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The collaboration between the states and the DOE's Energy Storage Research Program is proving to be an outstanding success. The selected projects show a good portfolio of advanced energy storage media: a ZnBr flow battery, the NaS battery, supercapacitors, and flywheels. The applications are equally varied: mitigation of substation congestion, grid frequency control, load management, and stabilization of a microgrid. The goal of these partnerships with the states is to demonstrate electric energy storage as a technically viable, cost-effective, and broadly applicable option for increasing the reliability of the electricity system and for electric energy management.

The present investigation utilizes a torsion-effusion method for measuring thermodynamic activity which differs from other torsion-effusion methods reported in the literature. Specifically, our attention is given to the concentration gradient of the solute which develops during the course of an experimental run. These concentration differences may be accounted for by solving the partial differential equation defining Fick's second law with known boundary conditions. With this approach, the concentration of solute at the bulk-gas interface can be determined and utilized in subsequent calculations rather than the bulk average concentration. Ignoring this concentration gradient may result in erroneous thermodynamic values. Measurements of the partial pressure of the volatile solute, Zn, in dilute ZnSn alloys, i.e. less than 5 at. %Zn, as a function of time were obtained at 772°K. On the basis of these data and the calculated concentration distribution of Zn during effusion utilizing the known diffusion coefficient of Zn as reported by Ma and Swalin, the activity coefficient and the Wagner self-interaction parameter of Zn are determined. Experimental values of γzn at dilute solution correlate well with those reported in the literature at higher Zn concentration. It was found that within the scatter of the experimental data, In γzn increases with decreasing Zn concentration. The intercept of the plot at pure Sn yields the limiting value of the activity coefficient of Zn, γzn0 = 2.20 ± 0.10 while the slope yields the Wagner self-interaction parameter of eznZn = −2.4 ± 1.0. Comparison with eznZn = −1.6 as predicted by the randomsolution model shows reasonable agreement. Since the ZnSn solutions do not deviate strongly from ideal behavior, the predicted value of eznZn = −1.8 determined by the first approximation of the quasichemical approach differs little from that predicted by the random-solution model. It is also shown in the Appendix that an approximate value of D for effusing component may be obtained using the present approach when such data are unknown.

Orr's treatment, which extends the thermodynamic model of Wagner and Schottky for CsCl-phases to large departure from stoichiometry, is presented. In this model, a composition-dependent disorder parameter z is obtained by minimizing the Gibbs free energy of the alloys. Since z is a complicated and implicit function of χ and α with χ being the difference between the concentration of the alloy and that of the stoichiometric alloy and α a basic parameter of the theoretical model, several approximations are introduced to describe the concentration dependence of z . For small values of α, the one-and-half approximation adequately describes the composition dependence of z even at relatively large departure from stoichiometry. Using this approximation, equations describing the activities and partial entropies of the component elements are derived. It is found that the activity data of Olander for β′-AuCd are in excellent agreement with theoretical values using α = 0.0026 and ln a Cd , o = −3.46. Moreover, partial entropies are found to be in good accord with the theoretical values calculated on the basis of α = 0.0026. For β'-AgMg, activity and partial entropy data of Trzebiatowski and Terpilowski also agree well with theoretical values utilizing α = 0.014 and ln a Mg , o = −5.14. It is also found that the α-function is not necessarily a suitable function for evaluating and assessing data of ordered intermetallic phases. Rather data of this kind should be evaluated and assessed in light of the theoretical model presented in this paper. The disorder parameter z is related to the long-range order parameter S which is then used to discuss the transition of the lattice from a substantially ordered state to a substantially disordered one at some critical concentration, χ c .

We present a new approach to the nonlinear equations for the phreatic surface of groundwater flow from or into a reservoir. The differential equation is converted into an equivalent integral equation, which is then solved by a method of iteration. We obtain exact results for both drawdown and infiltration, including the special case of groundwater penetration into dry soil.

We show that there exists a strong reciprocal relationship between the algebras associated with the wave equations of Bhabha and Nambu. The representations of the two groups obtained, O(6) and O(4, 2), respectively, are the simplest algebras which can describe supermultiplets of relativistic particles.