16 FREILING, CROCKER, AND ADAMS A sudden change in distribution type due to solidification therefore appears unlikely. What appears morelikely is that under different conditions the mass-transfer reactions are controlled by resistance in either vapor, surface, or condensed phases. Thus, in the first stage of condensation, fission-product diffusion through the vapor phase and condensation on the surface may be negligibly fast, and diffusion through the particle would be the rate-controlling step, At lower temperatures the diffusion through the particle may be negligibly slow, not so much because of solidification as because of the small diffusion coefficients existing at low temperatures. Vapor diffusion and surface deposition may then be the only processes requiring consideration. The transition point (or region) in such an instance would be different for every fission-product species. The transition points would occur more abruptly, the faster the cooling rate. Equilibrium distributions and sharp transition points are therefore mutually contradictory simplifications. Sharp transitions would favor mass-transfer resistance at the surface, Diffusion in the Vapor Phase Diffusion is usually treated by means of Fick’s first law, according to which the net number of molecules of type 1 crossing a unit surface in unit time is given by a vector equation that we will write in the form Jy =—Dy. V fyny where Dj, is the interdiffusion coefficient for type 1 molecules in gas molecules of type 2, n, is the number of type 1 molecules per unit vol- ume, and f, is the thermodynamic activity coefficient. Fick’s second law ony +V° Ji = 0 ot supplies the material-balance requirement. The activity coefficients are usually taken as unity. The interdiffusion coefficient D,. can be estimated from the Stefan— Maxwell equation D.. = 1" 1 moja(ny + ng) 2kT \” my where o,, = the mean collision diameter ['/ (0, + 0,)] yu. = the reduced molecular mass [m,m,/(m, + m,)] k = Boltzmann’s constant T = absolute temperature From the equation it is seen that D,, is proportional to T?, inversely proportional to the pressure, and independent of composition. By way of orientation, in air at 1 atm pressure and 0°C, Dj,is 0.611 cm?/sec