Thermodynamic Study of Mixed Anionic Solid Solutions Using Gradient Solid Electrolytes System K2CO3 - K2SO4

The thermodynamic properties of K2CO3 -KSO, solid solutions with hexagonal structure have been measured using a solid-state cell, incorporating a composite solid electrolyte with step-changes in composition. The cell with the configuration Pt, CO2' + O2' || K2CO3 | K2(CO3)x(SO4)1-x || CO2'' + O2'' + Pt X =1 X=X was investigated in the temperature range of 925 to 1165 K. The composite gradient solid electrolyte consisted of pure K2CO3 at one extremity and the solid solution under study at the other. The Nernstian response of the cell to changes in partial pressures of CO2 and O2 at the electrodes and temperature was demonstrated. The activity of K2CO3 in the solid solution was measured by three techniques. All three methods gave identical results, indicating unit transport number for K+ ions and negligible diffusion potential due to concentration gradients of carbonate and sulfate ions. The activity of K2CO3 exhibits positive deviation from Raoult's law. The excess Gibbs energy of mixing of the solid solution can be represented using a subregular solution model DELTAG(E) = X(1 - X)[5030X + 4715(1 - X)] J mol-1 By combining this information with the phase diagram, mixing properties of the liquid phase were obtained.

The concentration dependent cooperative friction coefficient of dilute polymer solutions at the theta point

We combine multiple scattering and renormalization group methods to calculate the leading order dimensionless virial coefficient k(s) for the friction coefficient of dilute polymer solutions under conditions where the osmotic second virial coefficient vanishes (i.e., at the theta point T-theta). Our calculations are formulated in terms of coupled kinetic equations for the polymer and solvent, in which the polymers are modeled as continuous chains whose configurations evolve under the action of random forces in, the velocity field of the solvent. To lowest order in epsilon=4-d, we find that k(s) = 1.06. This result compares satisfactorily with existing experimental estimates of k(s), which are in the range 0.7-0.8. It is also in good agreement with other theoretical results on chains and suspensions at T-theta. Our calculated k(s) is also found to be identical to the leading order virial coefficient of the tracer friction coefficient at the theta point. We discuss possible reasons for the difficulties encountered when attempting to evaluate k(s) by extrapolating prior renormalization group calculations from semidilute concentrations to the infinitely dilute limit. (C) 1996 American Institute of Physics.

The CaO-SrO-CuO-O-2 system: Phase equilibria and thermodynamic properties at 1123 K

Phase relationships in the CaO-SrO-CuO system in pure oxygen at 1.01 x 10(5) Pa pressure were determined by equilibrating different compositions at 1123 K for similar to 120 h and analyzing the phases present in the quenched samples using X-ray diffraction (XRD), optical and scanning electron microscopy, and energy dispersive analysis of X-rays (EDAX). Four solid solution series were observed in the system, The CawSr1-wO monoxide solid solution with rock-salt structure was found to exhibit an asymmetric miscibility gap, The mixing properties of the monoxide system were deduced using a subregular solution model, For the (CaxSr1-x)(2)CuO3 series, a complete solid solution range with orthorhombic space group Immm was obtained. Calcium substituted for strontium up to 68 at. % in SrCuO2+delta and 51.5 at. % in Sr14Cu24O41-delta. The tie lines between the solid solutions were determined accurately, The activity-composition relations in (CaxSr1-x)(2)CuO3, CaySr1-yCuO2+delta, and (Ca2Sr1-z)(14)Cu24O41-delta solid solutions were determined from experimental tie lines. Activities in the (CaxSr1-x)(2)CuO3 and CaySr1-yCuO2+delta series were close to the predictions of the Temkin model, The behavior of the (CazSr1-(z))(14)Cu24O41-delta solid solution was more complex, with the activity of SrCu(24/14)O-(41-delta/14) exhibiting both positive and negative deviations from ideality. Gibbs energy of formation of the CaCuO2+delta metastable phase at 1123 K was deduced from an analysis of the phase diagram.

Tie lines and activities in the system NiO-MgO-SiO2 at 1373 K

The isothermal section of the phase diagram for the system NiO-MgO-SiO2 at 1373 K is established, The tie lines between (NiXMg1-X)O solid solution with rock salt structure and orthosilicate solid solution (NiYMg1-Y)Si0.5O2 and between orthosilicate and metasilicate (NiZMg1-Z)SiO3 crystalline solutions are determined using electron probe microanalysis (EPMA) and lattice parameter measurement on equilibrated samples, Although the monoxides and orthosilicates of Ni and Mg form a continuous range of solid solutions, the metasilicate phase exists only for 0 < Z < 0.096, The activity of NiO in the rock salt solid solution is determined as a function of composition and temperature in the range of 1023 to 1377 K using a solid state galvanic cell, The Gibbs energy of mixing of the monoxide solid solution can be expressed by a pseudo-subregular solution model: Delta G(ex) = X(1 - X)[(-2430 + 0.925T)X + (-5390 + 1.758T)(1 - X)] J/mol, The thermodynamic data for the rock salt phase are combined with information on interphase partitioning of Ni and Mg to generate the mixing properties for the orthosilicate and the metasilicate solid solutions, The regular solution model describes the orthosilicate and the metasilicate solid solutions at 1373 K within experimental uncertainties, The regular solution parameter Delta G(ex)/Y(1 - Y) is -820 (+/-70) J/mol for the orthosilicate solid solution, The corresponding value for the metasilicate solid solution is -220 (+/-150) J/mol, The derived activities for the orthosilicate solid solution are discussed in relation to the intracrystalline ion exchange equilibrium between M1 and M2 sites. The tie line information, in conjunction with the activity data for orthosilicate and metasilicate solid solutions, is used to calculate the Gibbs energy changes for the intercrystalline ion exchange reactions, Combining this with the known data for NiSi0.5O2, Gibbs energies of formation of MgSi0.5O2, MgSiO3, and metastable NiSiO3 are calculated, The Gibbs energy of formation of NiSiO3, from its component oxides, is equal to 7.67 (+/-0.6) kJ/mol at 1373 K.

Limiting ionic conductance of symmetrical, rigid ions in aqueous solutions: Temperature dependence and solvent isotope effects

Limiting ionic conductance (Lambda(0)) of rigid symmetrical unipositive ions in aqueous solution shows a strong temperature dependence. For example, Lambda(0) more than doubles when the temperature is increased from 283 to 318 K. A marked variation also occurs when the solvent is changed from ordinary water (H2O) to heavy water (D2O). In addition, Lambda(0) shows a nonmonotonic size dependence with a skewed maximum near Cs+. Although these important results have been known for a long time, no satisfactory theoretical explanation exists for these results. In this article we present a simple molecular theory which provides a nearly quantitative explanation in terms of microscopic structure and dynamics of the solvent. A notable feature of this theory is that it does not invoke any nonquantifiable models involving solvent-berg or clatherates. We find the strong temperature dependence of Lambda(0) to arise from a rather large number of microscopic factors, each providing a small but nontrivial contribution, but all acting surprisingly in the same direction. This work, we believe, provides, for the first time, a satisfactory explanation of both the anomalous size and temperature dependencies of Lambda(0) of unipositive ions in molecular terms. The marked change in Lambda(0) as the solvent is changed from H2O to D2O is found to arise partly from a change in the dielectric relaxation and partly from a change in the effective interaction of the ion with the solvent.

Solutions of cubic equations in quadratic fields

Let K be any quadratic field with O-K its ring of integers. We study the solutions of cubic equations, which represent elliptic curves defined over Q, in quadratic fields and prove some interesting results regarding the solutions by using elementary tools. As an application we consider the Diophantine equation r + s + t = rst = 1 in O-K. This Diophantine equation gives an elliptic curve defined over Q with finite Mordell-Weil group. Using our study of the solutions of cubic equations in quadratic fields we present a simple proof of the fact that except for the ring of integers of Q(i) and Q(root 2), this Diophantine equation is not solvable in the ring of integers of any other quadratic fields, which is already proved in [4].

Beta-structure of polypeptides in non-aqueous solutions. I. Spectral characteristics of the polypeptide backbone

The optical rotatory features of the beta-structure of the polypeptides in non-aqueous solutions and films cast from these solutions have been investigated. The beta-structure of poly-S-benzyl-L-cysteine, poly-S-carbobenzoxy-L-cysteine and poly-S-benzyl-L-cysteine, poly-S-carbobenzoxy-L-cysteine and poly-O-carbo-bands of their films. The optical rotatory dispersion (ORD) and circular dichroism (CD) spectra of these polypeptides are found to be very similar in both film and solution. In solvents promoting the beta-structure, the polypeptides are characterized by CD troughs in the n-pi* transition region of the peptide chromophore. The ORD spectra are found to be positive in sign throughout the visible and accessible ultraviolet regions and are interpreted in terms of the possible existence of a relatively much larger positive pi-pi* CD bands as compared with the negative n-pi* band. The rotatory data obtained in the non-aqueous solution are compared with those obtained for other poly peptides in aqueous solutions, with respect to the type and extent of beta-structure present.

Beta-structure of polypeptides in non-aqueous solutions. II. Side-chain orientation

The specific side-chain orientations of the phenyl group in the polypeptides poly-S-benzyl-L-cysteine, poly-S-carbobenzoxy-L-cysteine and poly-O-carbobenzoxy-L-serine in the beta-structure have been studied by spectral measurements in solutions. All the three polypeptides exhibit aromatic CD bands, indicating the asymmetric placement of the side-chain phenyl rings when the polypeptide backbone takes up the antiparallel beta-structure. Supporting evidence for this is derived from n.m.r. spectra of the polypeptides, which show upfield shift of the phenyl protons due to the stacking of the aromatic rings. Molecular model building studies reveal the stacking of alternate phenyl groups along the polypeptide chain.

Activities of oxygen and lead in Pb-Ag O solutions

The reversible e.m.f. of galvanic cells: stainlesssteel,Ir,Pb+PbO|CaO+ZrO2|Ag+Pb+PbO,Ir,stainlesssteel,I and Pt,Ni+NiO|CaO+ZrO2|O(Pb+Ag),Cermet,Pt,II incorporating solid oxide electrolytes were measured as a function of alloy composition. In lead-rich alloys, the temperature dependence of the e.m.f. of cell I was also investigated. Since the solubility of oxygen in the alloy is small, the relative partial molar properties of lead in the binary Ag + Pb system can be calculated from the e.m.f. of this cell. The Gibbs free energies obtained in this study are combined with selected calorimetric data to provide a complete thermodynamic discription of liquid Ag + Pb Alloys. The activity coefficient of oxygen in the whole range of Ag + Pb alloys at 1273 K have been obtained from the e.m.f. of cell II; and these are found to deviate positively from Alcock and Richardson's quasichemical equation when the average co-ordination number of all the atoms is assigned a value of 2.

Chemical potential of germanium in its solid solutions with Cu, Ag and Au

Thin foils of copper, silver and gold were equilibrated with tetragonal GeO2 under controlled View the MathML source gas streams at 1000 K. The equilibrium concentration of germanium in the foils was determined by the X-ray fluorescence technique. The standard free energy of formation of tetragonal GeO2 was measured by a solid oxide galvanic cell. The chemical potential of germanium calculated from the experimental data and the free energies of formation of carbon monoxide and carbon dioxide was found to decrease in the sequence Ag + Ge > Au + Ge > Cu + Ge. The more negative value for the chemical potential of germanium in solid copper, compared to that in solid gold, cannot be explained in terms of the strain energy factor, electro-negativity differences or the vaporization energies of the solvent, and suggests that the d band and its hybridization with s electrons are an important factor in determining the absolute values for the chemical potential in dilute solutions. However, the variation of the chemical potential with solute concentration can be correlated to the concentration of s and p electrons in the outer shell.

Ion exchange equilibria between (Mn,Co)O solid solution and (Mn,Co)Cr2O4 and (Mn,Co)Al2O4 spinel solid solutions at 1100oC

The compositions of the (Mn,Co)O solid solution with rock salt structure in equilibrium with (Mn,Co)Cr2O4 and (Mn,Co)Al2O4 spinel solid solutions have been determined by X-ray diffraction measurements at 1100° C and an oxygen partial pressure of 10–10 atm. The ion exchange equilibria are quantitatively analysed, using values for activities in the (Mn,Co)O solid solution available in the literature, in order to obtain activities in the spinel solid solutions. The MnAl2O4-CoAl2O4 solid solution exhibits negative deviations from Raoult's law, consistent with the estimated cation disorder in the solid solution, while the MnCr2O4-CoCr2O4 solid solution shows slightly positive deviations. The difference in the Gibbs free energy of formation of the two pure chromites and aluminates derived from the results of this study are in good agreement with recent results obtained from solid oxide galvanic cells and gas-equilibrium techniques.

Thermodynamic properties of Fe3O4 FeV2O4 and Fe3O4 FeCr2O4 spinel solid solutions

Solid solutions of Fe304-FeV204 and Fe304-FeCr204 were prepared and equilibrated with Pt under controlled streams of CO/CO, gas mixtures at 1673 K. The concentration of Fe in Pt was used to determine the activity of Fe304 in the solid solutions. The activity of the second component was calculated by Gibbshhem integration. From these data, the Gibbs energy of mixing was derived for both systems. The experimental results and theoretical values which are determined from calculated cation distribution compare favorably in the case of vanadite solid solutions but not in the case of chromite solid solutions. The difference is attributed to a heat term arising from lattice distortion due to cation size difference. The positive heat of mixing will give rise to a miscibility gap in the system Fe304-FeCr204 at lower temperatures.

Phase relations and activities in the Co Ni O system at 1373 K

The tie-lines delineating equilibria between CoO-NiO and Co-Ni solid solutions in the ternary Co-Ni-O system at 1373 K have been determined by electron microprobe andedax point count analysis of the oxide phase equilibrated with the alloy. The oxygen potentials corresponding to the tie-line compositions have been measured using a solid oxide galvanic cell with calcia-stabilized zirconia electrolyte and Ni + NiO reference electrode. Activities in the metallic and oxide solid solution have been derived using a new Gibbs-Duhem integration technique. Both phases exhibit small positive deviations from ideality; the values ofG E/X 1 X 2 are 2640 J mol−1 for the metallic phase and 2870 J mol−1 for the oxide solid solution.

Tie lines and activities in the system CoO MgO SiO2 at 1373 K

The tie lines between (CoXMg1−X)O solid solution with rock salt structure and orthosilicate solid solution (CoYMg1−Y)-Si0.5O2, and between orthosilicate and metasilicate (CoZMg1-Z)SiO3 crystalline solutions, have been determined experimentally at 1373 K. The compositions of coexisting phases have been determined by electron probe microanalysis (EPMA) and lattice parameter measurement on equilibrated samples. The metasilicate solid solution exists only for 0 > Z > 0.213. The activity of CoO in the rock salt solid solution was determined as a function of composition and temperature in the range of 1023 to 1373 K using a solid-state galvanic cell: Pt, (CoXMg1−X)O+Co|(Y2O3)ZrO2|Co+CoO, Pt The free energy of mixing of (CoXMg1−X)O crystalline solution can be expressed by the equation ΔGE=X(1 −X)[(6048 − 2.146T)X+ (8745 − 3.09T)(1 −X)] J·mol−1 The thermodynamic data for the rock salt phase is combined with information on interphase partitioning of Co and Mg to generate the mixing properties for the ortho- and metasilicate solid solutions. For the orthosilicate solution (CoYMg1 −Y)Si0.5O2 at 1373 K, the excess Gibbs free energy of mixing is given by the relation ΔGE=Y(1 −Y)[2805Y+ 3261(1 −Y)] J·mol−1 For the metasilicate solution (CoZMg1 −Z)SiO3 at the same temperature, the excess free energy can be expressed by the relation ΔGE=Z(1 −Z)[2570Z+ 3627(1 −Z)] J·mol−1

An improved X-ray structural analysis for determining cation distribution in ZnFe2O4 and ZnFe2O4- Fe3O4 solid solutions

The distribution of zinc cation between crystallographically nonequivalent positions in ZnFe204 has been determined by anomalous X-ray scattering near the Zn K absorption edge. Measured intensity ratio with two energies close to the edge can be quantitatively explained only by assigning all zinc cations to the tetrahedral position in the approximately cubic close packed array of oxygen ions. A similar conclusion has also been reached for ZnxFe3-x04 solid solutions with x = 0.73, 0.54 and 0.35 employing the improved X-ray method. This is consistent with the EXAFS results which indicate an almost unchanged environmental structure around zinc cation in these solid solutions.