Use of a helical resonator as a capacitive transducer in vibrating reed measurements

A new design of the vibrating reed apparatus for studying the high-resonant overtones of very small samples is described. Using the high Q (∼10 ³) helical rf resonator as a capacitive transducer, great sensitivity has been obtained. The theoretical sensitivity of the detector is investigated with transmission-line theory, and the result shows that the Johnson-noise-limited sensitivity is proportional to the Q of the resonator instead of Q^1/2, as is the case of lumped LC-tuned circuit analyses. For a nonsuperconducting resonator, the Johnson-noise-limited minimum detectable displacement (Δd_min) at room temperature, with bandwidth B, is about 10^-7 Å √B/Hz, if the rf electrical field level is only limited by vacuum breakdown. An application of the apparatus in studying the temperature-dependent changes in the Young's modulus of single crystals of TaS₃ is shown.