By applying generalized two-dimensional (2D) correlation analysis as reported by Noda, we have systematically studied a kinetic model of parallel reactions. Given the related rate constants and absorption coefficients, the correlation between reactant and products are analyzed. The reactant–reactant, reactant–product, and product–product pairs are found to be synchronously correlated, and their intensities increase with increase of the rate constant and the absorption coefficient. On the other hand, only the reactant–product pairs show in the asynchronous spectra. Their intensities also depend proportionally on the rate constant and the absorption coefficient. The influence of signal-to-noise ratio (S/N) and overlapped spectra are further discussed. The resulting synchronous and asynchronous correlation spectra for the kinetic model appear to be weakly influenced by poor quality of the signal when the reference spectrum is set at zero. The ratio of asynchronous to synchronous correlation intensity yields a coherence spectrum. This spectrum remains a constant intensity for all the correlated peaks, being free from the influence of rate constant and absorption coefficient as well as being weakly disturbed by a small S/N ratio. It also provides a way to evaluate the extent of spectral overlap between two peaks. The coherence spectrum is useful to characterize the type of parallel reactions.
A Boltzmann-type kinetic model for misorientation distribution functions in two-dimensional fiber-texture polycrystalline grain growth
