[en] Ample experimental evidence is available in the literature on the geometry and the stability of local coordination for polyvalent metal ions in molten mixtures of their halides with alkali halides. Recent schemes for classifying this evidence are discussed. Dissociation of tetrahedral halocomplexes in good ionic systems can be viewed as a classical Mott problem of bound-state stability in a conducting matrix. More generally, structural coordinates can be constructed from properties of the component elements, to separate out systems with long-lived fourfold or sixfold coordination and to distinguish between these. (author). 11 refs, 1 fig

[en] We evaluate and extend an earlier proposal for a microscopic theory of the nonmetal-to-metal (NM-M) transition which occurs on dissolving an alkali metal in its molten halide. The transition is viewed as involving a balance between the free energy gain from the binding of valence electrons into localization centres and the excess free energy of the ionic assembly screened by the electrons. Using parameters estimated for solutions of potassium in potassium chloride and assuming that the elementary process of electronic trapping is the formation of F-centre-like clusters, Thomas-Fermi screening by metallic electrons is shown to lead to a very sharp NM-M transition at a concentration in the range of 25-30% added metal. Thermally activated hopping of the localized electrons and the evolution of the localization centres with composition are next crudely taken into account by allowing for an additional contribution to the inverse screening length, which is estimated from the electronic localization length. This is shown to lead to a progressive break-up of the localization clusters, accelerating into a NM-M transition in the same concentration range. This simplified theoretical scenario is consistent with the available experimental evidence. (author). 18 refs, 5 figs

[en] The correlations between long-wavelength fluctuations of concentration in a liquid binary alloy are determined by a balance between an elastic strain free energy and an Ornstein-Zernike effective interaction. The latter is extracted from thermodynamic data in the case of the Li-Pb system, which is well known to chemically order with stoichiometric composition corresponding to Li₄Pb. Strong attractive interactions between concentration fluctuations near the composition of chemical ordering originate from electronic charge transfer, which is estimated from the electron-ion partial structure factors as functions of composition in the liquid alloy. (author). 20 refs, 2 figs

[en] The continuous nonmetal-metal transition, which occurs on dissolving metals in molten salts, may be shifted to higher metal concentration in solutions involving polyvalent metal ions by the possibility that these metals go into lower oxidation states. We evaluate a microscopic model for these processes in the specific case of solutions of sodium metal in molten cryolite (AlF₃·3NaF). The structure of the ionic melt is understood and calculable at the microscopic level in terms of a dominant sixfold-coordinated trivalent state of the Al ion (the (AlF₆)^3-complex) with some admixture of a fourfold-coordinated trivalent state (the (AlF₄)^- complex). The sodium metal is assumed to enter the ionic liquid in the form of monovalent ions and electrons. Our calculations demonstrate how these added components break up the structure of the ionic melt to yield localization by the formation of Al ions in reduced valence states, and provide order-of-magnitude estimates for the free energy changes involved in these processes. Specifically, we find that with increasing metal concentration the equilibrium between (AlF₆)^3- and (AlF₄)^- shifts in favour of the latter, while Al³⁺ ions are released in the melt and bind the available electrons to form Al²⁺ and Al⁺ ions. The latter eventually become the most stable ones and also destabilize the (AlF₄)^- complex. This scenario is consistent with available macroscopic observations. We also briefly discuss how the treatment could be extended to examine other events that may arise with increasing metal content, such as the formation of dimers or small metal clusters. (author). 21 refs, 4 figs, 2 tabs

[en] Experimental evidence is available in the literature on the local coordination of divalent and trivalent metal ions by halogens in some 140 liquid mixtures of their halides with alkali halides. After brief reference to classification criteria for main types of local coordination, we focus on statistical mechanical models that we are developing for Al-alkali halide mixtures. Specifically, we discuss theoretically the equilibrium between (AlF₆)^3- and (AlF₄)^- complexes in mixtures of AlF₃ and NaF as a function of composition in the NaF-rich region, the effect of the alkali counterion on this equilibrium, the possible role of (AlF₅)^2- as an intermediate species in molten cryolite, and the origin of the different complexing behaviours of Al-alkali fluorides and chlorides. We also present a theoretical scenario for processes of structure breaking and electron localization in molten cryolite under addition of sodium metal. (author). 26 refs, 2 tabs

[en] An earlier statistical mechanical theory of complexing in molten mixtures of polyvalent metal halides and alkali halides is extended to situations in which an ionic equilibrium is established between two different types of complexes. The specific systems of interest are the mixtures of aluminium fluoride and sodium fluoride, in which early Raman scattering experiments by Gilbert, Mamantov and Begun have demonstrated coexistence of octahedral (AlF₆)^3- units and tetrahedral (AlF₄)^- units in the concentration range between 0.25 and 0.5 of AlF_3. Our treatment is based on a simple ionic model and involves (i) an evaluation of binding free energies for the two units in vacuo, showing that (AlF₆)^3- is strongly unstable against dissociation in this state, and (ii) a statistical mechanical theory of the liquid mixture, in which (AlF₆)^3- is stabilized by ionic screening interactions. The resulting ionic equilibrium in the liquid involves, in excellent agreement with the Raman data, strong suppression of dissociation for (AlF₆)^3-, except near the composition corresponding to criolite (AlF₃.3NaF). The temperature dependence of the ionic equilibrium is also evaluated, with special attention to molten criolite. Analogous calculations on aluminium-sodium chloride mixtures show that in these systems the equilibrium is completely shifted in favour of the (AlCl₄)^- species, as a consequence of its stabilization by halogen polarizability. (author). 13 refs, 1 fig., 4 tabs

[en] The stability of local fourfold coordination for divalent and trivalent metal ions in liquid mixtures of polyvalent metal halides and alkali halides is classified by means of structural coordinates obtained from properties of the elements. In parallel with earlier classifications of compound crystal structures and molecular shapes, the elemental properties are taken from first-principles calculations of valence electron orbitals in atoms, in the form of (i) the nodal radii of Andreoni, Baldereschi and Guizzetti or (ii) the pseudo-potential radii of Zunger and Cohen. As a third alternative we also consider a classification based on Pettifor's phenomenological chemical scale of the elements. The alternative structural classification schemes that are developed from these elemental properties are very successful in distinguishing molten mixtures in which the available experimental evidence indicates stability of ''complexes'', i.e. long-lived fourfold coordination of polyvalent metal ions. (author). 55 refs, 3 figs

[en] The propagation of zero sound in a spin-polarized Fermi gas under harmonic confinement is studied as a function of the mean-field interactions with a second Fermi gas. A local-density treatment is compared with the numerical solution of the Vlasov-Landau equations for the propagation of density distortions in a trapped two-component Fermi gas at temperature T=0.2 T_F. The response of the gas to the sudden creation of a sharp hole at its centre is also studied numerically

[en] Octahedral-type coordination by halogens in the liquid state has been reported for a number of trivalent metal ions from diffraction and Raman scattering experiments on their molten trihalides and from Raman scattering spectroscopy of liquid mixtures of trihalides with alkali halides. We analyze the available data on bond lengths and Raman frequencies by treating an isolated (MX₆)^3- species within a model which adopts charged-soft-sphere interionic potentials supplemented by an account of ionic polarization. The trivalent metal ions that we consider are M = La, Ce, Pr, Nd, Sm, Gd, Dy and Y for X = Cl and M = Al for X = F. The main result of the analysis is the prediction of trends in the soft-sphere repulsive parameters for the trivalent metal ions, leading to estimates of all the vibrational frequencies and the binding energy of such octahedral species. (author). 26 refs, 1 fig., 4 tabs

[en] We discuss theoretically (i) the effect of the alkali cation species on the ionic equilibrium between (AlF₆)^3- and (AlF₄)^- complexes in molten alkali fluoroaluminates, and (ii) the possible presence of (AlF₅)² - complexes in molten cryolite, in relation to very recent Raman scattering experiments by Gilbert and Materne. (author). 7 refs, 2 tabs