Integral equation theory description of phase equilibria in classical fluids

The relationship between short-range icosahedral order in metallic glasses and long-range order in icosahedral crystals is explored. Metallic-glass structure factors are assumed to describe liquids in metastable equilibrium just above the glass transition. A density-functional mean-field theory is then used to search for nearby crystalline states with a lower free energy. We find that undercooled liquids are metastable with respect to an icosahedral crystal, similar to the recently discovered icosahedral phase of Al-Mn. Conventional bcc and fcc crystals have an even lower free energy. The icosahedral phase is favored by the short-range icosahedral order present in the liquid. There is, however, an energetic cost associated with long-wavelength fluctuations forced in by the incommensurability of the icosahedral density waves. The theory predicts a rapid falloff of intensities in reciprocal space at small wave vectors, and a specific decoration of Penrose rhombahedra with atoms in real space. Our results are obtained via an exact mapping, in the density-functional framework, of the theory of icosahedral crystals onto the theory of conventional crystals in six dimensions.

Order in metallic glasses and icosahedral crystals

Binary mixtures of additive (d 12 = (d 1 + d 2)/2) and non-additive (d 12 ≠ (d 1 + d 2)/2) hard spheres have been studied with new integral equations. Accurate Monte Carlo results for some non-additive cases have been generated and tables of radial distribution functions are explicitly given. Comparison of structural and thermodynamic results demonstrates that an approximate integral equation recently proposed by Martynov and Sarkisov for one-component hard spheres significantly improves on the Percus-Yevick approximation also in the mixture case, without introducing free parameters. A simple further generalization gives a very good parameterization of the computer experiment results. An analytical fit of the equation of state for symmetric non-additive systems is also given.

Additive and non-additive hard sphere mixtures

Frameworks of clusters in alkali metal-gallium phases: Structure, bonding and properties

The occurrence of polyanions in a group of liquid ionic alloys, viz. alloys of the alkali metals with 13, 14, 15 and 16 elements (post-transition-metal groups 3, 4, 5 and 6), is discussed. It is shown that there are strong parallels with the corrresponding crystalline phases, in which polyanions such as .Pb4/4 , .Sb /1 and .Te2/2 exist, known for a long time as 'Zintl ions'. Little evidence exists for remnants of the diamond-lattice-type Zintl ion in liquid alkali-group-13 alloys, but in the alloys of Tl with K, Rb and Cs very long-range superstructures have been found, which are related to the occurrence of large, compact, polyhedral clusters in many crystalline phases. A stability rule, first proposed by Geertsma, relating the stability of the polyanions to the size of the cations, is universally observed. Furthermore it is shown that the range of the superstructure in the liquid is with remarkable precision proportional to the intercluster distance in the corresponding solids. The interpretation of the experimental data in terms of polyanion formation is discussed critically. There remains a paradox. Some sharp experimental features (superstructure peaks and maxima in the resistivities and stability functions) seem to indicate that the Zintl ions in the liquid are near perfect whereas specific heat results and ab initio computer simulations clearly show that the structure of the liquid is seriously blurred.

https://iopscience.iop.org/article/10.1088/0953-8984/8/34/003/pdf

Polyanions in liquid ionic alloys: a decade of research

Measurements of the resistivity rho of liquid Rb-Pb and Cs-Pb alloys as a function of composition and temperature are presented. Around the equiatomic composition, the resistivity reaches non-metallic values in both systems; equiatomic Cs-Pb ( rho =7000 mu Omega cm at T=620 degrees C) may be classified as a liquid semiconductor. This is explained in terms of the liquid structure of these alloys, in which the Pb ions presumably join in covalently bound clusters. With rising temperatures, these clusters disintegrate. As a consequence, the resistivity decreases rapidly. For the Cs-Pb system, a DSC (differential scanning calorimetry) survey of the liquidus temperature as a function of composition has been performed. A tentative Cs-Pb phase diagram is presented.

https://iopscience.iop.org/article/10.1088/0305-4608/16/7/012/pdf

Resistivity of liquid Rb-Pb and Cs-Pb alloys

Neutron diffraction experiments and measurements of the Knight shift and the electrical resistivity are presented for the liquid systems LiSn, NaPb, NaSn, LiGe, KPb and RbPb. They provide strong evidence for compound formation. There are indications for the existence of anion-clusters in all of these systems, except in LiSn.

Experimental results for liquid alkali-group IV alloys

The authors have measured the electrical resistivity of liquid K-Bi and Cs-Bi alloys as a function of composition and temperature. In both alloy systems strong indications for chemical compound formation were found: in a large composition range the resistivity attains values that are characteristic for Mott's 'regime of diffusive motion'. In K-Bi the octet compound K3Bi dominates. In Cs-Bi at 550 degrees C the resistivity reaches a maximum of more than 4000 mu Omega cm at a composition of 40 at.% Bi (T=550 degrees C). This is explained by assuming that the Bi ions form poly-anions (Zintl ions), quite possibly chain fragments Bin(n+2)- of variable length. The equi-atomic liquid alloy CsBi displays the unusual feature of a high resistivity (2000 mu Omega cm) combined with an almost negligible temperature dependence.

Resistivity of liquid K-Bi and Cs-Bi alloys

The electrical resistivity rho and the 7Li and 71Ga Knight shifts of liquid Li-Ga alloys were measured. The maximum value of rho on the isotherm at 775 K is 161.1 mu Omega cm at 32.6 at.% Ga. The temperature coefficient delta rho / delta T exhibits a negative minimum at this concentration. This value of rho for liquid Li-Ga alloys does not exceed values appropriate to the nearly free electron (NFE) model; resistivity values calculated by the Faber-Ziman formula are in fair agreement with experiment, though the peak position of the calculated isotherm of rho is shifted slightly to the Li-rich side. However, the experimental Knight shifts provide clear evidence of charge transfer from Li to Ga. The Knight shift KLi of 7Li decreases rapidly with the addition of Ga up to 30 at.% Ga where rho is maximum. Beyond this Ga concentration KLi becomes constant. On the other hand, the Knight shift of 71Ga, KGa, decreases almost linearly with the addition of Li up to 53 at.% Ga. This is attributed to increasing p character of the Ga conduction electrons if 7Li is added. For a more quantitative interpretation it will be necessary to incorporate charge transfer in the NFE model.

Resistivity and knight-shift of liquid li-ga alloys

The phase diagram and the electrical resistivity of liquid Na-Ga alloys were studied experimentally. Compound formation in the solid state was observed at 20 at.% and at 37 at.% Na. The latter composition closely corresponds to the stoichiometric compound Na22Ga39, reported recently by Ling and Belin. The present DSC and electrical resistivity measurements do not show the existence of a region of immiscibility around 70 at.% Na. The electrical resistivity ϱ shows a maximum value of 203.9 μΩ cm in the isothermal curve at 560° for an alloy containing 57 at.% Na. In the neighbourhood of this composition, the temperature derivative dϱ dT becomes slightly negative. The values of ϱ and dϱ dT remain within the metallic regime; yet, a description by the diffraction model is complicated by a lack of information on both liquid structure and ion-electron potentials.

J A Meijer

Papers

Resistivity of liquid Rb-Pb and Cs-Pb alloys

Experimental results for liquid alkali-group IV alloys

Resistivity of liquid K-Bi and Cs-Bi alloys

Resistivity and knight-shift of liquid li-ga alloys

The phase-diagram and the electrical-resistivity of liquid na-ga alloys