Metallic fluids, criticality, liquid-vapor

IJ. The Liquid-Vapor Critical Point Data of Fluid Metals and Semiconductors... 

Density and conductivity isotherms for fluid mercury are shown in Fig. 2.4 (Gotzlaff, 1988). These data are qualitatively similar to those of cesium shown in Fig. 2.3. An important quantitative difference, however, is the value of the conductivity in the immediate vicinity of the critical point. The conductivity of mercury near the critical point is about two orders of magnitude lower than that of cesium near its critical point. This simple comparison shows that there is no universal behavior of the electronic properties of fluid metals. Moreover, such data raise the possibility that a continuous MNM transition may be distinct from the liquid-vapor transition in some fluid metal systems. 

The other major difference between fluid metals and semiconductors concerns the phase behavior and the electronic character in various regions of the temperature-density plane. The low-temperature liquid-vapor equilibrium of semiconducting liquids involves two nonmetallic phases whereas the vapors of metallic elements are, by definition, in equilibrium with a liquid metal phase. The metallic state develops in fluid semiconductors when the temperature and pressure are high enough to disrupt the structural order responsible for semiconducting electronic structure. If this occurs near the critical region, there exists the possibility of rapid MNM transitions and strong interplay between the electronic properties and critical density fluctuations. In this respect, fluid metals and semiconductors behave similarly under extreme conditions whereas they are markedly different near their respective triple points. 

We have seen that the MNM transition and state-dependent interactions are central features of the phase behavior of fluid metals and semiconductors. The existence of a critical point forces us to deal not only with the discontinuous electronic transition coinciding with the liquid-vapor transition, but also with the continuous transition fl om metal to nonmetal implied by the trajectory shown in Fig. 2.2(a). Let us now consider some microscopic electronic mechanisms that could underlie such continuous transitions. We begin with a description of the metallic limit and the model of nearly-ffee-electrons. 

To go beyond this qualitative observation to a treatment of the equation of state data over the whole liquid-vapor density range is far more dii cult for metals than for insulating fluids like argon. The radieal changes in electronic structure associated with the MNM transition must be taken into account in going from one phase to the other. The situation near the critical point is especially complicated because of the strong state-dependence of the electronic structure. But at least at temperatures far below the critical point, the situation is much simpler. Therefore, let us first focus on this region. 

Mercury has the lowest known critical temperature (1478 °C) of any fluid metal. It is therefore particularly attractive to experimentalists. Mercury is also considerably less corrosive than many metals, especially the alkali metals discussed in the preceding chapter. These relatively favorable circumstances permit precise measurement of the electrical, optical, magnetic, and thermophysical properties of fluid mercury. With care, one can control temperatures accurately enough to determine the asymptotic behavior of physical properties as the liquid-vapor critical point is approached. Such truly critical data are especially valuable for exploring the relationship between the liquid-vapor and MNM transitions. Of the expanded metals exhibiting MNM transitions, mercury is therefore the most extensively investigated. It is the only expanded divalent metal whose critical region has proven to be experimentally accessible. 

The liquid-vapor transition of fluid metals forces one to search for the unity in physical science. The existence of the liquid-vapor critical point makes possible a continuous transition from a dilute atomic vapor to a dense metallic liquid. Thus a single set of experiments on a single pure... 

Dean, R A., R. S. Dougall, and L. S. Tong, 1971, Effect of Vapor Injection on Critical Heat Flux in a Subcooled R-l 13 (Freon) Flow, Proc. Int. Symp. on Two-Phase Flow Systems, Haifa, Israel. (6) Deane, C. W., and W. M. Rohsenow, 1969, Mechanism and Behavior of Nucleate Boiling Heat Transfer to the Alkali Liquid Metals, USAEC Rep. DSR 76303-65, Massachusetts Institute of Technology, Cambridge, MA Also in 1970, Liquid Metal Heat Transfer and Fluid Dynamics J. C. Chen and A. A. Bishop, Eds., ASME Winter Annual Meeting, New York. (4)... 

Besides the metals, there is another class of one-component fluid for which the molecular and electronic structure of the vapor phase is completely different from that of the liquid. These are the liquid pol)mers. The vapors of these materials consist of simple molecules, but on passing to the liquid state, a change in chemical binding leads to large chainlike structures. A polymeric Uquid differs from metals, in particular, in that it lacks the collective aspect of metallic binding. Still, one can also expect to find anomalous properties in the critical regions of such materials. 

Historically, the first experimental determinations of the vapor densities and pressures approaching the critical region of a metal were made for mercury. Bender (1915, 1918) carried out pioneering measurements of vapor densities up to about 1400 °C. The samples in these studies were enclosed in strong fused quartz capillaries. In 1932, Birch made the first measurements of the vapor pressure of mercury and obtained realistic values for the critical temperature and pressure. Birch found values = 1460 °C and = 1610 bar, results that are remarkably close to the most accurate values available today (Table 1.1). A number of groups in various countries have contributed subsequently to the pool of pVT data currently available (Hensel and Franck, 1966, 1968 Kikoin and Senchenkov, 1967 Postill et al., 1968 Schonherr et al., 1979 Yao and Endo, 1982 Hubbard and Ross, 1983 Gotzlaff, 1988). The result is that the density data for mercury are now the most extensive and detailed available for any liquid metal. Data have been obtained by means of isothermal, isobaric, or isochoric measurements, but as we have noted in Sec. 3.5, those obtained under constant volume (isochoric conditions) tend to be preferable. In Fig. 4.10 we present a selection of equation-of-state data that we believe to be the most reliable now available for fluid... 

Inclusion of selenium in a book on fluid metals is justified by its status as a borderline metal at high temperatures and pressures. Also, as we have discussed in chapter 2, the dramatically different molecular structure of the low-temperature liquid and the vapor means that selenium is an excellent example of a system with strongly state-dependent interactions. Structural evolution of the liquid as it is heated to the region of the critical point must inevitably lead to interesting changes in the physical properties. 

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