Microwave firing of ceramics is said to improve their physical
properties by creating an inverted temperature gradient: since the
microwaves can penetrate deeply into the ceramic to heat it, the heat
source is spread evenly throughout, while the heat sink is
concentrated at the surface, where cool air cools the surface of the
ceramic.  Consequently, water is driven out of the ceramic before it
hardens, avoiding the creation of steam bubbles that create
microscopic cracks in the ceramic.

David Reid, an amazing hacker, recently figured out that he could cast
aluminum and pot-metal in his kitchen microwave by making clay molds
with graphite and magnetite mixed into the clay.  Apparently graphite
absorbs microwaves quite well at room temperature and until it gets
fairly hot, while magnetite doesn't absorb them that well until it's
already relatively hot --- but continues to absorb them until it's hot
enough to melt the metal.  (http://home.c2i.net/metaphor/mvpage.html)

Unfortunately he didn't get it hot enough to cast steel or fire
ceramics; the magnetite melted.  He's still trying to solve this
problem.

I speculate that a small microwaveable vacuum chamber could help with
home microwave-firing by diminishing the heat loss due to convection.
(Reid used ceramic wool and taped over the ventilation port in the
microwave to help with this.)  Perhaps a simple bell jar, with a
ceramic base, a non-microwave-absorbing rubber seal for the bell-jar
to rest on, and a little nylon valve and hose fitting to let you pump
the air out before you put the thing into the microwave.

Used microwave ovens are available cheaply in the US: craigslist
currently lists several for $35, $20, $50, $15, $20, $20, $35.  By
contrast, small electric kilns seem to start around $500 new and $200
used.

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