Pure liquid metals

Selected values of rLv and the temperature coefficient a LV (= d T[ v/dT) are given in Table 4.1, taken from the reference compilation (Eustathopoulos et al. 1999) in 

In the case of Fe and Si, although xlv values at the melting point measured by several authors are not very different, a high difference in r LV values is observed. For this reason two values of t lv are given in Table 4.1 characteristic of low and high values quoted in the literature. 

Equation (1.15), when applied to monoatomic liquids, predicts that the molar surface energy rLV- m (with Qm = Na. w) is proportional to the heat of evaporation of the liquid, Le, and to a structural parameter m,. If mi is the same for all metals, tlv is expected to scale with the quantity Le / Qm. It was shown in (Eustathopoulos et al. 1998) that equation (1.15), valid in principle only at OK, holds also at TF. As Qm is proportional to vm2/3 (vm denoting the molar volume), one obtains  

Skapski (1948,1956) used as a basis in (Eustathopoulos et al. 1998) to derive equation (4.1). Note that because the ratio Le/TF for pure metals is approximately constant, correlations between tLv(Tf) and TF/vm2/3 are also to be expected and have been found to hold (Keene 1993). 

The temperature coefficient of surface energy, a LV, is given by (Eustathopoulos et al. 1998)  

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The electrolysis apparatus operates well above the melting point of aluminum (660 °C), and liquid aluminum has a higher density than the molten salt mixture, so pure liquid metal settles to the bottom of the reactor. The pure metal is drained through a plug and cast into ingots. 

Similar relationships can be written for the dissolution of hydrogen and oxygen. These relationships are expressions of Sievert s law which can be stated thus the solubility of a diatomic gas in a liquid metal is proportional to the square root of its partial pressure in the gas in equilibrium with the metal. The Sievert s law behaviour of nitrogen in niobium is illustrated in Figure 3.8. The law predicts that the amount of a gas dissolved in a metal can be reduced merely by reducing the partial pressure of that gas, as for example, by evacuation. In practice, however, degassing is not as simple as this. Usually, Sievert s law is obeyed in pure liquid metals only when the solute gas is present in very low concentrations. At higher concentrations deviations from the law occur. 

Some experimental data for thermal conductivities of pure liquid metals are shown in Figure 4.22, and data for some binary metallic alloys are shown in Figure 4.23. These values will, in general, be lower than the thermal conductivities of the corresponding solid forms of the metals and alloys. 

Figure 4.22 Thermal conductivity of some pure liquid metals as a function of temperature. Reprinted, by permission, from T. lida and R. I. L. Guthrie, The Physical Properties of Liquid Metals, p. 241. Copyright 1988 by Oxford University Press.

The surface energy of molten oxides has been studied less extensively than that of pure liquid metals. For instance, the surface energy of molten AI2O3, which is the most widely studied oxide, has been measured by 12 teams (Ikemiya et al. 1993) while that of Fe has been measured by 28 (Keene 1993). One reason for this difference is the experimental difficulties arising from the high melting point of many oxides but... 

Measurements of the surface energy of pure liquid metals performed in the last decades by different investigators and different techniques have led to values of... 

Figure 6.2. Experimental contact angles for pure liquid metal/oxide systems (taken from references given in the figure) versus calculated values of molar fraction of oxygen in the liquid metal caused by dissolution of the oxide. From (Eustathopoulos and Drevet 1998) [17].

Table 7.10. Wetting by Cu of metal-like carbides in a high vacuum at 1100°C(Ramqvist 1965). The equilibrium molar fraction of carbide metal Me dissolved in Cu, X c(Cu), is calculated from equation (7.16). Data for AG (reference state pure liquid metal Me) come from (Rosenqvist 1983) except for Mo2C and HfC (Kubaschewski and Alcock 1979). Data for AHMe(Cu) come from (Niessen et al. 1983).

Nachtrieb, N. H. Transport properties in pure liquid metals. S. 49 in Liquid Metals and Solidification, ASM (1958). 

Table I. Thermotransport of Isotopes in Pure Liquid Metals ...

On the surface tension of pure liquid metals at their melting points crj p, we use the following approximation ... 

Here AHx, the heat of formation of vacancies, is considered to be constant. The heat capacity of pure liquid metals decreases slightly with decreasing temperature. Using experimental values [2.13], one can calculate the entropy and enthalpy of the crystalline and liquid phase in the stable and metastable state. The entropy S and the enthalpy H are given by ... 

The sodium-lithium phase system has been studied by thermal analysis in the liquid and solid regions to temperatures in excess of 400°C. Two liquid phases separate at 170.6°C. with compositions of 3.4 and 91.6 atom % sodium. The critical solution temperature is 442° zt 10°C. at a composition of 40.3 atom % sodium. The freezing point of pure lithium is depressed from 180.5°C. to 170.6°C. by the addition of 3.4 atom % sodium, and the freezing point of pure sodium is depressed from 97.8° to 92.2°C. by the addition of 3.8 atom % lithium. From 170.6° to 92.2°C. one liquid phase exists in equilibrium with pure lithium. Regardless of the similarity in the properties of the pure liquid metals, the binary system deviates markedly from simple nonideal behavior even in the very dilute solutions. Correlation of the experimentally observed data with the Scatchard-Hildebrand regular solution model using the Flory-Huggins entropy correction is discussed. 

The Ziman-Faber model for liquid metals (Ziman, 1961 Faber and Ziman, 1965) has been widely used to describe the resistivity behaviour of amorphous metals. It is based on the nearly-free-electron approach and the Boltzmann transport equation. When all multiple two-site scattering corrections are neglected, the resistivity for a pure liquid metal can be represented by means of the equation... 

There have been several useful reviews of the theory for the electrical properties of pure liquid metals and we content ourselves with a brief summary of the present situation. Most of the relevant theoretical ideas to this section are due to Ziman and co-workers (see especially Ziman (1967)). 

A(K) structure factor, pure liquid metal E, activation energy... 

Although a liquid metal can be considered to be a random assembly of ions, the fact that the density of such a metal changes little upon melting implies that the packing characteristics of the solid survive into the liquid, and impose a mean nonuniform short-range distribution on the liquid. This distribution can be described, for a pure liquid metal, in terms of the mean number, n(r) dV, of ions to be found in volume element dV at r, given that an ion also resides at r = 0. The pair distribution function, g(r), is then given by... 

Measurements of A K) for pure liquid metals are readily made by X-ray diffraction and neutron-diffraction techniques. The only direct determinations of... 

For a pure liquid metal, we may write the excess surface energy, E of the liquid metal-vapor interface, as... 

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