THE APPLICATION OF MULTIPLE SCATTERING THEORY IN CALCULATING THE DEUTERIUM FLUX PERMEATING A Pd THIN FILM

Abstract

The multiple-scattering theory 2 is applied to the de Broglie wave of deuterons inside the palladium film. The formalism for band structure calculation and the reflection and transmission calculations for finite slices is presented. The latter is based on a double- layer scheme which obtains the reflection and transmission matrix elements for the multiplayer slice from those of a single layer. With a relative simple model for the potential of palladium crystal lattice, we calculate the band structures of probability wave of deuterons propagating in the palladium, as well as the transmission coefficients through finite periodic slices. Selective resonant tunneling theory is adopted when obtaining the scattering matrix T. Our calculations consist with experimental results which can not be explained by diffusion theory. 1 . Instead of the monotonic feature of the deuterium flux, the peaky deuterium flux appears at certain temperature, which is higher than the boiling point of the heavy water. This is unexpected if the diffusion model is applied to this permeation process. Based on the conventional diffusion theory, the diffusion coefficient increases dramatically when the temperature of the palladium increases. However, we observed the peaky feature repeatedly at certain temperature. The resonant feature shown in the experiments implies that the deuteron particles should be described by the probability wave. Therefore we introduced a general de Broglie wave function to characterize the interaction between the deuterium flux and the gas-loading D/Pd system. The phase factor of deuteron wave is the key for interference and resonance. The idea of the importance of the phase factor is also the core of selective resonant tunneling theory. Multiple-scattering theory was applied to implement the above concept in calculating the deuterium flux permeating the gas-loading Pd thin film. Multiple-scattering theory (MST) usually known as KKR (Korringa, Kohn, and Rostoker) approach, was developed mainly for the calculation of electronic band structures, although it originated from the study of classical waves. It was widely used in the research of de Broglie wave, elastic wave, electromagnetic wave and so on. The main idea of MST is to separate the complicated potential distributed in the three-dimensional space into non-overlapped regions (this is quite clear for periodic structure but not so easy for disordered systems). Each region is taken as a single scatterer and the incident waves on this scatterer are composed of the scattered waves of other scatterers and the incident waves far away while its scattered waves become part of incident waves on other scatterers. Such transformation between incident waves and scattered waves of different scatterers are achieved through the vector structure constant G. That's the keystone of MST. MST was developed into different kinds of equations when dealing with different problems. The concrete equations adopted in this paper were first brought forward by Modinos 3 in his work about the scattering problem