NUCLEAR-DEBRIS FORMATION 5 The first phase of this subprogram is virtually complete. We have available two models for prediction (a thermodynamic model anda radial-power-distribution model) and a means of modifying each semiempirically. The information flow in the system is shown schemati- cally in Fig. 2. Thermodynamic Equilibrium Model The thermodynamic equilibrium model developed by C. F, Miller has already been adequately described in detail in several publications®—’ and applied with some success to the case of reactor excursions by C. E, Miller, Jr.° Essentially it consists of distributing the available radionuclides in the nuclear cloud among the particles present according to the predicted equilibrium distribu- tion. The model takes 1400°C as the temperature below which particles are impenetrable to condensing nuclides. Unfortunately, adequate thermodynamic input data are not available to properly use and test the model in several critical cases (e.g., mass chains 89, 132, and 140 and their adjacent chains). Radial-power-distribution Model The radial-power-distribution model? is an amplification of suggestions by R. D, Cadle, R. C. Tompkins, and P. W. Krey, namely, that refractorily behaving nuclides distribute themselves among particles according to the available volume whereas volatilely behaving nuclides distribute themselves according to the available surface. By assuming that a collection of spherical particles exists and that all mass chains are distributed according to some power of the radius, one finds that the model predicts logarithmic correlations of radionuclide ratios for monodisperse samples. This is a happy result because radionuclide ratios observed in fractionated nuclear debris can be correlated logarithmically, at least as well as they can linearly, and the correlation parameters then become useful for model predictions. If one further assumesa particle distribution such that the mass is distributed lognormally with particle diameter with modal diameter x, and variance o’, one finds that all mass chains are distributed among the particles with variance o” and modal diameters given by x, exp [(b, ~1) 0°]. Here b, is a slope correlation parameter. This per- mits a great simplification in the calculations and makes hand calculation feasible, whereas, in the case of the thermodynamic equilibrium model, a computer is required. Although the thermodynamic equilibrium model is a more fundamental approach, the assumptions, simplifica- tions, and approximations involved in its use, together with the state of the available input data, make the two approaches, at least for the present, of competitive reliability. The radial-power model has a great advantage in being presently applicable to air-, tower-, and surface-burst predictions. The semiempirical aspect of the radial-power-distribution model consists of the way it utilizes empirical correlation parameters (ob-