Thermodynamic properties of Pb2PtO4 and PbPt2O4 and phase equilibria in the system Pb–Pt–O

The compounds Pb2PtO4 and PbPt2O4 were synthesized from an intimate mixture of yellow PbO and Pt metal powders by heating under pure oxygen gas at 973 K for periods up to 600 ks with intermediate grinding and recompacting. Both compounds were found to decompose on heating in pure oxygen to PbO and Pt, apparently in conflict with the requirements for equilibrium phase relations in the ternary system Pb–Pt–O. The oxygen chemical potential corresponding to the three-phase mixtures, Pb2PtO4 + PbO + Pt and PbPt2O4 + PbO + Pt were measured as a function of temperature using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the solid electrolyte and pure oxygen gas at 0.1 MPa pressure as the reference electrode. The standard Gibbs free energies of formation of the ternary oxides were derived from the measurements. Analysis of the results indicated that the equilibrium involving three condensed phases Pb2PtO4 + PbO + Pt is metastable. Under equilibrium conditions, Pb2PtO4 should have decomposed to a mixture of PbO and PbPt2O4. Measurement of the oxygen potential corresponding to this equilibrium decomposition as a function of temperature indicated that decomposition temperature in pure oxygen is 1014(±2) K. This was further confirmed by direct determination of phase relations in the ternary Pb–Pt–O by equilibrating several compositions at 1023 K for periods up to 850 ks and phase identification of quenched samples using X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). Only one ternary oxide PbPt2O4 was stable at 1023 K under equilibrium conditions. Alloys and intermetallic compounds along the Pb–Pt binary were in equilibrium with PbO.

Hydrothermal phase equilibria in Ln2O3-H2O-CO2 systems for Tm, Yb and Lu

Phase diagrams for Tm2O3-H2O-CO2. Yb2O3-H2O-CO2 and Lu2O3-H2O-CO2 systems at 650 and 1300 bars have been investigated in the temperature range of 100–800°C. The phase diagrams are far more complex than those for the lighter lanthanides. The stable phases are Ln(OH)3, Ln2(CO3)3.3H2O (tengerite phase), orthorhombic-LnOHCO3, hexagonal-Ln2O2CO3. LnOOH and cubic-Ln2O3. Ln(OH)3 is stable only at very low partial pressures of CO2. Additional phases stabilised are Ln2O(OH)2CO3and Ln6(OH)4(CO3)7 which are absent in lighter lanthanide systems. Other phases, isolated in the presence of minor alkali impurities, are Ln6O2(OH)8(CO3)3. Ln4(OH)6(CO3)3 and Ln12O7(OH)10,(CO3)6. The chemical equilibria prevailing in these hydrothermal systems may be best explained on the basis of the four-fold classification of lanthanides.

Force-free equilibria of magnetized jets

Force-free equilibrium configurations of magnetic-pressure-dominated magnetized supersonic jets confined by slowly varying external pressure are investigated analytically. For the case where internal dissipation mechanisms are active, the lowest-energy field configuration is found to be the superposition of an axisymmetric mode and a helical mode with a wavelength equal to 5 times the jet radius, and the pressure below which the nonaxisymmetric mode becomes energetically favorable is given as 2700 times the product of the 4th power of the magnetic helicity per unit length and the -6th power of the magnetic flux. A model of the total and polarized emission of such a configuration is developed and applied to the extended well-collimated astronomically resolved jet NGC 6251. The model is shown to reproduce significant features such as transverse oscillations of the ridge line, width oscillations and emission knots, the projected magnetic-field configuration, oscillations of the degree of polarization, and the distribution of the Faraday rotation measure.

Uplink Power Control and Base Station Association in Multichannel Cellular Networks

A combined base station association and power control problem is studied for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one cell (i.e., base station). A distributed association and power update algorithm is proposed and shown to converge to a Nash equilibrium of a noncooperative game. We consider network models with discrete mobiles (yielding an atomic congestion game), as well as a continuum of mobiles (yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lack of system optimality, we propose pricing mechanisms. It is shown that these mechanisms can be implemented in a distributed fashion.

Metal-spinel-corundum three phase equilibria in the system Ni-Cr-Al-O at 1373 K

The tie-lines representing the inter-crystalline ion exchange equilibria between the NiCr2O4-NiAl2O4 spinet solid solution and Cr2O3-Al2O3 corundum solid solution are determined by electron microprobe andEDAX pointcountanalysis of the oxide phases equilibrated with metallic Ni at 1373 K. The component activities in the spinet solid solution are derived from the tie-lines and thermodynamic data for Cr2O3-Al2O3 solid solution available in the literature. The Gibbs energy of mixing of the spinet solid solution calculated from the experimental data is discussed in relation to the values derived from the cation distribution models which assume random mixing of cations on both tetrahedral and octahedral sites. Positive deviation from the models is observed indicating significant positive enthalpy contribution arising form the size mismatch between Al+3 and Ni+2 ions on the tetrahedral site and Al+3, Ni+2 and Cr+3 on the octahedral site. Variation of the oxygen potential for threephase equilibrium involving metallic nickel, spinet solid solution and corundum solid solution is computed as a function of composition of the solid solutions at 1373 K. The oxygen potential exhibits a minimum at aluminum cationic fraction eta(Al)/(eta(Al) + eta(Cr)) = 0.524 in the oxide solid solutions.

Chemical potentials of oxygen for fayalite-quartz-lron and fayalite-quartz-magnetite equilibria

The oxygen potentials corresponding to fayalite-quartz-iron (FQI) and fayalite-quartz-magnetite (FQM) equilibria have been determined using solid-state galvanic cells: Pt,Fe + Fe2SiO4 + SiO2/(Y2O3)ZrO2/Fe + \r"FeO,\l"Pt and Pt, Fe3O4 + Fe2SiO4 + SiO2/(Y2O3)ZrO2/Ni + NiO, Pt in the temperature ranges 900 to 1400 K and 1080 to 1340 K, respectively. The cells are written such that the right-hand electrodes are positive. Silica used in this study had the quartz structure. The emf of both cells was found to be reversible and to vary linearly with temperature. From the emf, Gibbs energy changes were deduced for the reactions: 0.106Fe (s) + 2Fe0.947O (r.s.) + SiO2 (qz) → Fe2SiO4 (ol) δG‡= -39,140+ 15.59T(± 150) J mol-1 and 3Fe2SiO4 (ol) + O2 (g) → 2Fe3O4 (sp) + 3SiO2 (qz) δG‡ = -471,750 + 160.06 T±} 1100) J mol-1 The “third-law≓ analysis of fayalite-quartz-wustite and fayalite-quartz-magnetite equilibria gives value for δH‡298 as -35.22 (±0.1) and -528.10 (±0.1) kJ mol-1, respectively, independent of temperature. The Gibbs energy of formation of the spinel form of Fe2SiO4 is derived by com-bining the present results on FQI equilibrium with the high-pressure data on olivine to spinel transformation of Fe2SiO4.

Use of metastable equilibria for determination of Gibbs energy of solids

Attempts are made to measure activities of both components of a binary alloy (A�B) at 650 K using a solid-state galvanic cell incorporating a new composite solid electrolyte. Since the ionic conductivity of the composite solid electrolyte is three orders of magnitude higher than that of pure CaF2, the cell can be operated at lower temperatures. The alloy phase is equilibrated in separate experiments with flourides of each component and fluorine potential is measured. The mixture of the alloy (A�B) and the fluoride of the more reactive component (BF2) is stable, while (A�B) + AF2 mixture is metastable, Factors governing the possible use of metastable equilibria have been elucidated in this study. In the Co�Ni system, where the difference in Gibbs energies of formation of the fluorides is 21.4 kJ/mol, emf of the cell with metastable phases at the electrode is constant for periods ranging from 90 to 160 ks depending on alloy composition. Subsequently, the emf decreases because of the onset of the displacement reaction. In the Ni�Mn system, measurement of the activity of Ni using metastable equilibria is not fully successful at 650 K because of the large driving force for the displacement reaction (208.8 kJ/mol). Critical factors in the application of metastable equilibria are the driving force for displacement reaction and diffusion coefficients in both the alloy and fluoride solid solution.

Multicomponent multiphase equilibria

A method has been developed for the computation of multicomponent multiphase equilibrium. This method is essentially a modification of White’s element potentials method. It has been found that if the search for equilibrium is confined to a physically significant zone, a solution of the equilibrium problem can be obtained even with a poor initial guess.

Chemical potential of oxygen for iron-rutile-ilmenite and iron-ilmenite-ulvospinel equilibria

The chemical potential of oxygen corresponding to the iron-rutile-ilmenite (IRI) and iron-ilmenite-ulvospinel (IIU) equilibria has been measured employing solid-state galvanic cells,$$Pt, Fe + TiO_2 + FeTiO_3 //(Y_2 O_3 ) ZrO_2 //Fe + FeO, Pt$$ and $${\text{Pt, Fe + FeTiO}}_{\text{3}} {\text{ + Fe}}_{\text{2}} {\text{TiO}}_{\text{4}} {\text{//(Y}}_{\text{2}} {\text{0}}_{\text{3}} {\text{) ZrO}}_{\text{2}} {\text{//Fe + FeO, Pt}}$$ in the temperature range of 875 to 1275 K and 900 to 1373 K, respectively. The cells are written such that the right-hand electrodes are positive. The electromotive force (emf) of both the cells was found to be reversible and to vary linearly with temperature over the entire range of measurement. The chemical potential of oxygen for IRI equilibrium is represented by Δμo2(IRI) = -550,724 - 29.445T + 20.374T InT(±210) J mol−1 (875 <-T<- 1184 K) = -620,260 + 369.593T - 27.716T lnT(±210) J mol−1 (1184 <-T<- 1275 K) and that for IIU equilibrium by Δμo2(IIU) = -501,800 - 49.035T + 20.374T lnT(±210) J mol−1 (900 <-T<- 1184 K) = -571,336 + 350.003T− 27.716T lnT(=−210) J mol-1 (1184 <-T<- 1373 K) The standard Gibbs energy changes for IRI and IIU equilibria have been deduced from the measured oxygen potentials. Since ilmenite contains small amounts of Ti³+ ions, a correction for the activity of FeTiO3 has been incorporated by assuming ideal mixing on each cation sublattice in the FeTiO3-Ti2O3 system. Similarly, the ulvospinel contains some Fe³+ ions and a correction for the activity of Fe2TiO4 has been included by modeling the Fe2TiO4-Fe3O4 system. The third-law analysis of the results obtained for IRI equilibrium gives ΔH 298 0 = -575 (±1.0) kJ mol-1 and for IIU equilibrium yields ΔH 298 0 = -523.7 (±0.7) kJ mol−1}. The present results suggest that Fe2+ and Ti4+ cations mix almost ideally on the octahedral site of spinel lattice in Fe2TiO4, giving rise to a configurational contribution of 2R In 2 (11.5256 J mol-1 K-1) to the entropy of Fe2TiO4.

On the Nash-Williams′ Lemma in Graph Reconstruction Theory

A generalization of Nash-Williams′ lemma is proved for the Structure of m-uniform null (m − k)-designs. It is then applied to various graph reconstruction problems. A short combinatorial proof of the edge reconstructibility of digraphs having regular underlying undirected graphs (e.g., tournaments) is given. A type of Nash-Williams′ lemma is conjectured for the vertex reconstruction problem.

Thermodynamics and phase equilibria in the Ga---Sb system

The optimum values of the solution parameters of a multiparameter integral free-energy function have been determined using experimental data from the Ga-Sb system. The equation is represented as DELTAG(xs) = x(1 - x)[(1 - x)(a1 + a2T + a3T ln T) + x(a4 + a5T + a6T ln T) + x(1 - x)(a7 + a8T + a9xT)].The integral and the corresponding partial form of the free energy function have been found to be of use when interpreting the high temperature thermodynamic data, atomic interactions and phase equilibria in the Ga-Sb system.

Thermodynamics and phase equilibria in the system Ga---In using multi-parameter functions

A four and a five-parameter functions are used to analyse and interpret the high and low temperature thermodynamic data and phase equilibria in the Ga-In system.

A non-cooperative game-theoretic approach to channel assignment in multi-channel multi-radio wireless networks

Channel assignment in multi-channel multi-radio wireless networks poses a significant challenge due to scarcity of number of channels available in the wireless spectrum. Further, additional care has to be taken to consider the interference characteristics of the nodes in the network especially when nodes are in different collision domains. This work views the problem of channel assignment in multi-channel multi-radio networks with multiple collision domains as a non-cooperative game where the objective of the players is to maximize their individual utility by minimizing its interference. Necessary and sufficient conditions are derived for the channel assignment to be a Nash Equilibrium (NE) and efficiency of the NE is analyzed by deriving the lower bound of the price of anarchy of this game. A new fairness measure in multiple collision domain context is proposed and necessary and sufficient conditions for NE outcomes to be fair are derived. The equilibrium conditions are then applied to solve the channel assignment problem by proposing three algorithms, based on perfect/imperfect information, which rely on explicit communication between the players for arriving at an NE. A no-regret learning algorithm known as Freund and Schapire Informed algorithm, which has an additional advantage of low overhead in terms of information exchange, is proposed and its convergence to the stabilizing outcomes is studied. New performance metrics are proposed and extensive simulations are done using Matlab to obtain a thorough understanding of the performance of these algorithms on various topologies with respect to these metrics. It was observed that the algorithms proposed were able to achieve good convergence to NE resulting in efficient channel assignment strategies.

Phase equilibria in the system CaO-CoO-SiO2 and Gibbs energies of formation of the quaternary oxides CaCoSi2O6, Ca2CoSi2O7, and CaCoSiO4

Phase relations in the pseudoternary system CaO-CoO-SiO2 have been established at 1323 K. Three quaternary oxides were found to be stable: CaCoSi2O6 with clinopyroxene (Cpx), Ca2CoSi2O7 with melilite (Mel), and CaCoSiO4 with olivine (Ol) structures. The Gibbs energies of formation of the quaternary oxides from their component binary oxides were measured using solid-state galvanic cells incorporating yttria-stabilized zirconia as the solid electrolyte in the temperature range of 1000-1324 K. The results can be summarized as follows: CoO (rs) + CaO (rs) + 2SiO(2) (Qtz) --> CaCoSi2O6 (Cpx), Delta G(f)(0) = -117920 + 11.26T (+/-150) J/mol CoO (rs) + 2CaO (rs) + 2SiO(2) (Qtz) --> Ca2CoSi2O7 (Mel), Delta G(f)(0) = -192690 + 2.38T (+/-130) J/mol CoO (rs) + CaO (rs) + SiO2 (Qtz) --> CaCoSiO2 (Ol), Delta G(f)(0) = -100325 + 2.55T (+/-100) J/mol where rs = rock salt (NaCl) structure and Qtz = quartz. The uncertainty limits correspond to twice the standard error estimate. The experimentally observed miscibility gaps along the joins CaO-CoO and CaCoSiO4-Co2SiO4 were used to calculate the excess free energies of mixing for the solid solutions CaxCo1-xO and (CayCo1-y)CoSiO4:Delta G(E) = X(1 - X)[31975X + 26736 (1 - X)] J/mol and Delta G(E) = 23100 (+/-250) Y(1 - Y) J/mol. A T-X phase diagram for the binary CaO-CoO was computed from the thermodynamic information; the diagram agrees with information available in the literature. The computed miscibility gap along the CaCoSiO4-Co2SiO4 join is associated with a critical temperature of 1389 (+/-15) K. Stability fields for the various solid solutions and the quaternary compounds are depicted on chemical-potential diagrams for SiO2, CaO, and CoO at 1323 K.