The quality factor (Q) for different resonators at several overtones has been determined between 1.5 K and 300 K. These measurements form the basis for an improved interpretation of the limitation on Q. It is concluded that between 6 K and 20 K the main limitation in Q is due to the crystal itself. Data for different overtones permit the elimination of damping effects of the crystal supports. Measurements have been carried out on crystals with different roughness characteristics. These roughness characteristics have been measured using optical interferometry. Better control of surface roughness and crystal quality could lead to a Q of about 100 million in the liquid helium region. This value would be for a 11-MHz, 7th overtone crystal having a diameter of 15 mm.
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