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#7, #9, #11, #12
All these deformed cones swelled or ballooned out in the same way and in the same location, which leads me to the conclusion that this is not a matter of some random particle in the clay just happening to get, by some coincidence, trapped in the center base of each of these effected cones.
I suspect, therefore, the problem is likely still a bit of moisture retention.
Also, although I used the same amount of clay for each cone, there was some variation. Cones #7 and #9 were skipped. Though fired for 10 minutes, #10 did not balloon. It just so happens that #10 is also a bit taller and skinnier.
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So, the base was not as chunky, therefore probably dried out better during the pre-heating.
So, I will continue with a new batch, doubling the preheating time to ten minutes instead of 5.
My theory is that the clay, at the thicker base does not heat through all the way. The radiant heat from the kiln heats the surface very rapidly sealing in a bit of moisture which builds up pressure.
As the clay heats up more and becomes plastic, the pressure from inside causes the base to balloon out. If the cone base is thin enough it can dry out more easily and rapidly so no moisture gets trapped, so no ballooning of the narrower cones.
Increasing the preheating time should, theoretically, resolve the problem.
I'm also interested in a type of metal alloy called Invar.
Invar does not expand when heated. This is actually due to the composition, when heated Invar both expands AND contracts on a molecular level, which perfectly balances out.
I was thinking, by perhaps adding small amounts of powdered sand or calcium or something to the clay, as moisture leaves during the firing process, so that the clay tends to shrink, the added powder could release gas that would fill the space left by the escaping moisture, or create enough internal pressure to counteract the shrinkage due to the rapid drying, ...or something like that.
This particular clay seems to not shrink much to begin with anyway, but I was just thinking.
A zero shrinkage ceramic similar to Invar would probably be useful in some way. Though shrinkage during firing of clay is not exactly the same thing as thermal expansion when heated.