Stable Diamagnetic Levitation of Pyrolytic Graphite

For only a suprisingly small investment, it is possible to see something acheive stable, passive levitation in your home. All that's required are good Neodymium supermagnets and some pyrolytic graphite from SciToys.com. The problem arises in that as soon as you see a little you'll inevitably want more because it's just so awesome. The magnets are easily obtained from any number of sites, including Engineered Concepts, SciToys, Ebay, and Wondermagnet.

1/2 inch or 3/8 inch cubes would be good for a first experiment, both for levitation and to get some idea of how rare-earth magnets act before you buy anything larger. I've been lucky enough to just get nastily pinched by the one inch supermagnets I work with, but it still hurts like hell. Try and imagine having two of the 45-pound weight plates from the gym sitting on a few square millimeters of your skin - that's what big magnets pinch like. And the more they traumatize and flatten the pinch site, the closer they get and the harder they pull. But that only becomes a factor with the magnets that cost more than $10 each or so.

First arrange the magnets so that the north and south poles on the magnets face opposite directions, and then put them into a checkerboard pattern. This image from a magnetic field simulation I ran shows what the resulting magnetic field will resemble. The program calculated that N40 neodymium magnets in this arrangement will create a magnetic field peaking at 7000 gauss (it also took ten hours to generate a 3d field map). This arrangement of magnets can be tesselated indefinitely if you want to levitate more or larger pieces of graphite.

The next step (assuming you bought from scitoys) is to cut the graphite up. Before you do, you can try a mini-experiment to see how amazingly thermally conductive it is: Hold the piece by one end and gently push the other edge into an ice cube - ice cold will run up it's length within seconds; In it's plane, pyrolytic graphite has about 4 times the thermal conductivity of copper. Through the plane, however, it has about one tenth that of copper. Most of it's other properties exhibit a similar anisotropy, including strength. A single-edge disposable razor blade is probably the best way to cut it.

Hold the graphite vertically on a hard, flat surface. Push the razor blade into the edge, putting the tip of the blade as close as you can to the center of the carbon. Push gently and it should slip right into one corner. Rock gently back and forth to get a cleave started across the whole chip; You'll hear a sound that's like paper crumpling and wood splintering as the graphene sheets break apart. Once started, just keep gently pushing down and eventually chip will pop in two.

If you want to make the chips smaller, it depends on how thin they are. If they are extremely thin, you may be able to saw them apart in a reasonable time using the razor blade. If they are much thicker than a piece of paper, you're better off trying to score the chip about half a millimeter deep on either side and gently increasing pressure until it breaks at the cuts.

Now just let go of the chip(s) over the magnets, and voila - they will scoot to the point of lowest potential and sit there!

Here comes the physics

At room temperature, materials are either ferromagnetic, paramagnetic, or diamagnetic. These represent how their magnetic permeability compares to that of open space.

• Ferromagnetic materials are strongly attracted to magnets, and have permeabilities >> 1. They respond to magnets by creating their own strong field, aligned the same way as the magnetizing field.
• Paramagnetic materials are weakly attracted to magnets, and their permeabilities are slightly greater than one, maybe 1.0002. They respond the same way as ferromagnets, just weakly. They create a small field aligned with the magnetizing field.
• Diamagnetic materials are weakly repelled from magnets, and have permeabilities slightly less than one; Pyrolytic graphite has a permeability of .9996 through it's plane. Their electrons respond to magnetic fields by orienting themselves in the opposite direction, creating a weak magnetic field in the opposite direction.

So you can see that if a strong enough magnetic field is applied to a diamagnet, it will cancel earth's gravity and take off. So how does it not fall off the top of the magnets?

The reason for that lies in the shape of the magnetic field created by arranging multiple magnets. It's a bit difficult to see in the picture above, but near the centers of the magnets, the magnetic field goes straight up (creating a higher field farther away), while it goes parallel to the faces as you approach the edges. As a result, at any given height there is more repulsion from the centers of the magnets than their edges. Since the chips are always trying to retreat from the source of the repulsion, they move to the interior corners where the field is least at any given height. This creates a potential well, where the outer edges of the magnet array have fields extending highest, those in the middle have smaller peaks over their centers, and interior edges/corners the lowest of all.