O. Akinlade

Assessment of size effect on the surface properties of some binary liquid alloys

Abstract The effect of size in the calculation of the surface properties of some liquid binary alloys has been studied using the theoretical model developed by Prasad et al. (Phys. Chem. Liq. 27 (1994) 179). The systems studied include Na–Cs, Sn–Ga and Cu–Ni, which manifest a tendency to phase separation, in addition to Li–Ba and Na–Te, which exhibit a tendency to compound formation. Our results indicate that for those systems studied with phase separating tendencies, effects due to size considerations are quite significant. In general, we infer from our calculations that for the same value of order energy W / K B T , the effect of size is to reduce the surface concentration and to increase the surface tension, while the reverse holds when size effects are neglected. Compound forming systems do not follow this trend as the impact of size appears to depend both on the relative sizes of the alloying components and the degree of compound formation in the alloy.

Thermodynamics of liquid Al-Fe alloys

Abstract We have used a complex formation model to study chemical short range order due to atomic level interactions in liquid Al–Fe alloys. Assuming the existence of a complex of the form FeAl3, we use the model to deduce information on thermodynamic properties of the alloy such as the Gibbs free energy of mixing, the thermodynamic activity and the enthalpy of mixing. In our approach, we first model the Gibbs free energy in terms of interaction parameters. Subsequently, we use the parameters to describe properties such as the concentration– concentration fluctuations in the long wavelength limit, the Warren-Cowley short range order parameter and the chemical diffusion. Underlying the present calculations is the fact that for Al–Fe liquid alloys, a reasonable degree of chemical short range order although of a weak nature persists throughout the whole concentration range.

Bulk and surface properties of liquid In-Cu alloys

Abstract In–Cu is a weak interacting system (the excess free energy of mixing G M xs ≈−0.2 RT at equiatomic composition) but the composition dependence of the thermodynamic properties exhibit interesting features. G M xs is negative in the Cu-rich region and positive for the In-rich end. Similarly other thermodynamic properties are asymmetric about the equiatomic composition. Such an interesting feature is explained here on the basis that a complex of the form Cu 4 In exists in the bulk phase. Its energetics are used to study the surface composition of the In–Cu liquid alloys. Our study indicates that the surface is enormously rich with indium concentrations throughout the composition of the alloys.

Concentration fluctuations and thermodynamic properties of ternary liquid alloys

Abstract We have reformulated the complex formation model of Bhatia and Hargrove [Phys. Rev. B10 (1974) 3186] such that the extension makes it possible for us to explain the thermodynamic properties of compound forming ternary liquid alloys. The results obtained for the concentration–concentration fluctuations can be used to compute the Warren Cowley short-range order parameter for the same alloy. We make the assumption that a ternary liquid alloy consisting of A, B and C atoms forms complexes A i B j , A k C l , B u C v and A a B b C c . Based on this assumption, analytic expressions are derived for such thermodynamic quantities as the free energy of mixing G M , enthalpy of mixing H M , the concentration–concentration fluctuations in the long wavelength limit S c m c n (0) ( m , n =1, 2) and the activity, a i using the Flory approximation. We solve the derived expressions and thus obtain numerical results for the concentration dependence of these thermodynamic quantities for the ternary liquid Al–Cu–Zr alloys. Finally, a critical discourse of results obtained are given with a view to highlight the information that can be obtained from and limitations of our theoretical model.

SYNCHRONIZATION OF CROSS-WELL CHAOS IN COUPLED DUFFING OSCILLATORS

Numerical simulations have been used to investigate the synchronization behavior of a unidirectionally coupled pair of double-well duffing oscillators (DDOs). The DDOs were simulated in their structurally stable chaotic zone and their state variables were found to completely synchronized. The essential feature of the transition to the synchronous state is shown to correspond to a boundary crisis in which the cross-well chaotic attractor is destroyed.

Demixing tendencies in some Sn-based liquid alloys

Abstract We study the demixing tendencies observed in some Sn-based liquid alloys, specifically, Ga–Sn, Al–Sn and Fe–Sn liquid alloys using a phenomenological model. With the aid of the model, we investigate the concentration dependence of thermodynamic properties viz: activity, free energy of mixing, enthalpy of mixing, entropy of mixing and the chemical diffusion. The parameters that characterize the model, enable us to describe the energetics of the system in terms of the concentration–concentration fluctuations in the long wavelength limit. We deduce from our study that of the three liquid alloys, the thermodynamic properties of Fe–Sn are most asymmetric as a function of concentration, the observed asymmetry is explained on the basis of the size effect. From the results for Ga–Sn and Al–Sn, we infer that with increase in the atomic number of the element in group III that is added to liquid Sn, there is a reduced tendency for segregation. We deduce within the present framework that In–Sn would be a hetero-coordinated system. This deduction is in agreement with available experimental data.

Thermodynamic investigation of viscosity in Cu–Bi and Bi–Zn liquid alloys

Abstract We use a recently proposed formalism that relates thermodynamic properties and viscosity to investigate the role of energetics and size effects on Cu–Bi and Bi–Zn liquid alloys. Our calculations indicate that the model works quite well for Cu–Bi, while the results for Bi–Zn are not of similar quality. Furthermore, we show that size effects are more significant for Bi–Zn liquid alloys.

CORRELATION BETWEEN BULK AND SURFACE PHENOMENA IN Ga-(Bi,In) AND In-Bi LIQUID ALLOYS

Thermodynamic models are used to correlate the bulk and surface properties of mixing of Ga-(Bi,In) and In-Bi liquid alloys. It provides useful insight into the energetics of binary alloys (Ga-Bi, Ga-In and In-Bi) which are constituent components of ternary Ga-In-Bi alloys. The positive deviation of the properties of Ga-Bi and Ga-In alloys from the ideal mixing condition and negative deviation for In-Bi are discussed in terms of the interaction energies and hence a consistent set of different thermodynamic functions are obtained as a function of composition. Our calculations indicate that the surface of Ga-Bi is richer with Bi- atoms than in In-Bi. However, in atoms segregate to the surface of the Ga-In alloys.

Ordering Phenomena in Na-Ga and Na-Sn Molten Alloys

Abstract The quasilattice approximation (QLA) has been applied to study the alloying behaviour of Na-Ga and Na-Sn molten alloys by assuming the formation of complexes of the form Na5Ga8 and Na4Sn3. This has been used to obtain the concentration dependence of the free energy of mixing, the long wavelength limit of the concentration-concentration fluctuations and the ordering parameter α1. Our calculations yield for both alloys, qualitative agreement with experiment about the concentrations at which phase separation or compound formation occurs in the alloy. In the case of Na-Ga, however, because of the relatively large asymmetry in the concentration dependence of its free energy of mixing and possibly the nature of the complex chosen, the calculated results when compared with experiment are not as good as that for Na-Sn. For Na-Ga, we have also calculated the higher order conditional probabilities using the four atom cluster model (FACM) this has made it possible to calculate another value for α1. A compar...

Thermodynamics and structure of liquid metals from the charged hard-sphere reference fluid

Abstract Perturbative variational calculations of thermodynamic and structural properties of liquid metals, based on the use of ab initio and highly reliable nonlocal pseudopotentials for the electron-ion interactions and of the fluid of charged hard spheres as a reference system, have been reported recently for the liquid alkali metals from Na to Cs near the freezing point. We extend in this work the above-mentioned calculations in two directions. Firstly, we discuss the predicted temperature dependence of the liquid structure factor for the same alkali metals over a limited temperature range above the freezing point. Secondly, we examine the usefulness of the approach for metals with relatively strong electron-ion interactions, namely Li and several polyvalent metals (Mg, Cd, Al, In, Tl and Pb). The charged hard-sphere reference system leads to lower values of the Helmholtz free energy and to slightly improved values of the excess entropy for all the liquid metals that we evaluate, even though polyvalent ones overall appear to be relatively close to fluids of neutral hard spheres. For the liquid alkali metals at elevated temperatures, the calculated structure factors are of similar quality as in our previous work, that is, they show a systematic shift in the positions of peaks and valleys to slightly larger wave numbers and peak heights that are somewhat underestimated with increasing temperature. However, for liquid polyvalent metals, our approach yields quite good agreement with experiment for the positions of maxima and minima in the liquid structure factor, while it tends to overemphasize somewhat these structures.