The objectives of this program are to: Evaluate the frequency instabilities of quartz crystal resonators as a function of temperature and Q-factors; Show the feasibility of low temperature quartz oscillators; and Determine the dynamic thermal behavior of SAW quartz oscillators and precise crystal orientation and wave propagation direction with minimized sensitivities. The measurements of the frequency noise of different quartz resonators at room temperature show a correlation between 1/f noise levels and Q-factors, following 1/Q to the 4th power law. This new property was confirmed by measuring the 1/f noise level of a pair of resonators at 300 K, 4.2 K and 1 K. A first theoretical study enables to explain the 1/Q to the 4th power law from the phonon-phonon interactions due to the crystal anharmonicities. Under fast temperature variations frequency shifts are observed in SAW delay lines, which are proportional to the time derivative of the temperature. This dynamic thermal behavior was evaluated for ST cut quartz and found comparable to that one of AT-cut quartz BAW resonators. Therefore such a thermal sensitivity is not admissible for fast warm-up oscillator applications and must be lowered. (Author)

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