Diamondium pearls（Grade D） are actually made from Moissanite .It is Single Crystal Silicon Carbide.
In nature, there are primarily three types of SiC, that is 3C-SiC, 4H-SiC and 6H-SiC
The crystal structure of Moissanite consists of a hexagonal lattice formed by silicon and carbon atoms(6H-SiC), with each unit cell containing six silicon atoms and six carbon atoms. This structure gives Moissanite its hardness and fire similar to that of diamonds.
These three structures have different thermal conductivities.

That means the thermal conductivity of Moissanite is more than twice that of ALN(Aluminum nitride).

All the above data and information come from the following references:

1.Harris, G.L. 1995 Thermal conductivity of SiC, 5-6.
2. Goldberg Yu., Levinshtein M.E., Rumyantsev S.L.2001 Properties of Advanced Semiconductor Materials GaN, AlN, SiC, BN, SiC, SiGe, 93-148.

3. Amirthan G, Udaya A, Balasubramanian M. 2011 Thermal conductivity studies on Si / SiCceramic composites. 09 003.
4. M.S. Aziz, Z. Mohammed, R.I. Alip. 2018. Faculty of Electrical Engineering. The Effect of SiC Polytypes on the HeatDistribution Efficiency of a Phase Change Memory.