Degree Of Dynamical Disorder Research Articles

Order and disorder in irreversible decay processes.

Dynamical disorder motivates fluctuating rate coefficients in phenomenological, mass-action rate equations. The reaction order in these rate equations is the fixed exponent controlling the dependence of the rate on the number of species. Here, we clarify the relationship between these notions of (dis)order in irreversible decay, n A → B, n = 1, 2, 3, …, by extending a theoretical measure of fluctuations in the rate coefficient. The measure, Jn-Ln (2)≥0, is the magnitude of the inequality between Jn, the time-integrated square of the rate coefficient multiplied by the time interval of interest, and Ln (2), the square of the time-integrated rate coefficient. Applying the inequality to empirical models for non-exponential relaxation, we demonstrate that it quantifies the cumulative deviation in a rate coefficient from a constant, and so the degree of dynamical disorder. The equality is a bound satisfied by traditional kinetics where a single rate constant is sufficient. For these models, we show how increasing the reaction order can increase or decrease dynamical disorder and how, in either case, the inequality Jn-Ln (2)≥0 can indicate the ability to deduce the reaction order in dynamically disordered kinetics.

Vibrational Origin of the Thermal Stability in the High-Performance Piezoelectric Material GaAsO4

Theoretical calculations and experiments show the absence of libration modes of the tetrahedra in GaAsO(4), the most α-quartz-type distorted material. In consequence, the degree of dynamic disorder at high temperature is very low, making GaAsO(4) of high interest for high-temperature applications. This paper shows the importance of the theoretical calculations of vibration in oxide materials. In this way, it could be possible to extend this result to other materials and predict the thermal stability of the materials and their potential applications at high temperature.