Pyknometric volume measurement of a quasispherical resonator

Abstract

We have measured the internal volume of a 1 litre, diamond-turned copper quasispherical resonator with a fractional uncertainty of approximately 1 part in 106 using two independent techniques. This is in response to the need for a uniquely accurate measurement of resonator volume, for the purpose of measuring the Boltzmann constant in pursuit of the redefinition of the kelvin. The first technique is a pyknometric measurement using water as a liquid of known density. We describe the development of a procedure that results in stable, reproducible volume measurements. We provide a detailed discussion of the factors that affect the water density, such as dissolved gases. The second technique is microwave resonance spectroscopy. Here, we measure the resonant frequencies of the TM1n modes and relate them to the dimensions of the resonator. We evaluate the frequency perturbations that arise from the coupling waveguides and the electrical resistivity of the copper surface. The results of the microwave measurements show evidence of a dielectric coating on the surface. We propose that this is an oxide layer and estimate its thickness from the microwave data. Finally, we compare the volume estimates from the two methods, and find that the difference is within the combined uncertainty.