Thermodynamic consistency of the interaction parameter formalism

The apparent contradiction between the exact nature of the interaction parameter formalism as presented by Lupis and Elliott and the inconsistencies discussed recently by Pelton and Bale arise from the truncation of the Maclaurin series in the latter treatment. The truncation removes the exactness of the expression for the logarithm of the activity coefficient of a solute in a multi-component system. The integrals are therefore path dependent. Formulae for integration along paths of constant Xi,or X i/Xj are presented. The expression for In γsolvent given by Pelton and Bale is valid only in the limit that the mole fraction of solvent tends to one. The truncation also destroys the general relations between interaction parameters derived by Lupis and Elliott. For each specific choice of parameters special relationships are obtained between interaction parameters.

Thermodynamic measurements of b.c.c. Cr-Mn solid solutions at 1373 K

Thermodynamics of Cr-Mn alloys have been studied by Eremenko et al (l) using a fused salt e.m.f.technique. Their results indicate positive deviations from ideality at 1023 K. Kaufman (2) has independently estimated negative enthaipy and excess entropy for the b.c.c. Cr-Mn alloys, such that at high temperatures, the entropy term predominates over the enthalpy term giving positive deviations from ideality. Recently the thermodynamic properties of the alloys have been measured by 3acob (3) using a Knudsen cell technique in the temperature range of 1200 to 1500 K. The results indicate mild negative deviations from ideality over the entire composition range. Because of the differences in the reported results and Mn being a volatile component in the alloys which leads to surface depletion under a dynamic set up, an isopiestic technique is used to measure the properties of the alloys.

Representation of Thermodynamic Properties of Dilute Multi-Component Solutions--Options and Constraints

The different formalisms for the representation of thermodynamic data on dilute multicomponent solutions are critically reviewed. The thermodynamic consistency of the formalisms are examined and the interrelations between them are highlighted. The options are constraints in the use of the interaction parameter and Darken's quadratic formalisms for multicomponent solutions are discussed in the light of the available experimental data. Truncatred Maclaurin series expansion is thermodynamically inconsistent unless special relations between interaction parameters are invoked. However, the lack of strict mathematical consistency does not affect the practical use of the formalism. Expressions for excess partial properties can be integrated along defined composition paths without significant loss of accuracy. Although thermodynamically consistent, the applicability of Darken's quadratic formalism to strongly interacting systems remains to be established by experiment.

Thermodynamic partial properties of Na2O in Nasicon solid solution, Na1+xZr2SixP3-xO12

The thermodynamic activity of sodium oxide (Na2O) in the Nasicon solid solution series, Na1+xZr2SixO12, has been measured in the temperature range 700�1100 K using solid state galvanic cells: Pt|CO2 + O2|Na2CO3?Na1+xZr2SixP3-xO12?(Y2O3)ZrO2?In + In2O3|Ta, Pt for 1 = ? = 2.5, and Pt?CO2 + O2?Na2CO3?ß-alumina?Na1+xZr2SixP3-xO12?Ar + O2?Pt for x = 0, 0.5, 2.5, and 3. The former cell, where the Nasicon solid solution is used as an electrolyte along with yttria-stabilized zirconia, is well suited for Nasicon compositions with high ionic conductivity. In the latter cell, ß-alumina is used as an electrolyte and the Nasicon solid solution forms an electrode. The chemical potential of Na2O is found to increase monotonically with x at constant temperature. The partial entropy of Na2O decreases continuously with x. However, the partial enthalpy exhibits a maximum at x = 2. This suggests that the binding energy is minimum at the composition where ionic conductivity and cell volume have maximum values.

Thermodynamic Stability of Potassium-beta-Alumina

The activity of K sub 2 O in a mixture of alpha -alumina and potassium beta -alumina has been determined using a solid state galvanic cell in the temperature range 600-1000K. The cell is written such that the right hand electrode is positive. The solid electrolyte consisted of a dispersion of alpha -alumina ( approx 15 vol.%) in a matrix of K beta -alumina. The emf of the cell was found to be reversible and to vary linearly with temperature. From the emf and auxiliary data on In sub 2 O sub 3 and K sub 2 O from the literature, the activity of K sub 2 O in the two-phase mixture is obtained. The standard free energy of formation of K beta -alumina from component oxides is given. Graphs.

Thermodynamic properties of RhO2

A solid-state electrochemical cell, with yttria-stabilized zirconia as the electrolyte and pure O-2 gas at 0.1 MPa as the reference electrode, has been used to measure the oxygen chemical potential corresponding to the equilibrium between beta-Rh2O3 and RhO2 in the temperature range from 850 to 1050K. Using standard Gibbs energy of formation of beta-Rh2O3 available in the literature and the measured oxygen potential, the standard Gibbs free energy of formation of RhO2 is derived as a function of temperature: Delta G(f)degrees(RhO2)(+/- 71)/J mol(-1) = 238,418 + 179.89T Using an estimated value of Delta C-p degrees; for the formation reaction of RhO2 from its elements, the standard enthalpy of formation, standard entropy and isobaric heat capacity of RhO2 at 298.15 K are evaluated: Delta H-f degrees (298.15 K)(+/- 164)/kJ mol(-1) = -244.94, S degrees (298.15 K)(+/- 3.00)/J mol(-1) K-1 = 45.11 and C-p degrees(298.15 K)(+/- 2.6)1mol(-1) K-1 =64.28. (C) 2010 Elsevier B.V. All rights reserved.

Thermodynamic properties of the system toluene — 1, 1, 1-trichloroethane

Data on molar excess enthalpy on mixing at 298.15 K and 308.15 K, vapor-liquid equilibrium, latent heats of vaporization at 91.444 kPa and vapor pressures for the system toluene – 1, 1, 1-trichloroethane are presented. A simple adiabatic calorimeter designed for molar excess enthalpy measurements is described, tested and used. On présente, dans le cas du système toluène – 1, 1, 1-trichloréthane, des résultats relatifs aux grandeurs suivantes: a) enthalpie molaire d'excès à 298.15 K et 308.15 K; b) équilibre liquid-vapeur; c) chaleurs latentes de vaporisation à une pression absolue de 91.444 kP; d) pressions de vapeur. On décrit un calorimètre adiabatique simple, conçu pour mesurer l'enthalpie molaire d'excès, dont on a fait l'essai.

Thermodynamic properties of the systems benzene-chloroethanes

This paper presents the experimental data on vapor-liquid equilibrium and heats of mixing of mixtures of benzene with 1, e-dichloroethane, 1, l, 1 -trichloroethane, and lt1,2,2-tetrachloroethane.A literature survey revealed that the heats of mixing of benzene-l,2-dichloroethane have been studied and Table I shows the extent of study on this system.

Thermodynamic Properties of Niobium Oxides

Thermodynamic properties of three oxides of niobium have been measured using solid state electrochemical cells incorporating yttria-doped thoria (YDT) as the electrolyte in the temperature range T = (1000 to 1300) K. The standard Gibbs energies of formation of NbO, NbO2, and NbO2.422 from the elements can be expressed as: Delta(f)G(NbO)(o) +/- 547/J . mol(-1) = -414 986 + 86.861(T/K) Delta(f)G(NbO2)(o) +/- 548/J . mol(-1) = -779 864 + 164.438(T/K) Delta(f)G(NbO2.422)(o) +/- 775/J . mol(-1) = -911 045 + 197.932(T/K) The results are discussed in comparison with thermodynamic data reported in the literature. The new results refine data for NbO and NbO2 presented in standard data compilations. There are no data in thermodynamic compilations for NbO2.422 (Nb12O29). In the absence of the heat capacity and enthalpy of formation measurements, only the Gibbs energy of formation of NbO2.422 can be assessed. The free energy of formation of stoichiometric Nb2O5 is evaluated on the basis of measurements on NbO2.422 and information available in the literature on phase boundary compositions and isothermal variation of nonstoichiometric parameter with oxygen potential for Nb2O5-x. The results suggest a minor revision of data for Nb2O5. A minimum in the Gibbs energy of mixing for the system Nb-O occurs in the nonstoichiometric domain of Nb2O5-x with x = 0.036.

Thermodynamic properties of strontium titanates Sr2TiO4, Sr3Ti2O7, Sr4Ti3O10, and SrTiO3

The chemical potentials of SrO in two-phase fields (TiO2 + SrTiO3) (SrTiO3 + Sr4Ti3O10) (Sr4Ti3O10 + Sr3Ti2O7) and (Sr3Ti2O7 + Sr2TiO4) of the pseudo-binary system (SrO + TiO2) have been measured in the temperature range (900 to 1250) K relative to pure SrO as the reference state using solid-state galvanic cells incorporating single crystal SrF2 as the electrolyte The cells were operated under pure oxygen at ambient pressure The standard Gibbs free energies of formation of strontium titanates SrTiO3 Sr4Ti3O10 Sr3Ti2O7 and Sr2TiO4 from their component binary oxides were derived from the reversible electromotive force (EMF) of the cells For the formation of the four compounds from their component oxides TiO2 with rutile structure and SrO the standard Gibbs free energy changes are given by Delta G((ox))(SrTiO3) +/- 89/(J mol(-1)) = -121878 + 3 881(T/K) Delta G((ox))(Sr4Ti3O10) +/- 284/(J mol(-1)) = -409197 + 14 749(T/K) Delta G((ox))(Sr3Ti2O7) +/- 190/(J mol(-1)) = -285827 + 10 022(T/K) Delta G((ox))(Sr2TiO4) +/- 110/(J mol(-1))= -159385 + 3 770(T/K) The reference state for solid TiO2 is the rutile form The results of this study are in good agreement with Gibbs free energy of formation data reported in the literature for SrTiO3 but differ significantly with data for Sr4Ti3O10 For Si3Ti2O7 and Si2TiO4 experimental measurements are not available in the literature for direct comparison with the results obtained in this study (C) 2010 Elsevier Ltd All rights reserved

Phase relationships in the system Ni-W-O and thermodynamic properties of NiWO,

The phase diagram of the Ni-W-O system at 1200 K was established by metallographic and X-ray identification of the phases present after equilibration at controlled oxygen potentials. The oxygen partial pressures over the samples were fixed by metered streams of CO+CO2 gas mixtures. There was only one ternary oxide, nickel tungstate (NiWO4), in the Ni-W-O system at a total pressure of 1 atm, and this compound decomposed to a mixture of Ni+WO2.72 on lowering the oxygen potential. The Gibbs' free energy of formation of NiWO4 was determined from the measurement of the e.m.f. of the solid oxide galvanic cell, Pt, Ni+NiWO4+WO2.72/CaO-ZrO2/Ni+NiO, Pt and thermodynamic properties of tungsten and nickel oxides available in the literature. For the reaction, NiO(s)+WO3(s)rarrNiWO4(s) DeltaG°=–10500–0.708 T (±250) cal mol–1.

A Thermodynamic Proposal for the Exposition of Critically and other Subtle Features in Self-Deflagrating Ammonium Perchlorate Systems

A first comprehensive investigation on the deflagration of ammonium perchlorate (AP) in the subcritical regime, below the low pressure deflagration limit (LPL, 2.03 MPa) christened as regime I$^{\prime}$, is discussed by using an elegant thermodynamic approach. In this regime, deflagration was effected by augmenting the initial temperature (T$_{0}$) of the AP strand and by adding fuels like aliphatic dicarboxylic acids or polymers like carboxy terminated polybutadiene (CTPB). From this thermodynamic model, considering the dependence of burning rate ($\dot{r}$) on pressure (P) and T$_{0}$, the true condensed (E$_{\text{s,c}}$) and gas phase (E$_{\text{s,g}}$) activation energies, just below and above the surface respectively, have been obtained and the data clearly distinguishes the deflagration mechanisms in regime I$^{\prime}$ and I (2.03-6.08 MPa). Substantial reduction in the E$_{\text{s,c}}$ of regime I$^{\prime}$, compared to that of regime I, is attributed to HClO$_{4}$ catalysed decomposition of AP. HClO$_{4}$ formation, which occurs only in regime I$^{\prime}$, promotes dent formation on the surface as revealed by the reflectance photomicrographs, in contrast to the smooth surface in regime I. The HClO$_{4}$ vapours, in regime I$^{\prime}$, also catalyse the gas phase reactions and thus bring down the E$_{\text{s,g}}$ too. The excess heat transferred on to the surface from the gas phase is used to melt AP and hence E$_{\text{s,c}}$, in regime I, corresponds to the melt AP decomposition. It is consistent with the similar variation observed for both the melt layer thickness and $\dot{r}$ as a function of P. Thermochemical calculations of the surface heat release support the thermodynamic model and reveal that the AP sublimation reduces the required critical exothermicity of 1108.8 kJ kg$^{-1}$ at the surface. It accounts for the AP not sustaining combustion in the subcritical regime I$^{\prime}$. Further support for the model comes from the temperature-time profiles of the combustion train of AP. The gas and condensed phase enthalpies, derived from the profile, give excellent agreement with those computed thermochemically. The $\sigma _{\text{p}}$ expressions derived from this model establish the mechanistic distinction of regime I$^{\prime}$ and I and thus lend support to the thermodynamic model. On comparing the deflagration of strand against powder AP, the proposed thermodynamic model correctly predicts that the total enthalpy of the condensed and gas phases remains unaltered. However, 16% of AP particles undergo buoyant lifting into the gas phase in the `free board region' (FBR) and this renders the demarcation of the true surface difficult. It is found that T$_{\text{s}}$ lies in the FBR and due to this, in regime I$^{\prime}$, the E$_{\text{s,c}}$ of powder AP matches with the E$_{\text{s,g}}$ of the pellet. The model was extended to AP/dicarboxylic acids and AP/CTPB mixture. The condensed ($\Delta $H$_{1}$) and gas phase ($\Delta $H$_{2}$) enthalpies were obtained from the temperature profile analyses which fit well with those computed thermochemically. The $\Delta $H$_{1}$ of the AP/succinic acid mixture was found just at the threshold of sustaining combustion. Indeed the lower homologue malonic acid, as predicted, does not sustain combustion. In vaporizable fuels like sebacic acid the E$_{\text{s,c}}$ in regime I$^{\prime}$, understandably, conforms to the AP decomposition. However, the E$_{\text{s,c}}$ in AP/CTPB system corresponds to the softening of the polymer which covers AP particles to promote extensive condensed phase reactions. The proposed thermodynamic model also satisfactorily explains certain unique features like intermittent, plateau and flameless combustion in AP/ polymeric fuel systems.

A thermodynamic protocol for explaining subcriticality and other subtle features in self-deflagrating solids

A novel universal approach to understand the self-deflagration in solids has been attempted by using basic thermodynamic equation of partial differentiation, where burning mte depends on the initial temperature and pressure of the system. Self-deflagrating solids are rare and are reported only in few compounds like ammonium perchlorate (AP), polystyrene peroxide and tetrazole. This approach has led us to understand the unique characteristics of AP, viz. the existence of low pressure deflagration limit (LPL 20 atm), hitherto not understood sufficiently. This analysis infers that the overall surface activation energy comprises of two components governed by the condensed phase and gas phase processes. The most attractive feature of the model is the identification of a new subcritical regime I' below LPL where AP does not burn. The model is aptly supported by the thermochemical computations and temperature-profile analyses of the combustion train. The thermodynamic model is further corroborated from the kinetic analysis of the high pressure (1-30 atm) DTA thermograms which affords distinct empirical decomposition rate laws in regimes I' and 1 (20-60 atm). Using Fourier-Kirchoff one dimensional heat transfer differential equation, the phase transition thickness and the melt-layer thickness have been computed which conform to the experimental data.