Under conditions that need not be very carefully controlled it is possible to cool water to temperatures as cold as -6C without the water freezing. If an ice crystal is then introduced into the water, or if the water is given a mechanical shock, it will then freeze, with the freeze front propagating through the water at a speed of a few cm/sec.
There is a nice video of this here.
The heat capacity of supercooled water in this temperature range ought not be far from 1 cal/gm/C, while the heat of fusion of ice ought not be far from 80 cal/gm/C. This implies that only a small fraction of the water should freeze.
The first experiment would be to verify this, perhaps by sawing the ice that results in half, and looking at it under a magnifying glass or microscope. One expects to find ice with considerable structural integrity, yet consisting mostly of water-filled voids.
Other experiments might be suggested by the first. If the ice turns out to be solid through and though, we would certainly have a calorimetric challenge.
If interested in this project, talk to Jim Reardon.