Edited for clarity

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20 hours ago, Tyler Miller said:

You can do this too by hand--the steps can be reversed if you have known or desired values and work back to ingredients.  Usually pretty easy.  Just simple algebra.

When it comes to optimizing a variable / variables in your glaze subject to a number of constraints, things get a bit more complicated. Solving a linear programming problem in many variables is not something I'd want to do by hand. I'm not suggesting that you have to do this - usually a good working knowledge of your materials and some common sense will get you in the right ball park - but if its possible to get quantitative bounds  by letting a computer run through some algorithm, that's information I'd want to know when I'm playing with a recipe.

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Pieter,

It's not as bad as you think, but I will say it's a skill kindof like factoring or picking prime numbers out of a series.  Not necessarily intuitively learned.  A lot of mid-20th C academic publications, pre-glaze software, presume the skill.

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I learned by hand as well, and I agree that it gives a much better understanding of the process, but I have no problem using the computer. It's no different than using a calculator- I can calculate big numbers by hand, but why waste the time and risk the mistakes? Once you understand the process, the result is what's important, not the process.

Even if the UMF only provides a means of comparative notation, that defines it as data. The glaze recipe is data. UMF is data. The raw glaze is data. The fired test is data. All of it is information needed to determine the qualities of a glaze.

da·ta
ˈdadə,ˈdādə/
noun
  1. facts and statistics collected together for reference or analysis.
    synonyms: facts, figures, statistics, details, particulars, specifics; More
    • COMPUTING
      the quantities, characters, or symbols on which operations are performed by a computer, being stored and transmitted in the form of electrical signals and recorded on magnetic, optical, or mechanical recording media.
    • PHILOSOPHY
      things known or assumed as facts, making the basis of reasoning or calculation.

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Neil, 

my understanding is that data isn't derived from analysis, but is the thing analyzed.  The raw recipe is the data, the UMF a form of notation to facilitate analysis.

(x + y)^2 and x^2 +2xy+ y^2 are the same thing, but one facilitates a  easier math.  

The same is true in chem.  2 g of a substance plus 8 g of a substance = 7.5 g of a new substance and 2.5 of a new substance can be expressed more generally as:

x mol substance + y mol substance = w mol new sub + z mol new sub

Datum/data means "a given thing/things."  The raw material by which is worked on.  I believe your above definition supports that, though perhaps ambiguously.  Especially iay the final definition--data is the basis of calculation.

Edited by Tyler Miller

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2 hours ago, neilestrick said:

Even if the UMF only provides a means of comparative notation, that defines it as data. The glaze recipe is data. UMF is data. The raw glaze is data. The fired test is data. All of it is information needed to determine the qualities of a glaze.

Yes.... this.  Thanks for beating me to it, Neil.

best,

................john

 

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Okay, let's put this all to rest.  Firstly, I think the word you are looking for, John and Neil, is information.  Equivocating information and data is false.  All data is information, but not all information is data.

 
A glaze recipe and UMF provide, and come from, the same data, but not the same information.  A good parallel example would perhaps be Roman vs modern Arabic numerals.  The Arabic decimal system makes apparent mathematical associations not otherwise accessible in Roman numerals.  The number is the same, how you work with it is not.  Modern arabic numerals provide additional arithmetic information which otherwise has to mentally supplied.  The same is true with Leibniz vs Newtonian calculus notation.
 
A % by weight of oxides analysis gives the same data as a UMF, but the UMF provides additional information--the molarity.  This makes things like lithia easier to account for since Lithium is literally the lightest metal.
 
Now, to get back to Pieter, John, and Dick's point.  Running scads of UMF calculations through a simulator is to my mind useless.  The information gained is merely didactic (i.e. an expression of second hand knowledge), and such "hands-on" training is not so much hands on, but learning by rote.  Test tiles are superior for this kind of learning--for me.  If you feel this isn't the case, that's fine, de gustibus and all that.  But it's not gaining first hand knowledge, and certainly isn't a means to test hypotheses.  It aids in interpretation, but itself is not a test.  As such, I don't feel it's useful or necessary to run loads of tests through, just a few empirically significant ones.
 
This gets to my point that there's nothing you can do with a glaze sim that you can't by hand.  By hand, it's a question of being good with the necessary math skills--some aren't for everybody and that's fine.  Factoring, trig, and calculus aren't for everyone either.  No stigma there.
 
As for my preference for by hand.  It comes down to this:  glaze sims are buggy, ugly, inelegantly coded, and non-intuitive to use.  That's my feeling.  I also don't like that it's difficult and problematic to input my own ingredients into some.  And my own feeling is, if I'm not doing original glaze research, there's no point in glaze calcs at all.  I should just get a book of recipes and call it a day.
 
I also have a tendency to want to own my own mistakes and not be beholden to those of others.  And even the best glaze calculators out there are riddled with them.  Some not so insignificantly.
 
So, to summarize, not all information is data, but all data is information--though not necessarily useful as such.  Spectroscopic data on mineral composition expressed in something absurd like Ångstroms is of no help to me, although latent within that raw data is useful information.
 
Glaze calcs by hand are in no way inferior to those by machine.  And I'll bet a whole pile of dead potters would agree with me on that.  There aren't many conclusions to be made from running scads of glaze calcs.  Original research can be harder with some programs.  And the errors aren't your own.
 
Glaze calcs are also not necessary at all to make good glazes--a recipe book and test tiles work for the vast majority.  I think everyone here is an artist first, ceramic engineer fifth or sixth (if at all).
 
You may have your preferences and I respect them, but I think the truths behind mine are valid.  You're also not going to trip up a classical philosophy guy on the nature of data. 
 
peace.
Edited by Tyler Miller

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Tyler, you are obviously able to work in ceramics in a more philosophical way than many of us, and I don't mean that to be a negative. I hope you didn't read my comments to mean that I find your method to be inferior. On the contrary, I love working with numbers, but it's just not the way I work any more. My current schedule is too busy to allow for mixing tests for fun or doing calculations by hand. I find that working with UMF on the computer is very good for time management, and can prevent me from wasting a lot of time mixing non-functional glazes. Yes, there's something to be learned from the failures, but when I'm working towards something specific, I'm usually too pressed for time to care about that. I also think that you can't rule out the UMF as part of the whole package. Yes, test tiles alone can be the path to a good glaze, but I find UMF to be the best way to tweak a glaze to make it perfect, or to fix a problematic glaze. It's not just for original formulation. It's improbable that I would take a glaze from a book and use it as is. All glazes need tweaking for your clay body and firing schedule, and the UMF is a great way to to that.

These discussions are what make this forum great!:D

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On 9/16/2017 at 9:14 PM, Tyler Miller said:

In my experience, the more technology is involved with something, the further removed you are from the realities of what you're working on.   An example is wood working.  A table saw, router, and screws, removes the carpenter from the nature and feel of the wood.  One upon a time, all carpentry was done with wedges, froes, chisels, planes, etc.  Ripping (sawing with the grain) was unheard of.  You used a froe and riving brake for that.  Items and structures this way are inherently stronger than and superior to those made with sawn timber.  It was the law that parliamentary furniture in the UK had to be made with split timbers until it wasn't feasible to do so anymore.

Yikes, what a pile of misinformation Tyler. I can only conclude that you are more of an armchair woodworker than an actual woodworker.   Yes, ripping  has been around for 100s of years, they where used to make planks for everything from table tops to walk ways and yes, even buildings. Back in the day ripping was a two man job using a pit saw which was invented during the medieval times in the UK.

That parliamentary law you speak of was created by King George I in  1691 to impede American Colonists from using prime timber because Great Britain had depleted its forests  and they feared that their ships would not have timber available for masts. 

Riving was done primarily for items such as legs and tool handles, and yes because it is stronger.  A technique still used today by many fine woodworkers. Many primitive tables where made from riven wood mainly because the only tool available to the one making the table was an axe.

The table saw was invented by an Amish woman in 1813 along with the circular saw blade.  Planes were in vented a few years later in the 1820s. Planes were the precursor to the router which was invented around 1915.

Today, there are many fine woodworkers (myself included) that do not use screws or nails to build fine furniture and use riven wood where its needed.

Using modern tools does not remove a woodworker or a potter  from the nature and feel of the wood or clay.  In fact far from it,  it just simplifies a  task that wants to be accomplished.

If you want to calculate glaze formulas by hand I think that's wonderful and its what you should continue to do, in fact I admire you for it. But to proclaim that your way of calculating glaze is better then those that use software is a bit pretentious. 

If you are saying in your first paragraph that the use of modern tools and software removes one from the skill at hand then I would suggest that you stop using an electric or foot powered wheels and  a kiln that is heated by electric or gas and return to hand building pots and fire them in a pit. Then you can honestly say you are not removed "from the realities of what you're working on."

 

 

 

 

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Ron,  I suggest you check your facts again.  George I was not reigning in the UK in 1691--that would be William and Mary.  The law has nothing to do with the colonies, either.  There were laws on the books as late as 1894 stipulating that woods like fir used for commercial purposes had to be split.  For reasons of quality--America wasn't a colony then.  The table saw is as old as at least 1777 (when the first patent was issued--to Samuel Miller, not an Amish woman). Yet despite this early invention, it was still considered inferior.  Specialty items like barrels and casks are still made from split woods like oak and chestnut for this reason. Planes have been around for FAR longer than 1820.  Like, they've been found at Pompeii.  And rip sawing was indeed historically unheardof for a long time because it was unnecessary and uneconomical.

Seriously, whoever told you that stuff shot you a line.  The facts are easily verifiable and not even close to what you've said here--with the exception of the router, that did hit the market in 1915.

I fewl the need to clarify that my original comments were meant to fall along a time scale much greater than the history of America.  The world didn't begin with the Jamestown settlement.

As far as removing the woodworker from the grain and feel of yhe wood, I stand by that.  Using a handplane requires an awareness of the grain an industrial drum sander doesn't.  

And so you know my money and mouth are in the same place, I'm building a cabin by hand using materials found locally (except mortar and nails) and an accompanying updraft wood fire kiln.  I also regularly use wild clays from that property and locally sourced minerals in my clay work.  Oh and I built my own wooden kick wheel.

As for saying by hand is better, I didn't say that.  I said i prefer it and that you can do everything a calculator can do.  Which is true, not pretense.

 

Edited by Tyler Miller
Information added, incomplete thoughts fleshed out.

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