We report measurements of the temperature dependence of the surface resistivity of highquality YBa2Cu307 crystals at 5.95 GHz. A narrow transition with 89-K onset is observed.Resistivity in the normal state is found to be R", 126&10 Q. %'e establish an upper limit for the resistivity at 77 K of 1.0&10 0 and at 2 K of 1.5&10 A. The dissipation in four crystals with a total area of about 20 mm2 is measured to be nearly independent of peak microwave magnetic field over the range of 0.5 to 93 G in sharp contrast to the strong field dependence observed in bulk sintered samples. Dissipation of microwaves in superconductors is due to the interaction of the oscillating fields with the unpaired
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