Derivation and consistency of the partial functions of the ternary system involving interaction coefficients

The logarithm of activity coefficients of the components of the ternary system is derived based on the Maclaurin infinite series, which is expressed in terms of the integral property of the system and subjected to appropriate boundary conditions. The derivation of the functions involves extensive summation of various infinite series pertaining to the first-order interaction coefficients that have been shown completely to remove any truncational error. Since the conventional equations involving interaction coefficients are internally inconsistent, a consistent form of the partial functions is developed in the article using the technique just described. The thermodynamic consistency of the functions based on the Maxwell and the Gibbs-Duhem relations has been established. The derived values of the logarithmic activity coefficients of the components have been found to be in agreement with the thermodynamic data of the Fe-Cr-Ni system at 1873 K and have been found to be independent of the compositional paths.

Distribution of phosphorus and oxygen between liquid steel and basic oxygen steelmaking slag

The efficiency of dephosphorisation is governed by the thermodynamic behaviour of phosphorus and oxygen in molten metal, and P2O5 and FeO in slag. The equilibrium distribution of phosphorus and oxygen, for a wide range of chemical compositions simulating the evolution of slag composition during a typical BOF blow, has been experimentally determined. A mathematical model for estimation of the activity coefficients, as a function of the chemical composition, was also attempted.

A new formalism for representation of binary thermodynamic data

The applicability of a formalism involving an exponential function of composition x1 in interpreting the thermodynamic properties of alloys has been studied. The excess integral and partial molar free energies of mixing are expressed as: $$\begin{gathered} \Delta F^{xs} = a_o x_1 (1 - x_1 )e^{bx_1 } \hfill \\ RTln\gamma _1 = a_o (1 - x_1 )^2 (1 + bx_1 )e^{bx_1 } \hfill \\ RTln\gamma _2 = a_o x_1^2 (1 - b + bx_1 )e^{bx_1 } \hfill \\ \end{gathered} $$ The equations are used in interpreting experimental data for several relatively weakly interacting binary systems. For the purpose of comparison, activity coefficients obtained by the subregular model and Krupkowski’s formalism have also been computed. The present equations may be considered to be convenient in describing the thermodynamic behavior of metallic solutions.

Vapour composition and activities in Mg-Zn liquid alloy at 923 K

Vapour species effusing from a magnesia Knudsen cell containing Mg-Zn alloy at 923 K were condensed on a water cooled copper plate. The equilibrium composition of the vapour phase over the alloy was determined from chemical analysis of the condensate. The activity coefficients of both components in the alloy have been derived from the data using a modified Gibbs-Duhem relation. The ratio of saturation vapour pressures of pure Zn and Mg obtained from the analysis of alloy data agree well with values from the literature, providing an internal check on the accuracy of data obtained in this study. Both components of the alloy exhibit negative deviations from Raoult's law. The concentration-concentration structure factor of Bhatia and Thomton at zero wave vector, evaluated from the measurements, indicate the presence of MgZn2 type complex in the liquid state. The associated regular solution model has been used for the thermodynamic description of liquid Mg-Zn alloys.

Volume effects and associations in liquid alloys

The regular associated solution model for binary systems has been modified by incorporating the size of the complex as an explicit variable. The thermodynamic properties of the liquid alloy and the interactions between theA ?B type of complex and the unassociated atoms in anA-B binary have been evaluated as a function of relative size of the complex using the activity coefficients at infinite dilution and activity data at one other composition in the binary. The computational procedure adopted for determining the concentration of clusters and interaction energies in the associated liquid is similar to that proposed by Lele and Rao. The analysis has been applied to the thermodynamic mixing functions of liquid Al-Ca alloys believed to contain Al2Ca associates. It is found that the size of the cluster significantly affects the interaction energies between the complex and the unassociated atoms, while the equilibrium constant and enthalpy change for the association reaction exhibit only minor variation, when the equations are fitted to experimental data. The interaction energy between unassociated free atoms remains virtually unaltered as the size of the complex is varied between extreme values. Accurate data on free energy, enthalpy, and volume of mixing at the same temperature on alloy systems with compound forming tendency would permit a rigorous test of the proposed model.

Vapor-liquid equilibriums: systems methyl ethyl ketone-p-xylene and chlorobenzene-p-xylene

Vapor-liquid equilibrium data have been measured for the binary systems methyl ethyl ketone-p-xylene and chlorobenzene-p-xylene, at 685 mmHg pressure. The activity coefficients have been evaluated taking Into consideration the vapor-phase nonideallty. The f-x-y data have been subjected to a thermodynamic consistency test and the activity coefficients have been correlated by the Wilson equation.

Surface tension of some binary organic solutions of alkylbenzenes and 1-alkanols

The surface tensions of binary mixtures of 1-alkanols (Cl-Cd with benzene, toluene, or xylene were measured. The results were correlated with the activity coefficients calculated through the group contribution method such as UNIFAC, with the maximum deviation from the experimental results less that 5%. The coefficients of the correlation are correlated with the chain length.

Thermodynamics of oxygen in liquid copper-tin alloys

The activity coefficients of oxygen in copper-tin alloys at 1 1 00°C have been measured by two different equilibrium methodsthe cell Pt, Ni + NiO I ZrOz solid electrolyte I O[Cu + Sn], cermet. Pt and the equilibrium between Cu + Sn alloys and SnO + SiO, slags established via SnO vapour. The results from both types of measurement confirm the work of Block and co-workers and show that other data are in error. The deoxidation equilibria for Sn in liquid copper, with solid SnO, as deoxidation product, have been evaluated at temperatures of interest in copper smelting.

Thermodynamic study of oxygen in liquid lead tin alloys

The activity coefficients of oxygen in liquid lead-tin alloys have been measured between 550 and 1100°C by use of solid oxide galvanic cells Pt, Ni-NiO I Zr02 Solid electrolyte I 0 (Pb + Sn), Cermet, Pt Pt, Fe-FeO I Zr02 Solid electrolyte I O(Pb + Sn), Cermet, Pt Alcock and Richardson's quasi-chemical equation, with the coordination number of atoms set to 2, is found to predict successfully the activity coefficients of oxygen in these alloys.The relative partial molar enthalpy and entropy of oxygen ?t 1 atom per cent in the alloys have been calculated from ttva variation of the activity coefficient with temperature. The addition of tin to an unsaturated solution of oxygen in lead is shown to decrease significantly both the partial molar enthalpy and entropy of oxygen. As the measurements were restricted to a narrow range between 750-1100'C in lead-rich alloys, however, the pronounced variation of the partial molar enthalpy of oxygen with temperature at constant alloy composition predicted by the quasi-chemical model could not be verified.

Quasichemical equations for oxygen and sulphur in liquid binary alloys

An equation has been derived for predicting the activity coefficient of oxygen or sulphur in dilute solution in binary alloys, based on the quasichemical approach, where the metal atoms and the oxygen atoms are assigned different bond numbers. This equation is an advance on Alcock and Richardson's earlier treatment where all the three types of atoms were assigned the same coordination number. However, the activity coefficients predicted by this new equation appear to be very similar to those obtained through Alcock and Richardson's equation for a number of alloy systems, when the coordination number of oxygen in the new model is the same as the average coordination number used in the earlier equation. A second equation based on the formation of “molecular species” of the type XnO and YnO in solution is also derived, where X and Y atoms attached to oxygen are assumed not to make any other bonds. This equation does not fit experimental data in all the systems considered for a fixed value of n. Howover, if the strong oxygen-metal bonds are assumed to distort the electronic configuation around the metal atoms bonded to oxygen and thus reduce the strength of the bonds formed by these atoms with neighbouring metal atoms by approximately a factor of two, the resulting equation is found to predict the activity coefficients of oxygen that are in good agreement with experimental data in a number of binary alloys.

Prediction of activities of oxygen in dilute quaternary solutions using binary data

Equations are developed for predicting the activity coefficients of oxygen dissolved in ternary liquid alloys. These are extensions of earlier treatments, and are based on a model in which each oxygen atom is assumed to make four bonds with neighboring metal atoms. It is also postulated that the strong oxygen-metal bonds distort the electronic configuration around the metal atoms bonded to oxygen, and that the quantitative reduction of the strength of bonds made by these atoms with all of the adjacent metal atoms is equivalent to a factor of approximately two. The predictions of the quasichemical equation which is derived agree satisfactorily with the partial molar free energies of oxygen in Ag-Cu-Sn solutions at 1200°C reported in literature. An extension of this treatment to multicomponent solutions is also indicated.

Alloy/Oxide Equilibria in Iron--Vanadium--Oxygen and Iron--Niobium--Oxygen Systems

An experimental characterization of three-phase equilibria in Fe--V--O and Fe--Nb--O systems at 1823, 1873 and 1923K has been carried out using a solid state cell and by analysis of quenched samples. The oxygen potentials corresponding to these three-phase equilibria were monitored by a solid state cell incorporating Y sub 2 O sub 3 doped ThO sub 2 with Cr + Cr sub 2 O sub 3 as reference electrode. Similar measurements were carried out for Fe--Nb--O alloys in equilibrium with a mixture of FeNb sub 2 O sub 6 and NbO sub 2 . These measurements permit evaluation of interaction parameters (e exp V sub O = --6590/T + 2.892 and e exp Nb sub O = --4066/T + 1.502) and activity coefficients of vanadiun and niobium in dilute solution (ln gamma exp O sub V = --35 320/T + 12.68 and ln gamma sub Nb exp O = --12 386/T + 4.34) in liquid iron. The results obtained in this study resolve a number of discrepancies in thermodynamic data reported in the literature, especially regarding the activity coefficients of V and Nb and the stability ranges for V sub 2 O sub 3 and VO sub 1+x . 18 ref.--AA

Nonlinear Enzyme Kinetics Can Lead to High Metabolic Flux Control Coefficients: Implications for the Evolution of Dominance

In a classic study, Kacser & Burns (1981, Genetics 97, 639-666) demonstrated that given certain plausible assumptions, the flux in a metabolic pathway was more or less indifferent to the activity of any of the enzymes in the pathway taken singly. It was inferred from this that the observed dominance of most wild-type alleles with respect to loss-of-function mutations did not require an adaptive, meaning selectionist, explanation. Cornish-Bowden (1987, J. theor. Biol. 125, 333-338) showed that the Kacser-Burns inference was not valid when substrate concentrations were large relative to the relevant Michaelis constants. We find that in a randomly constructed functional pathway, even when substrate levels are small, one can expect high values of control coefficients for metabolic flux in the presence of significant nonlinearities as exemplified by enzymes with Hill coefficients ranging from two to six, or by the existence of oscillatory loops. Under these conditions the flux can be quite sensitive to changes in enzyme activity as might be caused by inactivating one of the two alleles in a diploid. Therefore, the phenomenon of dominance cannot be a trivial ''default'' consequence of physiology but must be intimately linked to the manner in which metabolic networks have been moulded by natural selection.

Photocatalytic activity of Ag-substituted and impregnated nano-TiO2

Ag-substituted (Ag sub) and Ag-impregnated (Ag imp), anatase phase nano-TiO2 have been synthesized by solution combustion technique and reduction technique, respectively. The catalysts were characterized extensively by powder XRD, TEM, XPS, FT-Raman, UV absorption, FT-IR, TGA, photoluminescence, BET surface area and isoelectric pH measurements. These catalysts were used for the photodegradation of dyes and for the selective photooxidation of cyclohexane to cyclohexanone. The photoactivities of the combustion-synthesized catalysts were compared with those of commercial Degussa P 25 (DP 25) TiO2, and Ag-impregnated DP 25 (Ag DP). For the photocatalytic degradation of dyes, unsubstituted combustion-synthesized TiO2 (CS TiO2) exhibited the highest activity, followed by 1% Ag imp and 1% Ag sub. For the photoconversion of cyclohexane, the total conversion of cyclohexane and the selectivity of cyclohexanone followed the order: 1% Ag sub > DP 25 > CS TiO2 > 1% Ag imp > 1% Ag DP. The kinetics of the photodegradation of dyes and of the photooxidation of cyclohexane were modeled using Langmuir–Hinshelwood rate equation and a free radical mechanism, respectively, and the rate coefficients were determined. The difference in activity values of the catalysts observed for these two reactions and the detailed characterization of these catalysts are described in this study.

Optical properties and CCN activity of aerosols in a high-altitude Himalayan environment: Results from RAWEX-GVAX

The seasonality and mutual dependence of aerosol optical properties and cloud condensation nuclei (CCN) activity under varying meteorological conditions at the high-altitude Nainital site (2km) in the Indo-Gangetic Plains were examined using nearly year-round measurements (June 2011 to March 2012) at the Atmospheric Radiation Measurement mobile facility as part of the Regional Aerosol Warming Experiment-Ganges Valley Aerosol Experiment of the Indian Space Research Organization and the U.S. Department of Energy. The results from collocated measurements provided enhanced aerosol scattering and absorption coefficients, CCN concentrations, and total condensation nuclei concentrations during the dry autumn and winter months. The CCN concentration (at a supersaturation of 0.46) was higher during the periods of high aerosol absorption (single scattering albedo (SSA)<0.80) than during the periods of high aerosol scattering (SSA>0.85), indicating that the aerosol composition seasonally changes and influences the CCN activity. The monthly mean CCN activation ratio (at a supersaturation of 0.46) was highest (>0.7) in late autumn (November); this finding is attributed to the contribution of biomass-burning aerosols to CCN formation at high supersaturation conditions.