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Diamond is one of the best thermal conductors you can get. If the diamond is crushed into dust and spread out over a flat surface, but still held fairly compact (for instance in a small petri dish), would it still conduct as well as before?

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Diamond dust (or dust of any other material) won't conduct heat anywhere close to as well as the solid material.

At a molecular level the dust isn't in very good contact with other grains of dust. There is plenty of separation and air in between the particles that will retard heat conductivity. If you were to compress the dust so significantly that it did conduct as well, I'm certain the pressure would be great enough to cause the dust to bond with other dust into a larger solid.

For more a more technical treatment of the thermal conductivity of powder beds, see this paper.

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Thank you, this is what I suspected. I just wanted to make sure. –  ageattack Jan 5 at 6:15
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You should accept the answer if you feel it properly answers your question. –  DanteTheEgregore Jan 5 at 6:23
    
Thank you for the reminder, I'm new to this site. –  ageattack Jan 5 at 20:01
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It is highly unlikely that diamond dust would be anywhere near in thermal conductivity, what a solid diamond exhibits.

The thermal conductivity of diamond, is extremely dependent on the quality of the diamond, both as to crystal defects, and also impurity doping.

At room Temperature, a typical Type I diamond was measured, giving a thermal conductivity of about 10 Watts per deg C per cm; at least double what silver or copper give. But the conductivity, typically peaks (for all diamonds) at much lower Temperatures, about 100 kelvins, where it is 3 to 4 times the 300 K value. Conductivity is best for Type IIa diamonds, with a 100 k value of around 100 W/deg/cm.

Measured conductivity values seem to indicate that the simple isotropic homogenious model of heat flow is not followed in diamond.

The very highest quality (white) gem diamonds, are usually type IIa. To the best of my recollection, I believe the Cullinan diamond was type IIa. (largest ever found).

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