Electric and magnetic susceptibilities of gaseous oxygen: Present data and modern theory compared

Abstract

We used a cross capacitor to measure the relative dielectric permittivity ${\ensuremath{\epsilon}}_{r}$ of ${\mathrm{O}}_{2}$ at 273, 293, and $323\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and at pressures up to $6.5\phantom{\rule{0.3em}{0ex}}\mathrm{MPa}$. Simultaneously we measured oxygen's complex refractive index $n$ using a quasispherical cavity resonator at frequencies between 2.4 and $7.3\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. The combined results from these measurements determine oxygen's frequency-dependent, relative magnetic permeability ${\ensuremath{\mu}}_{r}(f,p,T)$ with an uncertainty of less than 1% of $({\ensuremath{\mu}}_{r}\ensuremath{-}1)$ at pressures above $2\phantom{\rule{0.3em}{0ex}}\mathrm{MPa}$. Regression of these data to a model for oxygen's impact---broadened microwave spectrum allowed us to determine two quantities that are, in principle, amenable to calculation: the molar magnetic susceptibility in the limits of zero pressure and zero frequency ${\ensuremath{\chi}}_{M00}^{\mathrm{meas}}\ensuremath{\equiv}{\ensuremath{\chi}}_{M}(0,0,293.15\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ and the second magnetic virial coefficient ${b}_{\ensuremath{\mu}}$. With oxygen's electronic $g$ factor constrained to $2.0039\ifmmode\pm\else\textpm\fi{}0.0003$ (the value known from laser magnetic resonance, EPR, and molecular beam experiments) we obtained ${\ensuremath{\chi}}_{M00}^{\mathrm{meas}}=(42.92\ifmmode\pm\else\textpm\fi{}0.06)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{3}\phantom{\rule{0.2em}{0ex}}{\mathrm{mol}}^{\ensuremath{-}1}$ and ${b}_{\ensuremath{\mu}}=\ensuremath{-}1.8\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\mathrm{mol}}^{\ensuremath{-}1}$. The result for ${\ensuremath{\chi}}_{M00}^{\mathrm{meas}}$ is consistent with a recent ab initio calculation ${\ensuremath{\chi}}_{M00}^{\mathrm{meas}}∕{\ensuremath{\chi}}_{M00}^{\mathrm{calc}}=0.9998\ifmmode\pm\else\textpm\fi{}0.0014$. Our measurements of oxygen's magnetic susceptibility are the first made relative to the susceptibility of helium calculated ab initio. All previous measurements were made relative to the diamagnetic susceptibility of water. These previous measurements, published in 1943 or earlier, span the wider range $0.975<{\ensuremath{\chi}}_{M00}^{\mathrm{meas}}∕{\ensuremath{\chi}}_{M00}^{\mathrm{calc}}<1.019$. Our measurements of ${\ensuremath{\epsilon}}_{r}$ determine the static molecular dielectric polarizability of oxygen: $(1.7456\ifmmode\pm\else\textpm\fi{}0.0003)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\phantom{\rule{0.3em}{0ex}}\mathrm{F}\phantom{\rule{0.2em}{0ex}}{\mathrm{m}}^{2}$, which deviates by $+0.7$ and $\ensuremath{-}0.1%$ from two recent ab initio calculations.