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calculated thermal expansion

Karl P. Platt on wed 4 jun 97

Let's preface this by saying that anyone who's interested can get brain
curdling details on how one would go about deriving thermal expansion
co-efficients in Robert Mongomery's Design and Analysis of Experiments,
John Wiley & Sons, 1984.

Clearly being able to calculate thermal expansion, elasticity,
temperature/viscosity relations, index of refraction, etc., etc. of a
glaze, glass, ceramic, plastic, etc. has a lot of intuitive appeal.
Unfortunately, there are very strict limits as to how such things might
be useful.

The factors of English and Turner and Winkelmann and Schott were
developed to be used with commercial glassware compositions. Both of
these groups of factors assume that there is a linear relationship
between composition and thermal expansion -- adding 1% of Na2O will
raise the expansion of the mixture (glass) by such-and-so amount. The

A(glass)= A1xP1 + A2xP2.....AxPx

Where A is the "factor" and P is the mass% of the glaze/glass component.

A number of different workers apart from W&S and E&T have proposed
physical property/composition factors (Gilard & Dubrul, Kumar,
Takahashi, Clark & Turner, Narai-Szabo, Huggins, Huggins&Sun, Demkina,
Mayer & Haas or Appen). However, note that all derived numbers which
assign quite different values to the contribution of any oxide.
Obviously there's something else at work. Actually there are a couple
things.

First is that the relationships between concentration and properties is
not linear. Second is that the ranges of composition studied were
different.

Gilard and Dubril came up with a better fit by using a a quadratic
(non-linear) form of the additive relationship (A=A'1xP1+A''xP^2).

As to the range of compositions, we should look at how these factors are
derived. We want to study the relation ship between Na2O,CaO,Al2O3 and
SiO2. One would melt a range of compositions with varying quantities of
these components, make rods and measure their thermal expansion. The
compositions are then arranged in a group of equations one atop the
other as follows

A=wNa2O+xCaO+yAl2O3+zSiO2
A1=W1Na2O..........etc.

The as,ws,xs,ys,and zs are arranged into matrices and solved in a manner
referred to as Linear Regression to obtain the factors. Note: A number
of the workers above used quite unique (and non-linear) schemes of their
own to get the factors to fit reality a bit better. It is well
established in the world of Linear Regression that going outside the
range of parameters going into these calculations will give hinkey
results. This is exactly what happens.

As a student I went through this routine to derive Karl's factors. They
worked great within the ranges of composition used, but once outside
reality was highly elusive. My numbers, all of which were based on
soda-lime glass, also bore no relation to the numbers of anyone else --
but they worked for my ranges of composition. I went through this again
in 1993-1994 and came up with a plausible set of numbers that worked
well with the compositions I was working with -- I also have/had a huge
selection of samples to work with -- 2 or 3 different compositions were
measured and entered into the scheme daily. This helped a great deal as
errors (in weighing, refractory solution, the effect of heavy additions
of colorants, etc,) were "balanced out".

Ceramic glazes are another animal entirely and calculating anything
resembling what really happens is highly elusive -- see Hall's paper for
the circuitous details. This is particularly true of the glaze contains
any B2O3, mixed alkalies(common) or heavy quantities of RO components.

B2O3 is well known to show "anamolous" behavior in glasses/glazes. Real
simply, this is because it can exist in a number of different
relationships with oxygen. Frequently, in small amounts the B ion sits
between 4 oxygens and acts like a weak replacement for SiO2. When B2O3
replaces an alkali or RO component, the expansion of the glass will be
reduced as more network former is added. However, if it replaced SiO2,
expansion rises as the B2O3 glass is much more weakly held together than
SiO2 based glass. With larger additions of B2O3 and in the presence of
higher amounts of the alkalies, B2O3 tends to situate itself in between
on 3 oxygens -- this formation is highly weak and highly expansive.
The details of all this are actually somewhat more convoluted, but the
point is that the presence of B2O3 has dramatic effects that cannot be
simply factored under all circumstances. Hall's work reflects this
clearly where it shows he had _different groups_ of factors that
depended on composition.

Glazes are by nature a world apart from glass. This is mainly due to the
fact that they contain more or less crystalline material -- Ron noted
this. The crystalline material can have thermal expansions all over the
ball park and any effort to factor these in would keep an army of PhDs
busy for several careers.

There's also the whole matter of heat-treatment. Remember that ceramic
glazes (and bodies) are very seldom composed of completely reacted
materials and that firing for longer or shorter periods of time at any
temperature can produce vastly differing results.

As well in ceramic glaze one needs to consider the effects of glaze/body
reactions, which can be very significant in fluid glazes. There's also
the matter of volatilization of the alkalies, B2O3 or Pbo that can have
dramatic effects.

Yes, it often occurs that a calculated number goes in the right
direction -- of course adding more SiO2 will generally raise the
expansion of a glass/glaze. Yes adding more alkali will generally raise
the expansion, etc...... These facts remain independent of any factoring
schemes. This, I'd suggest, makes developing an intuition in respect to
the effects of different approaches one might take to modify a glaze and
equally, if not more valuable strategy obtaining a desired result --
i.e. non-crazed glaze.

The calculated numbers are, at best, a crutch and at worst simply bad
information on which one may make desicions -- bad data is worse than no
data in decision making.

To be honest, I have this spreadsheet I've built over the past 7 years
to do my calculations for me -- I love the late 20th century. It
includes calculated thermal expansion using E&T, W&S and Appen's
numbers. The results are always very different from each other and
experience shows Appen's numbers are the most reliable -- by the way, if
you can find Appen's book (it's in German) it is a wonderful resource
and accounts for many coloring oxides.

OK -- I'm stopping for now as I've been invited to go have bobo de
camarao and this is a Brasilian dish I _adore_

We could go on, and it may be worthwhile.....who knows.....

Abracos,

Karl

David Hewitt on sat 7 jun 97

In message , "Karl P. Platt" writes
>----------------------------Original message----------------------------

>
>As a student I went through this routine to derive Karl's factors. They
>worked great within the ranges of composition used, but once outside
>reality was highly elusive. My numbers, all of which were based on
>soda-lime glass, also bore no relation to the numbers of anyone else --
>but they worked for my ranges of composition. I went through this again
>in 1993-1994 and came up with a plausible set of numbers that worked
>well with the compositions I was working with -- I also have/had a huge
>selection of samples to work with -- 2 or 3 different compositions were
>measured and entered into the scheme daily. This helped a great deal as
>errors (in weighing, refractory solution, the effect of heavy additions
>of colorants, etc,) were "balanced out".
>

I have not tried to develop my own Coefficients of Expansion like Karl,
but I have done some testing to see if any of the coefficients of the
well known ceramists made any sense when compared to some actual glaze
tests.
These tests are available for anyone to see as an Article in the
Education section of the IMC site
URL http://www.ceramicsoftware.com
We found useful correlation as the article states. It was of course
inevitably for a limited range of compositions, but I would not dismiss
its usefulness because of this.

Karl lists many problem areas which I think are all valid areas for
concern. If any one would wish to read more on these 'areas of concern'
I do not think they could do better than by reading James D McLindon's
paper to the State University of New York College of Ceramics in June
1965. The 'Literature Survey' in this report, I think, covers most if
not all of the points Karl has raised. McLindon goes on to develop some
revised coefficients and tests on a series of Ferro glaze frits and
demonstrates that these give better correlation with measured expansions
than the factors used by Winkelmann and Schott. The concluding sentence
is:-
'The overall result of this paper is a greater significance in
estimating the relative effect of oxides in compounding glazes for
adjustment of fit to a body'.
He wisely does not claim to predict the degree of significance, but I am
sure he would not wish to suggest ignoring the figures produced by
calculation.

McLindon's coefficients ( Cubical Thermal Expansion x10-7) are as
follows:-
SiO2 1.1
Al2O3 1.95
B2O3 0.87
Na2O 11.4
K2O 9.0
PbO 2.4
ZnO 3.0
CaO 4.5
BaO 3.9
TiO2 4.5
ZrO2 2.1

Another paper from the New York State University by Dennis N Coon (Vol 2
1980) 'The relationship between thermal expansion and composition of
commercial glazes' deals at some length with the non linearity with
composition of some of the oxide expansion coefficients and the
practice, in the absence of anything better, of the use of average
factors. This includes in its Conclusions the following:-

'... If the need was to replace a glaze with one of similar expansion,
the model presented could be used to effectively screen out the
completely unacceptable candidates. However, the dilatometric method
would still be required for the final decision.'

Or you have to actually test a glaze to see if it fits, but calculation
can help.
Finally it concludes:-

'Further research must be directed towards increasing the accuracy of
the factors. Knowing the exact relationship which exists between the
factor and composition would eliminate the the use of average factors.
This effect of the other oxides present on the factors must also be
defined before the required accuracy can be obtained. if these
relationships were defined, it would not be unrealistic to expect
accuracy in the range required to eliminate dilatometric expansion
testing.'

Does anyone want a research project? Or perhaps someone is already
working on it
--
David Hewitt
David Hewitt Pottery ,
South Wales, NP6 1DQ, UK. Tel:- +44 (0) 1633 420647
URL http://www.ceramicsoftware.com/education/people/hewitt.htm

Ron Roy on sat 7 jun 97

Karl wrote on June 4 -

>The calculated numbers are, at best, a crutch and at worst simply bad
>information on which one may make decisions -- bad data is worse than no
>data in decision making.

Not so with calculated expansion as I have explained once - anyone who
wants to do some experiments that will prove the point just say so. The
statement - bad data is worse than none is true but - this does not apply
in this case as I (and obviously others) have found from experience. There
are unexpected results in some cases but there are reasons for this. The
question is - which data is good and which bad. To say that all the data is
bad is simply not true. To say that most of the data is bad is not true. To
even say half the data is useless is not true.

The fault is in using a single expansion/contraction rate for each oxide in
every system. I am not trying to oversimplify the problem - there is much
work to be done on this aspect of glaze calculation.

I find it a most useful crutch and use it almost daily to formulate glazes
which fit. In fact if I had to do this without calculated expansion I would
be feeling around in the dark again.

The alternative is going back to no data - throwing the baby out with the
bath water - a backward step. Ask anyone who has used calculated expansion
to help solve fit problems. I am not saying there is no skill involved -
blush - and I do say the more you know the better the results will be. I
can also say that at entry level there is an immediate benefit -
calculation opens doors to understanding because it fosters curiosity and
inquiry.

Ron Roy
Evenings, call 416 439 2621
Fax, 416 438 7849
Studio: 416-752-7862.
Email ronroy@astral.magic.ca

Karl P. Platt on sun 8 jun 97

>Not so with calculated expansion as I have explained once - anyone who
>wants to do some experiments that will prove the point just say so.

I'm game, have furnaces, kilns, materials, a frit factory up the road
and a lab with dilatometers available in the next room. This'll have to
fit in between other activites, and might be a little delayed.

>The fault is in using a single expansion/contraction rate for each >oxide in ev

This is a good point. C.W. Babcock, yet another worker who's tried to
come-up with a universal system of calculating thermal expansion (and
other physical properties), wrote a book called Glass Technology
Methods. I bought a copy in a used book store in Austin, TX in the 80's.
Babcock was affiliated with Owens-Illinois and published prodigiously in
the literature. His calculations scheme was based on applying a
different sets of factors that depend on where a given composition fell
on the phase diagram that represented the composition field for the
glass (glaze) in question. The thermal expansion numbers are no less
reasonable than any others.

K -- really burnt, but satisfied after the weekend's glassmaking
workshop in portuguese.