The Critical Region of Single-Component Fluids

It is difficult to determine directly the liquid-vapor coexistence curves of metals by measurement of the coexisting densities of the two phases. Rather, the curves have been established indirectly from the intercepts of measured isochores (Figs. 3.17 and 4.10) with the vapor pressure curve Psat versus T. The coexistence curves determined in this way for cesium and rubidium are presented in Fig. 6.1. This figure shows a plot of the reduced densities of the coexisting liquid, p lPc, and vapor, PvIPc as a function of the reduced temperature TjT. The plot also shows the mean densities, = (l/2)(pi, + py), known as the diameters.  

The reduced plots for rubidium and cesium coincide accurately, suggesting that a law of corresponding states is valid for these two members of the alkali group. The curves for the alkali metals are, however, extremely asymmetric and therefore quite different from those of argon and xenon. The diameters exhibit strong curvature over substantial temperature ranges. Asymmetric coexistence curves are a common characteristic of fluid systems that show a MNM transition under variation of the conduction electron concentration. The metal-ammonia solutions (Chieux and Sienko, 1970) and electron-hole liquid (Thomas et al., 1978) 

The coexistence curves of cesium, rubidium, and mercury violate a century-old empirical rule known as the Law of Rectilinear Diameters (Cailletet and Mathias, 1886). According to this rule, a plot of the diameter, versus T, should be linear right up to the critical point. In contrast, renormalization group theory predicts that the temperature derivative of the diameter, dp /dT, should diverge at least as fast as the constant-volume specific heat c . Specifically, as the reduced temperature T = (T — T)/Tc goes to zero, the diameter varies as 

The linear term describes the background rectilinear diameter common to all fluids. The critical exponent in the term depends on the 

As mentioned previously, analysis of the diameter data of molecular fluids led to the suggestion that many-body interactions are responsible for the anomalous term in these fluids. In particular, it is believed that the symmetry-breaking due to many-body dispersion forces may be understood in terms of a state-dependent effective pair interaction (Goldstein and Parola, 1988). There is a natural connection between this explanation and the observation of large amplitude diameter anomalies in cesium, rubidium, and mercury. In the metals, it is the MNM transition that changes the interparticle interaction with the 

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