Experimental data of powder reaction rate can be expressed in terms of the generalized scale of the diffusivity taken as an index of the reactivity from the analytical use of the concentric spherical model and the unreacted core model offered recently. The kinetic equations derived from these models are modified to both the simple form for the rapid analysis and the precise form for the samples with wide size distributions. Powder reactivity can never be assessed by the conventional kinetic theory commonly used for the powder reaction. In order to investigate the nature of diffusivity, thermal behaviors of the proton in diamond lattice are simulated on the basis of the direct molecular orbital dynamics theory.