iandol on mon 9 sep 02
Dear Autumn Downey,
I appreciate that you are only relaying information which was given to =
you by David hewitt. But I feel I must ask the rest of the group if this =
is a good or a poor statement.
>Mayer & Havas give the following figures in % Wt. Cubic x10^-7/oC. To =
convert to Linear coefficients, divide by 3.<
I have never seen coefficients of expansion given in terms of Mass, in =
common parlance "Weight", say kilos or pounds. Furthermore, if the =
values had been given in volumetric terms, would it not be the case that =
it we should take the Cube Root to obtain the linear value.
I am highly suspicious. Who are Mayer and Havas?
Best regards and thanks for this contribution.
Ivor Lewis.
Gavin Stairs on tue 10 sep 02
Hi Ivor,
I can answer part of this. The conversion is by means of the binomial
cubic expansion for small quantities, in which the linear term is the only
one to survive in any significance, since all the other terms multiply the
large quantity by a very small quantity. So, divide by 3.
(X + dx)^3 = X^3 + 3*X^2*dx + 3*X*dx^2 + dx^3 = V + dV. dV = 3*X^2*dx +
3*X*dx^2 +dx^3. Now Consider as unit volume and length: X=1, V=1, and
discard the dx terms in degree greater than 1: dV=3*dx. The correct
visualization is to consider the unit cube with plates of dx thickness
applied to each of three sides. This leaves little notches on three edges
(the squared terms) and on the corner (the cubed term). These are
neglected, leaving only the three slabs (the linear term). In use, the
linear coefficient only expands on one axis, so the cubic basis is only
expanded linearly. This preserves the unitary approximation over any
non-unit length. The dimensions that correspond are
^3*^-1 and *^-1, so I share your
curiosity about the mass, although that would follow by linear
correlation. So the mass usage may be a matter of measurement convenience
on the part of the original investigators. They probably measured out a
mass of the material in question, and then measured volumetric change by
some technique that I am not familiar with. Actually, today the best
measurement would be by powder x-ray diffraction or some such, giving a set
of crystal axis linear coefficients.
I am actually more skeptical about the whole methodology of using pure
substances for the base data. We do not use pure substances, except for
the dominant species such as silica, alumina, phosphate and boria glasses,
and even then it is usually as some form of mixture, as aluminosilicate,
etc. All the other stuff is used as participants in the glass matrix, and
in characteristically smaller quantities. I think it would make much
better sense to measure the coefficient of a glass in which the target
oxide concentration varies over the range of normal usage ("good glass", if
you like). The useful coefficients can then be extracted by statistical
means. This is a doable experiment for all of our usual materials, but it
requires careful technique to obtain usable data. One of the good effects
of using this kind of methodology is that it is perfectly possible to
explore the behavior of multiphase material in this way. However, the
number of data points required will quickly expand beyond all reasonable
bounds unless some sensible restrictions are applied.
Gavin
At 03:39 AM 09/09/2002 +0930, you wrote:
>Dear Autumn Downey,
>
>I appreciate that you are only relaying information which was given to =
>you by David hewitt. But I feel I must ask the rest of the group if this =
>is a good or a poor statement.
>
> >Mayer & Havas give the following figures in % Wt. Cubic x10^-7/oC. To =
>convert to Linear coefficients, divide by 3.<
>
>I have never seen coefficients of expansion given in terms of Mass, in =
>common parlance "Weight", say kilos or pounds. Furthermore, if the =
>values had been given in volumetric terms, would it not be the case that =
>it we should take the Cube Root to obtain the linear value.
>
>I am highly suspicious. Who are Mayer and Havas?
>
>Best regards and thanks for this contribution.
>
>Ivor Lewis.
>
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Gavin Stairs
Stairs Small Systems
525 Canterbury Road
London, Ontario
Canada N6G 2N5
telephone: (519) 434-8555.
email: stairs@stairs.on.ca
iandol on wed 11 sep 02
Dear Gavin Stairs,
Thank you for that exposition .
I understand what you have said but find that in the summation of the =
information you give...<squared terms) and on the corner (the cubed term). These are neglected, =
leaving only the three slabs (the linear term).>>... the "three slabs" =
you describe are square terms not linear terms. I am sure we can only =
solve this issue if we know about the experimental methodology for =
obtaining the basic information.
If weight is to be converted into a linear term then density must come =
into the calculation somewhere.
I suspect glasses are isotropic. But where there are crystals the =
parameters of the crystal lattice will influence the CoE so that is not =
uniform in each axial direction.
I agree that doing the work on a range of glasses may be the best thing =
which can be done. This may be the only way of presenting our ceramic =
constituency with information which has real practical value. Otherwise =
we are guessing and our computer programs only enable us to get a more =
precise guess.
It would certainly seem, if the qualities and properties of a glaze must =
be preserved, that those afflicted by these destructive wonders of =
nature may have to search for, or compound, a clay which will act as a =
substrate without inducing crazing at the selected maturity temperature.
Thanks for your input.
Best regards,
Ivor
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