Models oxygen potential

Vapor pressures and vapor compositions in equilibrium with a hypostoichiometric plutonium dioxide condensed phase have been calculated for the temperature range 1500 I H 4000 K. Thermodynamic functions for the condensed phase and for each of the gaseous species were combined with an oxygen-potential model, which we extended from the solid into the liquid region to obtain the partial pressures of O2, 0, Pu, PuO and Pu02 as functions of temperature and of condensed phase composition. The calculated oxygen pressures increase rapidly as stoichiometry is approached. At least part of this increase is a consequence of the exclusion of Pu +... 

The process we have followed Is Identical with the one we used previously for the uranium/oxygen (U/0) system (1-2) and Is summarized by the procedure that Is shown In Figure 1. Thermodynamic functions for the gas-phase molecules were obtained previously (3) from experimental spectroscopic data and estimates of molecular parameters. The functions for the condensed phase have been calculated from an assessment of the available data, Including the heat capacity as a function of temperature (4). The oxygen potential Is found from extension Into the liquid phase of a model that was derived for the solid phase. Thus, we have all the Information needed to apply the procedure outlined In Figure 1. 

In the oxygen-potential model that was used for the U/0 system (l -2), two equilibria for the solid were considered. One of these equilibria is analogous to Eq. (11) and the other involved the U6+ ion. We are unaware of evidence for the existence of the Pu6+ ion in the oxide system. No PUO3 molecule was identified in the matrix-isolation studies (29) although, with similar experimental methods, the UO3 molecule was easily observed (30). 

Oxygen Potential for Liquid PuO . To extend the oxygen-potential model from the solid to the liquid phase, we assume that Eqs. (11— 14) apply to the liquid with new values of the model parameters. 

The solidus, the liquidus, the oxygen-potential model for the solid Pu/0 system, and the oxygen-potential model for the liquid Pu/0 system each depend upon the temperature and composition. Because the oxygen-potential model has a greater effect on the vapor pressure and composition at high temperature than do the solidus and liquidus, we have fixed the functional forms and the parameter values for the oxygen-potential model. We choose the IAEA solidus (32) and determine the liquidus that is consistent with it and with the two parts of the oxygen-potential model. The calculated liquidus, which is based on the liquid model parameters, is very close to the IAEA liquidus (33). 

The liquidus, which is consistent with Eq. (21) and the two parts of the oxygen-potential model, may be represented by the following equation for 2416 < T < 2701 K ... 

The evaluation of the Integral In Eq. (23) differs from the corresponding Integral for the U/0 system because of the differences In the oxygen-potential models. In particular, the neglect of Pu6"1", but not U +, leads to the problem that In p((>2) for the Pu/O system becomes Infinite as x goes to zero. However, the Integral In Eq. (23) remains finite and has been evaluated (21). 

With the currently available information, the largest uncertainty is in the oxygen-potential model and the parameter values within the model. A recent assessment of the Pu/0 system (42) has indicated that the values of the parameters used in the Blackburn model yield slightly smaller oxygen potentials than those of Alexander (22), those of Tetenbaum (22-42) and those extrapolated from the data of Woodley (43). A reevaluation of the model parameters would allow a better fit to these experimental data ... 

P. E. Blackburn, M. Tetenbaum, and M.-L. Saboungi. Valuable comments on the oxygen potential model by Dr. R. E. Woodley are also gratefully acknowledged. 

The Anderson—Hyde dislocation model differs from the earher model based on the cooperative diffusion mechanism described by Andersson and Wadsley (1966), in which CS planes, e.g. in rutile, were diought to be produced by cation migration during reduction.The reduced oxygen potential at die surface means an enhanced Ti-potential and dierefore die Ti ions diffuse cooperatively into the crystal down diis Ti-potential gradient. However, diere is no experimental evidence to support this hypodiesis. This mechanism is also less hkely since diis would involve a large number of cations. 

Both L coefficients and / factors can, in principle, be calculated from microscopic models. For the evaluation of L,j, the random-alloy model [J. R. Manning (1968) A. R. Allnatt, A. B. Lidiard (1987)] is sometimes used. For the evaluation of thermodynamic factors, one takes advantage of the empirical rule that in extended solid solutions AO-BO, the cation vacancy concentration and the oxygen potential are related to each other as... 

Let us present D explicitly for the condition d//0 = 0, omitting all details of the lengthy derivation. By application of Manning s random-alloy model [A. R. Allnatt, A.B. Lidiard (1987)], and by inserting Eqns. (5.126) and (5.131) into Eqn. (5.132), for a constant oxygen potential across the diffusion zone, a Darken type equation is obtained... 

Yakabe, H., Hishinuma, M. and Yasuda, I., Static and transient model analysis on expansion behavior of LaCiO under an oxygen potential gradient, Journal of The Electrochemical Society 147, 2000, 4071. 

Table III are similar to their counterparts in the U/0 system ( ) Ionization was shown to be of minor importance for the U/0 system in the temperature and composition ranges of interest. Furthermore, the results obtained from the oxygen-potential model alone indicate that the vapor composition for the Pu/O system will be as oxygen-rich or more oxygen-rich than that for the U/0 system. A very oxygen-rich equilibrium vapor gives less ionization because of the relatively high ionization potentials of 0 and 02 Thus, we conclude that ionization may be neglected for the temperature and composition ranges of interest and have not included ionization effects in our calculations.

It is possible to interpret the potential equation in model wine solution experimentally by studying the impact of factors such as temperature (potential decreases as temperature increases, AFh = -f-40 mV per 20°C), oxygen (potential increases with the quantity of dissolved oxygen, AFh = 250 mV per 6 mg/1), and, to a lesser extent, pH (variations are very small in the pH range of wine). 

Ligno-cellulosic biomass is a resource from which liquid hydrocarbon fuels potentially may be derived. Pyrolyzing the wood yields gas and liquid products, but a relatively large percentage of the original wood carbon can be lost to a low value char by-product. Furthermore, like the model oxygenates described above, the EHI of the pyrolysis liquid products is substantially less than 1. 

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