Density, liquid alloys

Surface tension and density of liquid alloys have been studied by Moser et al. (2006). Measurements by maximum bubble pressure and dilatometric techniques were carried out in an extensive range of temperatures on liquid alloys close to the ternary eutectic Sn3 3Ag0 76Cu with different Sb additions, which decrease surface tension and density. The experimental data were discussed in comparison also with values calculated on the basis of different models. 

Potassium, a soft, low density, silver-colored metal, has high thermal and electrical conductivities, and very low ionization energy. One useful physical property of potassium is that it forms liquid alloys with other alkali metals such as Na, Rb, and Cs. These alloys have very low vapor pressures and melting points. 

Considerable evidence exits of the survival of Zintl ions in the liquid alloy. Neutron diffraction measurements [5], as well as molecular dynamics simulations [6, 7], give structure factors and radial distribution functions in agreement with the existence of a superstructure which has many features in common with a disordered network of tetrahedra. Resistivity plots against Pb concentration [8] show sharp maxima at 50% Pb in K-Pb, Rb-Pb and Cs-Pb. However, for Li-Pb and Na-Pb the maximum occurs at 20% Pb, and an additional shoulder appears at 50% Pb for Na-Pb. This means that Zintl ion formation is a well-established process in the K, Rb and Cs cases, whereas in the Li-Pb liquid alloy only Li4Pb units (octet complex) seem to be formed. The Na-Pb alloy is then a transition case, showing coexistence of Na4Pb clusters and (Pb4)4- ions and the predominance of each one of them near the appropiate stoichiometric composition. Measurements of other physical properties like density, specific heat, and thermodynamic stability show similar features (peaks) as a function of composition, and support also the change of stoichiometry from the octet complex to the Zintl clusters between Li-Pb and K-Pb [8]. 

In this work we study a number of isolated clusters which may be relevant for understanding the clustering in the liquid alloys. Of course, the behaviour of those clusters in the alloy may be more complicated due to the interaction with the condensed medium, but by studying free clusters we expect to obtain useful information about the tendency of the atoms to cluster in the alloy. A preliminary calculation [9] using the Density Functional Formalism (DFT) [10, 11] and a simplified model for the cluster structure [12] has confirmed the high stability of the A4Pb and A4Pb4 species (with A = Li, Na, K, Rb, Cs). However, the drastic simplification of the cluster structure used in that model calls for more accurate calculations. Consequently, in this work we report the results of ab initio molecular-dynamics DFT calculations. 

The variations of abundance in the mass spectrum of small Pb clusters have been explained by ab initio density functional calculations. A study of free clusters formed by Pb and Na helps to explain the observation of an exceptionally abundant NagPb cluster in gas phase experiments. It also gives strong support to the presence of Na4Pb and Na4Pb4 clusters in the liquid alloys. 

To test the validity of the hard sphere approach we first consider the equiatomic alloy, NaK, which is a relatively simple liquid alloy and for which X-ray and neutron diffraction data have been obtained (Henniger et aL, 1966). In addition data are available for the density and Xj over the whole range of composition (Abowitz and Gordon (1962)). As for the one component case, the final answer will depend on the choice of which in turn relates to the choice of Ri and R2. Ashcroft and Lekner (1966) found that for pure Na and pure K, a close fit with experiment was obtained with % = 0.45 so that Ri = 3.28A (Na) and R2 = 4.06A(K). Presumably these would alter somewhat in the alloy due to the change in electron density. However, in the absence of any theory of this effect, we shall retain these hard sphere diameters so that if the density is taken as 0.87 g cm which corresponds to 373 K, (alloy) = 0.451. With these assumptions for Ri and R2, Enderby and North (1968) calculated ajj(q) from the hard sphere PY theory. In Figure 7.15 we compare the experiment X-ray diffraction data with the theoretical curve derived from the calculated a j(q) and the published values of the x-ray form factors (Hanson et al (1964)). The measurement of agreement, particularly around the first peak, is encouraging and shows that for this alloy at least the PY hard-sphere description is a very useful first approximation. 

Only minimal data have been reported on the density of liquid alloys containing R metals. Measurements of for the R-R alloy Pr-Nd indicate this to be an ideal substitutional alloy, one obeying Vegard s Rule ... 

If the metal liquid system does not contain any components that provoke the exchange reactions in an electrochemical cell, the EMF method is well suited for such a system. The problem of liquation (or phase separation) is less serious, but the big difference of the sp>ecific density of alloying effects on the rate of establishment of thermodynamic equilibrium and distorts the potentiometric measurements. 

TABLE 3 Reference Summary for Liquid Alloy Density Data... 

Nearly all experimental eoexistenee eurves, whether from liquid-gas equilibrium, liquid mixtures, order-disorder in alloys, or in ferromagnetie materials, are far from parabolie, and more nearly eubie, even far below the eritieal temperature. This was known for fluid systems, at least to some experimentalists, more than one hundred years ago. Versehaflfelt (1900), from a eareflil analysis of data (pressure-volume and densities) on isopentane, eoneluded that the best fit was with p = 0.34 and 8 = 4.26, far from the elassieal values. Van Laar apparently rejeeted this eonelusion, believing that, at least very elose to the eritieal temperature, the eoexistenee eurve must beeome parabolie. Even earlier, van der Waals, who had derived a elassieal theory of eapillarity with a surfaee-tension exponent of 3/2, found (1893)... 

Figure. 3 (a) Partial pair correlation function.s gij(B.) in liquid K-Sb alloys, (b) Total, partial, and local electronic densities of states in liquid Ko.soSbo.so- Cf. text. 

Liquid liquid interfacial tension, and density difference, in the immiscible (monotectic) alloy (Al34 5Bi<55 5)95Si5 (mass%) have been measured by Kaban and Hoyer (2006). Addition of Si to the binary Al-Bi alloy increases the interfacial tension between the Al-and Bi-rich liquid phases. 

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