A Shapley Value Analysis to Coordinate the Formation of Procurement Networks

In this paper we address the problem of forming procurement networks for items with value adding stages that are linearly arranged. Formation of such procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions. Research in supply chain management has emphasized that such decisions need to take into account the fact that suppliers and buyers are intelligent and rational agents who act strategically. In this paper, we view the problem of procurement network formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a fair manner. We study the implications of using the Shapley value as a solution concept for forming such procurement networks. We also present a protocol, based on the extensive form game realization of the Shapley value, for forming these networks.

Gibbs free energies of formation of ZnAl2O4 and ZnCr2O4

The standard free energies of formation of zinc aluminate and chromite were determined by measuring the oxygen potential over a solid CuZn alloy, containing 10 at.−% Zn, in equilibrium with ZnO, ZnAl2O4+Al2O3(χ) and ZnCr2O4+Cr2O3, in the temperature range 700–900°C. The oxygen potential was monitored by means of a solid oxide galvanic cell in which a Y2O3 ThO2 pellet was sandwiched between a CaOZrO2 crucible and tube. The temperature dependence of the free energies of formation of the interoxidic compounds can be represented by the equations, The heat of formation of the spinels calculated from the measurements by the “Second Law method” is found to be in good agreement with calorimetrically determined values. Using an empirical correlation for the entropy of formation of cubic spinel phases from oxides with rock-salt and corundum structures and the measured high temperature cation distribution in ZnAl2O4, the entropy of transformation of ZnO from wurtzite to rock-salt structure is evaluated.

Potentiometric determination of the Gibbs free energy of formation of cadmium and magnesium chromites

The standard Gibbs free energy of formation of magnesium and cadmiumchromites have been determined by potentiometric measurements on reversiblesolid-state electrochemical cells [dformula (Au-5%Cd, , Au-5%Cd; Pt, + , CaO-ZrO[sub 2], + ,Pt; CdO, , CdCr[sub 2]O[sub 4] + Cr[sub 2]O[sub 3])] in the temperature range 500°–730°C, and [dformula Pt, Cr + Cr[sub 2]O[sub 3]/Y[sub 2]O[sub 3]-ThO[sub 2]/Cr + MgCr[sub 2]O[sub 4] + MgO, Pt] in the temperature range 800°–1200°C. The temperature dependence of the freeenergies of formation of the ternary compounds can be represented by theequations [dformula CdO(r.s.) + Cr[sub 2]O[sub 3](cor) --> CdCr[sub 2]O[sub 4](sp)] [dformula Delta G[sup 0] = - 42,260 + 7.53T ([plus-minus]400) J] and [dformula MgO(r.s.) + Cr[sub 2]O[sub 3](cor) --> MgCr[sub 2]O[sub 4](sp)] [dformula Delta G[sup 0] = - 45,200 + 5.36T ([plus-minus]400) J] The entropies of formation of these spinels are discussed in terms of cationdisorder and extent of reduction of Cr3+ ions to Cr2+ ions. Thermodynamicdata on the chromates of cadmium and magnesium are derived by combiningthe results obtained in this study with information available in the literatureon high temperature, high pressure phase equilibria in the systems CdO-Cr2O3-O2 and MgO-Cr2O3-O2.

Gibbs free energy of formation of magnesium stannate

he thermodynamic properties of the spinel Mg2SnO4 have been determined by emf measurements on the solid oxide galvanic cell,View the MathML source in the temperature range 600 to 1000°C. The Gibbs' free energy of formation of Mg2SnO4 from the component oxides can be expressed as View the MathML source,View the MathML source These values are in good agreement with the information obtained by Jackson et al. [Earth Planet. Sci. Lett.24, 203 (1974)] on the high pressure decomposition of magnesium stannate into component oxides at different temperatures. The thermodynamic data suggest that the spinel phase is entropy stabilized, and would be unstable below 207 (±25)°C at atmospheric pressure. Based on the information obtained in this study and trends in the stability of aluminate and chromite spinels, it can be deduced that the stannates of nickel and copper(II) are unstable.

Gibbs free energies of formation of indium (III) oxide and sulphate

Emf measurements on the galvanic cell Pt, Ta, In + In,O, / Tho,-Y,03 / Cu + C+O, Pt were used to obtain the standard free energy of formation of 1%03fr om 600 to 900°C. Differential thermal analysis was used to detect the decomposition of In2(S0,), under controlled SO2 + O2 + Ar mixtures in thqtemperature range 640-8wC. X-ray diffraction analysis indicated that the decomposition product was 1%03 without an oxywlphate intermediate. The following equations were obtained for the variation of the standard free-energy change(Jlmole) with temperature:

Gibbs energy of formation of lead zirconate

The Gibbs energy of formation of zirconia-saturated lead zirconate was determined by emf measurements on the solid state cells and at 800 to 1400 K. The results obtained differ significantly from those reported in the literature based on vapor-pressure measurements, using Knudsen effusion and transportation techniques and assuming that the vapor phase consisted entirely of monomeric PbO molecules. A reanalysis of the data obtained in the earlier vapor-pressure studies, using mass-spectrometric measurements on polymeric PbO species in the gas phase, gives Gibbs energies of formation of lead zirconate which are in better agreement with those obtained in this study. Recent electrochemical measurements using CaO-ZrO2 and PbF2 solid electrolytes are in good agreement with the present study. The results obtained in this study are also consistent with the phase diagram which shows decomposition of the zirconate to tetragonal zirconia and a liquid phase rich in PbO at 1843 K.

Gibbs energy formation of lead titanate

The Gibbs energy of formation of titania-saturated lead titanate has been determined by e.m.f. measurements on the solid state cell;Pt,Ir,Pb + Pb1−xTiO3−x + TiO2(rutile)/CaO-ZrO2/Ni + NiO,Pt in the temperature range 1075–1350 K. The results obtained are significantly different from those reported in the literature based upon vapour pressure measurements, employing Knudsen effusion and transportation techniques, and assuming that the vapor phase consisted entirely of monomeric PbO molecules. A reanalysis of the data obtained in the earlier vapor pressure studies using mass spectrometric measurements on polymeric PbO species in the gas phase, gives Gibbs energies of formation of lead titanate which are in better agreement with those obtained in this study. Earlier electrochemical measurements by Mehrotra et al. and more recent electrochemical measurements by Schmahl et al. both employing CaO-ZrO2 solid electrolytes are in good agreement with the present study. The electro-chemical measurements by Schmahl et al. using PbF 2 solid electrolyte give a slightly more positive Gibbs energy of formation. There was no evidence supporting the formation of compounds other than Pb1−xTiO3−x from yellow PbO and rutile form of TiO2 in the temperature range covered in this study.Résumé L'enthalpie libre de formation du titanate de plomb saturé en oxyde de titane a été déterminée par des mesures de FEM de la pile: Pt,Ir,Pb + Pb1−xTiO3−x + TiO2(rutile)/CaO-ZrO2/Ni + NiO,Pt dans le domaine de températures 1075–1350 K. Les résultats obtenus, different appréciablement de ceux publiés, déterminés par mesures de tensions de vapeur (techniques de transport et d'effusion de Knudsen) en supposant que la phase gazeuse etait uniquement constituée de molécules monomériques de PbO. Une réanalyse des résultats de la littérature, à partir de mesures par spectrométrie de masse sur les polymères de PbO gazeux, donne des enthalpies libres de formation du titanate de plomb se rapprochant de celles obtenues dans cette étude. Les mesures de Mehrotra et al. et plus récemment de Schmahl et al. utilisant toutes deux l'électrolyte CaO-ZrO2 concordent bien avec celles de la présente étude. Les mesures de Schmahl et al., à l'aide de l' électrolyte solide PbF2, donnent une enthalpie de formation légèrement plus positive. Pour la gammede températures étudiée, rien ne permet de supposer que des composés autres que Pb1−x TiO3−x puissent se former à partir du PbO Gaune) et du rutile (TiO2).

Potentiometric determination of the Gibbs energies of formation of lead aluminates

The Gibbs energies of formation of three compounds in the PbO-Al2O3 system—2PbO · Al2O3, PbO · Al2O3, andPbO· 6Al2O3—have been determined from potentiometric measurements on reversible solid-state galvanic cells [dformula Pt, Ir | Pb, alpha-Al[sub 2]O[sub 3], PbO [center-dot] 6Al[sub 2]O[sub 3] | ZrO[sub 2]-CaO | NiO, Ni | Pt] [dformula Pt | NiO, Ni | ZrO[sub 2]-CaO | Pb, PbO [center-dot] 6Al[sub 2]O[sub 3], PbO [center-dot] Al[sub 2]O[sub 3] | Ir, Pt] and [dformula Pt | NiO, Ni | ZrO[sub 2]-CaO | Pb, PbO [center-dot] Al[sub 2]O[sub 3], 2PbO [center-dot] Al[sub 2]O[sub 3] | Ir, Pt] in the temperature range 850–1375 K. The results are discussed in the light of reported phase diagrams for the PbO-Al2O3system. The partial pressures of different lead oxide species, PbnOn, n = 1–6, in the gas phase in equilibrium withthe aluminates are calculated by combining the results of this study with the mass-spectrometric data of Drowart et al.(1) for polymerization equilibria in the gas phase. The concentration of oxygen in lead in equilibrium with the aluminatesare also derived from the results and the literature data on the Gibbs energy of solution of oxygen in liquid lead.

Gibbs energy of formation of nickel orthosilicate (Ni2SiO4)

Two solid state galvanic cells:Pt, Ni + Ni2Si04 + Si02/(Y203)Zr02/Ni + + NiO, Pt (1) and Pt, Ni + NizSiOj + Si02/CaF2/Ni + + NiO, Pt (11) have been employed for the determination of the Gibbs' energy of formation of nickel orthosilicate(Ni2Si04) from nickel oxide and quartz. The emf of cell (I) was reversible and reproducible in the temperature range 925 to 1375K whereas emf of cell (11) drifted with time and changed polarity. From the results of cell (I), the Gibbs' energy of formation of nickel silicate is obtained as,2Ni0 (r.s.) + Si02 (quartz) + Ni2Si04 (olivine)Gibbs' energy of formation of the spinel form of Ni2Si04 is obtained by combining the data for olivine obtained in this study with high pressure data on olivine to spinel transition reported in the literature. The complex time dependence of the emf of cell (11) can be rationalised on the basis of formation of calcium silicates from calcium oxide, generally present as an impurity in the calcium fluoride electrolyte, and silica. The emf of cell (11) is shown to be the function of the activity of calcium oxide at the electrolyte/ electrode interface. The results provide strong evidence against the recent suggestion of mixed anionic conduction in calcium fluoride.

Measurement of Gibbs energies of formation of CoF2 and MnF2 using a new composite dispersed solid electrolyte

Gibbs energies of formation of CoF2 and MnF2 have been measured in the temperature range from 700 to 1100 K using Al2O3-dispersed CaF2 solid electrolyte and Ni+NiF2 as the reference electrode. The dispersed solid electrolyte has higher conductivity than pure CaF2 thus permitting accurate measurements at lower temperatures. However, to prevent reaction between Al2O3 in the solid electrolyte and NiF2 (or CoF2) at the electrode, the dispersed solid electrolyte was coated with pure CaF2, thus creating a composite structure. The free energies of formation of CoF2 and MnF2 are (± 1700) J mol−1; {fx37-1} The third law analysis gives the enthalpy of formation of solid CoF2 as ΔH° (298·15 K) = −672·69 (± 0·1) kJ mol−1, which compares with a value of −671·5 (± 4) kJ mol−1 given in Janaf tables. For solid MnF2, ΔH°(298·15 K) = − 854·97 (± 0·13) kJ mol−1, which is significantly different from a value of −803·3 kJ mol−1 given in the compilation by Barinet al.

Gibbs energies of formation of intermetallic phases in the systems Pt Mg, Pt Ca and Pt Ba and some applications

The standard Gibbs energies of formation of platinum-rich intermetallic compounds in the systems Pt-Mg, Pt-Ca, and Pt-Ba have been measured in the temperature range of 950 to 1200 K using solid-state galvanic cells based on MgF2, CaF2, and BaF2 as solid electrolytes. The results are summarized by the following equations: ΔG° (MgPt7) = −256,100 + 16.5T (±2000) J/mol ΔG° (MgPt3) = −217,400 + 10.7T (±2000) J/mol ΔG° (CaPt5) = −297,500 + 13.0T (±5000) J/mol ΔG° (Ca2Pt7) = −551,800 + 22.3T (±5000) J/mol ΔG° (CaPt2) = −245,400 + 9.3T (±5000) J/mol ΔG° (BaPt5) = −238,700 + 8.1T (±4000) J/mol ΔG° (BaPt2) = −197,300 + 4.0T (±4000) J/mol where solid platinum and liquid alkaline earth metals are selected as the standard states. The relatively large error estimates reflect the uncertainties in the auxiliary thermodynamic data used in the calculation. Because of the strong interaction between platinum and alkaline earth metals, it is possible to reduce oxides of Group ILA metals by hydrogen at high temperature in the presence of platinum. The alkaline earth metals can be recovered from the resulting intermetallic compounds by distillation, regenerating platinum for recycling. The platinum-slag-gas equilibration technique for the study of the activities of FeO, MnO, or Cr2O3 in slags containing MgO, CaO, or BaO is feasible provided oxygen partial pressure in the gas is maintained above that corresponding to the coexistence of Fe and “FeO.”

Gibbs energies of formation of rare earth MPt5 compounds

The Gibbs energies of formation of MPt5 (MNd, Dy, Ho, Er) intermetallic compounds were determined in the temperature range 900–1100 K using the solid state cell Ta,M+MF3¦CaF2¦MPt5+Pt+MF3,Ta For M ≡ Sm, a mixture of Gd + GdF3 was used as the reference electrode. In the case of Eu, a mixture of Eu + EuF2 served as the reference electrode. The trifluorides of Sm and Eu are not stable in equilibrium with the metal. The fluoride phase coexisting with a SmPt5 + Pt mixture is SmF3, whereas EuF2 is the equilibrium phase in contact with EuPt5 + Pt. All the MPt5 compounds studied (except EuPt5) exhibit similar stability. Europium is divalent in the pure metal and trivalent in EuPt5. The energy required for the promotion of divalent Eu to the trivalent state accounts for the less negative Gibbs energy of formation of EuPt5. The enthalpies of formation of all the MPt5 compounds obtained in this study are in good agreement with Miedema's model.