Small-Angle Scattering of X Rays from Carbon Dioxide in the Vicinity of Its Critical Point

Abstract

Intensity measurements of x rays scattered at small angles by carbon dioxide are reported for various equilibrium states in the critical neighborhood of the temperature–density diagram. From our studies we have observed that (1) the $K^2$ dependence in a plot of reciprocal relative scattered intensity ${\mathrm{(I}}_s^{\text{−1}})$ versus scattering angle is obeyed over the following ranges: ${\text{2.66\hspace{0.17em}×\hspace{0.17em}10}}^{\text{−4}}{\AA }^{\text{−2}}{\mathrm{\hspace{0.17em}<\hspace{0.17em}K}}^2{\text{\hspace{0.17em}=\hspace{0.17em}(16π}}^2{\mathrm{\hspace{0.17em}/\hspace{0.17em}\lambda }}^2){\sin }^2{\text{(θ\hspace{0.17em}/\hspace{0.17em}2)\hspace{0.17em}<\hspace{0.17em}8.06\hspace{0.17em}×\hspace{0.17em}10}}^{\text{−3}}{\AA }^{\text{−2}}{\text{, 0.343°\hspace{0.17em}≤\hspace{0.17em}T\hspace{0.17em}−\hspace{0.17em}T}}_c{\text{\hspace{0.17em}≤\hspace{0.17em}5.64}}_0°\mathrm{K}\text{, 87.5\hspace{0.17em}≤\hspace{0.17em}ρ\hspace{0.17em}≤\hspace{0.17em}356.5}$ amagat, and along the liquid side of the coexistence curve and (2) the temperature dependence of the isothermal compressibility ${\mathrm{(\beta }}_T)$ and the long‐range correlation length ${\mathrm{(\xi }}_s)$ have the forms: ${\beta }_T{\mathrm{\hspace{0.17em}=\hspace{0.17em}f\epsilon }}^{\mathrm{-\gamma }}$ and ${\xi }_s{\mathrm{\hspace{0.17em}=\hspace{0.17em}\xi }}_0{\epsilon }^{\mathrm{-\nu }}$ , where ${\mathrm{\epsilon \hspace{0.17em}=\hspace{0.17em}(T\hspace{0.17em}-\hspace{0.17em}T}}_c{\mathrm{)\hspace{0.17em}/\hspace{0.17em}T}}_c$ ; $\mathrm{f,\; \gamma }$ and $\nu$ are constants with respect to temperature. We have obtained ${\text{γ\hspace{0.17em}=\hspace{0.17em}1.32}}_{\text{−0.10}}^{\text{+0.09}}$ and $\text{ν\hspace{0.17em}=\hspace{0.17em}0.67\hspace{0.17em}±\hspace{0.17em}0.05}$ at the critical isochore, and ${\nu }_{\mathrm{liquid}}\text{\hspace{0.17em}≈\hspace{0.17em}0.58}$ along the liquid side of the coexistence curve. Using an empirical equation of the form $I_s^{\text{−1}}{\mathrm{\propto [\tau \hspace{0.17em}-\hspace{0.17em}\tau }}_{\mathrm{sp}}{\mathrm{(\rho )]}}^{\gamma }$ with ${\tau }_{\mathrm{sp}}{\mathrm{\hspace{0.17em}=\hspace{0.17em}T}}_{\mathrm{sp}}{\mathrm{\hspace{0.17em}/\hspace{0.17em}T}}_c$ and $T_{\mathrm{sp}}$ being the pseudospinodal temperature, we have obtained $\text{γ\hspace{0.17em}=\hspace{0.17em}1.20\hspace{0.17em}±\hspace{0.17em}0.09}$ at $\text{ρ\hspace{0.17em}=\hspace{0.17em}268.3}$ amagat and $\text{γ\hspace{0.17em}=\hspace{0.17em}1.13±0.09}$ at $\text{ρ\hspace{0.17em}=\hspace{0.17em}192.4}$ amagat. Moderate success is obtained in testing a more general scaling equation for $I_s$ .