Phase Relations in the System Cu-Gd-O and Gibbs Energy of Formation of CuGd204

The phase relations in the system Cu-Gd-O have been determined at 1273 K by X-ray diffrac- tion, optical microscopy, and electron microprobe analysis of samples equilibrated in quartz ampules and in pure oxygen. Only one ternary compound, CuGd2O4, was found to be stable. The Gibbs free energy of formation of this compound has been measured using the solid-state cell Pt, Cu2O + CuGd2O4 + Gd2O3 // (Y2O3) ZrO2 // CuO + Cu2O, Pt in the temperature range of 900 to 1350 K. For the formation of CuGd2O4 from its binary component oxides, CuO (s) + Gd2O3 (s) → CuGd2O4 (s) ΔG° = 8230 - 11.2T (±50) J mol-1 Since the formation is endothermic, CuGd2O4 becomes thermodynamically unstable with respect to CuO and Gd2O3 below 735 K. When the oxygen partial pressure over CuGd2O4 is lowered, it decomposes according to the reaction 4CuGd2O4 (s) → 4Gd2O3 (s) + 2Cu2O (s) + O2 (g) for which the equilibrium oxygen potential is given by Δμo 2 = −227,970 + 143.2T (±500) J mol−1 An oxygen potential diagram for the system Cu-Gd-O at 1273 K is presented.

An experimental study on acoustic emission energy as a quantitative measure of size independent specific fracture energy of concrete beams

Notched three point bend specimens (TPB) were tested under crack mouth opening displacement (CMOD) control at a rate of 0.0004 mm/s and during the fracture process acoustic emissions (AE) were simultaneously monitored. It was observed that AE energy could be related to fracture energy. An experimental study was done to understand the behavior of AE energy with parameters of concrete like its strength and size. In this study, AE energy was used as a quantitative measure of size independent specific fracture energy of concrete beams and the concepts of boundary effect and local fracture energy were used to obtain size independent AE energy from which size independent fracture energy was obtained. (C) 2010 Elsevier Ltd. All rights reserved.

Gibbs energy of formation of orthorhombic CaZrO3

The Gibbs free energy of formation of the orthorhombic form of CaZrO3(o) from monoclinic ZrO2(m) and periclase CaO(p) has been determined as a function of temperature in the range 950-1225 K, using an electrochemical cell incorporating single-crystal CaF2 as the solid electrolyte. The results are corrected for the small solid solubility of CaO in ZrO2. For the reaction, ZrO2(m) + CaO(p) --> CaZrO3(o), DELTAG(phi) = -31590 -13.9T(+/- 180) J mol-1. The ''second-law'' enthalpy of formation of CaZrO3 obtained from the results of this study at a mean temperature of 1090 K is in excellent agreement with the high-temperature solution calorimetric measurements of Muromachi and Navrotsky at 1068 K (J. Solid State Chem., 72 (1988) 244), and the average value of the bomb and acid solution calorimetric studies of Lvova and Feodosev (Zh. Fiz. Khim., 38 (1964) 28), Korneev et al. (Izv. Akad. Nauk SSSR, Neorg. Mater., 7 (1971) 886) and Brown and Bennington (Thermochim. Acta, 106 (1986) 183). The standard entropy of CaZrO3(o) at 298.15 K from the free energy data is 96.4 (+/- 3.5) J K-1 mol-1. The results of this study are discussed in comparison with high-temperture e.m.f. measurements reported in the literature on cubic zirconia solid solutions.

A critical assessment of the standard molar gibbs free energy of formation of NiWO4

Three independent studies have been reported on the free energy of formation of NiWO4. Results of these measurements are analyzed by the �third-law� method, using thermal functions for NiWO4 derived from both low and high temperature heat capacity measurements. Values for the standard molar enthalpy of formation of NiWO4 at 298·15 K obtained from �third-law� analysis are compared with direct calorimetric determinations. Only one set of free energy measurements is found to be compatible with calorimetric enthalpies of formation. The selected value for ?f H m 0 (NiWO4, cr, 298·15 K) is the average of the three calorimetric measurements, using both high temperature solution and combustion techniques, and the compatible free energy determination. A new set of evaluated data for NiWO4 is presented.

Effect of magnetic field on the binding energy of a hydrogenic donor in a vertical bar z vertical bar(2/3) quantum well

We have calculated the binding energy of a hydrogenic donor in a quantum well with potential shape proportional to \z\(2/3) as a function of the width of the quantum well and the barrier height under an applied uniform magnetic field along the a axis. As the well width decreases, the binding energy increases initially up to a critical well width (which is nearly the same for all magnetic fields) at which there is a turnover. The results are qualitatively similar to those of a hydrogenic donor in a rectangular well. We have also calculated [rho(2)](1/2) and [z(2)](1/2) for the donor electron. [rho(2)](1/2) is found to be strongly dependent on the magnetic field for a given well width and weakly dependent on the well width and the barrier height, for a given value of magnetic field [z(2)](1/2) is weakly dependent on the applied magnetic field. The probability of finding the donor electron inside the well shows a rapid decrease as the well width is reduced at nearly the well width at which the binding energy shows a maximum.

Determination of the Gibbs energy of diamond using a solid state cell

he chemical potential of carbon in diamond, relative to its value in graphite, has been directly determined using a solid state electrochemical cell incorporating single crystal CaF2 as the solid electrolyte. The cell can be represented as Pt, C(graphite) + CaC2 + CaF2double vertical barCaF2double vertical barCaF2 + CaC2 + C(diamond), Pt The reversible emf of this cell is directly related by the Nernst equation to the Gibbs free energy change for the conversion of diamond to graphite. The difference in the chemical potential of carbon in the two crystal structures varies linearly with temperature in the range 940 to 1260 K ?C(diamond) ? ?C(graphite) = 1100 + 4.64T (±50) J mol?1 On the average, the values given by the equation are 320 J mol?1 less positive than the currently accepted ones based on calorimetric studies. The difference is primarily in the enthalpy term.

Flat connections, geometric invariants and energy of harmonic functions on compact Riemann surfaces

A geometric invariant is associated to the space of fiat connections on a G-bundle over a compact Riemann surface and is related to the energy of harmonic functions.

Measurement of Gibbs energy of formation of Ca2PbO4 using a solid-state cell with three electrodes

Phase relations in the system Ca-Pb-O at 1100 K have been determined by equilibrating 18 compositions in the ternary and identifying the phases present in quenched samples by X-ray diffraction and energy dispersive X-ray analysis (EDX). Only one ternary compound Ca2PbO4 was found to be present. The compound coexists with CaO and PbO. The intermetallic compounds Ca2Pb, Ca5Pb3 and CaPb and liquid alloys are in equilibrium with CaO. The standard Gibbs energies of formation of Ca2PbO4 (880 - 1100 K) and Pb3O4 (770 - 910 K) were determined using solid-state cells based on yttria-stabilized zirconia as the solid electrolyte. Pure oxygen gas at 0.1 MPa was used as the reference electrode. For measurements on Ca2PbO4, a novel cell design with three electrodes in series, separated by solid electrolyte membranes, was used to avoid polarization of the electrode containing three solid phases. Two three-phase electrodes were used. The first absorbs the electrochemical flux of oxygen from the reference electrode to the measuring electrode. The other three-phase electrode, which is unaffected by the oxygen flux through the solid electrolyte, is used for electromotive force (EMF) measurement. The results from EMF studies were cross-checked using thermogravimetry (TG) under controlled oxygen partial pressures. The stability of Pb3O4 was investigated using a conventional solid-state cell with RuO2 electrodes. The results can be summarized by the following equations: 2CaO + PbO +1/2O(2) --> Ca2PbO4 Delta(r)G degrees/J mol(-1) = (- 128340 + 93.21 T/K) +/- 200 3PbO + 1/2O(2) --> Pb3O4 Delta(r)G degrees/J mol(-1) = (- 70060 + 77.5 T/K) +/- 150

Absolute Entropy and Energy of Carbon Dioxide Using the Two-Phase Thermodynamic Model

The two-phase thermodynamic (2PT) model is used to determine the absolute entropy and energy of carbon dioxide over a wide range of conditions from molecular dynamics trajectories. The 2PT method determines the thermodynamic properties by applying the proper statistical mechanical partition function to the normal modes of a fluid. The vibrational density of state (DoS), obtained from the Fourier transform of the velocity autocorrelation function, converges quickly, allowing the free energy, entropy, and other thermodynamic properties to be determined from short 20-ps MD trajectories. The anharmonic effects in the vibrations are accounted for by the broadening of the normal modes into bands from sampling the velocities over the trajectory. The low frequency diffusive modes, which lead to finite DoS at zero frequency, are accounted for by considering the DoS as a superposition of gas-phase and solid-phase components (two phases). The analytical decomposition of the DoS allows for an evaluation of properties contributed by different types of molecular motions. We show that this 2PT analysis leads to accurate predictions of entropy and energy of CO2 over a wide range of conditions (from the triple point to the critical point of both the vapor and the liquid phases along the saturation line). This allows the equation of state of CO2 to be determined, which is limited only by the accuracy of the force field. We also validated that the 2PT entropy agrees with that determined from thermodynamic integration, but 2PT requires only a fraction of the time. A complication for CO2 is that its equilibrium configuration is linear, which would have only two rotational modes, but during the dynamics it is never exactly linear, so that there is a third mode from rotational about the axis. In this work, we show how to treat such linear molecules in the 2PT framework.

Estimation of surface free energy of pyrites by contact angle measurements

The surface properties of coal-pyrite play a major role in determining its separation from coal in processes such as flotation. The solution pH is an important parameter in determining the surface properties of both coal and coal-pyrite such as surface free energy and zeta-potential. In the present investigation, the effect of pH on the surface free energy of pyrites from different sources was studied. The surface free energy of solids is made up of two components, i.e. the dispersive surface free energy and the acid-base interaction energy. Various methods have been used by previous researchers to evaluate these two components for different solids. In the present study, a new approach was developed and used to study the surface free energy of pyrite surfaces. Results indicate that the dispersion surface free energy of various pyrites is independent of pH while the acid-base interaction energy is strongly dependent on the pH. The acid-base interaction energy is different for each pyrite sample and also the change with pH varies with the type of pyrite. Coal-pyrite was found to be more hydrophobic than ore-pyrite which may be attributed to the presence of carbon in coal-pyrites. The acid-base interaction energy varied little with pH for coal pyrites than ore-pyrite. Comparison of acid-base interaction energy with zeta-potential measurements shows a good correlation between the minimum in acid-base interaction energy and the pHpzc.

Standard Gibbs energy of formation of Pb2Ru2O6.5

Lead ruthenate is used as a bifunctional electrocatalyst for both oxygen evolution and reduction and as a conducting component in thick-film resistors. It also has potential applications in supercapacitors and solid oxide fuel cells. However, thermodynamic properties of the compound have not been reported in the literature. The standard Gibbs energy of formation has now been determined in the temperature range from 873 to 1123 K using a solid-state cell incorporating yttria-stabilized zirconia (YSZ) as the electrolyte, a mixture of PbO + Pb2Ru2O6.5 + Ru as the measuring electrode, and Ru + RuO2 as the reference. The design of the measuring electrode is based on a study of phase relations in the ternary system Pb–Ru–O at 1123 K. For the reaction,S0884291400095625_eqnU1 the standard enthalpy of formation and standard entropy at 298.15 K are estimated from the high-temperature measurements. An oxygen potential diagram for the system Pb–Ru–O is composed based on data obtained in this study and auxiliary information from the literature