$\alpha -\beta$ and $\beta -\gamma$ phase boundaries of solid oxygen observed by adiabatic magnetocaloric effect

The magnetic-field-temperature phase diagram of solid oxygen is investigated by the adiabatic magnetocaloric effect (MCE) measurement with pulsed magnetic fields. Relatively large temperature decrease with hysteresis is observed at just below the $\beta -\gamma$ and $\alpha -\beta$ phase-transition temperatures owing to the field-induced transitions. The magnetic field dependence of these phase boundaries are obtained as $T_{\beta \gamma }\left(H\right)=43.8-1.55\times {10}^{-3}{H}^2$ K and $T_{\alpha \beta }\left(H\right)=23.9-0.73\times {10}^{-3}{H}^2$ K. The magnetic Clausius-Clapeyron equation quantitatively explains the $H$ dependence of $T_{\beta \gamma }$, but does not $T_{\alpha \beta }$. The MCE curve at $T_{\beta \gamma }$ is of typical first order, while the curve at $T_{\alpha \beta }$ seems to have both characteristics of first- and second-order transitions. We discuss the order of the $\alpha -\beta$ phase transition and propose possible reasons for the unusual behaviors.

Figure 1

Schematic setting of the MCE measurement for condensed oxygen.

Figure 2

MCE curves of condensed oxygen in (a) 90 to 45 K and in (b) 45 to 0 K. Phase boundaries at zero field [$T_{\gamma \mathrm{L}}\left(0\right)$, $T_{\beta \gamma }\left(0\right)$, $T_{\alpha \beta }\left(0\right)$] are shown by dotted lines.

Figure 3

(a) Temperature changes at 50 T as a function of $T_0$. The blue curve shows the estimated value by Eq. (4). Corresponding amounts of (b) heat and (c) entropy. Entropy is normalized by the gas constant, $R=8.31{\mathrm{J}\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$.

Figure 4

Enlarged MCE results at around (a) $T_{\beta \gamma }$ and (b) $T_{\alpha \beta }$. Black dashed curves are the quadratic function shown for the phase boundaries.