[AlleyCat]

I am looking for a material to be used in the cavity of an Xray tube.   I will need to enclose an electronic circuit in this material.   It will be a high temperature device (550 C) and have a really high dielectric constant.   Using Aluminum Nitrate in the material has been used with some success.   The material should be free of air pockets as well.   

[Enthalpy]

Welcome, AlleyCat!

Free of air is a reasonable demand. In ceramics, it results from good sintering.

Is it aluminium nitrate Al(NO₃)₃ or nitride AlN? The nitride is a known technical ceramic.

550°C is damn hot for electronics. I know no semiconductor operating or even surviving at this temperature. Some resistors, vacuum valves, special-made capacitors may work. Or is the circuit cooler? In oilfield operations, electronics operates shortly at +180°C with special precautions. The usual uneasy limit is +125°C.

Do you expect some X-ray shielding properties from the material? AlN is transparent, BN more so. Heavy elements shield more at identical weight.

The permittivity changes with temperature. Shall it be kept, or even be constant, to 550°C? That would restrict the choice. For instance the titanates and niobates of Ba, Zr, Ba+Zr or Pb+Zr have ε>1000 but only at room temperature and low frequency, with big losses, microphonic and memory effect.

Some permittivities:
8-15     AlN
9        Al₂O₃, common ceramic
27       Ta₂O₅
41       Nb₂O₅
40-200   BN, available ceramic
85+      TiO₂, available ceramic
29       ZrO₂, available ceramic (contains also HfO₂ usually, and must be stabilized with some Y₂O₃)
Good     HfO₂

[AlleyCat]

Hi Enthalpy

I am sorry the material we use is Aluminum Nitride.   We use it for the high resistivity to voltage.   The temperature of 550 C is only a small instance of time and we might be able to work around it.   I noticed that boron nitride is a much higher permeability than Aluminum Nitride.  Our electronics is mostly DC so it doesn't really have a frequency.   

Regards

[Enthalpy]

If you seek a high permittivity (ε, not permeability μ) at DC and room temperature, then barium-and-strontium titanate would outperform the others. It's the material used for type II and III ceramic capacitors for high capacity per volume unit.
https://en.wikipedia.org/wiki/Ceramic_capacitor#Class_2_ceramic_capacitors

Unless you have special needs for the capacitive material, like a quick energy storage line
http://www.chemicalforums.com/index.php?topic=72911.msg266311#msg266311
the standard choice would be to buy commercial capacitors and assemble them in a circuit. Varied shapes exist, including for high voltage
https://en.wikipedia.org/wiki/Ceramic_capacitor#Ceramic_power_capacitors
and you can combine them in series, arrange the geometry as you want. Outgassing depends only on the capping material: with epoxy resin it should be fine, sleeves of PVC or polyamide must be avoided.
http://www.avx.com/products/ceramic-capacitors/high-voltage/
https://psearch.en.murata.com/capacitor/lineup/index.html search "screw termination type"
https://www.vishay.com/capacitors/ceramic/high-voltage/
https://www.ceramtec.com/high-voltage-ceramic-capacitors/