Is there a Diamond in Jupiter's Center?

In this thread on the Sun, Chronos asked, “Next Question?” Well…http://boards.straightdope.com/sdmb/showpost.php?p=14932018&postcount=24

Arthur C. Clarke, in a couple of his works of fiction – yes, I know the difference! – posits a very large diamond at the heart of the planet Jupiter. An earth-sized diamond!

Is there any current support for this notion? Is it wholly hogwash, or vaguely possible, or at a stage of “nobody knows?”

Probably not, according to this source.

The simulation suggests that the core is made of layers of metals, rocks and ices of methane, ammonia and water, while above it is an atmosphere of mostly hydrogen and helium. At the center of the rocky core is probably a metallic ball of iron and nickel, just like Earth’s core.

Vaguely possible, sure. There’s certainly enough pressure down there. But I’m not sure why there would be a concentration of any sort of carbon in the center, rather than other materials like hydrogen (which makes up most of Jupiter) or iron (which is heavy enough that it’d sink to the center). Even if there were a lot of carbon in the center of Jupiter, I’d expect it to be much more impure than anything we’d properly call a diamond.

I would like to propose the novel idea that Jupiter’s core is actually made of cubic zirconium.

[tangent]

Just curious… How much carbon do we think our sun is currently chewing on?

Could there or should there be any correlation to the percentage of elements the sun is busy making heavier elements with, and Jupiter’s atmosphere/core? I assume the gas giants accreted from the same nebula remains, but I’ve never given thought to how homogenous the gasses/elements were in the neighborhood of our eventual solar system—right before our sun went nova.

[/tangent]

Elemental composition of the Sun

Composition of Jupiter: (from here)
[ul] [li] H2: 89.8±2.0%[/li] [li] He: 10.2±2.0%[/li] [li] CH4: 0.3±0.1%[/li] [li] NH3: 0.026±0.004%[/li] [li] HD: 0.0028±0.001%[/li] [li] C2H6: 0.00058±0.00015%[/li] [li] H2O: 0.0004% (varies with pressure)[/ul][/li]
(By way of comparison, the composition of the Earth, from Answers.com: "Earth’s solid mass is about 32% iron, 30% oxygen, 15% silicon, 14% magnesium, 3% sulfur, 2% nickel, 1.5% calcium, and 1.4% aluminum. Much of the iron and nickel are in the planetary core, which is 89% iron and 6% nickel. The atmosphere consists of 78% nitrogen and 21% oxygen, with traces of other gases including carbon dioxide (0.3%). ")