Arrhenius plot

Abstract: An extensive set of laboratory annealing data, relating the reduction in mean confined track length of induced fission tracks in Durango apatite (Mexico) to annealing temperature and time, has been used to construct an empirical mathematical description of the annealing process. Firstly, Laplacian smoothing splines are used to reveal the gross nature of the dependence of the length reduction, r , on logarithm of time (ln( t )) and inverse absolute temperature ( T −1 ). This suggests that contours of equal length reduction in an Arrhenius plot can be described by parallel or only slightly fanning straight lines. In seeking a more rigorous description, we construct a series of models relating some function g ( r ) and another function f {ln( t ), T −1 }, which contain most previously published relationships, as well as a number of novel forms. Within this composite model, both parallel and fanning Arrhenius plots are considered. The models are fitted and compared using formal statistical methods. None of the previously suggested relationships satisfactorily describe the data, and a novel form is proposed with g ( r )=ln(1− r ) for the parallel Arrhenius plot. The best fitting model accounts for 96.7% of the variation of g ( r ), but residual plots show some structure; suggesting that some improvement in the model is possible. The best fanning model accounts for 98.0% of the variation in g ( r ), and gives a significantly better fit than the parallel model, with residual plots showing no obvious structure. The degree of fanning is much less than in most previously published Arrhenius plots for apatite, which may be due to the presence of apatites of various compositions in those previous studies, whereas the present study relates to only a single composition. The slight amount of fanning observed in this study may be an artefact introduced by several intermediate steps between the physical processes taking place during annealing and their manifestation as the reduction in mean track length.

Abstract: Hydrothermal synthesis of CeO2 and AlO(OH) were conducted using a flow type apparatus over the range of temperature from 523 to 673 K at 30 MPa. Nanosize crystals were formed at supercritical conditions. The mechanism of nanoparticle formation at supercritical conditions was discussed based on the metal oxide solubility and kinetics of the hydrothermal synthesis reaction. The reaction rate of Ce(NO3)3 and Al(NO3)3 was evaluated using a flow type reactor. The Arrhenius plot of the first order rate constant fell on a straight line in the subcritical region, while it deviated from the straight line to the higher values above the critical point. The solubility of Ce(OH)3 and AlO(OH) was estimated by using a modified HKF model in a wide range of pH and temperature. In acidic conditions, where hydrothermal synthesis reaction is concerned, solubility gradually decreased with increasing temperature and then drastically dropped above the critical point. The trend of the solubility and the kinetics around the critical point could be explained by taking account of the dielectric constant effect on the reactions. There are two reasons why nanoparticle are formed at supercritical conditions. Larger particles are produced at subcritical conditions due to Ostwald ripening; that could not be observed in supercritical water because of the extremely low solubility. Second reason is the faster nucleation rate in supercritical water because of the lower solubility and the extremely fast reaction rate.