The substance best known for expanding, rather than condensing, as it freezes is, of course, water. The reason for this unusual phenomenon is that as they freeze, the water molecules form a tetrahedral lattice.
Wait, one might ask, what's a tetrahedral lattice?
To understand this, we have to look a little closer at the water molecule itself. As many know, the molecule is made of one Oxygen and two Hydrogen atoms bonded together.
It looks something like this:
Where "O" represents the Oxygen atom, "H" the Hydrogen atom, and the slashes the bonds between them. The two dots above the O represent its UNSHARED ELECTRON PAIR, a critical influence on the molecule's shape.
The bonds between the H's and O are made of electrons, which repel each other. Because there are three sets of electrons (Those bonding the H's to the O, AND the O's unshared pair, you following?) they arrange themselves into a roughly triangular shape.
A Tetrahedron (as in tetrahedral lattice) is a three-dimensional shape made of four triangles with edges touching. (Like a pyramid with a triangle for a base, can you visualize it?). So, we can begin to see a connection here.
The REASON the molecules form tetrahedrons is because of their charge. The water molecule has positive and negative sides, like a battery or magnet. In fact, the Oxygen atom (the top of the triangle) is negative, and the Hydrogen atoms (The base of the triangle) are positive.
We know that when two magnets are placed close together, they align themselves so that the POSITIVE side of one is touching the NEGATIVE side of the other. Water molecules are no different! They arrange themselves so that H's are near O's and vice versa. Only there are more than two water molecules; there are 3.54x10^22 in a single gram! (For those unfamiliar with scientific notation, that's 3,540,000,000,000,000,000,000,000 water molecules.) This attraction is responsible for many of water's unique properties, including why it expands when frozen.
Because there are so many molecules, their arrangement forms a pattern. Each molecule connects to two more molecules, each of which connects to two more after that...
Because of the charges we discussed earlier, the arrangement is remarkably definite and orderly. This kind of ordered, three-dimensional arrangement is called a LATTICE.
In this case, a tetrahedral lattice!
So, we now know what a tetrahedral lattice is, why does it make water expand when it freezes?
This is because the lattice can only hold its shape when the molecules have LOW ENERGY (I.e. low temperature)... in fact, only when they are frozen! Water molecules above 32 degrees F have so much energy that they can BREAK FREE of the lattice and move about freely, which actually allows them to get CLOSER TOGETHER. When they go below 32 degrees, however, they are forced back into shape.
This is why ice condenses when it melts, and expands when it freezes.
It should be noted that liquid water does NOT expand as it gets colder. water at 41 degrees F is DENSER than water at 42 degrees F; it is only when freezing that this phenomenon occurs. In fact, ice at 21 degrees F is denser than ice at 22 degrees F!
Now that we understand water, what other substances expand when frozen? Because of the lattice requirement, they are few and less known than water. Examples include Silicon, which is used in various electronic an technological applications, Bismuth, which in alloys and compounds can be found in chemical and pharmaceutical applications, as well as Antimony and Gallium.