Why does a substance expands upon freezing? What conditions necessitate this? For example, how does the slope of sublimation or fusion curve in a P-T diagram affect this?
The reason for this, simply put, is because of the structure of the lattice formed by the molecules upon freezing. For substances that exhibit this expansion upon freezing, the lattice structure happens to take up more space than when it is a liquid. For example, water (due to the formation/angle of the hydrogen bonds with the oxygen atom) has a hexagonal lattice structure when it's frozen, which takes up much more space than its liquid water molecule free-roaming state.
I agree that ice has more free space in its solid form. All the bonds, polar bonds, and nuclei form a lattice. Most frozen substances contain less free space than the liquid phase. Well, I think the better way to think of it is as solid water has a high amount of free space compared to other similar solids. Entropy would drive the electrons into the free spaces, since there are probably low energy states for e pairs in the open spaces. It must be that the drive for the lattice structure is high. So ice maybe in a fine balancing act. Change, the energetics of the lattice structure a bit and the hole thing could collapse. The interested reader can look up other forms of ice that form under various pressures. These may be the above "hypothetical" collapsed forms. I have looked up some of these other forms. Ice III is the one the forms most readily. It has something like 1.1 kg /L for its density. Something you would expect.