The crystal's size is in turn dependent on its temperature and any stresses applied to the crystal. So, if we can control the temperature of the sapphire very well, as well as eliminating stresses and vibrations the crystal can ring stably at a single unchanging frequency. Cryogenic sapphire possesses unique electrical, thermal and mechanical properties which make it exceptionally suitable as a resonator at the heart of a high stability oscillator. The natural consequence of this long energy storage time is that the sapphire can only interact with radiation which falls very close to its resonant frequency. For the particular mode we use in the resonator, the bandwidth of the resonance is less than 10 Hz wide at the operating frequency of 12 GHz.
Sapphire exhibits very low thermal expansion at cryogenic temperatures.
The temperature dependence of the magnetic susceptibility of the impurites causes the speed of light in the material to increase as the temperature increases. At a particular temperature this increasing speed of light exactly compensates the increasing size of the resonator such that the optical path length becomes independent of temperature. If we operate the oscillator at this particular temperature then we will be insensitive to temperature fluctuations of the sapphire. Nonetheless we still control the temperature of the resonator to a few 10s of millions of a degree. Finally the high rigidity of sapphire gives us good immunity to vibrations and tilts of the system.