On the mass rate of reactions in solids

In a previous paper, Hume and Colvin showed that the mass rate of decomposition occurring in crystalline particles was a function of three quantities, namely, the rate of nucleation, the rate of linear propagation and the size and shape of the particle. For a study of the energetics of the reaction, the second of these quantities is of primary importance, so that special attention was directed to the derivation of this quantity, under such conditions that a knowledge of the nucleation rate was unnecessary. In the case of the dehydration of certain salt hydrates invacuo , the rate of nucleation is so large that the entire surface of all the crystals is rapidly covered and the subsequent mass rate can be predicted from simple geometrical considerations. On the other hand, if the rate of nucleation is not so large that this simplification can be made, then the whole course of the reaction will be determined by the progressive formation of nuclei as the reaction proceeds. In many cases it is possible by visual observation to obtain qualitative information as to the manner of nucleation. For example, it might be found that decomposition proceeded from points on the surface or at the corners or edges of the crystals. The question can be treated generally if it is assumed that in a mass of crystalline particles the total number of points capable of becoming nucleation centres isn 0 and that each of these points has the same probability of becoming active. At timet , let there ben t points still unaffected. Then the number of nuclei formed during the time intervaldt is given by —dn t —kn t .dt , wherek is a constant. Hencen t =n 0 e -kt . and the number of points where nucleation has occurred isn 0 (1-e -kt . If the reaction spreads with a constant velocityu from the nuclei which are formed, the rate of the mass reaction will be given bydm /dt =n 0 .f (k, t, u ).